raising taxes to balance the budget - Economics - Stanford University
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RAISING TAXES TO BALANCE THE BUDGET: HOW EFFECTS ON OUTPUT AND LABOR SUPPLY COMPLICATE THE MATTER May 9, 2011 Gregory Hirshman Department of Economics Stanford University Stanford, CA 94305 [email protected] Under the direction of Prof. Robert Hall
ABSTRACT The United States and many major European countries currently are running large budget deficits, and most of these countries also confront significant national debt. Many are now seeking to restore fiscal discipline by cutting spending, raising taxes, or doing both. In this thesis, I explore what would occur if the United States or any of seven major European countries (France, Germany, Italy, the United Kingdom, Greece, Spain, and Sweden) attempted to balance its budget simply by raising taxes. I also determine what would occur if a country decided to balance its budget by using tax increases to accomplish half of its budget fix and cutting government spending to do the rest. To pursue this analysis, I first employ a simple static model to gain some understanding of how changes in tax rates affect how much people work. I then develop a more realistic and sophisticated dynamic general equilibrium model and gradually add refinements to it. With that model, I find that if government spending is not reduced, all countries except Sweden, which has only a small budget deficit, are either incapable of achieving a balanced budget in one year or could do so only by suffering dire economic consequences. Even if cuts in government spending account for 50% of the budget fix, all countries under analysis (except Greece which is unable to balance its budget under any of the four scenarios I posit) would experience at least some loss in output, and many would face considerable hardship. Keywords: Labor supply, tax rates, government spending, budget deficit, United States, Continental Europe, Scandinavia Acknowledgements: I thank Professor Robert Hall for overall guidance. I thank Professor Geoffrey Rothwell for suggestions on my study design. I also thank my parents who helped me edit this thesis and my brother Brian who helped me develop my MATLAB code.
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Table of Contents Chapter 1: Introduction .................................................................................................................. 6 Chapter 2: Literature Review ....................................................................................................... 16 2.1. Labor Supply Across Countries ...................................................................................... 16 2.1.1. The Effect of Tax Rates ......................................................................................... 16 2.1.2. The Effect of the Way that Government Spends its Revenue ............................... 19 2.1.3. The Effect of Labor Unions, Labor Market Regulations, and Productivity .......... 22 2.1.4. The Effect of Income Inequality ............................................................................ 24 2.2. Background of the Dynamic General Equilibrium Model .............................................. 25 2.2.1. The Neoclassical Starting Point ............................................................................. 25 2.2.2. Dynamic Modeling ................................................................................................ 27 Chapter 3: A Static Model of Tax Rates and Labor Supply ........................................................ 29 3.1. Background ..................................................................................................................... 29 3.2. Theoretical Framework ................................................................................................... 30 3.3. My Key Equilibrium Relation ........................................................................................ 37 3.4. Explanation of Results .................................................................................................... 39 Chapter 4: My Dynamic General Equilibrium Model ................................................................. 45
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4.1. How the Dynamic Model Improves upon the Simple Static Model ............................... 45 4.2. Introduction to the Dynamic General Equilibrium Model .............................................. 46 Chapter 5: Employing My Dynamic Model ................................................................................ 50 5.1. The Trivial Case: No Taxes ............................................................................................ 50 5.2. The Model with Taxes .................................................................................................... 50 5.3. Changing the Tax Rate in the Dynamic General Equilibrium Model ............................ 51 5.3.1. Increasing the Tax Rate from 20% to 30% ............................................................ 51 5.3.2. Decreasing the Tax Rate from 20% to 10% ........................................................... 57 5.3.3. Varying the Magnitude of the Change in the Tax Rate ......................................... 61 5.4. Removing the Consumption-Work Complementarity .................................................... 64 5.5. Assuming a Lower Wage Elasticity of Labor Supply .................................................... 66 Chapter 6: Alternative Scenarios for Government Spending....................................................... 69 6.1. Government Spending on Wasteful Projects .................................................................. 69 6.2. The Concept of μ.............................................................................................................. 72 6.3. Results from Introducing μ into the Model ..................................................................... 73 6.3.1. Increasing the Tax Rate from 20% to 30% ............................................................ 73 6.3.2. Decreasing the Tax Rate from 20% to 10% ........................................................... 75
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6.4. Implications of μ ............................................................................................................. 75 Chapter 7: Welfare Analysis ........................................................................................................ 77 7.1. Welfare Analysis over a Lifetime in the Baseline Case ................................................. 77 7.1.1. Utility Changes Caused by a Change in the Tax Rate ........................................... 78 7.1.2. Consumption Gain and Loss Equivalents Caused by Changes in the Tax Rate .... 79 7.1.3. Hours Worked Gain and Loss Equivalents Caused by Changes in the Tax Rate .. 81 7.2. Welfare Analysis Between the Steady States in the Baseline Case ................................ 83 7.2.1. Utility Changes Caused by a Change in the Tax Rate ........................................... 83 7.2.2. Consumption Gain and Loss Equivalents Caused by Changes in the Tax Rate .... 84 7.2.3. Hours Worked Gain and Loss Equivalents Caused by Changes in the Tax Rate .. 86 7.3. Welfare Analysis Assuming No Complementarity or a Less Elastic Labor Supply ...... 88 7.4. Welfare Analysis Assuming Different Values of μ ........................................................ 90 Chapter 8: Applying My Model to Real World Scenarios .......................................................... 92 8.1. The Economic Situation in the Eight Countries Under Consideration ........................... 92 8.2. Scenarios for Balancing the Budget in One Year ........................................................... 93 8.2.1. Assuming Lump Sum Transfers with No Change in Spending ............................. 94 8.2.2. Assuming Lump Sum Transfers with Spending Cuts 50% of the Budget Fix ...... 96
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8.2.3. Assuming μ = 0.50 with No Change in Spending .................................................. 99 8.2.4. Assuming μ = 0.50 with Spending Cuts 50% of the Budget Fix ......................... 100 8.2.5. The Consequences of Using Tax Increases to Balance the Budget ..................... 103 8.3. A Closer Look at the Case of the United States ............................................................ 103 8.4. Laffer Curves for the United States .............................................................................. 106 8.5. Balancing the Budget in the Long Run ......................................................................... 112 Chapter 9: Conclusion ................................................................................................................ 118 References .................................................................................................................................. 122 Appendix A: Matlab Code ......................................................................................................... 126 Appendix B: Results Spreadsheets ............................................................................................ 131
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Chapter 1: Introduction The United States and many major European countries are currently running large budget deficits, and most of these countries also confront significant national debt. As a consequence, many are now trying to restore fiscal discipline after providing generous entitlements, state pensions, and other government benefits for many years. Although tax rates have increased in recent decades in most advanced industrial countries, the resulting increase in government revenues has been greatly outpaced by the increase in government expenditures. Many countries must now cut spending, raise taxes, or do both. In this thesis, I intend to explore what would occur if the United States or any of the seven major European countries (France, Germany, Italy, the United Kingdom, Greece, Spain, and Sweden) attempted to balance its budget simply by raising its taxes. I also seek to determine what would occur if each of those countries decided to balance its budgets by using tax increases to accomplish half of the budget fix and by cutting government spending to do the rest. Can these countries succeed in balancing their budgets? If so, what would be the economic costs in terms of aggregate output and labor supply? To pursue this investigation, I will first develop a simple static model to gain some understanding of how changes in tax rates affect how much people work. I will then create a more realistic and sophisticated dynamic general equilibrium model and gradually refine it. With that model, I will return to my principle research questions. As historical background for this thesis, it is useful to understand the changes in labor supply that have occurred in the United States, Continental Europe, and Scandinavia. In the early 1970s, hours worked in the market sector by persons between the ages of 15 and 64 was approximately equal in the United States, Continental Europe (which I define as France,
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Germany, and Italy), and Scandinavia (which I define as Denmark, Finland, Norway, and Sweden) (Prescott 2004). By the mid-1990s, however, Continental Europeans worked only about 70% as much as Americans, and Scandinavians worked about 85% as much as Americans (Prescott 2004). In the past decade, the proportional labor supply differences between both Continental Europe and the United States and between Scandinavia and the United States have remained relatively constant (Rogerson 2006). What caused the large decrease in the relative labor supply in Continental Europe between the early 1970s and today, and why did the Scandinavian labor supply decrease less dramatically? Prescott (2004) created a model of the G-7 economies which suggested that the large decrease in the relative labor supply in Continental Europe was due primarily to differences in tax rates. His model allowed him to indirectly calculate the Frisch elasticity of labor supply, the elasticity of hours worked with respect to the wage rate given a constant marginal utility of consumption. He found it to be “nearly 3,” an estimate at the upper end of the literature on labor supply elasticity. This value implied that individuals would react strongly to changes in tax rates. Therefore, he found it logical that when tax rates in Continental Europe and the United States were comparable during the 1970s, their labor supplies were similar. As tax rates in Continental Europe increased markedly over the next 25 years, its relative labor supply fell dramatically. While Prescott’s model fit the empirical data on the labor supplies in the G-7 countries during both 1970-1974 and 1993-1996, it did not fit the data for the Scandinavian countries during those periods. Tax rates were higher in Scandinavia in the mid-1990s than in Continental Europe, yet labor supply was also higher. This apparently contradicted Prescott’s prediction that people would react strongly to increases in tax rates by reducing the supply of labor. Prescott
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had made numerous assumptions which might have to be relaxed or modified to allow economists to understand more fully the factors which affect labor supply across additional countries. In this thesis, I seek to develop a more effective and realistic model first by building on Prescott’s model and then creating my own dynamic general equilibrium model which avoids several of his oversimplifications. My thesis is organized as follows. Chapter 2 begins with a review of the literature on the causes of the relative changes in the labor supply between the United States, on the one hand, and Continental Europe and Scandinavia on the other. It then reviews literature which provides the foundation for my dynamic general equilibrium model. Chapter 3 develops a simple static model based on Prescott (2004). This model employs a less restrictive utility function, and it allows me to derive an original equilibrium relation between hours worked and the effective marginal tax rate and to estimate the Frisch elasticity of labor supply directly. Using this model, I find that the Frisch elasticity of labor supply in the G-7 countries was 2.97. This suggests that the vast majority of the change in the relative labor supply between the United States and Continental Europe might indeed be explained by higher tax rates in Continental Europe. My estimate of the Frisch elasticity of labor supply corroborates Prescott’s indirect calculation. Chapter 4 explains why a number of the underlying assumptions made in the simple static model are gross oversimplifications. For example, that model did not take into account interactions between economic variables across time periods, and it assumed that all non-military government expenditures substitute on a one-to-one basis for private consumption, implying that there was only one consumption good. I then develop a new dynamic general equilibrium model
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and explain why it represents a significant improvement. My presentation provides only an outline of how my calculations were actually performed. It was necessary to encode the model in Matlab because those calculations were far too complex to be performed by hand. That code is presented in Appendix A. Chapter 5 applies my dynamic model to the baseline case in which I assume that (1) the elasticity labor supply is 1.9, (2) consumption-work complementarity exists, and (3) all tax revenue is spent on lump sum transfer payments to individuals regardless of hours worked. The first two assumptions are based on Hall (2009a), and the rationale for them is discussed in chapter 5. The third assumption is derived from Prescott (2004), and the rationale for it is discussed in chapter 3. Chapter 5 explores how an arbitrary increase or decrease in the tax rate would, in the baseline case, affect economic variables including output, hours worked, the real interest rate, the pre-tax wage, consumption, the capital stock, the economy’s discounter, and the rental price of capital. It employs a time horizon of 80 years. An increase in the tax rate is shown to lead to a long run decrease in output, hours worked, consumption, and the capital stock while a decrease in the tax rate produces a long run increase in output, hours worked, consumption, and the capital stock. The largest changes occur during the first year after the changes in the tax rate. Thereafter, the variables gradually approach their long term steady states. The real interest rate and pre-tax wage are unchanged in the long run. Appendix B presents the results spreadsheets for changing the tax rate from 20% to 30% or from 20% to 10% in the baseline case Chapter 5 then examines three related issues. It demonstrates that, starting from an initial postulated tax rate of 20%, each 10% increase in the final tax rate from 0% to 90% has an
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increasingly large effect on the magnitude of the changes produced in output, hours worked, consumption, and the capital stock. It shows that removing the assumption of consumption-work complementarity or assuming a less elastic labor supply of 0.5 reduces the magnitude of these changes. Chapter 6 considers alternative scenarios for the amount that individuals value government spending. The assumption that all tax revenue is spent on lump sum transfers to individuals regardless of hours worked is an oversimplification since it is unrealistic to assume that individuals value all government spending as much as direct transfer payments. Therefore, I consider two other scenarios. The first is the extreme case in which all tax revenue is spent on projects which do not affect the individual’s marginal utility of consumption in any way. The second scenario is more complex. It is designed to reflect the possibility that a fraction of government spending might provide utility to individuals by increasing their ability to consume while the remainder might be spent on projects which do not affect the individual’s marginal utility. I introduce a variable, μ, which represents the fraction of tax revenue spent on programs which correspond to the individuals’ consumption preferences. In this scenario, the benefit individuals derive from government spending still does not depend on hours worked, but it does depend on the value of μ. The analysis of the results of the changes in tax rates in these scenarios is based on two competing economic effects: the substitution effect and the income effect. The substitution effect is the change in the amount that individuals work given a change in the after-tax wage, holding the marginal utility of consumption constant. The income effect is the change in the
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amount that individuals work because changes in the tax rate make them richer or poorer affecting their marginal utility of consumption. Because in chapter 5 I assumed that all government revenue was spent on lump sum transfers to individuals regardless of hours worked, the income effect was absent. Regardless of the tax rate, tax revenue was fully rebated to individuals. No income was lost, so only the substitution effect influenced hours worked. A lower after-tax wage reduced the incentive to work (marginal utility of consumption being held constant) because individuals would increase their consumption less by working an additional hour. Therefore in chapter 5, increasing the tax rate always led to a decrease in output and hours worked and decreasing the tax rate always led to an increase in output and hours worked. When some or all of government revenue is spent on projects which do not affect the individual’s marginal utility of consumption, the income effect becomes relevant. This is because a tax increase will make individuals poorer. When individuals are able to consume less, each unit of consumption is more valuable, so a tax increase will make individuals value each unit of consumption more. Their marginal utility of consumption will increase. Thus, there will be two opposing effects of a tax increase on labor supply when only a fraction of tax revenue is spent on programs which correspond to the individuals’ consumption preferences. The substitution effect will tend to make individuals work less and the income effects will tend to make them work more. The smaller the value of μ, the greater the income effect. For small values of μ, the income effect dominates in my model, so an increase in the tax rate will cause an increase in labor supply and output. For larger values of μ, the income effect is smaller and the substitution effect dominates, so an increase in the tax rate will cause a decrease in labor supply and output. For a tax decrease, the results are the reverse.
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Chapter 7 explores the effects of tax rate changes on the utility, or welfare, of individuals. First, it presents the changes in welfare produced by changes in the tax rate over the course of an 80 year lifetime. Then it examines the difference between the initial and final steady states. The latter expresses the full impact of the tax changes, but it does not take into account the intervening changes between years 2 and 79, and so it overestimates actual welfare changes which result. This chapter concludes by considering how altering assumptions about the consumption-work complementarity, the elasticity of labor supply, and the nature of government spending would affect welfare changes over the 80 year lifetime. In my baseline case, increasing tax rates reduces welfare and decreasing tax rates increases welfare. This occurs regardless of assumptions made about how individuals value government spending, about whether consumption-complementarity exists, or about whether labor supply is relatively elastic or inelastic, although these assumptions do affect the magnitude of the changes. To provide a more intuitive sense of the magnitude of the welfare changes which I calculate, I consider consumption change equivalents and hours worked change equivalents. Consumption change equivalents express how much more or less consumption an individual would need to have if he continued to work as much as he had at the initial tax rate to attain the utility he actually achieves when the tax rate is increased or decreased. Hours worked change equivalents express how much more or less an individual would need to work if he continued to consume as much as had did at the initial tax rate to attain the utility he actually achieves when the tax rate is increased or decreased. An important finding in this chapter is that the lower the value of μ, the greater the magnitude of the change in welfare caused by a given change in the tax rate. While a low value of μ may imply that an increase in the tax rate will increase output and labor supply, welfare will
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be reduced dramatically when μ is small. In fact, for a given tax rate increase, the higher the value of μ, the smaller the decrease in welfare despite the fact that output and labor supply will be more negatively affected when μ is large. Conversely, for a given tax rate decrease, the higher the value of μ, the smaller the increase in welfare despite the fact that output and labor supply will be more positively affected when μ is large. With this background, chapter 8 returns to the original research questions. I consider eight countries: the United States, the four largest European economies (France, Germany, Italy, and the United Kingdom), the two largest European economies with very high deficit to GDP ratios (Greece and Spain) and the largest Scandinavian economy (Sweden). My first goal is to use my model to predict how much these countries would have to raise taxes in order to balance their budgets within one year. I examine various scenarios incorporating different assumptions about government spending to determine how such assumptions would affect the size of the necessary tax increases and the resulting effects on output and labor supply. I pursue the case of the United States in greater depth, presenting the Laffer Curves which my model generates under different assumptions about government spending. The Laffer curve generated when μ = 0 is particularly interesting because it does not reach a peak before the marginal tax rate is 0.80. Finally, I compute how much the United States would have to raise taxes in order to balance its budget in the long run, taking into account both the short term and the long term impact of tax rate increases on output. Regardless of whether tax revenue is assumed to be spent on lump sum transfers to individuals regardless of hours worked or whether individuals value government spending ½ as much as their own consumption (μ = 0.50), all countries except Sweden, which has only a small budget deficit, are either incapable of achieving a balanced budget in one year through tax
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increases alone or would suffer dire economic consequences as a result of the necessary tax increases. If a reduction in government spending accounts for 50% of the budget fix and tax revenue is assumed to be spent on lump sum transfers to individuals regardless of hours worked, Germany, Greece, and Spain could not balance their budgets. Of the remaining countries, only Sweden could avoid serious economic repercussions. If the reduction in government spending accounts for 50% of the budget fix and if individuals value government spending ½ as much as their own consumption (μ = 0.50), 7 of the 8 countries can balance their budgets. Greece’s budget deficit is so severe and its current tax rates are so high that even under these conditions, it cannot balance its budget. All the countries which can balance their budgets would experience reductions in output, and Germany and Spain would face devastating hardship. In the case of the United States, whose 2009 deficit to GDP ratio was 11% and whose debt to GDP ratio was 53%, I demonstrate that assuming no consumption-work complementarity or a less elastic labor supply would lead to a lower values for tax rate necessary to balance the budget and smaller consequent decreases in output and hours work. The greater the share of the budget fix made up by decreases in government spending, the smaller the necessary increases in the tax rate and the smaller the decreases in output and hours work. The smaller the value of μ, the smaller the necessary increase in the marginal tax rate to balance the budget, and the smaller the decreases in output and hours worked. In my baseline case, I find that for the United States even to achieve a deficit to GDP ratio of 3% without a reduction in spending would require such a large increase in its tax rate that a depression would result. Furthermore, despite the relatively low marginal tax rate of the United States, it would be impossible for it to achieve a budget surplus of 3% simply by raising tax rates without reducing government spending. Because my model demonstrates that only
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about 90% of the decrease in output which occurs in a country over an 80 year lifetime is experienced during the first year after a tax rate increase, I find that the long run fall in output caused by a tax increase would be even larger than the short run fall in output. Therefore, still larger tax increases would be necessary to achieve balanced budgets in the long run, causing greater economic harm. For example, although the United States could balance its budget in one year under the baseline assumptions if it were willing to endure the resulting economic hardship, it would be impossible for it to balance its budget in the long run simply by raising taxes. Chapter 10 presents my conclusions and suggests potential avenues for further research.
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Chapter 2: Literature Review I begin by reviewing literature which analyzes four aspects of the relative changes in the labor supply between the United States, on the one hand, and Continental Europe and Scandinavia on the other. The first is the effect of tax rates on the relative labor supplies. The second is the way that patterns of government expenditures help explain why over the past two decades relative labor supply has been higher in Scandinavia than in Continental Europe despite higher taxes. The third is the influence of labor unions, labor market regulations, and output per hour worked on labor supply. The fourth is the impact of the level of income inequality on labor supply. I then review literature which provides background for Hall (2009a) since this paper provides the foundation for the dynamic model I develop in this thesis. 2.1. Labor Supply Across Countries 2.1.1. The Effect of Tax Rates Prescott (2004) spurred intense debate in the economic community over the impact of differences in tax rates on the observed differences in relative labor supply across countries. He defined labor supply as hours worked per person aged 15-64 in the market sector. He only counted those hours which resulted in taxed labor income. Paid vacations, sick leave, holidays, and time spent working in the underground economy or at home were specifically excluded. Prescott created a model for the G-7 countries following standard macroeconomic theory and analyzed a stand-in household that faced a decision over how much to work and how much to consume. He derived an equilibrium relation between hours worked and the effective
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marginal tax rate on labor income. He explained the way he estimated tax rates and justified his why his estimates were reasonable. One of his key simplifying assumptions was that all tax revenue, except for that used for pure public consumption, was returned to households in lump sum payments independent of household income or hours worked. He defended this assumption by asserting that most public expenditures in the G-7 countries are substitutes for private consumption. This assumption allowed his model to consider only one consumption good. Prescott noted that although this was reasonable for the G-7 countries, it was not valid if a broader set of countries was to be considered. For example, in Scandinavia greater government expenditures on programs like child care for working parents necessitated treating some publicly provided goods separately from privately consumed goods. Rogerson (2006) extended Prescott’s analysis to include multiple consumption goods. His paper is discussed later in subsection 2.1.2. In Prescott’s analysis of the G-7 countries during the periods of 1970-1974 and 19931996, he found the Frisch elasticity of labor supply was “nearly 3,” implying that individuals would react strongly to changes in tax rates and that the vast majority of the differences in labor supply between the United States and Continental Europe could be explained by the higher taxes in Continental Europe. He noted that his model estimated the labor supply among the G-7 countries very well during the mid-1990s and quite well during the early 1970s. Prescott’s finding of an elasticity of labor supply of “nearly 3” is at the extreme upper end of values found in the literature. Many economists believe that the elasticity is actually much lower. Pistaferri (2003) based his estimate of labor supply elasticity on data on how workers’ expectations of their wages change as tax rates change. He calculated the Frisch elasticity of labor supply to be 0.70. Studying the decline in hours worked among lottery winners, Kimball and Shapiro (2003) estimated the Frisch elasticity of labor supply to be about
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one. Mulligan (1998) found the elasticity to be not much greater than one. His work is controversial, however, because, unlike most authors, he included data on older workers who earn lower wages, work fewer hours, and tend to be more responsive to changes in tax rates. Rogerson and Wallenius (2008) sought to explain the variation which exists in estimates of the Frisch elasticity of labor supply by dividing the relevant papers into two groups. Those which use microeconomic models typically calculate elasticities ranging from 0.05 to 1.25. Those papers that use macroeconomic models typically find values between 2.25 and 3.00. Low values derived from microeconomic models would imply that differences in tax rates between the United States and Continental Europe could only explain a small part of the differences in the changes in relative labor supply because these values imply that the number of hours worked would not be strongly affected by changes in tax rates. The high values derived from macroeconomic models, however, would imply that differences in tax rates between the United States and Continental Europe could explain most of the differences in the changes in relative labor supply. In the papers considered above, home production was not considered to contribute to labor supply. Olovsson (2009) pointed out, however, that while market work per person is about 10% higher in the United States than in Sweden, the total number of hours worked differs by only 1% when hours worked at home are included. He developed a model which demonstrated that differences in tax rates could account for most of the discrepancy in market work and home production between the United States and Sweden. He noted that taxes affect the amount of home production because service taxes raise the price of market-produced services while labor taxes reduce the economic return to market work, increasing the relative return to home production. Because tax rates are much higher in Sweden than in the United States, there is a
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greater incentive for Swedes to substitute home production for market work. Freeman and Schettkat (2005) came to similar conclusions. They found that while Americans work significantly more hours per week in the market sector than Europeans, Americans and Europeans work about the same number of hours per week when home production is included. Their analysis indicated that higher taxes in Europe played a key role in creating this situation. 2.1.2. The Effect of the Way that Government Spends its Revenue While tax rates definitely affect labor supply, it seems likely that other factors contribute to the differences in relative labor supply among the United States, Continental Europe, and Scandinavia. One of these factors is the pattern of government expenditures, which helps account for the fact that labor supply is higher in Scandinavia than it is in Continental Europe despite higher tax rates in Scandinavia. Rogerson (2006) explored this issue by employing a version of the standard neoclassical growth model which takes into account different types of government spending. Instead of making Prescott’s assumption that all government expenditures are lump sum transfers independent of hours worked, Rogerson divided government expenditures into four categories, depending on whether they were used (1) to finance lump sum transfers independent of hours worked, (2) to hire workers at market wages who produced nothing which households valued, (3) to subsidize consumption, or (4) to subsidize leisure. He found that taxes which funded government expenditures to hire unproductive workers or to subsidize consumption had no effect on hours worked, but taxes expended on lump sum transfers and subsidies for leisure had a negative effects on hours worked. Those spent on subsidies for leisure had the largest effect. Rogerson concluded that it is essential to consider how the government spends its revenue in order to determine the effect of tax rates on labor supply because different types of expenditures lead to different effects.
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Rogerson (2007) applied this analysis to the “anomaly” of Scandinavia. Scandinavia had both higher tax rates and higher labor supplies than Continental Europe in the mid-1990s. This appeared to contradict the theory that higher tax rates lead to lower labor supply. Rogerson found, however, that the elasticity of labor supply varies among countries depending on their patterns of government expenditures. If the elasticity of labor supply in Scandinavia is low enough relative to that in Continental Europe, this could explain how Scandinavian countries could simultaneously have higher tax rates and higher labor supplies. Scandinavian taxes for government expenditures would have a less negative effect on labor supply than taxes in Continental Europe. By assuming more than one consumption good in the economy, Rogerson was able to distinguish between government transfers to individuals regardless of hours worked, government transfers affected by hours worked, and government transfers which did not affect the individual’s marginal utility of consumption. If higher taxes fund disability payments which can be received only by an individual who is not working, for example, they might have a strongly negative effect on labor supply. On the other hand, if the higher taxes were used to fund day care of children of working parents, they might have a much smaller adverse effect on labor supply. Rogerson also pointed out that higher taxes would lead to larger differences on the labor supply in activities for which there are strong non-market substitutes. This point was also stressed by Davis and Henrekson (2005). These authors considered, for example, the case of a family who wished to paint their home, an activity for which there is a strong non-market substitute. If the family hires professional painters, the transaction is subject to taxation. If it paints the house itself, taxes are avoided. The higher the taxes, the greater the incentive to avoid
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the market alternative. Other activities, such as auto production, are difficult to carry out outside the market sector. The effect of higher tax rates on labor supply in such activities would be expected to be smaller. Building on this analysis, Rogerson explained how Scandinavian countries could have higher marginal tax rates and still have higher labor supply. Compared to Continental Europe, they have substantially higher rates of government employment. This government employment often serves as an implicit transfer to the government employee, although it does not affect the marginal utility of consumption for the vast majority of households. Higher government employment in the service sector in Scandinavia provides a larger transfer of market services to households, increasing hours worked in the market sector. For example, Rogerson noted that Scandinavian countries spend a much higher percentage of government revenue on services such as child and elderly care. Such jobs often have strong non-market substitutes. The same work which counts toward labor supply in Scandinavia when it is performed by government employees does not count in Continental Europe, where it is often completed outside of the market sector. Rosen (1996) noted that child care subsidies have had an especially large impact on labor supply by encouraging labor force participation by women in Sweden. With Sweden’s high marginal tax rates, it would be difficult for these mothers to work in the market sector and purchase child care in the private market. Child care subsidies, however, tend to offset this income tax penalty. Rosen noted that such child care subsidies are a major reason why female participation in the labor market is much higher in Scandinavia than in Continental Europe and thus a major reason why hours worked in Scandinavia are higher than they might otherwise be.
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2.1.3. The Effect of Labor Unions, Labor Market Regulations, and Productivity Differences in the power of labor unions, the stringency of labor market regulations, and relative productivity also affect relative labor supply across countries. Alesina et al. (2005) argued that differences in the power of labor unions and in the stringency of labor market regulations, rather than differences in tax rates, explain the majority of the differences in labor supply between Continental Europe and the United States. They noted that the strength of unions increased dramatically in Continental Europe during the 1970s and 1980s, the period which witnessed the large decrease in its relative labor supply. They cited Alesina and Glaesar (2004), which argued that American racial fractionalization and European political instability led to Americans being much less open to the socialist/Marxist left than Europeans and therefore less supportive of organized labor. Alesina et al. argued that because of their power, unions in Continental Europe were able during economic shocks to push successfully for a reduction in hours worked as an alternative to increased unemployment, employing slogans like “work less–work all.” This might not have been an optimal response to the economic conditions, but union power often rested on the size of union membership, making such policies appealing to them. Hunt and Katz (1998) pointed out that the reduction of the standard workweek did not lead to any significant increase in overtime work in Europe. Therefore, the diminished standard workweek reduced labor supply. Alesina et al. pointed out that unions demanded higher wages to compensate for lower hours worked and keep total income constant. This led to even sharper declines in labor supply because it was difficult for employers to increase hourly wages without making cuts in total hours of employment. Nickell (1998) noted that unions also succeeded in lobbying for much
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higher unemployment compensation in Europe, which reduced the marginal loss of consumption for the unemployed. This made unemployment less undesirable. It reduced the incentive to seek employment and pressured employers to raise wages in order to provide incentives to work. The resulting higher wages reduced the incentive for employers to hire more workers. Rogerson (2006) pointed out another reason for the decrease in the labor supply of Continental Europe and Scandinavia relative to that of the United States. As countries develop, individuals tend to work less. More advanced nations have lower labor supplies because their citizens can achieve a similar standard of living while working fewer hours and enjoying more leisure. As consumption increases, the marginal utility of consumption decreases. Individuals thus have less incentive to work longer hours when they receive higher wages. In the early 1970s, output per hour worked in Continental Europe and Scandinavia was significantly lower than in the United States. By the mid-1990s, productivity in Continental Europe and Scandinavia had caught up (Prescott 2004, Pilarski 2008). Thus, in the early 1970s, Continental Europeans and Scandinavians had an extra incentive to work because of their lower output per worker. By the mid-1990s, this difference no longer existed. If Continental Europeans and Scandinavians worked about as much as Americans when they had an extra incentive, they would be expected to work less without it. According to Pissarides (2007), one of the reasons for the dramatic decrease in the relative labor supply of Continental Europe over this period is that the comparison is between the time of exceptional economic and productivity growth which Europe experienced from the end of World War II to the early 1970s and the normal steady state of the mid-1990s.
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2.1.4. The Effect of Income Inequality A final factor contributing to the fact that Americans work more than Europeans is that there is greater income inequality in the United States. As Formby et al. (2004) pointed out, the distribution of wages is more even, for example, in Germany than in the United States. In addition, government transfers from the wealthy to the poor are greater in Germany, so disposable income inequality is even less in Germany relative to the United States than wage income inequality (Gottschalk and Smeeding 1997). Bell and Freeman (2001) explained the fact that Americans work more than Germans by analyzing forward-looking labor supply responses to differences in earnings inequality. They argued that workers often choose additional current hours of work because they hope to gain promotions and higher pay in the future. Since earnings are more unequally distributed in the United States than in Germany, extra work has a greater potential payoff in the United States, and this leads to more hours worked. According to Bell and Freeman, the argument that greater earnings inequality leads to more hours worked rests on three premises: (1) that individuals can rise in the percentile distribution of earnings by working more hours, (2) that individuals base how much they work currently on assumptions they make about how much they expect to earn in the future as a result of their current work, and (3) that the greater the inequality of income, the larger the marginal change in an individual’s earnings given the same change in his position in the percentile distribution of income. Using data on earnings and hours worked in the market sector in the United States and Germany, they found (1) that the greater the number of hours an individual worked, the greater his expected earnings in both the United States and in Germany, but with a greater expected benefit in the United States and (2) that in both countries full time workers work more hours in occupations which have greater wage inequality. This provided evidence that that
25
the difference in income inequality between the United States and Germany was a significant factor in the difference in hours worked in the market sector between the two countries. 2.2. Background of the Dynamic General Equilibrium Model 2.2.1. The Neoclassical Starting Point Hall (2009a) sought to estimate the output and consumption multiplier effects which quantify how much output and consumption change given an increase in government purchases. Hall initially developed a static neoclassical model with a standard macroeconomic utility function in which individuals receive positive utility from consumption and negative utility from work. In his model, technology was estimated using the Cobb-Douglass production function, and the real wage was assumed to be determined by the marginal product of labor. Employing this model, Hall calculated the output multiplier to be 0.4 and the consumption multiplier to be -0.6. These values differ significantly from the empirical data which indicate that the output multiplier is about 1 and the consumption multiplier is about 0. Recognizing this, Hall considered additional factors to make his model more reflective of reality. The first was the endogenous markup of price over cost, which reflects the fact that firms in the real world have market power. Assuming sticky prices, this power is higher in economic slumps and lower in booms. Markups are thus countercyclical, as Rotemberg and Woodford (1992) demonstrated. Augmenting his neoclassical model with a constant-elasticity relationship between markup and output, Hall computed the output multiplier to be 0.5 and the consumption multiplier to be -0.5, a step in the right direction. He then considered unemployment and the employment function, noting that many general equilibrium models have difficulty explaining fluctuations in labor supply if they do not
26
explicitly consider unemployment. Monica Merz (1995) and David Andolfatto (1996) made significant progress by building on the work of Mortensen and Pissarides (1994) by explicitly allowing for unemployment in otherwise neoclassical models. Blanchard and Galí (2007) succeeded in introducing unemployment in the New Keynesian Model. Hall (2009b) built on the Mortensen-Pissardes model by allowing for a broad variety of bargaining solutions between jobseekers and employers and replacing their linear preferences with standard macroeconomic preferences. Hall (2009a) then used an employment function, which he had previously developed in Hall (2009b). This function incorporates two components. The first is the fraction of the population which is employed as a result of the interaction between jobseekers and employers. The second is the Frisch supply function for hours worked per employed worker, which explicitly takes unemployment into account. Chetty et al. (2011) illustrated why, in measuring labor supply elasticities, it is important to consider both how much people respond to changes in the tax rates conditional on employment and how many people choose to be employed when tax rates change. Using his employment function, Hall calculated a labor supply elasticity much higher than that which he had found using the standard neoclassical model. This value was more in line with labor supply elasticity calculated by Kydland and Prescott (1982). Although that value had been criticized for by Mankiw et al. (1985) and Eichenbaum et al. (1988) as being too high, Hall stated that in light of recent work, it appeared reasonable. With this basis, he reestimated the output multiplier to be 0.8 and the consumption multiplier to be -0.2, values even closer to the empirical data. The last factor which Hall added to his static model was the consumption-work complementarity, which reflects the fact that as an individual works more hours in the market
27
sector, his marginal utility of consumption rises. As an individual has the less time for home production, he places greater value on consumption in the market. Aguiar and Hurst (2005) and Hurst (2008) analyzed consumption patterns upon retirement. Their data supported the notion of complementarity between consumption and work. There is a significant drop in consumption of goods and services in the market when individuals cease\ to work, apparently because they have the opportunity to spend more time on home production and therefore have less need to make purchases in the market. Browning and Crossley (2001) and Low et al. (2008) studied declines in consumption in the market during periods of unemployment. Their work also supported the notion of consumption-work complementarity. Employing the preferences used in Hall and Milgrom (2008) to account for consumption-work complementarity, Hall calculated an output multiplier of 0.97 and a consumption multiplier of -0.03. These values were consistent with empirical evidence. 2.2.2. Dynamic Modeling: Building on his static model, Hall then constructed a dynamic model assuming that individuals smooth consumption over their lifetimes instead of simply consuming their present incomes. This dynamic model resulted in lower output multipliers for government purchases because temporary government purchases were offset by future tax increases, and individuals prepared for such increases by cutting current consumption to smooth their consumption by saving to meet the anticipated tax increases. In his model, Hall employed standard treatment of capital adjustment costs, the rental price of capital, the equivalence of capital demand and capital supply, the law of motion for capital, the economy’s discounter, and the Euler equation. He also assumed that after an initial increase in government purchases, government spending would be reduced each year thereafter until it asymptotically approached the pre-shock level and that the
28
capital stock after government spending would also return to the pre-shock level. Using this model, Hall computed an output multiplier of 0.98 and a consumption multiplier of -0.03. He found that if he removed his assumptions about endogenous markup or assumed a lower labor supply elasticity, this had a large effect on his calculations, but if he assumed no consumptionwork complementarity, this had only a small effect. Many economists have taken issue with the idea that all individuals smooth consumption over their lifetime. One of Keynes’s major contributions to macroeconomics was the idea that current consumption depends heavily on current income. Nevertheless, it appears reasonable to assume that some individuals have full access to capital markets and can smooth lifetime consumption although other may be credit constrained and thus consume current income. Galí et al. (2007) followed this logic in employing a standard New Keynesian model for government purchases. They considered a population in which a fraction of individuals, λ, consumed all of its labor income while the remainder smoothed lifetime consumption. The output and consumption multipliers depend strongly on the value of λ. Higher values lead to much larger multipliers. López-Salido and Rabanal (2006) built on the leading New Keynesian model of Christiano et al. (2005), employing a similar assumption about the existence of two groups of individuals, one of which consumes current income while the other smoothes lifetime consumption. López-Salido and Rabanal agreed that the output and consumption multipliers depend strongly on the value of λ, finding that a higher λ leads to much larger multipliers. When Coenen and Straub (2005) employed the model of Smets and Wouters (2003) and assumed two groups, they confirmed that the value of λ affected their calculation of the multipliers, although their multipliers were much lower than those computed by Galí et al. and López-Salido and Rabanal.
29
Chapter 3: A Static Model of Tax Rates and Labor Supply
Before developing a dynamic general equilibrium model to analyze how tax rates and the
patterns of government spending affect labor supply, it is useful to employ a simpler model and to understand the economic theory behind it. In this chapter, I develop such a model based on the work of Prescott (2004). I present background information for this model, discuss the model’s theoretical framework, and derive its key equilibrium relation. Finally, I explain the results obtained using this model. 3.1. Background Prescott (2004) created a static model of the G-7 economies which explained that the change in the relative labor supply between the United States and Continental Europe between the early 1970s and the mid-1990s was largely a result of differences in tax rates. His model employed a utility function which established an equilibrium relation between hours worked and the effective marginal tax rate. It allowed for an indirect calculation of the Frisch elasticity of labor supply. Prescott found this elasticity to be “nearly 3,” an estimate at the upper end of the range of those in the macroeconomic literature. My simple static model builds on Prescott’s work, but it employs a less restrictive utility function. This allows me to derive an original equilibrium relation between the effective marginal tax rate and labor supply and to directly calculate the Frisch elasticity of labor supply to be 2.97. This model would tend to support Prescott’s conclusion that the vast majority of the differences in labor supply between the United States and Continental Europe can be explained by differences in the marginal tax rate.
30
3.2. Theoretical Framework In this chapter, I examine the major advanced industrial countries which comprise the G-7: Germany, France, Italy, the United Kingdom, Canada, Japan, and the United States. My data comes from the United Nations system of national accounts (SNA) statistics, OECD labor market statistics, and other sources on the purchasing power parity gross domestic product (GDP). I analyze the periods of 1970-1974 and 1993-1996 because Prescott provided all of the necessary data for them. Following the common procedure of labor economists, I define labor supply in this paper as the number of hours worked in the taxed market sector by people between the ages of 15 and 64. Its two principle components are the fraction of the target age population that works and the number of hours worked per person. Paid vacations, sick leave, and holidays are explicitly excluded. Time spent working in the underground economy or at home is similarly excluded. Only time working for taxable labor income is included. Table 3.1, adapted from Prescott (2004), presents labor supply statistics for the G-7 countries relative to those of the United States during 1970-1974 and 1993-1996. In the early 1970’s, labor supply in Continental Europe was about equal to that in the United States. During 1993-1996, labor supply in Continental Europe was only about 70% of that in the United States. What caused this large change? To answer that question, I have built on Prescott’s framework to develop a new model. I analyze a stand-in household that faces a decision about how much time to devote to labor or leisure and how much to consume or save. I use preferences similar to those of Prescott. The key difference in my model lies in the utility function I employ to treat the labor-leisure decision.
31
TABLE 3.1 LABOR SUPPLY FOR THE G-7 COUNTRIES
Hours Worked per Person Relative to the United States (U.S. = 100)*
Period
Country
1993-1996
Germany France Italy Canada United Kingdom Japan United States
75 68 64 88 88 104 100
1970-1974
Germany France Italy Canada United Kingdom Japan United States
105 105 82 94 110 127 100
*These data are for persons aged 15-64. Note that this table was adopted from Prescott (2004).
Prescott defined preferences for a stand-in household in the following manner:
log
log 100
(3.1)
where the variable c denotes consumption and h denotes hours of labor supplied to the market sector per person per week. Time is indexed by t. The discount factor 0 < β < 1 measures the value of future consumption and leisure relative to current consumption and leisure. The higher the value β, the more highly a person valued future consumption and leisure. The parameter α > 0 specifies the utility of leisure relative to consumption. Prescott (2004) assumed that a household has 100 hours of productive time per week, implying that (100 – h) hours were
32
devoted to leisure activity. In accordance with standard macroeconomic practice, his model considered time not spent participating in the market sector to be leisure, even though much of this “leisure” might have been spent working in the underground economy or in the nonmarket sector. What was important was that nonmarket production was not taxed. While Prescott’s utility function was simple and easy to use, it did not allow for a direct calculation of the Frisch elasticity of labor supply. I therefore employ the following utility function /
log
1
1/
(3.2)
where ψ denotes the Frisch elasticity of labor supply. The variables c, h, and β denote the same parameters as in Prescott’s model. While α still denotes the utility of leisure parameter, it is different in (3.2) than in (3.1) since I measure the labor-leisure decision in a different manner. Nevertheless, both utility functions reflect the fact that households obtain positive utility from consumption and negative utility from labor. In (3.2), I compute the negative utility of labor in a more complete manner in order to allow for the direct calculation of ψ. I adopt Prescott’s (2004) assumption that households own the capital and rent it to the firm. This is merely for convenience since the results would be the same if the firms owned the capital and rented it to the households, or if the firms were debt-financed. The law of motion for capital stock is 1 where k is the capital stock, x is investment, and δ is the depreciation rate.
(3.3)
33
My model economy also adopts Prescott’s assumption of a stand-in firm following a Cobb-Douglass production function (3.4) where y denotes output, c denotes consumption, and g denotes pure public consumption. The capital share parameter is 0 < θ < 1, and the total factor productivity parameter of country i at date t is Ait. The computation of Ait is irrelevant to the analysis in this paper. Following Prescott, the budget constraint for the household at date t is 1
1
1
1
(3.5)
where wt is the real wage rate, rt is the rental price of capital, τc is the consumption tax rate, τx is the investment tax rate, τh is the marginal labor income tax rate, τk is the capital income tax rate, and Tt represents government transfers. It is important to note that marginal and average labor income taxes are different. I am concerned specifically with the marginal labor income tax rate. To understand equation (3.5), it is useful to think of the left hand side as representing household expenditures and the right hand side as representing household revenue. Household expenditures are divided into after-tax consumption and after-tax investment. Household revenue comes from after-tax labor income, after-tax capital income, and transfers from the government. The δkt term is added on the right hand side of (3.5) because households receive a tax break for depreciation. That is, 1
34
.
Thus, after-tax capital income is equal to the income earned from renting out capital minus taxes paid on rental income less depreciation. My static model, like Prescott’s, assumes all tax revenue except for that which funds purely public consumption is returned to households in lump sum transfer payments which are independent of household income. It also assumes that government expenditures except for military expenditures substitute on a one-to-one basis for private consumption. I also follow Prescott’s lead in estimating pure public consumption g to be two times military’s share of employment times GDP and in assuming that there is only one consumption good. This is a reasonable assumption for the G-7 countries given the nature of their government expenditures. It is not, however, realistic when considering other countries. In Scandinavia, for example, greater government expenditure on programs like child care for working parents necessitates treating publicly provided goods separately from privately consumed goods. Like Prescott’s model, my model presumes a tax system far simpler than those used in any of the G-7 countries. As Prescott notes, however, taking a more complicated tax code into account would entail more difficult calculations but would not affect the inferences drawn from the model. In my model, like Prescott’s, households pay the taxes, so national income accounts have to be appropriately adjusted. Net taxes on the final product have to be calculated by subtracting subsidies from indirect taxes to remove net indirect taxes as a cost component of GDP. To understand this, consider the following example. Imagine a country with a single firm which produces one hat with a pre-tax price of $10.00. Output is $10.00. Suppose a $1.00 sales
35
tax is levied. The buyer must pay $11.00 for the hat. Suppose the buyer receives a $0.50 subsidy for buying the hat. It would really only cost him $10.50. Net taxes would equal indirect taxes less subsides, or $1.00 – $0.50 = $0.50. The output of the economy would still be $10.00. Again, following Prescott, my model assumes that two-thirds of indirect taxes net of subsidies fall directly on private consumption, while the remaining one-third is distributed evenly over private consumption and investment. Net indirect taxes on consumption, ITc, can therefore be expressed as 2 3
1 3
(3.6)
where C is private consumption expenditures, I is private investment, and IT is indirect taxes. Prescott expressed indirect taxes on consumption in this way because many indirect taxes, such as value-added taxes and sales taxes, fall directly on consumption, but others, such as property taxes on office buildings and sales taxes on equipment purchases for business, fall both on consumption and investment. In my model, like Prescott’s, personal consumption c is defined as (3.7) and output y as (3.8) where G is public consumption, Gmil is military expenditures, and GDP is gross domestic product. The consumption tax rate is
36
(3.9) For labor income, my model, like Prescott’s, accounts for two types of taxation. The first is the social security tax rate, which is expressed as Social Security Taxes 1
(3.10)
where the denominator is equivalent to the model economy’s output from labor. The second is the marginal labor income tax rate. To obtain the marginal labor income tax rate, it is first necessary to compute average income tax rate, which is expressed as
Direct Taxes Depreciation
(3.11)
where depreciation must be subtracted from output since households receive a tax break for it. Direct taxes are those paid by households. They do not include corporate taxes. Direct taxes, like social security taxes, are counted as private expenditures of households. Following Prescott, I estimate the marginal labor income tax rate, τh, by combining equations (3.10) and (3.11), yielding 1.6
.
(3.12)
The factor of 1.6 was derived by Prescott by employing the methodology of Feenberg and Coutts (1993) to estimate the marginal income tax rate in the United States during both 1970-1974 and 1993-1996. Their methodology used representative samples of the tax records to determine the marginal tax rate on labor income by determining how much tax revenue increased when household labor income increased by 1%.
37
3.3. My Key Equilibrium Relation In my equilibrium relation, I seek to express hours worked, h, as a function of the effective marginal tax rate on labor income, τ. I combine the marginal labor income tax rate and consumption tax rates to calculate the effective marginal tax rate on labor income. This tax rate specifies the fraction of labor income taken in the form of taxes, holding investment fixed. Prescott expressed it as
.
1
(3.13)
I then use two first order conditions to derive the equilibrium relation between hours worked and the effective marginal tax rate on labor income. The first condition reflects the fact that the marginal rate of substitution (MRS) between leisure and consumption is equal to their price ratio, which is the after-tax wage rate. Using the utility function in (3.2), / /
MRS
/
1/ /
1
.
Thus, /
1
.
(3.14)
The second condition is the profit-maximizing condition that wage equals the marginal product of labor (MPL). Again, using equation (3.2),
38
MPL
1
1
where final equality holds because according to equation (3.4),
, so
.
Thus, 1
.
(3.15)
I adopt Prescott’s value for θ of 0.3223 since this is the empirically determined average value for the countries under consideration. Combining the first order conditions given in equations (3.14) and (3.15), I derive the following equilibrium relation /
/
1
1
1 – 1 –
/
1 –
1 –
1–
1 – /
.
Rearranging this equation, I express my equilibrium relation for country i at date t as /
1 1
.
(3.16)
39
When Prescott subjected his utility function (equation 3.1) to same manipulations, his equilibrium relation was 1 1
.
(3.17)
1
This equation shares many of the same features of mine, but mine can be used to directly calculate the Frisch elasticity of labor supply while his cannot. My equilibrium relation, like Prescott’s, separates the intratemporal and intertemporal factors affecting labor supply. The (1 – τ) term reflects the intratemporal effects of taxes on the relative prices of consumption and leisure. On the other hand, the c/y term reflects intertemporal factors because if, for example, the effective tax rate is expected to rise in the future, c/y will be lower at present since households will have an incentive to save to smooth consumption. All other things equal, a lower value of c/y will be associated with a higher value of h. An expectation of a future tax increase will cause an increase in current labor supply. Similarly, if the level of the capital stock were low relative to the balanced growth path level, c/y would be lower since households would have the incentive to save in order to increase investment. This would again produce a higher value of h. 3.4. Explanation of Results To calculate α, the utility of leisure parameter, and ψ, the Frisch elasticity of labor supply, I rewrite (3.16) as follows /
1 1
40
/
1
1 1
/
1
1 1
/
.
since the values of c, y, θ, and τ are known for each country and
We may now let
time period considered. Then,
1
log log log
/
1 1
/
log
/
log
/
1 1
/
/
log
log α
1
log z
To run a regression, I express the equilibrium relation as
log
1 h
1
log
1
log
(3.18)
in order to account for unmodeled factors that affect labor supply. To appropriately estimate the values of [ψ/(ψ + 1)]*log(α) and [ψ/(ψ + 1)], however, I must use a two stage least squares regression. The independent variable z is endogenous because z contains the consumption to output ratio c/y, which is correlated with ε because changes in household preferences will influence consumption decisions. A change in ε will affect c/y, which in turn affects the labor supply. It is therefore necessary to use an instrumental variable. I
41
choose τ, the effective marginal tax rate on labor income, to be that instrument because, since τ is a component of z, it is clearly correlated with z. Furthermore, τ is uncorrelated with ε since I have assumed factors that determine tax rates are not affected by household preferences. In my model, changes in household preferences, which would affect labor supply through changes in c/y, should have no effect on τ, which is set independently by governments. Hence, I can express equation (3.18) as
log
1 h
1
log
1
log
(3.19)
where λ is the dummy variable for τ. Running a two stage least squares regression on (3.19), I find that [ψ/(ψ + 1)]*log(α) = 0.888 and that [ψ/(ψ + 1)] = 0.748. The values of [ψ/(ψ + 1)]*log(α) and [ψ/(ψ + 1)] are of no inherent interest, but I can use them to determine the values of α and ψ. I calculate ψ as follows
1
.748
.748
1
.748
.748
.748
.748
2.97.
. 748 1 .748
I calculate α as follows
1
log α
.888
42
log α
. 888
.
3.28
/
1
/.
It is useful to know how reliable these estimations of α and ψ are. Because I have calculated them indirectly, I have to be careful in estimating their standard errors. I cannot directly manipulate the standard errors for [ψ/(ψ + 1)]*log(α) and [ψ/(ψ + 1)] to obtain the standard errors for α and ψ. It is necessary instead to use bootstrap. Using 2,000 bootstrap repetitions, I determine the standard error of α to be 0.19 and the standard error of ψ to be 0.31. Since α = 3.28, the 95% confidence interval places it between 2.91 and 3.65. Since ψ = 2.97, the 95% confidence interval places it between 2.36 and 3.58. The null hypothesis that α = 0 is rejected since p-value for this hypothesis test less than 0.001. Similarly, the null hypothesis that ψ = 0 is rejected. I have firm evidence that households derive positive utility from leisure and that the Frisch elasticity of labor supply is not zero. Therefore, changes in the effective marginal tax rate will affect labor supply. Table 3.2 summarizes my results for the values and standard errors for α and ψ and the results of my hypothesis tests. Table 3.3 presents the labor supply estimated using (3.16), and the empirical OECD data for labor supply in the G-7 countries during the periods of 1970-1974 and 1993-1996. During 1993-1996, the difference between the estimated values and the empirical values is quite small. The average difference is only 1.4 hours per week, nearly identical to the average difference computed in Prescott (2004). During 1970-1974, the difference is also quite small except in the case of Japan and Italy, which are the outliers. The model performs rather well for the other 12 data points, especially considering the fact that it assumes a single value of the Frisch elasticity
43
TABLE 3.2 SUMMARY OF RESULTS FOR PARAMETERS OF INTEREST Parameter
Interpretation
Estimate (Standard Error)
α
Utility of leisure parameter
3.28
Null Hypothesis Value
p-value
0
≤0.001
0
≤0.001
(0.19) Frisch elasticity of labor supply
ψ
2.97 (0.31)
Note: Estimates based on 2 observations from each of the G-7 countries for a total of 14 observations.
TABLE 3.3 EMPIRICAL VERSUS ESTIMATED VALUES OF LABOR SUPPLY Labor Supply* Period
Country
1993-1996
Germany
19.3
19.6
France
17.5
Italy
1970-1974
Empirical Estimated
Difference (Estimated Less Empirical)
Prediction Factors Tax Rate τ
Cons./Output (c/y)
0.3
0.59
0.74
19.7
2.2
0.59
0.74
16.5
19.0
2.5
0.64
0.69
Canada
22.9
21.4
-1.5
0.52
0.77
United Kingdom
22.8
22.8
0.0
0.44
0.83
Japan
27.0
29.0
2.0
0.37
0.68
United States
25.9
24.6
-1.3
0.40
0.81
Germany
24.6
24.1
-0.5
0.52
0.66
France
24.4
25.3
0.9
0.49
0.66
Italy
19.2
28.2
9.0
0.41
0.66
Canada
22.2
25.6
3.4
0.44
0.72
United Kingdom
25.9
23.8
-2.1
0.45
0.77
Japan
29.8
36.4
6.6
0.25
0.60
United States
23.5
26.2
2.7
0.40
0.74
*Labor supply is measured in hours worked per person aged 15-64 per week.
44
of labor supply for all countries during both time periods. It is clear from Table 3.3 that during the early 1970’s, when tax rates in the United States and Continental Europe were similar, labor supplies in the United States and Continental Europe were similar as well. At the aggregate level when idiosyncratic factors are averaged out, it would appear that Americans and Continental Europeans had similar economic preferences during that time period. In the mid-1990’s, however, higher tax rates in Continental Europe apparently had produced relatively lower labor supplies. If a worker in Europe had earned 100 additional euros, he would have paid about 60 euros in direct or indirect taxes. If a worker had earned an extra $100 in the United States, he would have paid only $40 to the government. As a result, Americans had more incentive to work. Given my finding that the Frisch elasticity of labor supply was 2.97, the vast majority of the difference between the labor supply in the United States and that of France and Germany could be explained by differences in the effective marginal tax rates. My direct calculation of the Frisch elasticity of labor supply produces a value virtually identical to Prescott’s indirect calculation that it is “nearly 3.” These values imply that households react strongly to changes in effective marginal tax rates. It is interesting to note that my value of 3.28 for the utility of leisure parameter is much greater than Prescott’s value of 1.54. This is not surprising, however, because I employed a different utility function (equation (3.2) instead of equation (3.1)).
45
Chapter 4: My Dynamic General Equilibrium Model The simple static model presented in chapter 3 has several important limitations. In this chapter, I will explain why a number of its underlying assumptions are gross oversimplifications and why the dynamic general equilibrium model which I develop in this chapter represents a significant improvement. 4.1. How the Dynamic Model Improves upon the Simple Static Model While the simple static model seems to provide strong evidence that marginal tax rates themselves can have a profound effect on labor supply, it is highly oversimplified. First of all, while it takes into account interaction between variables, such as consumption, output, hours worked, and tax rates, within time periods, it does not take into account interactions across time periods. It is reasonable to expect that their values in one period will affect their values in subsequent periods. My dynamic general equilibrium model is designed to take such interactions into account. Second, the simple static model assumes that the Frisch elasticity of labor supply is equal for all countries during both time periods. This is unlikely since the G-7 countries have different cultural values and different non-tax government policies which would be expected to affect how much households choose to work. The dynamic general equilibrium model presented in section 4.2 is able to incorporate different values of the Frisch elasticity of labor supply for different countries. Third, the simple static model does not incorporate the idea of consumption-work complementarity. The dynamic general equilibrium model explicitly considers this complementarity in its utility function. Finally, the simple static model assumes all non-military government expenditures substitute on a one-to-one basis for private consumption. It is probably
46
more accurate to believe that different types of government expenditures will affect hours worked in a different ways. For example, it is unlikely that government expenditures for disability payments will have the same effect on labor supply as government funding of day care programs of children of working parents. In order to treat this problem, I introduce a parameter into the dynamic model in chapter 6 to reflect the varying amount that individuals value government expenditures. 4.2. Introduction to the Dynamic General Equilibrium Model My dynamic general equilibrium model builds on the model developed in Hall (2009a), applying aspects of that model to the analysis of the effect of tax rates and patterns of government expenditures on output and labor supply. The presentation of the dynamic general equilibrium model which follows in this section is an outline of how the calculations are actually performed in my model. The optimization problems entailed are far too complex and cumbersome to do by hand. It is necessary to encode the model with Matlab to perform the calculations. The Matlab program created for this thesis is presented in Appendix A. In my model, individual preferences are given by /
1
1/
/
/
/
1
1/
.
(4.1)
I sum from t = 0 to 79 because I have chosen to consider a lifespan of 80 years. This utility function incorporates the concept of the consumption-work complementarity by employing the χ parameter, which gives its magnitude. The variable c represents the consumption of goods and services, and σ describes the curvature of utility with respect to consumption. In addition, σ reflects is also the intertemporal elasticity of substitution and the reciprocal of the coefficient of
47
relative risk aversion. The variable h represents the volume of work, and ψ describes the curvature of utility with respect to the volume of work. When χ = 0, ψ represents the Frisch elasticity of labor supply. Finally, γ represents the magnitude of the disutility of work. Without taxation, the first-order condition that maximizes utility and optimizes the combination of consumption and work can be calculated with the following equality /
1
1
/
1/
/
1
/
1/
(4.2)
.
I derive equation (4.2), noting that optimal combination of consumption and work is found using /
the first-order condition
. If I assume a tax scheme consisting of a wage tax where
/
individuals receive a wage w and have to pay a fraction τ of their income in taxes, the individual’s after-tax wage is 1
. Then, the first order condition which maximizes an
individual’s utility becomes 1
/
1
1
1/
/
/
1
1/
/
.
(4.3)
In this paper, I consider three cases with respect to the way in which tax revenue is used by the government. In chapter 5, I analyze the case considered by Prescott (2004) in which all tax revenue is spent on lump sum transfer payments to individuals regardless of hours worked. In chapter 6, I analyze both the case in which all the tax revenue is expended on wasteful programs which do not affect the individual’s marginal utility of consumption and the case in which tax revenue is expended on programs to benefit individuals regardless of hours worked but only a certain fraction (μ) of that expenditure corresponds to their consumption preferences, the remainder (1– μ) being expended on projects that do not affect the individual’s marginal utility of consumption.
48
My dynamic general equilibrium model assumes technology in the economy is described by the Cobb-Douglas production function, so (4.4) where α is labor’s share of output and k is capital. I use the standard value of α = 0.70. In accordance with the literature on labor supply models, I assume competition and no capital adjustment costs. Capital then rents for the price (4.5) where bt is the rental price of capital, rt is the real interest rate and therefore the net marginal product of capital, and δ is the depreciation rate. I use the standard value of δ = 0.10. Capital demand in period t equals the capital supply as determined by the previous period, so 1
(4.6)
The law of motion for capital is given by
1
(4.7)
because at the end of each period, the sum of the output (yt) produced in the economy and the capital stock remaining from the previous period (kt-1) is allocated to consumption (ct), government purchases (gt), and the new capital stock (kt). The economy’s discounter is
,
/
1
1
1/
/
/
1
1
1/
/
(4.8)
49
where β is the ratio of the present value of consumption in period t+1 relative to consumption in period t. I use the standard value of β = 0.95. The Euler equation for consumption is 1
,
1
(4.9)
since the reciprocal of the economy’s discounter is equal to one plus the real interest rate. Finally, I assume that the initial capital stock in the economy is equal to its steady state level at the initial tax rate. I also assume that the capital stock at the end of period T is equal to its steady state level at the final tax rate. This assumption is reasonable since the capital stock will asymptotically approach its infinite-horizon solution for reasonably large values of T. I set T = 80 to model the effects of changing tax rates and the patterns of government expenditures over the course of an 80 year lifetime, but my model has the turnpike property so the value of T essentially irrelevant as long as it is greater than 20 because the vast majority of the changes take place within 20 years.
50
Chapter 5: Employing My Dynamic Model In this chapter, I apply my dynamic general equilibrium model. I assume that all tax revenue is spent on lump sum transfer payments to individuals regardless of hours worked. I explore the effects of changes in the tax rate on several important economic parameters and examine what happens if I assume no consumption-work complementarity or if I postulate a lower labor supply elasticity. 5.1. The Trivial Case: No Taxes I first consider the simplest case: no taxes. Predictably, the model shows no change over time in output (y), hours of work (h), the real interest rate (r), the wage (w), consumption (c), capital stock (k), the economy’s discounter (m), or the rental price of capital (b). 5.2. The Model with Taxes I then analyze the effect of taxes, assuming that all of the tax revenue is spent on lump sum transfer payments to individuals regardless of hours worked. I set the initial capital stock equal to the capital stock in the steady state under the initial tax rate and the final capital stock equal to the capital stock in the steady state under the final tax rate, but I allow the capital stock and the other parameters to vary during the intervening period. For example, I consider a country with a tax rate of 20% which decides to raise its tax rate to 30%. My model sets the capital stock in year 1 equal to the capital stock in the economy with a 20% tax rate in the steady state. It sets the capital stock in year 80 equal to the capital stock in that economy with a 30% tax rate in the steady state. Between years 1 and 80, the
51
capital stock and the other parameters vary until they approach their new steady states. I can track all parameters yearly through the 80 year lifetime. If the final tax rate equals the initial tax rate, the value of any parameter in year 1 will equal its value in year 80. Parameters change only if the tax rate changes (or if individuals’ preferences for government spending change, as discussed in chapter 6). 5.3. Changing the Tax Rate in the Dynamic General Equilibrium Model In this section, I first examine how the various parameters change when the tax rate increases from 20% to 30% in my baseline case in which all tax revenue is spent on lump sum transfer payments regardless of hours worked, the consumption-work complementarity holds, and the labor supply is elastic. Later I investigate how these parameters change when the tax rate decreases, for example, from 20% to 10% in the baseline case. The specific initial and final tax rates which I have chosen in my presentation have no special significance. They were chosen arbitrarily for illustrative purposes. 5.3.1. Increasing the Tax Rate from 20% to 30% If all tax revenue is spent on lump transfer payments, there is no income effect when the tax rate is changed. Therefore, when the tax rate increases, hours worked should decrease because decreasing after-tax wages decreases the incentive to work since the marginal utility of consumption remains constant. The decrease in after-tax wage lowers the marginal benefit of working. Consider the case in which the tax rate increases from 20% in year 1 to 30% in year 2 and remains at 30% through year 80. Table 5.1 presents a summary of the changes in the economic parameters while Results Spreadsheet 1, presented in Appendix B, gives the results in detail. As Appendix B shows, the pre-tax wage actually increases slightly from year 1 to year 2,
52
TABLE 5.1 RESULTS FROM THE TAX INCREASE FROM 20% TO 30%
Parameter
Interpretation
Percentage Change from Year 1 to Year 80
Percentage Change from Year 2 to Year 80
y h r w c k m b
Output Hours worked Real Interest Rate Pre-Tax Wage Consumption Capital Economy's Discounter Rental Price of Capital
–6.0% –6.0% 0.0% 0.0% –6.0% –6.0% n/a* n/a*
–0.6% +1.8% +15.7% –2.4% –1.5% –5.2% –0.7% +4.9%
*There is no value for m or b for year 1.
going from 0.935 to 0.958, reflecting the fact that the decrease in hours worked from 0.781 to 0.720 increases the marginal product of labor, assuming diminishing returns to labor. See Graphs 5.1 and 5.2. The increase in the pre-tax wage, however, does not even come close to compensating for the decrease in the after-tax wage caused by increase in the tax rate. After a large decrease in hours worked from year 1 to year 2 from 0.781 to 0.720, hours worked increases from its low point in year 2 to asymptotically approach the steady state value of 0.734 at a tax rate of 30%. This small increase in hours worked slightly lowers the pre-tax wage. In fact, the pre-tax wage decreases asymptotically to its steady state value of 0.935 in year 80. The after-tax wage is thus much lower at a tax rate of 30% than at a tax rate of 20%. The increase in the tax rate causes consumption to fall since the after-tax wage is lowered, causing individuals work and earn less. See Graph 5.3. Even if all tax revenue is rebated back to individuals, consumption falls because individuals work less when the tax rate is increased, so there is less income to consume. (The decrease in consumption is smaller,
53
GRAPH 5.1
Change in the pre‐tax wage over time when the wage tax rate increases from 20% to 30% Pre‐Tax Wage
0.96 0.955 0.95 0.945 0.94 0.935 0.93 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 Year Number
GRAPH 5.2
Change in hours worked over time when the wage tax rate increases from 20% to 30% Hours Worked
0.8 0.78 0.76 0.74 0.72 0.7 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 Year Number
54
GRAPH 5.3
Consumption
Change in consumption over time when the wage tax rate increases from 20% to 30% 0.85 0.84 0.83 0.82 0.81 0.8 0.79 0.78 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 Year Number
however, than it is when the tax revenue is spent solely on projects which do not affect the individual’s marginal utility of consumption.) The decrease in consumption is continuous from year 1 to year 80. Individuals work more hours and have a higher after-tax wage in year 1 than in year 2. Consumption falls from 0.838 in year 1 to 0.800 in year 2. Consumption in year 2 is higher, however, than in subsequent years because the slight increase in hours worked from year 2 to year 80 is more than offset by the decline in the after-tax wage which occurs over the period. Hence consumption falls from 0.800 in year 2 until it approaches its steady state of 0.788 in year 80. The model sets the initial capital stock at the steady state value obtained under the tax rate of 20%. Because higher tax rates decrease the incentive to work and therefore reduce hours worked, they lessen the amount of capital necessary for production. Since the capital stock in year 80 is set at the steady state value for the tax rate of 30%, the capital stock is lower in year 80 than it is in year 1, falling from 2.050 to 1.927. See Graph 5.4.
55
GRAPH 5.4
Change in the capital stock over time when the wage tax rate increases from 20% to 30%
Capital Stock
2.1 2.05 2 1.95 1.9 1.85 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 Year Number
To understand the changes in the real interest rate, it is important to recognize that, because this model assumes competitive markets, the real interest rate is set equal to the marginal product of capital. The increase in the tax rate leads to a large sudden decrease in hours worked between years 1 and 2, and because there are fewer hours of work in which to employ the capital stock, the marginal product of capital, and thus the real interest rate, falls from 0.053 in year 1 to 0.045 in year 3. See Graph 5.5. (The real interest rate is not defined in year 2 because the economy’s discounter is not defined for year 1. Consider equations (4.10) and (4.11):
,
/
1
1
1/
/
/
1
1
1/
/
and 1
,
1.
Since m is not defined in period 1, r cannot be defined in period 2.) As hours worked rebounds
56
GRAPH 5.5
Change in the real interest rate over time when the wage tax rate increases from 20% to 30% Real Interest Rate
0.054 0.052 0.05 0.048 0.046 0.044 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 Year Number
and the capital stock diminishes from year 2 to year 80, each unit of capital stock becomes more valuable, increasing its marginal product and thus the real interest rate until the real interest rate reaches its initial steady state value of 0.053 in year 80. The changes in output, the rental price of capital, and the economy’s discounter follow from the previous discussion. Output is an increasing function of hours worked and the capital stock. Because hours worked falls by a large amount from year 1 to year 2 while the capital stock also decreases, output drops precipitously from 1.043 to 0.986. See Graph 5.6. From year 2 to year 80, hours worked rebounds somewhat, but the capital stock decreases at a faster rate, so there is a slow but steady further decline in output from 0.986 to 0.980. The rental price of capital is defined as the real interest rate plus the depreciation rate. Since the model assumes a constant depreciation rate of 0.10 per year, the absolute changes in the rental price of capital equal the absolute changes in the real interest rate and reflect the same
57
GRAPH 5.6
Change in output over time when the wage tax rate increases from 20% to 30% 1.06
Output
1.04 1.02 1 0.98 0.96 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 Year Number
economic mechanisms. See Graph 5.7. There is no value for the rental price of capital until year 3. From year 3 to year 80, the changes in the rental price of capital mirror the changes in the real interest rate. The economy’s discounter is defined by the Euler equation as an inverse function of the real interest rate, so that when the real interest rate increases, the economy’s discounter decreases. The Euler equation is 1
,
1.
The discounter is only defined between years 2 to 79. It decreases asymptotically toward a steady state as the real interest rate increases over that period. See Graph 5.8. 5.3.2. Decreasing the Tax Rate from 20% to 10% The economic explanation of the changes in the parameters when the tax rate is lowered is simply the inverse of that of the changes when the tax rate is raised. For example, when the tax rate decreases in the baseline case, economic intuition suggests that hours worked should
58
GRAPH 5.7
Change in the rental price of capital over time when the wage tax rate increases from 20% to 30% Rental Price of Capital
0.154 0.152 0.15 0.148 0.146 0.144 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60 63 66 69 72 75 78 Year Number
Value of the Economy's Discounter
GRAPH 5.8
Change in the value of economy's discounter over time when the wage tax rate increases from 20% to 30% 0.958 0.956 0.954 0.952 0.95 0.948 2 5 8 11 14 17 20 23 26 29 32 35 38 41 44 47 50 53 56 59 62 65 68 71 74 77 Year Number
59
TABLE 5.2 RESULTS FROM THE TAX DECREASE FROM 20% TO 10%
Parameter
Interpretation
Percentage Change from Year 1 to Year 80
Percentage Change from Year 2 to Year 80
y h r w c k m b
Output Hours worked Real Interest Rate Pre-Tax Wage Consumption Capital Economy's Discounter Rental Price of Capital
+5.6% +5.6% 0.0% 0.0% +5.6% +5.6% n/a* n/a*
+0.5% –1.7% –11.1% +2.2% +1.3% +4.7% +0.6% –4.2%
*There is no value for m or b for year 1.
increase because there is more incentive to work. Given the same pre-tax wage, the after-tax wage rises. The increase in after-tax wage raises the marginal utility of work. Consider, for example, the case in which the tax rate decreases from 20% in year 1 to 10% in year 2 and remains at 10% through year 80. Table 5.2 presents a summary of the results while Results Spreadsheet 2, presented in the Appendix B, gives these results in detail. The pre-tax wage decreases slightly from year 1 to year 2 from 0.935 to 0.915 because, assuming diminishing returns to labor, an increase in hours worked from 0.781 to 0.839 results in a decrease the marginal product of labor. See Graphs 5.9 and 5.10. This decrease in the pre-tax wage, however, does not even come close to compensating for the increase in the after-tax wage caused by decrease in the tax rate. After the large increase hours worked from year 1 to year 2 (from 0.781 to 0.839), hours worked gradually decreases to asymptotically approach the steady state value of 0.825. This small decrease in hours worked slightly raises the pre-tax wage. In fact, the pre-tax wage increases asymptotically back to its steady state value of 0.935 in year 80. The after-tax wage is thus much higher due to the lower taxes. Similarly, the changes in other parameters
60
GRAPH 5.9
Change in the pre‐tax wage over time when the wage tax rate decreases from 20% to 10% Pre‐Tax Wage
0.94 0.935 0.93 0.925 0.92 0.915 0.91 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 Year Number
GRAPH 5.10
Change in hours worked over time when the wage tax rate decreases from 20% to 10% Hours Worked
0.86 0.84 0.82 0.8 0.78 0.76 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 Year Number
61
TABLE 5.3 RESULTS FROM THE CHANGING THE TAX RATE BY VARIOUS AMOUNTS
Parameter
Interpretation
y h r w c k
Output Hours worked Real Interest Rate Pre-Tax Wage Consumption Capital
Percentage Change from Year 1 to Year 80* Rate = 0%
Rate = 10%
Rate = 20%
Rate = 30%
Rate = 40%
+10.1% +10.1% 0.0% 0.0% +10.1% +10.1%
+5.6% +5.6% 0.0% 0.0% +5.6% +5.6%
0.0% 0.0% 0.0% 0.0% 0.0% 0.0%
–6.0% –6.0% 0.0% 0.0% –6.0% –6.0%
–12.6% –12.6% 0.0% 0.0% –12.6% –12.6%
*These columns present the percentage change for each parameter given an initial tax rate of 20% and a final tax rate indicated by each column heading.
Parameter
Interpretation
y h r w c k
Output Hours worked Real Interest Rate Pre-wage Wage Consumption Capital
Percentage Change from Year 1 to Year 80* Rate = 50%
Rate = 60%
Rate = 70%
Rate = 80%
Rate = 90%
–19.7% –19.7% 0.0% 0.0% –19.7% –19.7%
–27.8% –27.8% 0.0% 0.0% –27.8% –27.8%
–37.0% –37.0% 0.0% 0.0% –37.0% –37.0%
–48.3% –48.3% 0.0% 0.0% –48.3% –48.3%
–63.6% –63.6% 0.0% 0.0% –63.6% –63.6%
*These columns present the percentage change for each parameter given an initial tax rate of 20% and a final tax rate indicated by each column heading.
parallel those in the case of the tax increase with the obvious reversal of sign. The Graphs of those changes are the mirror image of those for the tax increase. Compare, for example, Graph 5.1 to 5.9 or Graph 5.2 to 5.10. 5.3.3. Varying the Magnitude of the Change in the Tax Rate It is also interesting to examine how much the parameters are affected by tax changes of varying magnitudes. I have analyzed data for the cases in which the initial tax rate is 20% and
62
GRAPH 5.11
Percentage Change in Output
Changes in output from year 1 to year 80 given an initial tax rate of 20% and various final tax rates 20.0% 0.0% ‐20.0% ‐40.0% ‐60.0% ‐80.0% 0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
Final Tax Rate
Percentage Change in Hours Worked
GRAPH 5.12
Changes in hours worked from year 1 to year 80 given an initial tax rate of 20% and various final tax rates 20.0% 0.0% ‐20.0% ‐40.0% ‐60.0% ‐80.0% 0%
10%
20%
30%
40%
50%
Final Tax Rate
60%
70%
80%
90%
63
Percentage Change in Consumption
GRAPH 5.13
Changes in consumptionfrom year 1 to year 80 given an initial tax rate of 20% and various final tax rates 20.0% 0.0% ‐20.0% ‐40.0% ‐60.0% ‐80.0% 0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
Final Tax Rate
Percentage Change in the Capital Stock
GRAPH 5.14
Changes in the capital stock from year 1 to year 80 given an initial tax rate of 20% and various final tax rates 20.0% 0.0% ‐20.0% ‐40.0% ‐60.0% ‐80.0% 0%
10%
20%
30%
40%
50%
Final Tax Rate
60%
70%
80%
90%
64
the final tax rate is 0%, 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, and 90%. See Table 5.3. A few results stand out. First, after 80 years the real interest rate and the pre-tax wage are in all cases unchanged. Second, output, hours worked, consumption, and the capital stock all increase when the tax rate is decreased and decrease when the tax rate is increased. Finally, each 10% increase in the final tax rate from 0% to 90% has an increasingly large effect on the magnitude of the resulting changes in output, hours worked, consumption, and the capital stock. In other words, the marginal loss in output, hours worked, consumption, and the capital stock between year 1 to year 80 is smallest when the final tax rate goes from 0% to 10%, larger when the final tax rate goes from 10% to 20%, and so on in an increasing fashion until the greatest marginal loss occurs largest when the final tax rate goes from 80% to 90%. See Graphs 5.11-5.14. This demonstrates that the disincentives of higher tax rates become more and more pronounced as those rates increase because individuals have less and less incentive to work as the government takes more and more of their income. For example, when the tax rate goes from 0% to 10%, individuals keep only 90% of their pre-tax wage instead of 100%. When the final tax rate is changed from 80% to 90%, individuals go from keeping 20% of their pre-tax wage to keeping only 10%, a much larger relative decrease. Thus, an increase in the final tax rate of a given percentage of income will have less of a negative effect on output, hours worked, consumption, and the capital stock when the tax rate is low than the same increase in terms of percentage of income when the tax rate is already high. 5.4. Removing the Assumption of Consumption-Work Complementarity One of the assumptions of my dynamic general equilibrium model is that there is a complementarity between consumption and work. This complementarity is reflected in
65
equation (4.1) /
1
/
/
/
1/
1
1/
where χ signifies the magnitude of the complementarity. I assume consumption-work complementarity in my baseline case because empirical evidence suggests that an individual’s consumption of goods and services in the market economy will indeed rise when he works more hours, holding marginal utility constant. If an individual works more, he will have less time for home production and will rely more on purchases in the market. The existence of consumptionwork complementarity is reflected, for example, in the data regarding the “retirement consumption puzzle.” Consumption of goods and services in the market decreases when individuals retire as retirees apparently devote more time to home production. Although it is logical to assume consumption-work complementarity, one can alter my model to remove this assumption. This yields a new utility function /
1
1/
/
1
1/
.
(5.1)
If the consumption-work complementarity is removed, the magnitude of the decreases in output, hours worked, consumption, and the capital stock caused by higher tax rates is smaller. This is because when higher tax rates induce individuals to works less, the consumption-work complementarity implies that they would decrease their market consumption by a larger amount because they would have more time for home production. If there were no complementarity, individuals would not reduce their market consumption as much. Larger decreases in consumption would result in larger decreases in output, hours worked, and the capital stock, so if
66
the complementarity is not assumed, these parameters will not decrease as much. For example, consider an increase in the tax rate from 20% to 30%. If the complementarity is assumed, the decrease in output, hours worked, consumption, and the capital stock is 6.0%. If the complementarity is not assumed, this decrease is 5.1%. Conversely, if there is a tax decrease and the consumption-work complementarity does not exist, the increase in output, hours worked, consumption, and the capital stock will be smaller. These results are summarized in Tables 5.4 and 5.5. 5.5. Assuming a Lower Wage Elasticity of Labor Supply Another key assumption of my model in the baseline case is that the wage elasticity of labor supply is 1.9. Labor supply elasticity is defined as the elasticity of hours worked with respect to the wage rate, given a constant marginal utility of consumption. Economists disagree about the actual magnitude of the labor supply elasticity. Empirical household data suggests that it may be between 0.2 and 1.0. Macroeconomic models, however, yield higher estimates. Hall (2009a) used an employment function which takes into account both the elasticity resulting from choices by workers about how much to work and from sticky wage compensation in the searchand-matching setup of Mortensen and Pissarides (1994). Hall found the labor supply elasticity to be 1.9. I have chosen to use that value in my baseline case rather than the value of 2.97 which I derived in chapter 3 with a less sophisticated static model, especially because 2.97 is at the extreme upper end of estimates of the labor supply elasticity found in the literature. If I had chosen to use a labor supply elasticity of 0.5, the changes in output, hours worked, consumption, and the capital stock for a given change in the tax rate would have been smaller because, although the same increase in the tax rate would cause the same change in the
67
TABLE 5.4 RESULTS FROM THE TAX INCREASE UNDER DIFFERENT ASSUMPTIONS Percentage Change from Year 1 to Year 80* Parameter
Interpretation
y h r w c k
Output Hours worked Real Interest Rate Pre-Tax Wage Consumption Capital
Base Case
No Complementarity
Less Elastic Labor Supply
–6.0% –6.0% 0.0% 0.0% –6.0% –6.0%
–5.1% –5.1% 0.0% 0.0% –5.1% –5.1%
–4.6% –4.6% 0.0% 0.0% –4.6% –4.6%
*These columns indicate the percentage change for each parameter given an initial tax rate of 20% and a final tax rate of 30%.
TABLE 5.5 RESULTS FROM THE TAX DECREASE UNDER DIFFERENT ASSUMPTIONS
Parameter
Interpretation
y h r w c k
Output Hours worked Real Interest Rate Pre-Tax Wage Consumption Capital
Percentage Change from Year 1 to Year 80* Base Case +5.6% +5.6% 0.0% 0.0% +5.6% +5.6%
No Complementarity +4.8% +4.8% 0.0% 0.0% +4.8% +4.8%
Less Elastic Labor Supply +4.3% +4.3% 0.0% 0.0% +4.3% +4.3%
*These columns indicate the percentage change for each parameter given an initial tax rate of 20% and a final tax rate of 10%.
after-tax wage, this would have caused in a smaller decrease in hours worked. If hours worked decreases by a smaller amount, output, consumption, and capital stock also decrease by smaller amounts. By the same logic, if a higher wage elasticity of labor supply is assumed, a given tax increase would decrease hours worked by a larger amount. Individuals will produce less, consume less, and require less capital. If the tax rate rises from 20% to 30%, assuming a wage
68
elasticity of labor supply of 1.9, the decrease in output, hours worked, consumption, and the capital stock is 6.0%. If the wage elasticity of labor supply is 0.5, the decline in those parameters is 4.6%. Conversely, if there is a tax decrease, a lower labor supply elasticity results in smaller increases in the parameters. These results are summarized in Tables 5.4 and 5.5.
69
Chapter 6: Alternative Scenarios for Government Spending In the previous chapter, I analyzed the results generated by my dynamic general equilibrium model assuming that all tax revenue was spent on lump sum transfers to individuals regardless of hours worked. In this chapter, I examine other possibilities. First, I consider the extreme case in which all tax revenue is spent on projects which do not affect the individual’s marginal utility of consumption. Next, I consider the case in which a certain fraction (μ) of tax revenue is spent on programs corresponding to individuals’ consumption preferences and the remainder (1– μ) is spent on projects that do not affect the individual’s marginal utility of consumption. This scenario reflects the fact that individuals usually do not value government spending as much as their own consumption, but rather value it less than their disposable income. 6.1. Government Spending on Wasteful Projects When all tax revenue is returned to individuals in the form of lump sum transfers regardless of hours worked, tax changes do not produce an income effect because in the model all individuals make the same wage and thus the lump sum transfer exactly equals the taxes paid. Tax changes only produce a substitution effect because individuals are not made richer or poorer by the changes. All the money paid to the government in taxes returns to individuals to spend as they please. Tax rate changes still have a substitution effect, however, because they change the after-tax wage from (1 – τi)w to (1 – τf)w, where τi is the initial tax rate and τf is the final tax rate. When the after-tax wage changes, the marginal utility of work changes, inducing individuals to work more if their after-tax wage is higher and to work less if their after-tax wage is lower.
70
Suppose, however, that all tax revenue is spent on projects which do not affect the individual’s marginal utility of consumption. A tax change will now have both an income effect and a substitution effect. Consider the base case of a tax increase from 20% to 30%. The tax increase will make individuals poorer. They will now only keep 70% of their wage instead of 80% of it. The remainder of their wage will be used by the government in ways that provide them no utility. The tax increase clearly makes them poorer. Since my model assumes diminishing returns to consumption, the poorer the individual is, the more he values a given unit of consumption. The income effect of the tax increase induces an individual to work more hours because his marginal utility of consumption increases when his income decreases. The substitution effect is also present with the tax increase. If the marginal utility of consumption were held constant, the individual making 70% of his wage after the tax increase instead of 80% would have less incentive to work. Each additional hour he spent working under the higher tax rate would produce less additional ability to consume. This is clearly true if the marginal utility of consumption is held constant, but when the income effect is present, the marginal utility of consumption changes. A lower after-tax wage does not necessarily result in less incentive to work. In fact, economic theory is ambiguous about the potential effect of an increase in the tax rate on labor supply in this case because it is ambiguous about whether the income effect or substitution effect will dominate (Kalemli-Ozcan and Weil 2010). The results from my model, presented in the right hand column in Table 6.1 (μ = 0), indicate that an increase in the tax rate from 20% to 30% increases labor supply (and output and the capital stock) when government revenue is assumed to be spent on projects which do not affect the individual’s marginal utility of consumption. Consumption is the economic parameter which still falls when the tax rate increases. This is because while individuals work more when the tax rate increases
71
TABLE 6.1 RESULTS FOR A TAX INCREASE FROM 20% TO 30% WITH DIFFERENT VALUES OF μ
Parameter
Interpretation
Percentage Change from Year 1 to Year 80 (μ = 1)
Percentage Change from Year 1 to Year 80 (μ = 0.75)
Percentage Change from Year 1 to Year 80 (μ = 0.50)
Percentage Change from Year 1 to Year 80 (μ = 0.25)
Percentage Change from Year 1 to Year 80 (μ = 0)
y h r w c k
Output Hours worked Real Interest Rate Pre-Tax Wage Consumption Capital
–6.0% –6.0% 0.0% 0.0% –6.0% –6.0%
–4.2% –4.2% 0.0% 0.0% –6.3% –4.2%
–2.0% –2.0% 0.0% 0.0% –6.6% –2.0%
+0.7% +0.7% 0.0% 0.0% –6.9% +0.7%
+3.9% +3.9% 0.0% 0.0% –7.1% +3.9%
*Assuming consumption-work complementarity and an elastic labor supply.
TABLE 6.2 RESULTS FOR A TAX DECREASE FROM 20% TO 10% WITH DIFFERENT VALUES OF μ
Parameter
Interpretation
Percentage Change from Year 1 to Year 80 (μ = 1)
Percentage Change from Year 1 to Year 80 (μ = 0.75)
Percentage Change from Year 1 to Year 80 (μ = 0.50)
Percentage Change from Year 1 to Year 80 (μ = 0.25)
Percentage Change from Year 1 to Year 80 (μ = 0)
y h r w c k
Output Hours worked Real Interest Rate Pre-Tax Wage Consumption Capital
+5.6% +5.6% 0.0% 0.0% +5.6% +5.6%
+3.6% +3.6% 0.0% 0.0% +5.9% +3.6%
+1.4% +1.4% 0.0% 0.0% +6.2% +1.4%
–1.0% –1.0% 0.0% 0.0% +6.4% –1.0%
–3.5% –3.5% 0.0% 0.0% +6.6% –3.5%
*Assuming consumption-work complementarity and an elastic labor supply.
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because the income effect dominates the substitution effect in this case, the increase in consumption which should result from the increase in the labor supply does not fully offset the decrease in consumption which results from the lower after-tax wage since the government is spending its revenue on projects which do not affect the individual’s marginal utility of consumption. My model also demonstrates that, under the same assumptions, a decrease in the tax rate decreases labor supply (and output and the capital stock) but increases consumption. See the right hand column in Table 6.2 (μ = 0). 6.2. The Concept of μ It is clearly unrealistic to assume that all tax revenue would be returned to individuals in the form of lump sum transfers for their own consumption. The government spends only a fraction of its revenue on direct transfers, and even some of that revenue is “lost” due to various inefficiencies. On the other hand, it is equally unrealistic to assume that all tax revenue would be spent on projects which did not in any way affect the individual’s marginal utility of consumption. It is more reasonable to assume that a certain fraction of government spending provides utility to individuals and that government spending increases the ability of individuals to consume to a certain extent, although the amount may be difficult to quantify. For example, if the government uses revenue for programs such as prescription drug coverage, individuals are likely to value such spending, but they would probably value it less than income which they could spend as they wished. Perhaps they would have used their wage in a similar way, but they might have bought different drugs or entirely different products. Prescription drug coverage would be of value to individuals, but it would not be a perfect substitute for personal income. On
73
the other hand, there are government programs, such as Social Security, do in fact provide direct income to individuals. To reflect this reality in a simplified form, I have introduced in my model a new variable, μ, which represents the fraction of government expenditures which corresponds to individuals’ consumption preferences. The remaining (1– μ) of tax revenue is presumed to be used for projects which do affect their marginal utility of consumption. Under this assumption, government spending can be thought of as a substitute, but not a perfect substitute, for individual consumption. In my model, however, government expenditures are still considered to benefit all individuals equally independent of hours worked. 6.3. Introducing μ into the Model I will now analyze the effect of varying the value of μ, considering first the case of a tax increase and then the case of a tax decrease. Specifically, I will examine how the variables in the economy react when μ is set as 1, 0.75, 0.50, 0.25, or 0. 6.3.1. Increasing the Tax Rate from 20% to 30% The parameter μ determines the magnitude of the income effect of a tax change. In the lump sum transfer case discussed in chapter 5 where μ = 1, all tax revenue is assumed to be spent in a way which corresponds to the individuals’ consumption preferences since individuals can spend their lump sum transfers as the wish. In this scenario tax changes do not affect the overall wealth of individuals, and there is no income effect. In the wasteful projects case discussed in section 6.1 where μ = 0, all tax revenue is spent on projects which did not affect the individual’s marginal utility of consumption, and tax changes have the largest possible income effect. My model indicates that under this assumption, the income effect dominates the substitution effect,
74
so that tax increases lead to increases in labor supply and tax decreases lead to decreases in labor supply. When 0 < μ < 1, a change in the tax rate will have an income effect equal to 1–
Δ
(6.1)
where Δτ represents the magnitude of the change in the tax rate. This is because a change in the tax rate has two effects. The amount that individuals have to pay in taxes changes by (Δτ)*wh, and the amount that government expenditures increases their consumption changes by μ*(Δτ)*wh. It is important to recognize that the income effect is dependent both on the value of μ and the magnitude of the change in the tax rate, but the substitution effect is dependent only on the magnitude of the tax rate. It is independent of μ. Therefore, when μ is small, the income effect may dominate the substitution effect. When μ is large, the substitution effect will dominate because the income effect is smaller. Table 6.1 presents the impact of a tax increase on various economic parameters given different values of μ. For larger values of μ, an increase in the tax rate reduces labor supply (and output and the capital stock). The decreased incentive to work caused by a lower wage is greater in magnitude than the increased incentive to work caused by the fact that higher tax rates make individuals poorer, so they value each marginal unit of consumption more. Consumption falls both because of reduced labor supply and because the lower after-tax wage decreases the ability to consume. For smaller values of μ, an increase in the tax rate increases labor supply (and output and the capital stock) because the income effect is large enough to dominate the substitution effect. The decreased incentive to work caused by a lower after-tax wage is smaller in magnitude than the increased incentive to work caused by the fact that higher tax rates make
75
individuals poorer, so they value each marginal unit of consumption more. Nevertheless, consumption still falls because the increase in labor supply is more than offset by the reduction in the after-tax wage. 6.3.2. Decreasing the Tax Rate from 20% to 10% Table 6.2 presents the impact of a tax decrease on various economic parameters given different values of μ. For larger values of μ, a decrease in the tax rate increases labor supply (and output and the capital stock) because the income effect is small enough so that the substitution effect is dominant. The effect of the increased incentive to work caused by a higher after-tax wage is greater in magnitude than the decreased incentive to work caused by lower tax rates making individuals richer, so they value each marginal unit of consumption less. Consumption rises both because of greater labor supply and because the higher after-tax wage increases the ability to consume. For smaller values of μ, a decrease in the tax rate decreases labor supply (and output and the capital stock) because the income effect is large enough to dominate the substitution effect. The effect of the increased incentive to work caused by a higher after-tax wage in these cases is smaller in magnitude than the decreased incentive to work caused by the fact that lower tax rates make individuals richer, so they value each marginal unit of consumption less. Consumption still rises, however, because the decrease in labor supply is more than offset by the increase in the after-tax wage. 6.4. Implications of μ As is evident from the previous section, the value of μ is critical in determining how a potential tax change will affect important economic parameters. If the value of μ is sufficiently small, increases in the tax rate may actually increase output and labor supply. If μ is higher,
76
increases in the tax rate will decrease output and labor supply. For the United States and for the major European countries which want to eliminate or reduce their deficits, the value of μ is critical in the analysis of whether the tax increases will cause major reductions in output and labor supply, or whether they will have little effect on output and labor supply or even increase them. In the discussion of μ, it is also essential, however, to consider the welfare of individuals in the economic analysis. As will be explained in chapter 7, individuals obtain positive utility from consumption and negative utility from working. If a government raises taxes and spends most or all of its revenue on projects which do not affect the individual’s marginal utility of consumption, this will lead to an increase in how much individuals work, but it will decrease their welfare. Consumption will fall despite the fact that individuals work more because the government will be taking income away from individuals which they could have spent as they pleased and spending it on projects that do not make individuals much better off. On the other hand, if a government raises taxes and spends most or all of its revenue in ways which correspond closely to individuals’ consumption preferences, they will work fewer hours, but they will not be so adversely affected. Consumption will fall, but individuals will work less, so the effect of a tax increase on welfare will not be as negative. This issue is examined in greater depth in section 7.4.
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Chapter 7: Welfare Analysis The effects of tax rate changes on the welfare of individuals are at least as important as their effects on output and labor supply. In this chapter, I first analyze the changes in welfare induced by changes in the tax rate over the course of a “lifetime” of 80 years. I then examine the welfare changes between the initial and final steady states. Although the latter examination allows me to investigate the full impact of the tax changes, it does not take into account changes between years 2 and 79, and so it provides an overestimate of the actual welfare changes. Finally, I consider how altering assumptions about consumption-work complementarity, about the elasticity of labor supply, and about how much individuals value government spending would affect welfare changes over the 80 year lifetime. 7.1. Welfare Analysis over a Lifetime in the Baseline Case In examining welfare changes in the dynamic model, it is important to understand the distinction between changes over the course of a lifetime of 80 years and changes between the initial and final steady states. Only the former reflects the level of welfare during the entire period. Suppose, for example, that an initial tax rate of 20% is raised to 30%. The calculation of welfare changes over the course of a lifetime of 80 years takes into account the fact that individuals do not immediately move from one steady state to another. The capital stock is higher when the tax rate is 20% than when it is 30%, but according to the dynamic model, the capital stock changes slowly over the 80 period to reach its new steady state value. Similarly, consumption and hours worked do not immediately reach their ultimate steady state levels. Because it takes about 20 years for them to asymptotically approach those levels, welfare
78
changes calculated over the entire course of 80 years will be smaller than the differences between the initial and final steady states might suggest. I express welfare changes in three ways. First, I examine the change in an individual’s utility if an initial tax rate, for example, of 20%, is increased to 30% or decreased to 10%. Second, I examine the consumption change equivalent of that utility change, holding hours worked constant. Third, I examine the hours worked change equivalent of the utility change, holding consumption constant. The consumption and hours worked equivalents provide an intuitive meaning to the magnitude of the utility changes which are otherwise expressed in units whose significance is difficult to grasp. 7.1.1. Utility Changes Caused by Changes in the Tax Rate Addressing the utility change produced when tax rates are changed is relatively straightforward. The utility function in my model is equation (4.1), which is reproduced below /
1
1/
/
/
/
1
1/
.
I can employ Results Spreadsheets 5.1 and 5.2 to find the values of consumption (c) and hours worked (h) for each of the 80 years when the tax rate is held constant at 20%, when it goes from 20% to 30%, and when it goes from 20% to 10%. With these values and the baseline values of other parameters (β = 0.95 σ = 0.4, ψ = 1.9, χ = 0.334, and γ = 1.103), I calculate the lifetime utility for an individual when the tax rate decreases to 10% to be -31.29, when the tax rate remains at 20% to be -31.53, and when the tax rate changes to 30% to be -32.02. Thus, the utility change which results from increasing the tax rate from 20% to 30% is -0.49 while the utility change from decreasing the tax rate from 20% to 10% is +0.24. In subsection 5.3.3, in
79
discussing the effects of changing the tax rate by various amounts, I noted that a given increase in the tax rate when the final tax rate is low will have less of an effect on output, hours worked, consumption, and the capital stock than the same change when the final tax rate is high. The welfare results manifest these phenomena. For example, there is a smaller percentage change in utility when the final tax rate increases from 10% to 20% (a decrease of 0.8%) than when the final tax rate is increases from 20% to 30% (a decrease of 1.6%). 7.1.2. Consumption Gain and Loss Equivalents Caused by Changes in the Tax Rate As these calculations have demonstrated, it is clear that individuals gain utility from tax cuts and lose utility from tax increases. It is difficult, however, to intuitively grasp the magnitude of these changes in terms of arbitrary units of utility. An alternative way to present them is to compute their consumption change equivalents. To compute the consumption change equivalent ĉ, it is necessary to perform the follow calculation ĉ ,
,
.
(7.1)
The expanded form of (7.1) is ĉ 1 1/
/
/
ĉ
/
/
1
1/ (7.2)
/
where
1
1/
/
/
/
1
1/
represents consumption at the initial tax rate of 20% in year t,
worked at the initial tax rate of 20% in year t, 10% or 30% in year t, and
represents hours
represents consumption at the final tax rate of
represents hours worked at the final tax rate of 10% or 30% in year
80
t. Since the values of all other variables are known, it is possible using computer software to compute ĉ. The consumption change equivalent ĉ expresses how much more or less consumption an individual would have to have over the course of an 80 year lifetime, if he worked as much as he would at a constant tax rate of 20%, to attain the utility he actually achieves when the tax rate changes to 30% or 10%. If an individual working as much as he would with a tax rate of 20% is to attain only the utility he would attain when the tax rate increases to 30%, he would have to consume less since he enjoys less utility at the 30% tax rate than he does at the 20% tax rate and he would have to attain that lower utility solely by reducing his consumption. Using equation (7.2), I calculate that ĉ = -0.012. This represents a decrease in consumption of 1.5% compared to consumption at the steady state at the 20% tax rate. In other words, the utility, or welfare, loss that individuals would suffer if the tax rate is increased from 20% to 30% is equivalent to a reduction of 1.5% in consumption if hours worked are held constant. Similarly, if an individual works as much as he would when the tax rate is 20% but is to attain the utility he would have when the tax rate decreases to 10%, that individual would have to consume more since he enjoys more utility at the 10% tax rate than he does at the 20% tax rate and would attain that higher utility solely by increasing his consumption. Using equation (7.2), I calculate that ĉ = 0.0060. This gain represents an increase in consumption of 0.7% compared to consumption at the steady state at the 20% tax rate. In other words, the utility, or welfare, gain that individuals would attain if the tax rate decreased from 20% to 10% is equivalent to an increase of 0.7% in consumption when hours worked are held constant. Table 7.1 presents the consumption change equivalents described in this section.
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TABLE 7.1 CONSUMPTION AND HOURS WORKED EQUIVALENTS OVER AN 80 YEAR LIFETIME
Final Tax Rate
Utility*
Consumption Change Equivalent*
Hours Worked Change Equivalent*
10% 20% 30%
-31.29 -31.53 -32.02
+0.7% 0% –1.5%
–1.0% 0% +2.2%
*Assuming all tax revenue is spent on lump sum transfers regardless of hours worked, an initial tax rate of 20%, the existence of the consumption-work complementarity, and an elastic labor supply.
7.1.3. Hours Worked Gain and Loss Equivalents Caused by Changes in the Tax Rate Another way to express the welfare change resulting from tax rate changes is to compute the hours worked gain or loss equivalent of the change in utility. Individuals value leisure and lose utility when they work more. Hours worked gain represents a loss in utility while an hours worked loss represents a gain in utility. To compute the hours worked gain or loss equivalent ĥ, it is necessary to perform the following calculation ,
ĥ
,
.
(7.3)
The expanded form of (7.3) is /
1
/
1/
ĥ 1 1/
/
ĥ
/
(7.4) /
1
1/
/
/
/
1
1/
82
where
again represents consumption at the initial tax rate of 20% in year t,
worked at the initial tax rate of 20% in year t, 10% or 30% in year t, and
represents hours
represents consumption at the final tax rate of
represents hours worked at the final tax rate of 10% or 30% in year
t. Since the values of all other variables are known, it is possible using computer software to compute ĥ. The hours worked equivalent ĥ expresses how many more or less hours an individual would have to work over the course of an 80 year lifetime, if he consumed as much as he would at a constant tax rate of 20%, to attain the utility he actually achieves when the tax rate changes to 30% or 10%. If an individual consuming as much as he would with a tax rate of 20% is to attain only the utility he would attain when the tax rate is 30%, he would have to work more since he enjoys less utility at the 30% tax rate than he does at the 20% tax rate and he would have to attain that lower utility solely by increasing his hours worked. Using equation (7.4), I calculate that ĥ = 0.016. This “loss” represents an increase of 2.2% in hours worked compared to the steady state at the 20% tax rate. In other words, the utility, or welfare, loss that individuals would attain if the tax rate increased from 20% to 30% is equivalent to an increase of 2.2% in hours worked when consumption is held constant. Similarly, if an individual consumes as much as he would when the tax rate is 20% but is to attain the utility he would have when the tax rate is 10%, that individual would work less since he enjoys more utility at the 10% tax rate than he does at the 20% tax rate and would attain that higher utility solely by decreasing his hours worked. Using equation (7.4), I calculate that ĥ = -0.0080. This “gain” represents a decrease of 1.0% in hours worked compared to the steady state at the 20% tax rate. In other words, the utility, or welfare, gain that individuals would attain if the tax rate decreased from 20% to 10% is equivalent to a decrease of 1.0% in hours worked
83
when consumption is held constant. Table 7.1 presents the hours worked change equivalents described in this section. 7.2. Welfare Analysis Between the Steady States in the Baseline Case I now analyze the welfare changes between the initial and final steady states produced by tax changes. Given an initial tax rate of 20%, I determine the change in the individual’s utility when the tax rate is increased to 30% or decreased to 10%. Then, I find the consumption change equivalent of the utility change, holding hours worked constant. Finally, I find the hours worked change equivalent of the utility change, holding consumption constant. 7.2.1. Utility Changes Caused by Changes in the Tax Rate Again the calculation of the utility gain or loss is straightforward. My utility function from equation (4.1) is /
1
/
/
/
1/
1
1/
.
Because I am now only interested in the welfare analysis between steady states, I can simplify the equation by removing the summation across time periods. This yields /
1
1/
/
/
/
1
1/
.
(7.5)
I use Results Spreadsheets 5.1 and 5.2 to determine the values of consumption (c) and hours worked (h) for the tax rates of 10%, 20%, and 30% at their steady state levels. At the tax rate of 10%, c and h are 0.89 and 0.83, respectively. At the tax rate of 20%, c and h are 0.84 and 0.78, respectively. At the tax rate of 30%, c and h are 0.79 and 0.73, respectively. With these values
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and the baseline values for the other parameters (σ = 0.4, ψ = 1.9, χ = 0.334, and γ = 1.103), equation (7.5) allows me to calculate the utility of an individual at the 10% tax rate to be -1.58, at the 20% tax rate to be -1.60, and at the 30% tax rate to be -1.64. Thus, the utility change when the tax rate increases from 20% to 30% is –0.039 and the utility change when tax rate decreases from 20% to 10% is +0.024. As discussed in subsection 5.3.3, a given increase in the final tax rate when that tax rate is low will have a smaller effect on output, hours worked, consumption, and the capital stock than when the final tax rate is high. This phenomenon is reflected in the welfare results. For example, there is a smaller percentage change in utility when the final tax rate increases from 10% to 20% (a decrease of 1.5%) than when the final tax rate is increases from 20% to 30% (a decrease of 2.4%). 7.2.2. Consumption Gain and Loss Equivalents Caused by Changes in the Tax Rate As in subsection 7.1.2, I will now determine the consumption and hours worked change equivalents of the utility changes in order to provide a more intuitive sense of the magnitude of the welfare effects of changes in the tax rate. To compute the consumption change equivalent between steady states, I manipulate equation (7.5) so that consumption (c) is on the left hand side and all other variables and parameters, including utility (U), are on the right hand side. Thus, /
1
/
1/
/
1 /
/
1/ 1
1
/
/
/
1
/
/
/
1/
1 1
1/ /
1 1
1/
85
/
1
1
1
/
/
1
1 1
1
1
1/
/
1
1
/
1
1 1
1
1/ /
/
1
1 1
1
1/ /
.
(7.6)
I can now calculate how much more or less consumption an individual would need in the steady state, when working as much as he would at a constant tax rate of 20%, to attain the utility he actually achieves when the tax rate changes to 30% or 10%. A tax rate increase from 20% to 30% will lower the individual’s utility and produce a consumption loss equivalent. Using the value of h corresponding to the steady state at the 20% tax rate (h = 0.78), the value of U corresponding to the individual’s utility at the 30% tax rate (U = -1.64), and the baseline values for the other parameters in equation (7.6), I calculate c = 0.82. This is less than the value of consumption in the steady state at the 20% tax rate (c = 0.84). Thus, the consumption loss equivalent of the decrease in utility resulting from raising the tax rate from 20% to 30% is 0.019, representing a 2.2% loss in consumption. In other words, the utility, or welfare, loss that individuals would experience if the tax rate increased from 20% to 30% is equivalent to a decrease of 2.2% in consumption when hours worked is held constant. Similarly, a tax rate decrease from 20% to 10% will raise the individual’s utility and produce a consumption gain equivalent. Using the value of h corresponding to the steady state at the 20% tax rate (h = 0.78), the value of U corresponding to the individual’s utility at the 10% tax rate (U = -1.58), and the baseline values for the other parameters in equation (7.6), I calculate
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TABLE 7.2 CONSUMPTION AND HOURS WORKED EQUIVALENTS BETWEEN STEADY STATES
Final Tax Rate
Utility*
Consumption Change Equivalent*
Hours Worked Change Equivalent*
10% 20% 30%
–1.58 –1.60 –1.64
+1.4% 0% –2.2%
–2.0% 0% +3.2%
*Assuming all tax revenue is spent on lump sum transfers regardless of hours worked, an initial tax rate of 20%, the existence of the consumption-work complementarity, and an elastic labor supply.
c = 0.85. This is greater than the value of consumption in the steady state at the 20% tax rate (c = 0.84). Thus, the consumption gain equivalent of the increase in utility from raising the tax rate from 20% to 10% is 0.012, representing a 1.4% gain in consumption. In other words, the utility, or welfare, gain that individuals would experience if the tax rate decreased from 20% to 10% is equivalent to an increase of 1.4% in their consumption when hours worked is held constant. Table 7.2 presents the consumption change equivalents described in this section. 7.2.3. Hours Worked Gain and Loss Equivalents Caused by Changes in the Tax Rate To compute the hours worked gain or loss equivalent between steady states, I manipulate equation (7.5) so that hours worked (h) is on the left hand side and all other variables and parameters, including utility (U), are on the right hand side. Thus, /
1 /
/
1/ /
/
/
1
/
1
1/
/
1
1/
1/
87
1
1
/
/
1
/
/
1
1
/
/
1
/
1
1/
1
1/
1
/
/
1
1
1/
/
1 1
1 1
1
1
/
1
1 1
1/ /
.
(7.7)
I can now calculate how much more or fewer hours an individual would need to work in the steady state, when consuming as much as he would at a constant tax rate of 20%, to attain the utility he actually achieves when the tax rate changes to 30% or 10%. A tax rate increase from 20% to 30% will lower the individual’s utility and produce an hours worked gain equivalent. Using the value of c corresponding to the steady state at the 20% tax rate (c = 0.84), the value of U corresponding to the individual’s utility at the 30% tax rate (U = -1.64), and the baseline values for the other parameters in equation (7.7), I calculate h = 0.81. This is more than the number of hours worked in the steady state at the 20% tax rate (h = 0.78). Thus, the hours worked gain equivalent of the decrease in utility from raising the tax rate from 20% to 30% is 0.025, representing a 3.2% increase in hours worked. In other words, the utility, or welfare, loss that individuals would experience if the tax rate increased from 20% to 30% is equivalent to an increase of 3.2% in hours worked when consumption worked is held constant. Similarly, a tax rate decrease from 20% to 10% will raise the individual’s utility and produce an hours worked loss equivalent. Using the value of c corresponding to the steady state
88
at the 20% tax rate (c = 0.84), the value of U corresponding to the individual’s utility at the 10% tax rate (U = -1.58), and the baseline values for the other parameters in equation (7.7), I calculate h = 0.77. This is less than the value of hours worked corresponding to the steady state at the 20% tax rate (h = 0.78). Thus, the hours worked loss equivalent to the increase in utility from lowering the tax rate from 20% to 10% is 0.016, representing a 2.0% decrease in hours worked. In other words, the utility, or welfare, gain that individuals would experience if the tax rate decreased from 20% to 10% is equivalent to a decrease of 2.0% in hours worked when consumption worked is held constant. Table 7.2 presents the consumption gain and loss equivalents described in this section. 7.3. Welfare Analysis Assuming No Complementarity or a Less Elastic Labor Supply Although the way in which consumption and hours worked equivalents of utility changes are calculated is not affected by assumptions about the consumption-work complementarity or the elasticity of labor supply, the utility changes caused by changes in the tax rate are indeed affected by these assumptions. As explained in section 5.4, removing the consumption-work complementarity results in tax changes having less of an effect on output, hours worked, consumption, and the capital stock. The resulting changes in utility will therefore also be smaller, and so the consumption and hours worked change equivalents will be smaller. When the consumption-work complementarity assumption is removed, the consumption loss equivalent when the tax rate is raised from 20% to 30% decreases from 1.5% to 1.3%, the consumption gain equivalent when the tax rate is lowered from 20% to 10% decreases from 0.7% to 0.6%, the hours worked gain equivalent when the tax rate is raised from 20% to 30% decreases from 2.2% to 1.8%, and the hours worked loss equivalent when the tax rate is lowered from 20% to 10%
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TABLE 7.3 EQUIVALENTS FOR VARIOUS ASSUMPTIONS OVER A LIFETIME
Final Tax Rate
Consumption Change Equivalent (Baseline Case)*
Consumption Change Equivalent (No Complementarity)
Consumption Change Equivalent (Less Elastic LS)
10% 20% 30%
+0.7% 0% –1.5%
+0.6% 0% –1.3%
+0.5% 0% –1.0%
*Assuming all tax revenue is spent on lump sum transfers regardless of hours worked, an initial tax rate of 20%, the existence of the consumption-work complementarity, and an elastic labor supply.
Final Tax Rate
Hours Worked Change Equivalent (Baseline Case)*
Hours Worked Change Equivalent (No Complementarity)
Hours Worked Change Equivalent (Less Elastic LS)
10% 20% 30%
–1.0% 0% +2.2%
–0.8% 0% +1.8%
–0.7% 0% +1.5%
*Assuming all tax revenue is spent on lump sum transfers regardless of hours worked, an initial tax rate of 20%, the existence of the consumption-work complementarity, and an elastic labor supply.
decreases from 1.0% to 0.8%. As explained in section 5.5, assuming a lower labor supply elasticity results in tax changes having less of an effect on output, hours worked, consumption, and the capital stock. Therefore, changes in utility are smaller, and so consumption and hours worked change equivalents are smaller. If less elastic labor supply is assumed, the consumption loss equivalent when the tax rate is raised from 20% to 30% decreases from 1.5% to 1.0%, the consumption gain equivalent when the tax rate is lowered from 20% to 10% decreases from 0.7% to 0.5%, the hours worked gain equivalent when the tax rate is raised from 20% to 30% decreases from 2.2%
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to 1.5%, and the hours worked loss equivalent when the tax rate is lowered from 20% to 10% decreases from 1.0% to 0.7%. Table 7.3 summarizes these results. 7.4. Welfare Analysis Assuming Different Values of μ If individuals value government spending a fraction μ times as much as their own consumption, then, as mentioned in section 6.4, the smaller the value of μ, the greater the impact of that a tax change on welfare. While an increase in the tax rate may lead to an increase in output and labor supply if the value of μ is sufficiently small, individuals will be worse off because they will consume less while working more. On the other hand, higher values of μ imply that individuals value government spending more. An increase in the tax rate may lead them to work and produce less, but their welfare will not be as negatively affected as it is when μ is low. For example, when the tax rate is increased from 20% to 30%, the consumption loss equivalent is 1.5% when μ = 1, 5.2% when μ = 0.50, and 10.6% when μ = 0. When the tax rate is increased from 20% to 30%, the hours worked gain equivalent is 2.2% when μ = 1, 6.8% when μ = 0.50, and 12.3% when μ = 0. This reasoning also applies to a decrease in the tax rate with the obvious reversal of sign. For example, when the tax rate is decreased from 20% to 10%, the consumption gain equivalent is 0.7% when μ = 1, 4.3% when μ = 0.50, and 9.4% when μ = 0. When the tax rate is decreased from 20% to 10%, the hours worked loss equivalent is 1.0% when μ = 1, 5.7% when μ = 0.50, and 11.3% when μ = 0. These results are summarized in Table 7.4.
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TABLE 7.4 EQUIVALENTS FOR VARIOUS VALUES OF μ OVER A LIFETIME Final Tax Rate
Consumption Change Equivalent (μ = 1)
Consumption Change Equivalent (μ = 0.50)
Consumption Change Equivalent (μ = 0)
10% 20% 30%
+0.7% 0.0% –1.5%
+4.3% 0.0% –5.2%
+9.4% 0.0% –10.6%
*Assuming an initial tax rate of 20% as well as consumption-work complementarity, and an elastic labor supply.
Final Tax Rate
Hours Worked Change Equivalent (μ = 1)
Hours Worked Change Equivalent (μ = 0.50)
Hours Worked Change Equivalent (μ = 0)
10% 20% 30%
–1.0% 0% +2.2%
–5.7% 0.0% +6.8%
–11.3% 0.0% +12.3%
*Assuming an initial tax rate of 20% as well as consumption-work complementarity, and an elastic labor supply.
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Chapter 8: Applying My Model to Real World Scenarios In this chapter, I address by principle research questions by applying my dynamic general equilibrium model to the analysis of real world problems. I use it to predict how much the United States and seven major European countries would have to raise taxes in order to balance their budgets in one year. These countries have budget deficits and substantial debt to GDP ratios, although some face more serious problems than others. I examine various scenarios incorporating different assumptions about government spending to determine how these assumptions would affect predictions about how much taxes would have to increase to eliminate the deficits within one year and assess the expected effects on output and labor supply. In the case of the United States, I pursue this analysis in greater depth. Then I present the Laffer Curves which my model generates for the United States under different assumptions about government spending. Finally, I analyze how much the United States would have to raise taxes in order to balance its budget in the long run, taking into account both the short term and the long term impacts of tax rate increases on output. 8.1. The Economic Situation in the Eight Countries Under Consideration In my analysis of the potential impact of trying to balance the budget within one year on output and hours worked, I consider eight countries: the United States, the four largest European economies (France, Germany, Italy, and the United Kingdom), the two largest European economies with very high deficit to GDP ratios (Greece and Spain) and the largest Scandinavian economy (Sweden). My data comes from the OECD Outlook Database Inventory for the year 2009, the most recent year for which such data is available. In that year, the United States faced a moderate debt to GDP ratio of 0.53 but a high deficit to GDP ratio of 0.11. Germany, Sweden,
93
TABLE 8.1 DEFICIT AND DEBT TO GDP RATIOS AMONG US AND EUROPEAN COUNTRIES
Country*
Deficit to GDP Ratio
Debt to GDP Ratio
France Germany Greece Italy Spain Sweden United Kingdom United States
0.08 0.03 0.14 0.05 0.11 0.01 0.11 0.11
0.61 0.44 1.26 1.07 0.46 0.38 0.75 0.53
*This data comes from the OECD Outlook Database Inventory for the year 2009.
and Spain had lower debt to GDP ratios of 0.44, 0.38, and 0.46 respectively. While the deficit to GDP ratios in Germany and Sweden were moderate at 0.03 and 0.01, respectively, the deficit to GDP ratio in Spain was as large as that of the United States at 0.11. France and the United Kingdom had slightly higher debt to GDP ratios of 0.61 and 0.75, respectively, and also faced considerable deficit to GDP ratios of 0.08 and 0.11, respectively. Italy and Greece had very high debt to GDP ratios of 1.07 and 1.26, although the deficit to GDP ratio in Italy was modest at 0.05 while in Greece it was very high at 0.14. Table 8.1 summarizes these statistics. 8.2. Scenarios for Balancing the Budget in One Year For each country, I will analyze the size of the increase in the tax rate necessary to balance the budget during the following year under each of four possible scenarios. The first is that all government spending consists of lump sum transfers regardless of hours worked and that there is no decrease in government spending. The second is that all government spending consists of lump sum transfers regardless of hours worked and that 50% of the budget fix comes from a decrease in government spending. The third is that individuals value government
94
spending ½ as much as their own consumption (μ = 0.50) and that there is no decrease in government spending. The fourth is that individuals value government spending ½ as much as their own consumption (μ = 0.50) and that 50% of the budget fix comes from a decrease in government spending. For each scenario in each country, I perform a two stage calculation. First, I calculate the tax rate which would be necessary to balance the budget within one year if it were possible to raise the tax rate without affecting output or hours worked. Then I employ my model to recalculate the necessary tax rate taking into account the expected effect of increases in the tax rate on output and hours worked. 8.2.1. Assuming Lump Sum Transfers with No Change in Spending I first create an algorithm to determine the tax rate necessary to balance the budget if the tax rate increases did not affect output. I will illustrate this algorithm using the case of the United States. I start by computing the tax revenue to GDP ratio. In 2009, it was 0.24 for the United States. Because the deficit to GDP ratio in 2009 was 0.11, the tax revenue to GDP ratio at current output necessary to balance the budget would have been 0.24
0.11
0.35.
The fractional increase in the tax rate necessary to balance the budget would therefore have been 0.35 0.24 0.24
0.47.
Next I determine the marginal tax rate in the United States. This is an estimate because there is no single marginal tax rate for all Americans. The income tax system in the United
95
States is progressive, as are the tax systems in all the countries under consideration. In this analysis, I will estimate the marginal tax rate by adding the marginal personal income tax rate and the social security tax rate on gross labor income for workers receiving each country’s average wage. For the United States, this yields a marginal tax rate of 0.34. I calculate the ratio of the marginal tax rate to the average tax rate in the United States (noting rounding errors) to be 0.34 0.24
1.44.
I then determine the marginal tax rate at current output necessary to balance the budget. (“Current” refers to the year 2009 since this is the most recent year for which I have data.) I assume that when the tax rate is raised to balance the budget, the ratio of the marginal tax rate to the average tax rate remains constant. The marginal tax rate at current output necessary in the United States to balance the budget would thus be 1.44 0.35
0.51.
As I have shown, however, an increase in the marginal tax rate would actually lead to a decrease in output when I assume that government revenue is spent on lump sum transfers to individuals regardless of hours worked. Therefore, this marginal tax rate of 0.51 would actually be insufficient to achieve a balanced budget. Using my model, I find that a marginal tax rate of 0.70 would actually have been necessary. This is because the increase of the marginal tax rate from 0.34 to 0.70 would lead to a drop in output of 28% and drop in hours worked of 37%. Such one-year decreases are far greater than those the United States experienced during the worst years of the Great Depression (King 1994). In 2009 if the United States had needed to balance
96
its budget in one year by raising taxes without cutting government spending, the result would have been disastrous. As Table 8.2 demonstrates, the United States was not the only country to be in such a difficult fiscal situation. Table 8.2 implies that it would have been impossible in 2009 for France, Germany, Greece, Italy, and Spain to balance their budgets in one year simply by raising tax rates, assuming that government revenue was used solely for lump sum transfers regardless of hours worked and that government spending did not decrease. France, Greece, Italy, and Spain all had substantial deficit to GDP ratios, so it may not be surprising that it would have been impossible for them to balance their budgets given those assumptions, but it may appear odd that Germany, with its moderate deficit to GDP ratio, could not have balanced its budget. Germany’s problem was that its marginal tax rate was already so high at 0.63 that a further tax increase would have had severe consequences for output. For this reason, Germany could not have simply taxed its way to a balanced budget within one year. The United Kingdom could only have managed to balance its budget in this scenario by raising its marginal tax rate from 0.39 to 0.63. This would have caused its output to fall by 19% and its hours worked to fall by 26%, devastating the country economically. Only Sweden, with its very low deficit to GDP ratio, could have balanced its budget by raising taxes without decreasing spending without facing severe economic repercussions. The increase of its marginal tax rate from 0.48 to 0.50 would have decreased its output and hours worked each by only 2%. 8.2.2. Assuming Lump Sum Transfers with Spending Cuts Constituting 50% of the Budget Fix I will again assume that all government spending consists of lump sum transfers regardless of hours worked, but now I will assume that 50% of the budget fix is derived from
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TABLE 8.2 BALANCING THE BUDGET WITH LUMP SUM TRANSFERS AND NO CHANGE IN SPENDING
Country*
Deficit to GDP Ratio
Debt to GDP Ratio
Tax Revenue to GDP Ratio
France Germany Greece Italy Spain Sweden United Kingdom United States
0.08 0.03 0.14 0.05 0.11 0.01 0.11 0.11
0.61 0.44 1.26 1.07 0.46 0.38 0.75 0.53
0.42 0.37 0.29 0.44 0.31 0.46 0.34 0.24
Tax Revenue to GDP Ratio at Current Output Necessary to Balance the Budget in 1 Year 0.49 0.40 0.43 0.49 0.42 0.48 0.45 0.35
Fractional Increase in the Tax Rate Necessary to Balance the Budget in 1 Year 0.18 0.08 0.47 0.12 0.36 0.03 0.32 0.47
*This data comes from the OECD Outlook Database Inventory for the year 2009.
Marginal Tax Rate, Marginal Tax Rate Resulting Resulting Accounting for Changes in at Current Output Change in Change in Country Output, Necessary to Necessary to Output³ Hours Worked³ Balance the Budget² Balance the Budget France 0.52 1.24 0.61 Unable4 N/A N/A Germany 0.63 1.71 0.68 Unable4 N/A N/A Greece 0.51 1.73 0.74 Unable4 N/A N/A Italy 0.54 1.23 0.60 Unable4 N/A N/A Spain 0.48 1.57 0.66 Unable4 N/A N/A Sweden 0.48 1.03 0.49 0.50 -0.02 -0.02 United Kingdom 0.39 1.13 0.51 0.63 -0.19 -0.26 United States 0.34 1.44 0.51 0.70 -0.28 -0.37 1. The marginal tax rate is assumed to be the sum of the marginal personal income tax and social security contribution rates on gross labor income for a worker receiving the average wage in the country. 2. Assuming that the ratio of the marginal tax rate to the average tax rate remains constant when the tax revenue to GDP ratio increases by the amount necessary to balance the budget. 3. Assuming government spending as lump sum transfers regardless of hours worked. 4. Unable means that there is no marginal tax rate which would allow the country to balance its budget. Current Marginal Tax Rate¹
Ratio of Marginal Tax Rate to Average Tax Rate
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TABLE 8.3 BALANCING THE BUDGET WITH LUMP SUM TRANSFERS AND SPENDING CUTS 50% OF BUDGET FIX
Country*
Deficit to GDP Ratio
Debt to GDP Ratio
Tax Revenue to GDP Ratio
France Germany Greece Italy Spain Sweden United Kingdom United States
0.08 0.03 0.14 0.05 0.11 0.01 0.11 0.11
0.61 0.44 1.26 1.07 0.46 0.38 0.75 0.53
0.42 0.37 0.29 0.44 0.31 0.46 0.34 0.24
Tax Revenue to GDP Ratio at Current Output Necessary to Balance the Budget in 1 Year 0.46 0.39 0.36 0.46 0.36 0.47 0.40 0.30
Fractional Increase in the Tax Rate Necessary to Balance the Budget in 1 Year 0.09 0.04 0.23 0.06 0.18 0.01 0.16 0.24
*This data comes from the OECD Outlook Database Inventory for the year 2009.
Marginal Tax Rate, Marginal Tax Rate Resulting Resulting Accounting for Changes in at Current Output Change in Change in Country Output, Necessary to Necessary to Output³ Hours Worked³ Balance the Budget² Balance the Budget 0.52 1.24 0.57 0.63 -0.10 -0.14 France 0.63 1.71 0.66 Unable4 N/A N/A Germany 0.51 1.73 0.63 Unable4 N/A N/A Greece 0.54 1.23 0.57 0.61 -0.07 -0.09 Italy 0.48 1.57 0.57 Unable4 N/A N/A Spain 0.48 1.03 0.49 0.49 -0.01 -0.01 Sweden 0.39 1.13 0.45 0.48 -0.06 -0.09 United Kingdom 0.34 1.44 0.43 0.46 -0.08 -0.11 United States 1. The marginal tax rate is assumed to be the sum of the marginal personal income tax and social security contribution rates on gross labor income for a worker receiving the average wage in the country. 2. Assuming that the ratio of the marginal tax rate to the average tax rate remains constant when the tax revenue to GDP ratio increases by the amount necessary to balance the budget. 3. Assuming government spending as lump sum transfers regardless of hours worked. 4. Unable means that there is no marginal tax rate which would allow the country to balance its budget. Current Marginal Tax Rate¹
Ratio of Marginal Tax Rate to Average Tax Rate
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decreases in government spending. The other 50% would have to come from an increase in the tax rate. Table 8.3 presents the results. Under these assumptions, it would have been necessary for the United States to raise its marginal tax rate from 0.34 to 0.46. This would have reduced output by 8% and hours worked by 11%. Under similar assumptions, France and Italy would have been able to balance their budgets as well. France would have had to raise its marginal tax rate from 0.52 to 0.63, reducing its output by 10% and hours worked by 14%. Italy would have had to raise its marginal tax rate from 0.54 to 0.61, reducing its output by 7% and its hours worked by 9%. Germany, Greece, and Spain could not have raised enough revenue from taxes to balance their budgets even if spending cuts had accounted for 50% of the budget fix. The United Kingdom would have had to increase its marginal tax rate from 0.39 to 0.48, causing a 6% drop in its output and a 9% drop in its hours worked. Sweden would only have had to increase its marginal tax rate from 0.48 to 0.49. This would have caused only a 1% drop in output and hours worked. 8.2.3. Assuming μ = 0.50 with No Change in Government Spending Next I assume that individuals value government spending ½ as much as their own consumption (μ = 0.50) and that there is no reduction in government spending in the effort to balance the budget. Table 8.4 presents the results. The United States would have needed to raise its marginal tax rate from 0.34 to 0.55. The increase is much smaller than the increase to the 0.70 marginal tax rate necessary if the government had spent its revenue on lump sum transfers regardless of hours worked. Output in the United States would have decreased by 7% and hours worked by 10%. These changes, although large, are smaller than the 28% decrease in output and 37% decrease in hours worked
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which would have resulted from the tax increase necessary if the government had spent its tax revenue on lump sum transfers regardless of hours worked. Even with μ = 0.50, Greece, Germany, and Spain would not have been able to balance their budgets without a decreases in government spending. All other countries could have done so, but Sweden is the only one which would not have suffered a considerable decrease in output and hours worked. France would have had to raise its marginal tax rate from 0.52 to 0.69, causing an 11% drop in output and a 16% drop in hours worked. Italy would have had to raise its marginal tax rate from 0.54 to 0.65, causing a 7% drop in output and a 10% drop in hours worked. The United Kingdom would have had to raise its marginal tax rate from 0.39 to 0.55, causing an 6% drop in output and an 9% drop in hours worked. Only Sweden, which would only have had to raise its tax rate only from 0.48 to 0.50 to balance its budget, would have endured minimal losses in output and hours worked of 1%. 8.2.4 Assuming μ = 0.50 with Spending Cuts Constituting 50% of the Budget Fix Now I will assume that individuals value government spending ½ as much as their own consumption (μ = 0.50) and that 50% of the budget fix comes from a decrease in government spending. Table 8.5 presents the results. Under these assumptions, all countries under consideration except Greece would have been able to balance their budgets. The United States would have had to increase its marginal tax rate from 0.34 to 0.44, leading to a 3% decrease in output and a 4% decrease in output. France, Italy, Sweden, and the United Kingdom would have faced decreases in output of between 1% and 4% and decreases in hours worked of between 1% and 6%. Germany and Spain would still have suffered greatly from the necessary tax rate increases. With a marginal tax rate
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TABLE 8.4 BALANCING THE BUDGET WITH μ = 0.50 AND NO CHANGE IN GOVERNMENT SPENDING
Country*
Deficit to GDP Ratio
Debt to GDP Ratio
Tax Revenue to GDP Ratio
France Germany Greece Italy Spain Sweden United Kingdom United States
0.08 0.03 0.14 0.05 0.11 0.01 0.11 0.11
0.61 0.44 1.26 1.07 0.46 0.38 0.75 0.53
0.42 0.37 0.29 0.44 0.31 0.46 0.34 0.24
Tax Revenue to GDP Ratio at Current Output Necessary to Balance the Budget in 1 Year 0.49 0.40 0.43 0.49 0.42 0.48 0.45 0.35
Fractional Increase in the Tax Rate Necessary to Balance the Budget in 1 Year 0.18 0.08 0.47 0.12 0.36 0.03 0.32 0.47
*This data comes from the OECD Outlook Database Inventory for the year 2009.
Marginal Tax Rate, Marginal Tax Rate Resulting Resulting Accounting for Changes in at Current Output Change in Change in Country Output, Necessary to Balance Necessary to Output³ Hours Worked³ the Budget² Balance the Budget France 0.52 1.24 0.61 0.69 -0.11 -0.16 Germany 0.63 1.71 0.68 Unable4 N/A N/A Greece 0.51 1.73 0.74 Unable4 N/A N/A Italy 0.54 1.23 0.60 0.65 -0.07 -0.10 Spain 0.48 1.57 0.66 Unable4 N/A N/A Sweden 0.48 1.03 0.49 0.50 -0.01 -0.01 United Kingdom 0.39 1.13 0.51 0.55 -0.06 -0.09 United States 0.34 1.44 0.51 0.55 -0.07 -0.10 1. The marginal tax rate is assumed to be the sum of the marginal personal income tax and social security contribution rates on gross labor income for a worker receiving the average wage in the country. 2. Assuming that the ratio of the marginal tax rate to the average tax rate remains constant when the tax revenue to GDP ratio increases by the amount necessary to balance the budget. 3. Assuming that individuals value government spending ½ as much as their own consumption (μ = 0.50). 4. Unable means that there is no marginal tax rate which would allow the country to balance its budget. Current Marginal Tax Rate¹
Ratio of Marginal Tax Rate to Average Tax Rate
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TABLE 8.5 BALANCING THE BUDGET ASSUMING μ = 0.50 AND SPENDING CUTS 50% OF BUDGET FIX
Country*
Deficit to GDP Ratio
Debt to GDP Ratio
Tax Revenue to GDP Ratio
France Germany Greece Italy Spain Sweden United Kingdom United States
0.08 0.03 0.14 0.05 0.11 0.01 0.11 0.11
0.61 0.44 1.26 1.07 0.46 0.38 0.75 0.53
0.42 0.37 0.29 0.44 0.31 0.46 0.34 0.24
Tax Revenue to GDP Ratio at Current Output Necessary to Balance the Budget in 1 Year 0.46 0.39 0.36 0.46 0.36 0.47 0.40 0.30
Fractional Increase in the Tax Rate Necessary to Balance the Budget in 1 Year 0.09 0.04 0.23 0.06 0.18 0.01 0.16 0.24
*This data comes from the OECD Outlook Database Inventory for the year 2009.
Marginal Tax Rate, Marginal Tax Rate Resulting Resulting Accounting for Changes in at Current Output Change in Change in Country Output, Necessary to Balance Necessary to Output³ Hours Worked³ the Budget² Balance the Budget France 0.52 1.24 0.57 0.59 -0.04 -0.06 Germany 0.63 1.71 0.66 0.72 -0.09 -0.13 Greece 0.51 1.73 0.63 Unable4 N/A N/A Italy 0.54 1.23 0.57 0.59 -0.03 -0.04 Spain 0.48 1.57 0.57 0.62 -0.08 -0.11 Sweden 0.48 1.03 0.49 0.49 -0.01 -0.01 United Kingdom 0.39 1.13 0.45 0.46 -0.02 -0.03 United States 0.34 1.44 0.43 0.44 -0.03 -0.04 1. The marginal tax rate is assumed to be the sum of the marginal personal income tax and social security contribution rates on gross labor income for a worker receiving the average wage in the country. 2. Assuming that the ratio of the marginal tax rate to the average tax rate remains constant when the tax revenue to GDP ratio increases by the amount necessary to balance the budget. 3. Assuming that individuals value government spending ½ as much as their own consumption (μ = 0.50). 4. Unable means that there is no marginal tax rate which would allow the country to balance its budget. Current Marginal Tax Rate¹
Ratio of Marginal Tax Rate to Average Tax Rate
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increase from 0.48 to 0.62, Spain’s output would have dropped 8%, and its hours worked would have fallen 11%. With a marginal tax rate increase from 0.63 to 0.72, Germany’s output would have dropped 9%, and its hours worked would have fallen 13%. 8.2.5. The Consequences of Using Tax Increases to Balance the Budget In all these scenarios, all countries except Sweden would have had to endure considerable economic hardship in order to balance their budgets within one year as a consequence of the necessary tax rate increase. Interestingly, under none of the scenarios would Greece have been able to balance its budget, demonstrating the seriousness of its budget crisis. It is important to appreciate that this analysis takes into consideration only the changes in output caused by the increase in the tax rate during the first year after that tax rate increase. My model demonstrates, however, that only about 90% of the decrease in output which occurs in a country over an 80 year lifetime is experienced during the first year. Thus, in the long run, the fall in output would be larger than that which the figures presented in Tables 8.2-8.5 suggest. If these tax increases were implemented, output would continue to fall in succeeding years, so that tax revenues would fall and budgets would again fall into deficit. Thus, even the tax increases I have suggested would not have balanced the budgets in the long run, as will be demonstrated in section 8.5. Larger tax increases would have been necessary to achieve balanced budgets in the long run, causing greater economic harm. 8.3. A Closer Look at the Case of the United States In this section, I will consider additional scenarios for the case of the United States. Again, the goal will be to eliminate the budget deficit within one year. The results are presented in Table 8.6.
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TABLE 8.6 VARIOUS SCENARIOS FOR THE US TO DEAL WITH ITS DEFICIT
Scenario for the United States1
Current Marginal Tax Rate
Marginal Tax Rate, Accounting for Changes in Output, Necessary to Achieve Scenario Goal
Resulting Change in Output
Resulting Change in Hours Worked
Balanced Budget, No Spending Cut
0.34
0.70
-0.28
-0.37
Balanced Budget, No Spending Cut (Prescott Tax Rate)2
0.35
0.71
-0.28
-0.38
Balanced Budget, No Complementarity
0.34
0.63
-0.20
-0.27
Balanced Budget, Less Elastic LS
0.34
0.56
-0.10
-0.14
Balanced Budget, Spending 25% of Budget Fix
0.34
0.54
-0.14
-0.19
Balanced Budget, Spending 50% of Budget Fix
0.34
0.46
-0.08
-0.11
Balanced Budget, Spending 75% of Budget Fix
0.34
0.40
-0.04
-0.06
Balanced Budget, No Spending Cut (μ = 0.25)
0.34
0.51
-0.01
-0.01
Balanced Budget, No Spending Cut (μ = 0.50)
0.34
0.55
-0.07
-0.10
Balanced Budget, No Spending Cut (μ = 0.75)
0.34
0.60
-0.16
-0.21
3% Deficit, No Spending Cut
0.34
0.54
-0.14
-0.19
3% Surplus, No Spending Cut
0.34
Unable3
N/A
N/A
1. Assuming the baseline case of consumption-work complementarity, an elastic labor supply, government spending as lump sum transfers regardless of hours worked, and the marginal tax rate computed in the same manner as in Tables 8.2-8.5 unless otherwise specified. 2. The Prescott tax rate is computed by summing the social security tax rate and 1.6 times the average income tax rate, as discussed in chapter 3. 3. Unable means that there is no marginal tax rate which would allow the United States to balance its budget.
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The first scenario considered is that which results from using the method of Prescott (2004) to determine the current marginal tax rate in the United States. Prescott added social security tax rate to 1.6 times the average income tax rate to obtain his estimate. He derived this factor of 1.6 by employing the methodology of Feenberg and Coutts (1993) to estimate the marginal income tax rate in the United States during both 1970-1974 and 1993-1996. This method yields a current marginal tax rate for the United States of 0.35 rather than 0.34, the value used in section 8.2. Using Prescott’s estimate, the marginal tax rate necessary to balance the budget would be 0.71. The resulting fall in output would be 28% and the fall in hours worked would be 38%. As would be expected given the small difference in the estimate of the marginal tax rate, these results are nearly identical to those in the section 8.2. Next I will consider the result of removing the consumption-work complementarity assumption. This would lead to a lower value for the tax rate necessary to balance the budget and smaller decreases in output and hours work because a given increase in the tax rate would have smaller effects on output and hours worked. Similarly, assuming a less elastic labor supply would lead to a lower value for the tax rate necessary to balance the budget since a lower labor supply elasticity implies that given changes in the tax rate would have smaller effects on output and hours worked. Clearly, the greater the share of the budget fix which is made up by decreases in government spending rather than increases in taxes, the smaller the necessary increases in the tax rate and the smaller the consequent decreases in output and hours work, as Table 8.6 demonstrates. Furthermore, the greater the value of μ, the smaller the income effect caused by an increase in the tax rate, and so the more negative the effect of a given tax increase on output
106
and labor supply. Therefore, the greater the value of μ, the larger the tax increase necessary to balance the budget and the larger the resulting decrease in output and hours worked. Even to achieve a deficit to GDP ratio of 3%, the United States would require a marginal tax rate of 0.54 if there were no decrease in government spending. This would induce a 14% decrease in output and a 19% decrease in hours worked. It is striking to note that, despite its relatively low marginal tax rate, the United States simply cannot achieve a budget surplus of 3% by raising tax rates unless it reduces government spending. In 2009, the debt to GDP ratio in the United States was 53%. It will be difficult for the United States to reduce this ratio significantly without cutting government spending. 8.4. The Laffer Curve for the United States In view of the ability of my model to predict the decline in output which results from various tax rate increases, it is interesting to use it to plot the Laffer Curves for the United States. Assuming that the government spends its tax revenue on lump sum transfers regardless of hours worked and that the current marginal tax rate in the United States is 0.34, I obtain the data presented in Table 8.7. To construct my Laffer Curve, I plot the data for final marginal tax rates between 0.00 and 0.80 in increments of 0.05. I stopped at the marginal tax rate of 0.80 because my computer was unable to solve my Matlab program for tax rates greater than 0.80. I compute final average tax rates assuming that the ratio of the marginal tax rate to the average tax rate remains constant. Using the current marginal tax rate, I compute the change in output and the change in hours worked associated with each final marginal tax rate. To determine total tax revenue, I take the product of the final average tax rate and the output for the United States. In Graph 8.1, I assumed that government spends its tax revenue on lump sum transfer payments
107
TABLE 8.7 LAFFER CURVE DATA FOR THE US ASSUMING LUMP SUM TRANSFERS
Current Marginal Tax Rate
Final Marginal Tax Rate
Final Average Tax Rate (τ)*
Change in Output
Change in Hours Worked
Total Tax Revenue (τ*y)
0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80
0.00 0.03 0.07 0.10 0.14 0.17 0.21 0.24 0.28 0.31 0.35 0.38 0.42 0.45 0.49 0.52 0.56
0.19 0.17 0.14 0.11 0.08 0.06 0.03 -0.01 -0.04 -0.07 -0.11 -0.15 -0.19 -0.23 -0.28 -0.33 -0.39
0.29 0.25 0.21 0.17 0.12 0.08 0.04 -0.01 -0.06 -0.10 -0.15 -0.20 -0.26 -0.31 -0.37 -0.43 -0.50
0.000 0.039 0.076 0.111 0.145 0.175 0.204 0.231 0.256 0.277 0.296 0.312 0.325 0.332 0.336 0.335 0.326
*Assuming the ratio of the marginal tax rate to the average tax rate remains constant.
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GRAPH 8.1
Total tax revenue for various marginal tax rates assuming government spending as lump sum transfer payments (μ = 1) 0.4
0.35
Total Tax Revenue
0.3
0.25
0.2
0.15
0.1
0.05
0 0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4 Tax Rate
0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.8
109
regardless of hours worked (the equivalent of μ = 1). This Laffer Curve reaches its peak at a tax rate of about 0.70, implying that the United States government would maximize total tax revenue by implementing a marginal tax rate of about 0.70, corresponding to an average tax rate of about 0.49. Of course, moving to such a high marginal tax rate would have devastating effects on output and hours worked. Output would drop about 30% and hours worked would drop about 40%. If I assume that individuals value government spending ½ as much as their own consumption (μ = 0.50), I obtain the data in Table 8.8. The total tax revenue would be much higher for a given tax rate than in the previous case because there is now an income effect which offsets a considerable amount of the substitution effect of the tax increase. A tax increase will therefore have less of a negative effect on output and labor supply (and a tax decrease will have less of a positive effect on output and labor supply). Graph 8.2 presents the Laffer Curve when μ = 0.50. This Laffer Curve reaches its peak at a tax rate of about 0.75, implying that the United States government would maximize total tax revenue by implementing a marginal tax rate of about 0.75, corresponding to an average tax rate of about 0.52. Moving to such a high marginal tax rate would have devastating effects on output and hours worked. Output would drop about 20% and hours worked would drop about 30%. If I assume that individuals’ marginal utility of consumption is unaffected by government spending (μ = 0), I obtain the data in Table 8.9. The Laffer Curve corresponding to this scenario, (Graph 8.3), is perhaps the most interesting. Because according to my model an increase in the tax rate actually increases labor supply when μ = 0, the Laffer Curve does not reach a peak between marginal tax rates of 0.00 and 0.80. In fact, until the marginal tax rate reaches approximately 0.65, the marginal increase in total tax revenue for each increase in the marginal
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TABLE 8.8 LAFFER CURVE DATA FOR THE US ASSUMING μ = 0.50
Current Marginal Tax Rate
Final Marginal Tax Rate
Final Average Tax Rate (τ)*
Change in Output
Change in Hours Worked
Total Tax Revenue (τ*y)
0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80
0.00 0.03 0.07 0.10 0.14 0.17 0.21 0.24 0.28 0.31 0.35 0.38 0.42 0.45 0.49 0.52 0.56
0.05 0.05 0.04 0.04 0.03 0.02 0.01 0.00 -0.02 -0.03 -0.05 -0.08 -0.11 -0.14 -0.18 -0.22 -0.28
0.07 0.07 0.06 0.05 0.04 0.03 0.01 0.00 -0.02 -0.05 -0.08 -0.11 -0.15 -0.19 -0.24 -0.31 -0.38
0.000 0.057 0.114 0.171 0.226 0.280 0.333 0.384 0.432 0.478 0.520 0.558 0.590 0.615 0.633 0.639 0.630
*Assuming the ratio of the marginal tax rate to the average tax rate remains constant.
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GRAPH 8.2
Total tax revenue for various marginal tax rates assuming μ = 0.5 for government spending 0.7
0.6
Total Tax Revenue
0.5
0.4
0.3
0.2
0.1
0 0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4 Tax Rate
0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.8
112
tax rate of 0.05 increases, meaning that, for example, the increase in total tax revenue when the marginal tax rate increases from 0.60 to 0.65 is greater than the increase in total tax revenue when the marginal tax rate increases from 0.55 to 0.60, and so on through the marginal tax increase from 0.00 to 0.05. Even when the marginal tax rate is increased beyond 0.65 to 0.80, total tax revenue continues to increase substantially. Although my computer was unable to solve my Matlab program for marginal tax rates greater than 0.80, it appears that total tax revenue might continue to increase as the marginal tax rate increases at least for some higher marginal tax rates. This implies that when μ = 0, individuals would have a strong incentive to work despite extremely high tax rates. Although the substitution effect would strongly decrease work incentives at such tax rates, the income effect would dominate. 8.5. Balancing the Budget in the Long Run Table 8.10 presents data about how much the United States would have to increase its tax rate to balance its budget, taking into account the resulting changes in output. The top half of the table presents the marginal tax rates necessary to balance the budget in year 80 after all of the effects of the tax rate increase on output have been realized. In contrast, the bottom half of the table presents the marginal tax rates necessary to balance the budget within one year. The data in the bottom half is identical to that presented earlier in Tables 8.2-8.5. As Table 8.10 reveals, the United States would be unable to balance its budget in year 80 when all of the effects of the tax rate increase on output have been realized if there are no cuts in government spending and if government spending consists of lump sum transfers regardless of hours worked. In this scenario, the marginal tax rate of 0.70 necessary to balance the budget in year 2 is actually the tax rate which produces the greatest government revenue, as discussed in section 8.4 and illustrated in Graph 8.1. Output in the United States in year 80, however, would be only about
113
TABLE 8.9 LAFFER CURVE DATA FOR THE US ASSUMING μ = 0
Current Marginal Tax Rate
Final Marginal Tax Rate
Final Average Tax Rate (τ)*
Change in Output
Change in Hours Worked
Total Tax Revenue (τ*y)
0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80
0.00 0.03 0.07 0.10 0.14 0.17 0.21 0.24 0.28 0.31 0.35 0.38 0.42 0.45 0.49 0.52 0.56
-0.11 -0.09 -0.08 -0.06 -0.05 -0.03 -0.01 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.13 0.13 0.11
-0.15 -0.13 -0.11 -0.09 -0.07 -0.05 -0.02 0.01 0.03 0.06 0.09 0.12 0.15 0.17 0.18 0.19 0.16
0.000 0.059 0.120 0.184 0.249 0.317 0.387 0.460 0.536 0.614 0.695 0.779 0.864 0.950 1.032 1.107 1.162
*Assuming the ratio of the marginal tax rate to the average tax rate remains constant.
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GRAPH 8.3
Total tax revenue for various marginal tax rates assuming μ = 0 for government spending 1.4
1.2
Total Tax Revenue
1
0.8
0.6
0.4
0.2
0 0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4 Tax Rate
0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.8
115
TABLE 8.10 VARIOUS SCENARIOS FOR THE US TO DEAL WITH ITS DEFICIT TO BALANCE THE BUDGET IN YEAR 80
Scenario for the United States1
Current Marginal Tax Rate
Marginal Tax Rate, Accounting for Changes in Output in the Long Run, to Balance the Budget
Change in Output
Surplus in Year 22
No Spending Cut, Lump Sum Transfers
0.34
Unable3
N/A
N/A
Spending 50% of Budget Fix, Lump Sum Transfers
0.34
0.47
-0.10
0.01
No Spending Cut, μ = 0.50
0.34
0.56
-0.08
0.01
Spending 50% of Budget Fix, μ = 0.50
0.34
0.44
-0.03
RAISING TAXES TO BALANCE THE BUDGET: HOW EFFECTS ON OUTPUT AND LABOR SUPPLY COMPLICATE THE MATTER May 9, 2011 Gregory Hirshman Department of Economics Stanford University Stanford, CA 94305 [email protected] Under the direction of Prof. Robert Hall
ABSTRACT The United States and many major European countries currently are running large budget deficits, and most of these countries also confront significant national debt. Many are now seeking to restore fiscal discipline by cutting spending, raising taxes, or doing both. In this thesis, I explore what would occur if the United States or any of seven major European countries (France, Germany, Italy, the United Kingdom, Greece, Spain, and Sweden) attempted to balance its budget simply by raising taxes. I also determine what would occur if a country decided to balance its budget by using tax increases to accomplish half of its budget fix and cutting government spending to do the rest. To pursue this analysis, I first employ a simple static model to gain some understanding of how changes in tax rates affect how much people work. I then develop a more realistic and sophisticated dynamic general equilibrium model and gradually add refinements to it. With that model, I find that if government spending is not reduced, all countries except Sweden, which has only a small budget deficit, are either incapable of achieving a balanced budget in one year or could do so only by suffering dire economic consequences. Even if cuts in government spending account for 50% of the budget fix, all countries under analysis (except Greece which is unable to balance its budget under any of the four scenarios I posit) would experience at least some loss in output, and many would face considerable hardship. Keywords: Labor supply, tax rates, government spending, budget deficit, United States, Continental Europe, Scandinavia Acknowledgements: I thank Professor Robert Hall for overall guidance. I thank Professor Geoffrey Rothwell for suggestions on my study design. I also thank my parents who helped me edit this thesis and my brother Brian who helped me develop my MATLAB code.
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Table of Contents Chapter 1: Introduction .................................................................................................................. 6 Chapter 2: Literature Review ....................................................................................................... 16 2.1. Labor Supply Across Countries ...................................................................................... 16 2.1.1. The Effect of Tax Rates ......................................................................................... 16 2.1.2. The Effect of the Way that Government Spends its Revenue ............................... 19 2.1.3. The Effect of Labor Unions, Labor Market Regulations, and Productivity .......... 22 2.1.4. The Effect of Income Inequality ............................................................................ 24 2.2. Background of the Dynamic General Equilibrium Model .............................................. 25 2.2.1. The Neoclassical Starting Point ............................................................................. 25 2.2.2. Dynamic Modeling ................................................................................................ 27 Chapter 3: A Static Model of Tax Rates and Labor Supply ........................................................ 29 3.1. Background ..................................................................................................................... 29 3.2. Theoretical Framework ................................................................................................... 30 3.3. My Key Equilibrium Relation ........................................................................................ 37 3.4. Explanation of Results .................................................................................................... 39 Chapter 4: My Dynamic General Equilibrium Model ................................................................. 45
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4.1. How the Dynamic Model Improves upon the Simple Static Model ............................... 45 4.2. Introduction to the Dynamic General Equilibrium Model .............................................. 46 Chapter 5: Employing My Dynamic Model ................................................................................ 50 5.1. The Trivial Case: No Taxes ............................................................................................ 50 5.2. The Model with Taxes .................................................................................................... 50 5.3. Changing the Tax Rate in the Dynamic General Equilibrium Model ............................ 51 5.3.1. Increasing the Tax Rate from 20% to 30% ............................................................ 51 5.3.2. Decreasing the Tax Rate from 20% to 10% ........................................................... 57 5.3.3. Varying the Magnitude of the Change in the Tax Rate ......................................... 61 5.4. Removing the Consumption-Work Complementarity .................................................... 64 5.5. Assuming a Lower Wage Elasticity of Labor Supply .................................................... 66 Chapter 6: Alternative Scenarios for Government Spending....................................................... 69 6.1. Government Spending on Wasteful Projects .................................................................. 69 6.2. The Concept of μ.............................................................................................................. 72 6.3. Results from Introducing μ into the Model ..................................................................... 73 6.3.1. Increasing the Tax Rate from 20% to 30% ............................................................ 73 6.3.2. Decreasing the Tax Rate from 20% to 10% ........................................................... 75
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6.4. Implications of μ ............................................................................................................. 75 Chapter 7: Welfare Analysis ........................................................................................................ 77 7.1. Welfare Analysis over a Lifetime in the Baseline Case ................................................. 77 7.1.1. Utility Changes Caused by a Change in the Tax Rate ........................................... 78 7.1.2. Consumption Gain and Loss Equivalents Caused by Changes in the Tax Rate .... 79 7.1.3. Hours Worked Gain and Loss Equivalents Caused by Changes in the Tax Rate .. 81 7.2. Welfare Analysis Between the Steady States in the Baseline Case ................................ 83 7.2.1. Utility Changes Caused by a Change in the Tax Rate ........................................... 83 7.2.2. Consumption Gain and Loss Equivalents Caused by Changes in the Tax Rate .... 84 7.2.3. Hours Worked Gain and Loss Equivalents Caused by Changes in the Tax Rate .. 86 7.3. Welfare Analysis Assuming No Complementarity or a Less Elastic Labor Supply ...... 88 7.4. Welfare Analysis Assuming Different Values of μ ........................................................ 90 Chapter 8: Applying My Model to Real World Scenarios .......................................................... 92 8.1. The Economic Situation in the Eight Countries Under Consideration ........................... 92 8.2. Scenarios for Balancing the Budget in One Year ........................................................... 93 8.2.1. Assuming Lump Sum Transfers with No Change in Spending ............................. 94 8.2.2. Assuming Lump Sum Transfers with Spending Cuts 50% of the Budget Fix ...... 96
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8.2.3. Assuming μ = 0.50 with No Change in Spending .................................................. 99 8.2.4. Assuming μ = 0.50 with Spending Cuts 50% of the Budget Fix ......................... 100 8.2.5. The Consequences of Using Tax Increases to Balance the Budget ..................... 103 8.3. A Closer Look at the Case of the United States ............................................................ 103 8.4. Laffer Curves for the United States .............................................................................. 106 8.5. Balancing the Budget in the Long Run ......................................................................... 112 Chapter 9: Conclusion ................................................................................................................ 118 References .................................................................................................................................. 122 Appendix A: Matlab Code ......................................................................................................... 126 Appendix B: Results Spreadsheets ............................................................................................ 131
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Chapter 1: Introduction The United States and many major European countries are currently running large budget deficits, and most of these countries also confront significant national debt. As a consequence, many are now trying to restore fiscal discipline after providing generous entitlements, state pensions, and other government benefits for many years. Although tax rates have increased in recent decades in most advanced industrial countries, the resulting increase in government revenues has been greatly outpaced by the increase in government expenditures. Many countries must now cut spending, raise taxes, or do both. In this thesis, I intend to explore what would occur if the United States or any of the seven major European countries (France, Germany, Italy, the United Kingdom, Greece, Spain, and Sweden) attempted to balance its budget simply by raising its taxes. I also seek to determine what would occur if each of those countries decided to balance its budgets by using tax increases to accomplish half of the budget fix and by cutting government spending to do the rest. Can these countries succeed in balancing their budgets? If so, what would be the economic costs in terms of aggregate output and labor supply? To pursue this investigation, I will first develop a simple static model to gain some understanding of how changes in tax rates affect how much people work. I will then create a more realistic and sophisticated dynamic general equilibrium model and gradually refine it. With that model, I will return to my principle research questions. As historical background for this thesis, it is useful to understand the changes in labor supply that have occurred in the United States, Continental Europe, and Scandinavia. In the early 1970s, hours worked in the market sector by persons between the ages of 15 and 64 was approximately equal in the United States, Continental Europe (which I define as France,
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Germany, and Italy), and Scandinavia (which I define as Denmark, Finland, Norway, and Sweden) (Prescott 2004). By the mid-1990s, however, Continental Europeans worked only about 70% as much as Americans, and Scandinavians worked about 85% as much as Americans (Prescott 2004). In the past decade, the proportional labor supply differences between both Continental Europe and the United States and between Scandinavia and the United States have remained relatively constant (Rogerson 2006). What caused the large decrease in the relative labor supply in Continental Europe between the early 1970s and today, and why did the Scandinavian labor supply decrease less dramatically? Prescott (2004) created a model of the G-7 economies which suggested that the large decrease in the relative labor supply in Continental Europe was due primarily to differences in tax rates. His model allowed him to indirectly calculate the Frisch elasticity of labor supply, the elasticity of hours worked with respect to the wage rate given a constant marginal utility of consumption. He found it to be “nearly 3,” an estimate at the upper end of the literature on labor supply elasticity. This value implied that individuals would react strongly to changes in tax rates. Therefore, he found it logical that when tax rates in Continental Europe and the United States were comparable during the 1970s, their labor supplies were similar. As tax rates in Continental Europe increased markedly over the next 25 years, its relative labor supply fell dramatically. While Prescott’s model fit the empirical data on the labor supplies in the G-7 countries during both 1970-1974 and 1993-1996, it did not fit the data for the Scandinavian countries during those periods. Tax rates were higher in Scandinavia in the mid-1990s than in Continental Europe, yet labor supply was also higher. This apparently contradicted Prescott’s prediction that people would react strongly to increases in tax rates by reducing the supply of labor. Prescott
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had made numerous assumptions which might have to be relaxed or modified to allow economists to understand more fully the factors which affect labor supply across additional countries. In this thesis, I seek to develop a more effective and realistic model first by building on Prescott’s model and then creating my own dynamic general equilibrium model which avoids several of his oversimplifications. My thesis is organized as follows. Chapter 2 begins with a review of the literature on the causes of the relative changes in the labor supply between the United States, on the one hand, and Continental Europe and Scandinavia on the other. It then reviews literature which provides the foundation for my dynamic general equilibrium model. Chapter 3 develops a simple static model based on Prescott (2004). This model employs a less restrictive utility function, and it allows me to derive an original equilibrium relation between hours worked and the effective marginal tax rate and to estimate the Frisch elasticity of labor supply directly. Using this model, I find that the Frisch elasticity of labor supply in the G-7 countries was 2.97. This suggests that the vast majority of the change in the relative labor supply between the United States and Continental Europe might indeed be explained by higher tax rates in Continental Europe. My estimate of the Frisch elasticity of labor supply corroborates Prescott’s indirect calculation. Chapter 4 explains why a number of the underlying assumptions made in the simple static model are gross oversimplifications. For example, that model did not take into account interactions between economic variables across time periods, and it assumed that all non-military government expenditures substitute on a one-to-one basis for private consumption, implying that there was only one consumption good. I then develop a new dynamic general equilibrium model
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and explain why it represents a significant improvement. My presentation provides only an outline of how my calculations were actually performed. It was necessary to encode the model in Matlab because those calculations were far too complex to be performed by hand. That code is presented in Appendix A. Chapter 5 applies my dynamic model to the baseline case in which I assume that (1) the elasticity labor supply is 1.9, (2) consumption-work complementarity exists, and (3) all tax revenue is spent on lump sum transfer payments to individuals regardless of hours worked. The first two assumptions are based on Hall (2009a), and the rationale for them is discussed in chapter 5. The third assumption is derived from Prescott (2004), and the rationale for it is discussed in chapter 3. Chapter 5 explores how an arbitrary increase or decrease in the tax rate would, in the baseline case, affect economic variables including output, hours worked, the real interest rate, the pre-tax wage, consumption, the capital stock, the economy’s discounter, and the rental price of capital. It employs a time horizon of 80 years. An increase in the tax rate is shown to lead to a long run decrease in output, hours worked, consumption, and the capital stock while a decrease in the tax rate produces a long run increase in output, hours worked, consumption, and the capital stock. The largest changes occur during the first year after the changes in the tax rate. Thereafter, the variables gradually approach their long term steady states. The real interest rate and pre-tax wage are unchanged in the long run. Appendix B presents the results spreadsheets for changing the tax rate from 20% to 30% or from 20% to 10% in the baseline case Chapter 5 then examines three related issues. It demonstrates that, starting from an initial postulated tax rate of 20%, each 10% increase in the final tax rate from 0% to 90% has an
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increasingly large effect on the magnitude of the changes produced in output, hours worked, consumption, and the capital stock. It shows that removing the assumption of consumption-work complementarity or assuming a less elastic labor supply of 0.5 reduces the magnitude of these changes. Chapter 6 considers alternative scenarios for the amount that individuals value government spending. The assumption that all tax revenue is spent on lump sum transfers to individuals regardless of hours worked is an oversimplification since it is unrealistic to assume that individuals value all government spending as much as direct transfer payments. Therefore, I consider two other scenarios. The first is the extreme case in which all tax revenue is spent on projects which do not affect the individual’s marginal utility of consumption in any way. The second scenario is more complex. It is designed to reflect the possibility that a fraction of government spending might provide utility to individuals by increasing their ability to consume while the remainder might be spent on projects which do not affect the individual’s marginal utility. I introduce a variable, μ, which represents the fraction of tax revenue spent on programs which correspond to the individuals’ consumption preferences. In this scenario, the benefit individuals derive from government spending still does not depend on hours worked, but it does depend on the value of μ. The analysis of the results of the changes in tax rates in these scenarios is based on two competing economic effects: the substitution effect and the income effect. The substitution effect is the change in the amount that individuals work given a change in the after-tax wage, holding the marginal utility of consumption constant. The income effect is the change in the
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amount that individuals work because changes in the tax rate make them richer or poorer affecting their marginal utility of consumption. Because in chapter 5 I assumed that all government revenue was spent on lump sum transfers to individuals regardless of hours worked, the income effect was absent. Regardless of the tax rate, tax revenue was fully rebated to individuals. No income was lost, so only the substitution effect influenced hours worked. A lower after-tax wage reduced the incentive to work (marginal utility of consumption being held constant) because individuals would increase their consumption less by working an additional hour. Therefore in chapter 5, increasing the tax rate always led to a decrease in output and hours worked and decreasing the tax rate always led to an increase in output and hours worked. When some or all of government revenue is spent on projects which do not affect the individual’s marginal utility of consumption, the income effect becomes relevant. This is because a tax increase will make individuals poorer. When individuals are able to consume less, each unit of consumption is more valuable, so a tax increase will make individuals value each unit of consumption more. Their marginal utility of consumption will increase. Thus, there will be two opposing effects of a tax increase on labor supply when only a fraction of tax revenue is spent on programs which correspond to the individuals’ consumption preferences. The substitution effect will tend to make individuals work less and the income effects will tend to make them work more. The smaller the value of μ, the greater the income effect. For small values of μ, the income effect dominates in my model, so an increase in the tax rate will cause an increase in labor supply and output. For larger values of μ, the income effect is smaller and the substitution effect dominates, so an increase in the tax rate will cause a decrease in labor supply and output. For a tax decrease, the results are the reverse.
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Chapter 7 explores the effects of tax rate changes on the utility, or welfare, of individuals. First, it presents the changes in welfare produced by changes in the tax rate over the course of an 80 year lifetime. Then it examines the difference between the initial and final steady states. The latter expresses the full impact of the tax changes, but it does not take into account the intervening changes between years 2 and 79, and so it overestimates actual welfare changes which result. This chapter concludes by considering how altering assumptions about the consumption-work complementarity, the elasticity of labor supply, and the nature of government spending would affect welfare changes over the 80 year lifetime. In my baseline case, increasing tax rates reduces welfare and decreasing tax rates increases welfare. This occurs regardless of assumptions made about how individuals value government spending, about whether consumption-complementarity exists, or about whether labor supply is relatively elastic or inelastic, although these assumptions do affect the magnitude of the changes. To provide a more intuitive sense of the magnitude of the welfare changes which I calculate, I consider consumption change equivalents and hours worked change equivalents. Consumption change equivalents express how much more or less consumption an individual would need to have if he continued to work as much as he had at the initial tax rate to attain the utility he actually achieves when the tax rate is increased or decreased. Hours worked change equivalents express how much more or less an individual would need to work if he continued to consume as much as had did at the initial tax rate to attain the utility he actually achieves when the tax rate is increased or decreased. An important finding in this chapter is that the lower the value of μ, the greater the magnitude of the change in welfare caused by a given change in the tax rate. While a low value of μ may imply that an increase in the tax rate will increase output and labor supply, welfare will
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be reduced dramatically when μ is small. In fact, for a given tax rate increase, the higher the value of μ, the smaller the decrease in welfare despite the fact that output and labor supply will be more negatively affected when μ is large. Conversely, for a given tax rate decrease, the higher the value of μ, the smaller the increase in welfare despite the fact that output and labor supply will be more positively affected when μ is large. With this background, chapter 8 returns to the original research questions. I consider eight countries: the United States, the four largest European economies (France, Germany, Italy, and the United Kingdom), the two largest European economies with very high deficit to GDP ratios (Greece and Spain) and the largest Scandinavian economy (Sweden). My first goal is to use my model to predict how much these countries would have to raise taxes in order to balance their budgets within one year. I examine various scenarios incorporating different assumptions about government spending to determine how such assumptions would affect the size of the necessary tax increases and the resulting effects on output and labor supply. I pursue the case of the United States in greater depth, presenting the Laffer Curves which my model generates under different assumptions about government spending. The Laffer curve generated when μ = 0 is particularly interesting because it does not reach a peak before the marginal tax rate is 0.80. Finally, I compute how much the United States would have to raise taxes in order to balance its budget in the long run, taking into account both the short term and the long term impact of tax rate increases on output. Regardless of whether tax revenue is assumed to be spent on lump sum transfers to individuals regardless of hours worked or whether individuals value government spending ½ as much as their own consumption (μ = 0.50), all countries except Sweden, which has only a small budget deficit, are either incapable of achieving a balanced budget in one year through tax
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increases alone or would suffer dire economic consequences as a result of the necessary tax increases. If a reduction in government spending accounts for 50% of the budget fix and tax revenue is assumed to be spent on lump sum transfers to individuals regardless of hours worked, Germany, Greece, and Spain could not balance their budgets. Of the remaining countries, only Sweden could avoid serious economic repercussions. If the reduction in government spending accounts for 50% of the budget fix and if individuals value government spending ½ as much as their own consumption (μ = 0.50), 7 of the 8 countries can balance their budgets. Greece’s budget deficit is so severe and its current tax rates are so high that even under these conditions, it cannot balance its budget. All the countries which can balance their budgets would experience reductions in output, and Germany and Spain would face devastating hardship. In the case of the United States, whose 2009 deficit to GDP ratio was 11% and whose debt to GDP ratio was 53%, I demonstrate that assuming no consumption-work complementarity or a less elastic labor supply would lead to a lower values for tax rate necessary to balance the budget and smaller consequent decreases in output and hours work. The greater the share of the budget fix made up by decreases in government spending, the smaller the necessary increases in the tax rate and the smaller the decreases in output and hours work. The smaller the value of μ, the smaller the necessary increase in the marginal tax rate to balance the budget, and the smaller the decreases in output and hours worked. In my baseline case, I find that for the United States even to achieve a deficit to GDP ratio of 3% without a reduction in spending would require such a large increase in its tax rate that a depression would result. Furthermore, despite the relatively low marginal tax rate of the United States, it would be impossible for it to achieve a budget surplus of 3% simply by raising tax rates without reducing government spending. Because my model demonstrates that only
15
about 90% of the decrease in output which occurs in a country over an 80 year lifetime is experienced during the first year after a tax rate increase, I find that the long run fall in output caused by a tax increase would be even larger than the short run fall in output. Therefore, still larger tax increases would be necessary to achieve balanced budgets in the long run, causing greater economic harm. For example, although the United States could balance its budget in one year under the baseline assumptions if it were willing to endure the resulting economic hardship, it would be impossible for it to balance its budget in the long run simply by raising taxes. Chapter 10 presents my conclusions and suggests potential avenues for further research.
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Chapter 2: Literature Review I begin by reviewing literature which analyzes four aspects of the relative changes in the labor supply between the United States, on the one hand, and Continental Europe and Scandinavia on the other. The first is the effect of tax rates on the relative labor supplies. The second is the way that patterns of government expenditures help explain why over the past two decades relative labor supply has been higher in Scandinavia than in Continental Europe despite higher taxes. The third is the influence of labor unions, labor market regulations, and output per hour worked on labor supply. The fourth is the impact of the level of income inequality on labor supply. I then review literature which provides background for Hall (2009a) since this paper provides the foundation for the dynamic model I develop in this thesis. 2.1. Labor Supply Across Countries 2.1.1. The Effect of Tax Rates Prescott (2004) spurred intense debate in the economic community over the impact of differences in tax rates on the observed differences in relative labor supply across countries. He defined labor supply as hours worked per person aged 15-64 in the market sector. He only counted those hours which resulted in taxed labor income. Paid vacations, sick leave, holidays, and time spent working in the underground economy or at home were specifically excluded. Prescott created a model for the G-7 countries following standard macroeconomic theory and analyzed a stand-in household that faced a decision over how much to work and how much to consume. He derived an equilibrium relation between hours worked and the effective
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marginal tax rate on labor income. He explained the way he estimated tax rates and justified his why his estimates were reasonable. One of his key simplifying assumptions was that all tax revenue, except for that used for pure public consumption, was returned to households in lump sum payments independent of household income or hours worked. He defended this assumption by asserting that most public expenditures in the G-7 countries are substitutes for private consumption. This assumption allowed his model to consider only one consumption good. Prescott noted that although this was reasonable for the G-7 countries, it was not valid if a broader set of countries was to be considered. For example, in Scandinavia greater government expenditures on programs like child care for working parents necessitated treating some publicly provided goods separately from privately consumed goods. Rogerson (2006) extended Prescott’s analysis to include multiple consumption goods. His paper is discussed later in subsection 2.1.2. In Prescott’s analysis of the G-7 countries during the periods of 1970-1974 and 19931996, he found the Frisch elasticity of labor supply was “nearly 3,” implying that individuals would react strongly to changes in tax rates and that the vast majority of the differences in labor supply between the United States and Continental Europe could be explained by the higher taxes in Continental Europe. He noted that his model estimated the labor supply among the G-7 countries very well during the mid-1990s and quite well during the early 1970s. Prescott’s finding of an elasticity of labor supply of “nearly 3” is at the extreme upper end of values found in the literature. Many economists believe that the elasticity is actually much lower. Pistaferri (2003) based his estimate of labor supply elasticity on data on how workers’ expectations of their wages change as tax rates change. He calculated the Frisch elasticity of labor supply to be 0.70. Studying the decline in hours worked among lottery winners, Kimball and Shapiro (2003) estimated the Frisch elasticity of labor supply to be about
18
one. Mulligan (1998) found the elasticity to be not much greater than one. His work is controversial, however, because, unlike most authors, he included data on older workers who earn lower wages, work fewer hours, and tend to be more responsive to changes in tax rates. Rogerson and Wallenius (2008) sought to explain the variation which exists in estimates of the Frisch elasticity of labor supply by dividing the relevant papers into two groups. Those which use microeconomic models typically calculate elasticities ranging from 0.05 to 1.25. Those papers that use macroeconomic models typically find values between 2.25 and 3.00. Low values derived from microeconomic models would imply that differences in tax rates between the United States and Continental Europe could only explain a small part of the differences in the changes in relative labor supply because these values imply that the number of hours worked would not be strongly affected by changes in tax rates. The high values derived from macroeconomic models, however, would imply that differences in tax rates between the United States and Continental Europe could explain most of the differences in the changes in relative labor supply. In the papers considered above, home production was not considered to contribute to labor supply. Olovsson (2009) pointed out, however, that while market work per person is about 10% higher in the United States than in Sweden, the total number of hours worked differs by only 1% when hours worked at home are included. He developed a model which demonstrated that differences in tax rates could account for most of the discrepancy in market work and home production between the United States and Sweden. He noted that taxes affect the amount of home production because service taxes raise the price of market-produced services while labor taxes reduce the economic return to market work, increasing the relative return to home production. Because tax rates are much higher in Sweden than in the United States, there is a
19
greater incentive for Swedes to substitute home production for market work. Freeman and Schettkat (2005) came to similar conclusions. They found that while Americans work significantly more hours per week in the market sector than Europeans, Americans and Europeans work about the same number of hours per week when home production is included. Their analysis indicated that higher taxes in Europe played a key role in creating this situation. 2.1.2. The Effect of the Way that Government Spends its Revenue While tax rates definitely affect labor supply, it seems likely that other factors contribute to the differences in relative labor supply among the United States, Continental Europe, and Scandinavia. One of these factors is the pattern of government expenditures, which helps account for the fact that labor supply is higher in Scandinavia than it is in Continental Europe despite higher tax rates in Scandinavia. Rogerson (2006) explored this issue by employing a version of the standard neoclassical growth model which takes into account different types of government spending. Instead of making Prescott’s assumption that all government expenditures are lump sum transfers independent of hours worked, Rogerson divided government expenditures into four categories, depending on whether they were used (1) to finance lump sum transfers independent of hours worked, (2) to hire workers at market wages who produced nothing which households valued, (3) to subsidize consumption, or (4) to subsidize leisure. He found that taxes which funded government expenditures to hire unproductive workers or to subsidize consumption had no effect on hours worked, but taxes expended on lump sum transfers and subsidies for leisure had a negative effects on hours worked. Those spent on subsidies for leisure had the largest effect. Rogerson concluded that it is essential to consider how the government spends its revenue in order to determine the effect of tax rates on labor supply because different types of expenditures lead to different effects.
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Rogerson (2007) applied this analysis to the “anomaly” of Scandinavia. Scandinavia had both higher tax rates and higher labor supplies than Continental Europe in the mid-1990s. This appeared to contradict the theory that higher tax rates lead to lower labor supply. Rogerson found, however, that the elasticity of labor supply varies among countries depending on their patterns of government expenditures. If the elasticity of labor supply in Scandinavia is low enough relative to that in Continental Europe, this could explain how Scandinavian countries could simultaneously have higher tax rates and higher labor supplies. Scandinavian taxes for government expenditures would have a less negative effect on labor supply than taxes in Continental Europe. By assuming more than one consumption good in the economy, Rogerson was able to distinguish between government transfers to individuals regardless of hours worked, government transfers affected by hours worked, and government transfers which did not affect the individual’s marginal utility of consumption. If higher taxes fund disability payments which can be received only by an individual who is not working, for example, they might have a strongly negative effect on labor supply. On the other hand, if the higher taxes were used to fund day care of children of working parents, they might have a much smaller adverse effect on labor supply. Rogerson also pointed out that higher taxes would lead to larger differences on the labor supply in activities for which there are strong non-market substitutes. This point was also stressed by Davis and Henrekson (2005). These authors considered, for example, the case of a family who wished to paint their home, an activity for which there is a strong non-market substitute. If the family hires professional painters, the transaction is subject to taxation. If it paints the house itself, taxes are avoided. The higher the taxes, the greater the incentive to avoid
21
the market alternative. Other activities, such as auto production, are difficult to carry out outside the market sector. The effect of higher tax rates on labor supply in such activities would be expected to be smaller. Building on this analysis, Rogerson explained how Scandinavian countries could have higher marginal tax rates and still have higher labor supply. Compared to Continental Europe, they have substantially higher rates of government employment. This government employment often serves as an implicit transfer to the government employee, although it does not affect the marginal utility of consumption for the vast majority of households. Higher government employment in the service sector in Scandinavia provides a larger transfer of market services to households, increasing hours worked in the market sector. For example, Rogerson noted that Scandinavian countries spend a much higher percentage of government revenue on services such as child and elderly care. Such jobs often have strong non-market substitutes. The same work which counts toward labor supply in Scandinavia when it is performed by government employees does not count in Continental Europe, where it is often completed outside of the market sector. Rosen (1996) noted that child care subsidies have had an especially large impact on labor supply by encouraging labor force participation by women in Sweden. With Sweden’s high marginal tax rates, it would be difficult for these mothers to work in the market sector and purchase child care in the private market. Child care subsidies, however, tend to offset this income tax penalty. Rosen noted that such child care subsidies are a major reason why female participation in the labor market is much higher in Scandinavia than in Continental Europe and thus a major reason why hours worked in Scandinavia are higher than they might otherwise be.
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2.1.3. The Effect of Labor Unions, Labor Market Regulations, and Productivity Differences in the power of labor unions, the stringency of labor market regulations, and relative productivity also affect relative labor supply across countries. Alesina et al. (2005) argued that differences in the power of labor unions and in the stringency of labor market regulations, rather than differences in tax rates, explain the majority of the differences in labor supply between Continental Europe and the United States. They noted that the strength of unions increased dramatically in Continental Europe during the 1970s and 1980s, the period which witnessed the large decrease in its relative labor supply. They cited Alesina and Glaesar (2004), which argued that American racial fractionalization and European political instability led to Americans being much less open to the socialist/Marxist left than Europeans and therefore less supportive of organized labor. Alesina et al. argued that because of their power, unions in Continental Europe were able during economic shocks to push successfully for a reduction in hours worked as an alternative to increased unemployment, employing slogans like “work less–work all.” This might not have been an optimal response to the economic conditions, but union power often rested on the size of union membership, making such policies appealing to them. Hunt and Katz (1998) pointed out that the reduction of the standard workweek did not lead to any significant increase in overtime work in Europe. Therefore, the diminished standard workweek reduced labor supply. Alesina et al. pointed out that unions demanded higher wages to compensate for lower hours worked and keep total income constant. This led to even sharper declines in labor supply because it was difficult for employers to increase hourly wages without making cuts in total hours of employment. Nickell (1998) noted that unions also succeeded in lobbying for much
23
higher unemployment compensation in Europe, which reduced the marginal loss of consumption for the unemployed. This made unemployment less undesirable. It reduced the incentive to seek employment and pressured employers to raise wages in order to provide incentives to work. The resulting higher wages reduced the incentive for employers to hire more workers. Rogerson (2006) pointed out another reason for the decrease in the labor supply of Continental Europe and Scandinavia relative to that of the United States. As countries develop, individuals tend to work less. More advanced nations have lower labor supplies because their citizens can achieve a similar standard of living while working fewer hours and enjoying more leisure. As consumption increases, the marginal utility of consumption decreases. Individuals thus have less incentive to work longer hours when they receive higher wages. In the early 1970s, output per hour worked in Continental Europe and Scandinavia was significantly lower than in the United States. By the mid-1990s, productivity in Continental Europe and Scandinavia had caught up (Prescott 2004, Pilarski 2008). Thus, in the early 1970s, Continental Europeans and Scandinavians had an extra incentive to work because of their lower output per worker. By the mid-1990s, this difference no longer existed. If Continental Europeans and Scandinavians worked about as much as Americans when they had an extra incentive, they would be expected to work less without it. According to Pissarides (2007), one of the reasons for the dramatic decrease in the relative labor supply of Continental Europe over this period is that the comparison is between the time of exceptional economic and productivity growth which Europe experienced from the end of World War II to the early 1970s and the normal steady state of the mid-1990s.
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2.1.4. The Effect of Income Inequality A final factor contributing to the fact that Americans work more than Europeans is that there is greater income inequality in the United States. As Formby et al. (2004) pointed out, the distribution of wages is more even, for example, in Germany than in the United States. In addition, government transfers from the wealthy to the poor are greater in Germany, so disposable income inequality is even less in Germany relative to the United States than wage income inequality (Gottschalk and Smeeding 1997). Bell and Freeman (2001) explained the fact that Americans work more than Germans by analyzing forward-looking labor supply responses to differences in earnings inequality. They argued that workers often choose additional current hours of work because they hope to gain promotions and higher pay in the future. Since earnings are more unequally distributed in the United States than in Germany, extra work has a greater potential payoff in the United States, and this leads to more hours worked. According to Bell and Freeman, the argument that greater earnings inequality leads to more hours worked rests on three premises: (1) that individuals can rise in the percentile distribution of earnings by working more hours, (2) that individuals base how much they work currently on assumptions they make about how much they expect to earn in the future as a result of their current work, and (3) that the greater the inequality of income, the larger the marginal change in an individual’s earnings given the same change in his position in the percentile distribution of income. Using data on earnings and hours worked in the market sector in the United States and Germany, they found (1) that the greater the number of hours an individual worked, the greater his expected earnings in both the United States and in Germany, but with a greater expected benefit in the United States and (2) that in both countries full time workers work more hours in occupations which have greater wage inequality. This provided evidence that that
25
the difference in income inequality between the United States and Germany was a significant factor in the difference in hours worked in the market sector between the two countries. 2.2. Background of the Dynamic General Equilibrium Model 2.2.1. The Neoclassical Starting Point Hall (2009a) sought to estimate the output and consumption multiplier effects which quantify how much output and consumption change given an increase in government purchases. Hall initially developed a static neoclassical model with a standard macroeconomic utility function in which individuals receive positive utility from consumption and negative utility from work. In his model, technology was estimated using the Cobb-Douglass production function, and the real wage was assumed to be determined by the marginal product of labor. Employing this model, Hall calculated the output multiplier to be 0.4 and the consumption multiplier to be -0.6. These values differ significantly from the empirical data which indicate that the output multiplier is about 1 and the consumption multiplier is about 0. Recognizing this, Hall considered additional factors to make his model more reflective of reality. The first was the endogenous markup of price over cost, which reflects the fact that firms in the real world have market power. Assuming sticky prices, this power is higher in economic slumps and lower in booms. Markups are thus countercyclical, as Rotemberg and Woodford (1992) demonstrated. Augmenting his neoclassical model with a constant-elasticity relationship between markup and output, Hall computed the output multiplier to be 0.5 and the consumption multiplier to be -0.5, a step in the right direction. He then considered unemployment and the employment function, noting that many general equilibrium models have difficulty explaining fluctuations in labor supply if they do not
26
explicitly consider unemployment. Monica Merz (1995) and David Andolfatto (1996) made significant progress by building on the work of Mortensen and Pissarides (1994) by explicitly allowing for unemployment in otherwise neoclassical models. Blanchard and Galí (2007) succeeded in introducing unemployment in the New Keynesian Model. Hall (2009b) built on the Mortensen-Pissardes model by allowing for a broad variety of bargaining solutions between jobseekers and employers and replacing their linear preferences with standard macroeconomic preferences. Hall (2009a) then used an employment function, which he had previously developed in Hall (2009b). This function incorporates two components. The first is the fraction of the population which is employed as a result of the interaction between jobseekers and employers. The second is the Frisch supply function for hours worked per employed worker, which explicitly takes unemployment into account. Chetty et al. (2011) illustrated why, in measuring labor supply elasticities, it is important to consider both how much people respond to changes in the tax rates conditional on employment and how many people choose to be employed when tax rates change. Using his employment function, Hall calculated a labor supply elasticity much higher than that which he had found using the standard neoclassical model. This value was more in line with labor supply elasticity calculated by Kydland and Prescott (1982). Although that value had been criticized for by Mankiw et al. (1985) and Eichenbaum et al. (1988) as being too high, Hall stated that in light of recent work, it appeared reasonable. With this basis, he reestimated the output multiplier to be 0.8 and the consumption multiplier to be -0.2, values even closer to the empirical data. The last factor which Hall added to his static model was the consumption-work complementarity, which reflects the fact that as an individual works more hours in the market
27
sector, his marginal utility of consumption rises. As an individual has the less time for home production, he places greater value on consumption in the market. Aguiar and Hurst (2005) and Hurst (2008) analyzed consumption patterns upon retirement. Their data supported the notion of complementarity between consumption and work. There is a significant drop in consumption of goods and services in the market when individuals cease\ to work, apparently because they have the opportunity to spend more time on home production and therefore have less need to make purchases in the market. Browning and Crossley (2001) and Low et al. (2008) studied declines in consumption in the market during periods of unemployment. Their work also supported the notion of consumption-work complementarity. Employing the preferences used in Hall and Milgrom (2008) to account for consumption-work complementarity, Hall calculated an output multiplier of 0.97 and a consumption multiplier of -0.03. These values were consistent with empirical evidence. 2.2.2. Dynamic Modeling: Building on his static model, Hall then constructed a dynamic model assuming that individuals smooth consumption over their lifetimes instead of simply consuming their present incomes. This dynamic model resulted in lower output multipliers for government purchases because temporary government purchases were offset by future tax increases, and individuals prepared for such increases by cutting current consumption to smooth their consumption by saving to meet the anticipated tax increases. In his model, Hall employed standard treatment of capital adjustment costs, the rental price of capital, the equivalence of capital demand and capital supply, the law of motion for capital, the economy’s discounter, and the Euler equation. He also assumed that after an initial increase in government purchases, government spending would be reduced each year thereafter until it asymptotically approached the pre-shock level and that the
28
capital stock after government spending would also return to the pre-shock level. Using this model, Hall computed an output multiplier of 0.98 and a consumption multiplier of -0.03. He found that if he removed his assumptions about endogenous markup or assumed a lower labor supply elasticity, this had a large effect on his calculations, but if he assumed no consumptionwork complementarity, this had only a small effect. Many economists have taken issue with the idea that all individuals smooth consumption over their lifetime. One of Keynes’s major contributions to macroeconomics was the idea that current consumption depends heavily on current income. Nevertheless, it appears reasonable to assume that some individuals have full access to capital markets and can smooth lifetime consumption although other may be credit constrained and thus consume current income. Galí et al. (2007) followed this logic in employing a standard New Keynesian model for government purchases. They considered a population in which a fraction of individuals, λ, consumed all of its labor income while the remainder smoothed lifetime consumption. The output and consumption multipliers depend strongly on the value of λ. Higher values lead to much larger multipliers. López-Salido and Rabanal (2006) built on the leading New Keynesian model of Christiano et al. (2005), employing a similar assumption about the existence of two groups of individuals, one of which consumes current income while the other smoothes lifetime consumption. López-Salido and Rabanal agreed that the output and consumption multipliers depend strongly on the value of λ, finding that a higher λ leads to much larger multipliers. When Coenen and Straub (2005) employed the model of Smets and Wouters (2003) and assumed two groups, they confirmed that the value of λ affected their calculation of the multipliers, although their multipliers were much lower than those computed by Galí et al. and López-Salido and Rabanal.
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Chapter 3: A Static Model of Tax Rates and Labor Supply
Before developing a dynamic general equilibrium model to analyze how tax rates and the
patterns of government spending affect labor supply, it is useful to employ a simpler model and to understand the economic theory behind it. In this chapter, I develop such a model based on the work of Prescott (2004). I present background information for this model, discuss the model’s theoretical framework, and derive its key equilibrium relation. Finally, I explain the results obtained using this model. 3.1. Background Prescott (2004) created a static model of the G-7 economies which explained that the change in the relative labor supply between the United States and Continental Europe between the early 1970s and the mid-1990s was largely a result of differences in tax rates. His model employed a utility function which established an equilibrium relation between hours worked and the effective marginal tax rate. It allowed for an indirect calculation of the Frisch elasticity of labor supply. Prescott found this elasticity to be “nearly 3,” an estimate at the upper end of the range of those in the macroeconomic literature. My simple static model builds on Prescott’s work, but it employs a less restrictive utility function. This allows me to derive an original equilibrium relation between the effective marginal tax rate and labor supply and to directly calculate the Frisch elasticity of labor supply to be 2.97. This model would tend to support Prescott’s conclusion that the vast majority of the differences in labor supply between the United States and Continental Europe can be explained by differences in the marginal tax rate.
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3.2. Theoretical Framework In this chapter, I examine the major advanced industrial countries which comprise the G-7: Germany, France, Italy, the United Kingdom, Canada, Japan, and the United States. My data comes from the United Nations system of national accounts (SNA) statistics, OECD labor market statistics, and other sources on the purchasing power parity gross domestic product (GDP). I analyze the periods of 1970-1974 and 1993-1996 because Prescott provided all of the necessary data for them. Following the common procedure of labor economists, I define labor supply in this paper as the number of hours worked in the taxed market sector by people between the ages of 15 and 64. Its two principle components are the fraction of the target age population that works and the number of hours worked per person. Paid vacations, sick leave, and holidays are explicitly excluded. Time spent working in the underground economy or at home is similarly excluded. Only time working for taxable labor income is included. Table 3.1, adapted from Prescott (2004), presents labor supply statistics for the G-7 countries relative to those of the United States during 1970-1974 and 1993-1996. In the early 1970’s, labor supply in Continental Europe was about equal to that in the United States. During 1993-1996, labor supply in Continental Europe was only about 70% of that in the United States. What caused this large change? To answer that question, I have built on Prescott’s framework to develop a new model. I analyze a stand-in household that faces a decision about how much time to devote to labor or leisure and how much to consume or save. I use preferences similar to those of Prescott. The key difference in my model lies in the utility function I employ to treat the labor-leisure decision.
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TABLE 3.1 LABOR SUPPLY FOR THE G-7 COUNTRIES
Hours Worked per Person Relative to the United States (U.S. = 100)*
Period
Country
1993-1996
Germany France Italy Canada United Kingdom Japan United States
75 68 64 88 88 104 100
1970-1974
Germany France Italy Canada United Kingdom Japan United States
105 105 82 94 110 127 100
*These data are for persons aged 15-64. Note that this table was adopted from Prescott (2004).
Prescott defined preferences for a stand-in household in the following manner:
log
log 100
(3.1)
where the variable c denotes consumption and h denotes hours of labor supplied to the market sector per person per week. Time is indexed by t. The discount factor 0 < β < 1 measures the value of future consumption and leisure relative to current consumption and leisure. The higher the value β, the more highly a person valued future consumption and leisure. The parameter α > 0 specifies the utility of leisure relative to consumption. Prescott (2004) assumed that a household has 100 hours of productive time per week, implying that (100 – h) hours were
32
devoted to leisure activity. In accordance with standard macroeconomic practice, his model considered time not spent participating in the market sector to be leisure, even though much of this “leisure” might have been spent working in the underground economy or in the nonmarket sector. What was important was that nonmarket production was not taxed. While Prescott’s utility function was simple and easy to use, it did not allow for a direct calculation of the Frisch elasticity of labor supply. I therefore employ the following utility function /
log
1
1/
(3.2)
where ψ denotes the Frisch elasticity of labor supply. The variables c, h, and β denote the same parameters as in Prescott’s model. While α still denotes the utility of leisure parameter, it is different in (3.2) than in (3.1) since I measure the labor-leisure decision in a different manner. Nevertheless, both utility functions reflect the fact that households obtain positive utility from consumption and negative utility from labor. In (3.2), I compute the negative utility of labor in a more complete manner in order to allow for the direct calculation of ψ. I adopt Prescott’s (2004) assumption that households own the capital and rent it to the firm. This is merely for convenience since the results would be the same if the firms owned the capital and rented it to the households, or if the firms were debt-financed. The law of motion for capital stock is 1 where k is the capital stock, x is investment, and δ is the depreciation rate.
(3.3)
33
My model economy also adopts Prescott’s assumption of a stand-in firm following a Cobb-Douglass production function (3.4) where y denotes output, c denotes consumption, and g denotes pure public consumption. The capital share parameter is 0 < θ < 1, and the total factor productivity parameter of country i at date t is Ait. The computation of Ait is irrelevant to the analysis in this paper. Following Prescott, the budget constraint for the household at date t is 1
1
1
1
(3.5)
where wt is the real wage rate, rt is the rental price of capital, τc is the consumption tax rate, τx is the investment tax rate, τh is the marginal labor income tax rate, τk is the capital income tax rate, and Tt represents government transfers. It is important to note that marginal and average labor income taxes are different. I am concerned specifically with the marginal labor income tax rate. To understand equation (3.5), it is useful to think of the left hand side as representing household expenditures and the right hand side as representing household revenue. Household expenditures are divided into after-tax consumption and after-tax investment. Household revenue comes from after-tax labor income, after-tax capital income, and transfers from the government. The δkt term is added on the right hand side of (3.5) because households receive a tax break for depreciation. That is, 1
34
.
Thus, after-tax capital income is equal to the income earned from renting out capital minus taxes paid on rental income less depreciation. My static model, like Prescott’s, assumes all tax revenue except for that which funds purely public consumption is returned to households in lump sum transfer payments which are independent of household income. It also assumes that government expenditures except for military expenditures substitute on a one-to-one basis for private consumption. I also follow Prescott’s lead in estimating pure public consumption g to be two times military’s share of employment times GDP and in assuming that there is only one consumption good. This is a reasonable assumption for the G-7 countries given the nature of their government expenditures. It is not, however, realistic when considering other countries. In Scandinavia, for example, greater government expenditure on programs like child care for working parents necessitates treating publicly provided goods separately from privately consumed goods. Like Prescott’s model, my model presumes a tax system far simpler than those used in any of the G-7 countries. As Prescott notes, however, taking a more complicated tax code into account would entail more difficult calculations but would not affect the inferences drawn from the model. In my model, like Prescott’s, households pay the taxes, so national income accounts have to be appropriately adjusted. Net taxes on the final product have to be calculated by subtracting subsidies from indirect taxes to remove net indirect taxes as a cost component of GDP. To understand this, consider the following example. Imagine a country with a single firm which produces one hat with a pre-tax price of $10.00. Output is $10.00. Suppose a $1.00 sales
35
tax is levied. The buyer must pay $11.00 for the hat. Suppose the buyer receives a $0.50 subsidy for buying the hat. It would really only cost him $10.50. Net taxes would equal indirect taxes less subsides, or $1.00 – $0.50 = $0.50. The output of the economy would still be $10.00. Again, following Prescott, my model assumes that two-thirds of indirect taxes net of subsidies fall directly on private consumption, while the remaining one-third is distributed evenly over private consumption and investment. Net indirect taxes on consumption, ITc, can therefore be expressed as 2 3
1 3
(3.6)
where C is private consumption expenditures, I is private investment, and IT is indirect taxes. Prescott expressed indirect taxes on consumption in this way because many indirect taxes, such as value-added taxes and sales taxes, fall directly on consumption, but others, such as property taxes on office buildings and sales taxes on equipment purchases for business, fall both on consumption and investment. In my model, like Prescott’s, personal consumption c is defined as (3.7) and output y as (3.8) where G is public consumption, Gmil is military expenditures, and GDP is gross domestic product. The consumption tax rate is
36
(3.9) For labor income, my model, like Prescott’s, accounts for two types of taxation. The first is the social security tax rate, which is expressed as Social Security Taxes 1
(3.10)
where the denominator is equivalent to the model economy’s output from labor. The second is the marginal labor income tax rate. To obtain the marginal labor income tax rate, it is first necessary to compute average income tax rate, which is expressed as
Direct Taxes Depreciation
(3.11)
where depreciation must be subtracted from output since households receive a tax break for it. Direct taxes are those paid by households. They do not include corporate taxes. Direct taxes, like social security taxes, are counted as private expenditures of households. Following Prescott, I estimate the marginal labor income tax rate, τh, by combining equations (3.10) and (3.11), yielding 1.6
.
(3.12)
The factor of 1.6 was derived by Prescott by employing the methodology of Feenberg and Coutts (1993) to estimate the marginal income tax rate in the United States during both 1970-1974 and 1993-1996. Their methodology used representative samples of the tax records to determine the marginal tax rate on labor income by determining how much tax revenue increased when household labor income increased by 1%.
37
3.3. My Key Equilibrium Relation In my equilibrium relation, I seek to express hours worked, h, as a function of the effective marginal tax rate on labor income, τ. I combine the marginal labor income tax rate and consumption tax rates to calculate the effective marginal tax rate on labor income. This tax rate specifies the fraction of labor income taken in the form of taxes, holding investment fixed. Prescott expressed it as
.
1
(3.13)
I then use two first order conditions to derive the equilibrium relation between hours worked and the effective marginal tax rate on labor income. The first condition reflects the fact that the marginal rate of substitution (MRS) between leisure and consumption is equal to their price ratio, which is the after-tax wage rate. Using the utility function in (3.2), / /
MRS
/
1/ /
1
.
Thus, /
1
.
(3.14)
The second condition is the profit-maximizing condition that wage equals the marginal product of labor (MPL). Again, using equation (3.2),
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MPL
1
1
where final equality holds because according to equation (3.4),
, so
.
Thus, 1
.
(3.15)
I adopt Prescott’s value for θ of 0.3223 since this is the empirically determined average value for the countries under consideration. Combining the first order conditions given in equations (3.14) and (3.15), I derive the following equilibrium relation /
/
1
1
1 – 1 –
/
1 –
1 –
1–
1 – /
.
Rearranging this equation, I express my equilibrium relation for country i at date t as /
1 1
.
(3.16)
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When Prescott subjected his utility function (equation 3.1) to same manipulations, his equilibrium relation was 1 1
.
(3.17)
1
This equation shares many of the same features of mine, but mine can be used to directly calculate the Frisch elasticity of labor supply while his cannot. My equilibrium relation, like Prescott’s, separates the intratemporal and intertemporal factors affecting labor supply. The (1 – τ) term reflects the intratemporal effects of taxes on the relative prices of consumption and leisure. On the other hand, the c/y term reflects intertemporal factors because if, for example, the effective tax rate is expected to rise in the future, c/y will be lower at present since households will have an incentive to save to smooth consumption. All other things equal, a lower value of c/y will be associated with a higher value of h. An expectation of a future tax increase will cause an increase in current labor supply. Similarly, if the level of the capital stock were low relative to the balanced growth path level, c/y would be lower since households would have the incentive to save in order to increase investment. This would again produce a higher value of h. 3.4. Explanation of Results To calculate α, the utility of leisure parameter, and ψ, the Frisch elasticity of labor supply, I rewrite (3.16) as follows /
1 1
40
/
1
1 1
/
1
1 1
/
.
since the values of c, y, θ, and τ are known for each country and
We may now let
time period considered. Then,
1
log log log
/
1 1
/
log
/
log
/
1 1
/
/
log
log α
1
log z
To run a regression, I express the equilibrium relation as
log
1 h
1
log
1
log
(3.18)
in order to account for unmodeled factors that affect labor supply. To appropriately estimate the values of [ψ/(ψ + 1)]*log(α) and [ψ/(ψ + 1)], however, I must use a two stage least squares regression. The independent variable z is endogenous because z contains the consumption to output ratio c/y, which is correlated with ε because changes in household preferences will influence consumption decisions. A change in ε will affect c/y, which in turn affects the labor supply. It is therefore necessary to use an instrumental variable. I
41
choose τ, the effective marginal tax rate on labor income, to be that instrument because, since τ is a component of z, it is clearly correlated with z. Furthermore, τ is uncorrelated with ε since I have assumed factors that determine tax rates are not affected by household preferences. In my model, changes in household preferences, which would affect labor supply through changes in c/y, should have no effect on τ, which is set independently by governments. Hence, I can express equation (3.18) as
log
1 h
1
log
1
log
(3.19)
where λ is the dummy variable for τ. Running a two stage least squares regression on (3.19), I find that [ψ/(ψ + 1)]*log(α) = 0.888 and that [ψ/(ψ + 1)] = 0.748. The values of [ψ/(ψ + 1)]*log(α) and [ψ/(ψ + 1)] are of no inherent interest, but I can use them to determine the values of α and ψ. I calculate ψ as follows
1
.748
.748
1
.748
.748
.748
.748
2.97.
. 748 1 .748
I calculate α as follows
1
log α
.888
42
log α
. 888
.
3.28
/
1
/.
It is useful to know how reliable these estimations of α and ψ are. Because I have calculated them indirectly, I have to be careful in estimating their standard errors. I cannot directly manipulate the standard errors for [ψ/(ψ + 1)]*log(α) and [ψ/(ψ + 1)] to obtain the standard errors for α and ψ. It is necessary instead to use bootstrap. Using 2,000 bootstrap repetitions, I determine the standard error of α to be 0.19 and the standard error of ψ to be 0.31. Since α = 3.28, the 95% confidence interval places it between 2.91 and 3.65. Since ψ = 2.97, the 95% confidence interval places it between 2.36 and 3.58. The null hypothesis that α = 0 is rejected since p-value for this hypothesis test less than 0.001. Similarly, the null hypothesis that ψ = 0 is rejected. I have firm evidence that households derive positive utility from leisure and that the Frisch elasticity of labor supply is not zero. Therefore, changes in the effective marginal tax rate will affect labor supply. Table 3.2 summarizes my results for the values and standard errors for α and ψ and the results of my hypothesis tests. Table 3.3 presents the labor supply estimated using (3.16), and the empirical OECD data for labor supply in the G-7 countries during the periods of 1970-1974 and 1993-1996. During 1993-1996, the difference between the estimated values and the empirical values is quite small. The average difference is only 1.4 hours per week, nearly identical to the average difference computed in Prescott (2004). During 1970-1974, the difference is also quite small except in the case of Japan and Italy, which are the outliers. The model performs rather well for the other 12 data points, especially considering the fact that it assumes a single value of the Frisch elasticity
43
TABLE 3.2 SUMMARY OF RESULTS FOR PARAMETERS OF INTEREST Parameter
Interpretation
Estimate (Standard Error)
α
Utility of leisure parameter
3.28
Null Hypothesis Value
p-value
0
≤0.001
0
≤0.001
(0.19) Frisch elasticity of labor supply
ψ
2.97 (0.31)
Note: Estimates based on 2 observations from each of the G-7 countries for a total of 14 observations.
TABLE 3.3 EMPIRICAL VERSUS ESTIMATED VALUES OF LABOR SUPPLY Labor Supply* Period
Country
1993-1996
Germany
19.3
19.6
France
17.5
Italy
1970-1974
Empirical Estimated
Difference (Estimated Less Empirical)
Prediction Factors Tax Rate τ
Cons./Output (c/y)
0.3
0.59
0.74
19.7
2.2
0.59
0.74
16.5
19.0
2.5
0.64
0.69
Canada
22.9
21.4
-1.5
0.52
0.77
United Kingdom
22.8
22.8
0.0
0.44
0.83
Japan
27.0
29.0
2.0
0.37
0.68
United States
25.9
24.6
-1.3
0.40
0.81
Germany
24.6
24.1
-0.5
0.52
0.66
France
24.4
25.3
0.9
0.49
0.66
Italy
19.2
28.2
9.0
0.41
0.66
Canada
22.2
25.6
3.4
0.44
0.72
United Kingdom
25.9
23.8
-2.1
0.45
0.77
Japan
29.8
36.4
6.6
0.25
0.60
United States
23.5
26.2
2.7
0.40
0.74
*Labor supply is measured in hours worked per person aged 15-64 per week.
44
of labor supply for all countries during both time periods. It is clear from Table 3.3 that during the early 1970’s, when tax rates in the United States and Continental Europe were similar, labor supplies in the United States and Continental Europe were similar as well. At the aggregate level when idiosyncratic factors are averaged out, it would appear that Americans and Continental Europeans had similar economic preferences during that time period. In the mid-1990’s, however, higher tax rates in Continental Europe apparently had produced relatively lower labor supplies. If a worker in Europe had earned 100 additional euros, he would have paid about 60 euros in direct or indirect taxes. If a worker had earned an extra $100 in the United States, he would have paid only $40 to the government. As a result, Americans had more incentive to work. Given my finding that the Frisch elasticity of labor supply was 2.97, the vast majority of the difference between the labor supply in the United States and that of France and Germany could be explained by differences in the effective marginal tax rates. My direct calculation of the Frisch elasticity of labor supply produces a value virtually identical to Prescott’s indirect calculation that it is “nearly 3.” These values imply that households react strongly to changes in effective marginal tax rates. It is interesting to note that my value of 3.28 for the utility of leisure parameter is much greater than Prescott’s value of 1.54. This is not surprising, however, because I employed a different utility function (equation (3.2) instead of equation (3.1)).
45
Chapter 4: My Dynamic General Equilibrium Model The simple static model presented in chapter 3 has several important limitations. In this chapter, I will explain why a number of its underlying assumptions are gross oversimplifications and why the dynamic general equilibrium model which I develop in this chapter represents a significant improvement. 4.1. How the Dynamic Model Improves upon the Simple Static Model While the simple static model seems to provide strong evidence that marginal tax rates themselves can have a profound effect on labor supply, it is highly oversimplified. First of all, while it takes into account interaction between variables, such as consumption, output, hours worked, and tax rates, within time periods, it does not take into account interactions across time periods. It is reasonable to expect that their values in one period will affect their values in subsequent periods. My dynamic general equilibrium model is designed to take such interactions into account. Second, the simple static model assumes that the Frisch elasticity of labor supply is equal for all countries during both time periods. This is unlikely since the G-7 countries have different cultural values and different non-tax government policies which would be expected to affect how much households choose to work. The dynamic general equilibrium model presented in section 4.2 is able to incorporate different values of the Frisch elasticity of labor supply for different countries. Third, the simple static model does not incorporate the idea of consumption-work complementarity. The dynamic general equilibrium model explicitly considers this complementarity in its utility function. Finally, the simple static model assumes all non-military government expenditures substitute on a one-to-one basis for private consumption. It is probably
46
more accurate to believe that different types of government expenditures will affect hours worked in a different ways. For example, it is unlikely that government expenditures for disability payments will have the same effect on labor supply as government funding of day care programs of children of working parents. In order to treat this problem, I introduce a parameter into the dynamic model in chapter 6 to reflect the varying amount that individuals value government expenditures. 4.2. Introduction to the Dynamic General Equilibrium Model My dynamic general equilibrium model builds on the model developed in Hall (2009a), applying aspects of that model to the analysis of the effect of tax rates and patterns of government expenditures on output and labor supply. The presentation of the dynamic general equilibrium model which follows in this section is an outline of how the calculations are actually performed in my model. The optimization problems entailed are far too complex and cumbersome to do by hand. It is necessary to encode the model with Matlab to perform the calculations. The Matlab program created for this thesis is presented in Appendix A. In my model, individual preferences are given by /
1
1/
/
/
/
1
1/
.
(4.1)
I sum from t = 0 to 79 because I have chosen to consider a lifespan of 80 years. This utility function incorporates the concept of the consumption-work complementarity by employing the χ parameter, which gives its magnitude. The variable c represents the consumption of goods and services, and σ describes the curvature of utility with respect to consumption. In addition, σ reflects is also the intertemporal elasticity of substitution and the reciprocal of the coefficient of
47
relative risk aversion. The variable h represents the volume of work, and ψ describes the curvature of utility with respect to the volume of work. When χ = 0, ψ represents the Frisch elasticity of labor supply. Finally, γ represents the magnitude of the disutility of work. Without taxation, the first-order condition that maximizes utility and optimizes the combination of consumption and work can be calculated with the following equality /
1
1
/
1/
/
1
/
1/
(4.2)
.
I derive equation (4.2), noting that optimal combination of consumption and work is found using /
the first-order condition
. If I assume a tax scheme consisting of a wage tax where
/
individuals receive a wage w and have to pay a fraction τ of their income in taxes, the individual’s after-tax wage is 1
. Then, the first order condition which maximizes an
individual’s utility becomes 1
/
1
1
1/
/
/
1
1/
/
.
(4.3)
In this paper, I consider three cases with respect to the way in which tax revenue is used by the government. In chapter 5, I analyze the case considered by Prescott (2004) in which all tax revenue is spent on lump sum transfer payments to individuals regardless of hours worked. In chapter 6, I analyze both the case in which all the tax revenue is expended on wasteful programs which do not affect the individual’s marginal utility of consumption and the case in which tax revenue is expended on programs to benefit individuals regardless of hours worked but only a certain fraction (μ) of that expenditure corresponds to their consumption preferences, the remainder (1– μ) being expended on projects that do not affect the individual’s marginal utility of consumption.
48
My dynamic general equilibrium model assumes technology in the economy is described by the Cobb-Douglas production function, so (4.4) where α is labor’s share of output and k is capital. I use the standard value of α = 0.70. In accordance with the literature on labor supply models, I assume competition and no capital adjustment costs. Capital then rents for the price (4.5) where bt is the rental price of capital, rt is the real interest rate and therefore the net marginal product of capital, and δ is the depreciation rate. I use the standard value of δ = 0.10. Capital demand in period t equals the capital supply as determined by the previous period, so 1
(4.6)
The law of motion for capital is given by
1
(4.7)
because at the end of each period, the sum of the output (yt) produced in the economy and the capital stock remaining from the previous period (kt-1) is allocated to consumption (ct), government purchases (gt), and the new capital stock (kt). The economy’s discounter is
,
/
1
1
1/
/
/
1
1
1/
/
(4.8)
49
where β is the ratio of the present value of consumption in period t+1 relative to consumption in period t. I use the standard value of β = 0.95. The Euler equation for consumption is 1
,
1
(4.9)
since the reciprocal of the economy’s discounter is equal to one plus the real interest rate. Finally, I assume that the initial capital stock in the economy is equal to its steady state level at the initial tax rate. I also assume that the capital stock at the end of period T is equal to its steady state level at the final tax rate. This assumption is reasonable since the capital stock will asymptotically approach its infinite-horizon solution for reasonably large values of T. I set T = 80 to model the effects of changing tax rates and the patterns of government expenditures over the course of an 80 year lifetime, but my model has the turnpike property so the value of T essentially irrelevant as long as it is greater than 20 because the vast majority of the changes take place within 20 years.
50
Chapter 5: Employing My Dynamic Model In this chapter, I apply my dynamic general equilibrium model. I assume that all tax revenue is spent on lump sum transfer payments to individuals regardless of hours worked. I explore the effects of changes in the tax rate on several important economic parameters and examine what happens if I assume no consumption-work complementarity or if I postulate a lower labor supply elasticity. 5.1. The Trivial Case: No Taxes I first consider the simplest case: no taxes. Predictably, the model shows no change over time in output (y), hours of work (h), the real interest rate (r), the wage (w), consumption (c), capital stock (k), the economy’s discounter (m), or the rental price of capital (b). 5.2. The Model with Taxes I then analyze the effect of taxes, assuming that all of the tax revenue is spent on lump sum transfer payments to individuals regardless of hours worked. I set the initial capital stock equal to the capital stock in the steady state under the initial tax rate and the final capital stock equal to the capital stock in the steady state under the final tax rate, but I allow the capital stock and the other parameters to vary during the intervening period. For example, I consider a country with a tax rate of 20% which decides to raise its tax rate to 30%. My model sets the capital stock in year 1 equal to the capital stock in the economy with a 20% tax rate in the steady state. It sets the capital stock in year 80 equal to the capital stock in that economy with a 30% tax rate in the steady state. Between years 1 and 80, the
51
capital stock and the other parameters vary until they approach their new steady states. I can track all parameters yearly through the 80 year lifetime. If the final tax rate equals the initial tax rate, the value of any parameter in year 1 will equal its value in year 80. Parameters change only if the tax rate changes (or if individuals’ preferences for government spending change, as discussed in chapter 6). 5.3. Changing the Tax Rate in the Dynamic General Equilibrium Model In this section, I first examine how the various parameters change when the tax rate increases from 20% to 30% in my baseline case in which all tax revenue is spent on lump sum transfer payments regardless of hours worked, the consumption-work complementarity holds, and the labor supply is elastic. Later I investigate how these parameters change when the tax rate decreases, for example, from 20% to 10% in the baseline case. The specific initial and final tax rates which I have chosen in my presentation have no special significance. They were chosen arbitrarily for illustrative purposes. 5.3.1. Increasing the Tax Rate from 20% to 30% If all tax revenue is spent on lump transfer payments, there is no income effect when the tax rate is changed. Therefore, when the tax rate increases, hours worked should decrease because decreasing after-tax wages decreases the incentive to work since the marginal utility of consumption remains constant. The decrease in after-tax wage lowers the marginal benefit of working. Consider the case in which the tax rate increases from 20% in year 1 to 30% in year 2 and remains at 30% through year 80. Table 5.1 presents a summary of the changes in the economic parameters while Results Spreadsheet 1, presented in Appendix B, gives the results in detail. As Appendix B shows, the pre-tax wage actually increases slightly from year 1 to year 2,
52
TABLE 5.1 RESULTS FROM THE TAX INCREASE FROM 20% TO 30%
Parameter
Interpretation
Percentage Change from Year 1 to Year 80
Percentage Change from Year 2 to Year 80
y h r w c k m b
Output Hours worked Real Interest Rate Pre-Tax Wage Consumption Capital Economy's Discounter Rental Price of Capital
–6.0% –6.0% 0.0% 0.0% –6.0% –6.0% n/a* n/a*
–0.6% +1.8% +15.7% –2.4% –1.5% –5.2% –0.7% +4.9%
*There is no value for m or b for year 1.
going from 0.935 to 0.958, reflecting the fact that the decrease in hours worked from 0.781 to 0.720 increases the marginal product of labor, assuming diminishing returns to labor. See Graphs 5.1 and 5.2. The increase in the pre-tax wage, however, does not even come close to compensating for the decrease in the after-tax wage caused by increase in the tax rate. After a large decrease in hours worked from year 1 to year 2 from 0.781 to 0.720, hours worked increases from its low point in year 2 to asymptotically approach the steady state value of 0.734 at a tax rate of 30%. This small increase in hours worked slightly lowers the pre-tax wage. In fact, the pre-tax wage decreases asymptotically to its steady state value of 0.935 in year 80. The after-tax wage is thus much lower at a tax rate of 30% than at a tax rate of 20%. The increase in the tax rate causes consumption to fall since the after-tax wage is lowered, causing individuals work and earn less. See Graph 5.3. Even if all tax revenue is rebated back to individuals, consumption falls because individuals work less when the tax rate is increased, so there is less income to consume. (The decrease in consumption is smaller,
53
GRAPH 5.1
Change in the pre‐tax wage over time when the wage tax rate increases from 20% to 30% Pre‐Tax Wage
0.96 0.955 0.95 0.945 0.94 0.935 0.93 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 Year Number
GRAPH 5.2
Change in hours worked over time when the wage tax rate increases from 20% to 30% Hours Worked
0.8 0.78 0.76 0.74 0.72 0.7 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 Year Number
54
GRAPH 5.3
Consumption
Change in consumption over time when the wage tax rate increases from 20% to 30% 0.85 0.84 0.83 0.82 0.81 0.8 0.79 0.78 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 Year Number
however, than it is when the tax revenue is spent solely on projects which do not affect the individual’s marginal utility of consumption.) The decrease in consumption is continuous from year 1 to year 80. Individuals work more hours and have a higher after-tax wage in year 1 than in year 2. Consumption falls from 0.838 in year 1 to 0.800 in year 2. Consumption in year 2 is higher, however, than in subsequent years because the slight increase in hours worked from year 2 to year 80 is more than offset by the decline in the after-tax wage which occurs over the period. Hence consumption falls from 0.800 in year 2 until it approaches its steady state of 0.788 in year 80. The model sets the initial capital stock at the steady state value obtained under the tax rate of 20%. Because higher tax rates decrease the incentive to work and therefore reduce hours worked, they lessen the amount of capital necessary for production. Since the capital stock in year 80 is set at the steady state value for the tax rate of 30%, the capital stock is lower in year 80 than it is in year 1, falling from 2.050 to 1.927. See Graph 5.4.
55
GRAPH 5.4
Change in the capital stock over time when the wage tax rate increases from 20% to 30%
Capital Stock
2.1 2.05 2 1.95 1.9 1.85 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 Year Number
To understand the changes in the real interest rate, it is important to recognize that, because this model assumes competitive markets, the real interest rate is set equal to the marginal product of capital. The increase in the tax rate leads to a large sudden decrease in hours worked between years 1 and 2, and because there are fewer hours of work in which to employ the capital stock, the marginal product of capital, and thus the real interest rate, falls from 0.053 in year 1 to 0.045 in year 3. See Graph 5.5. (The real interest rate is not defined in year 2 because the economy’s discounter is not defined for year 1. Consider equations (4.10) and (4.11):
,
/
1
1
1/
/
/
1
1
1/
/
and 1
,
1.
Since m is not defined in period 1, r cannot be defined in period 2.) As hours worked rebounds
56
GRAPH 5.5
Change in the real interest rate over time when the wage tax rate increases from 20% to 30% Real Interest Rate
0.054 0.052 0.05 0.048 0.046 0.044 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 Year Number
and the capital stock diminishes from year 2 to year 80, each unit of capital stock becomes more valuable, increasing its marginal product and thus the real interest rate until the real interest rate reaches its initial steady state value of 0.053 in year 80. The changes in output, the rental price of capital, and the economy’s discounter follow from the previous discussion. Output is an increasing function of hours worked and the capital stock. Because hours worked falls by a large amount from year 1 to year 2 while the capital stock also decreases, output drops precipitously from 1.043 to 0.986. See Graph 5.6. From year 2 to year 80, hours worked rebounds somewhat, but the capital stock decreases at a faster rate, so there is a slow but steady further decline in output from 0.986 to 0.980. The rental price of capital is defined as the real interest rate plus the depreciation rate. Since the model assumes a constant depreciation rate of 0.10 per year, the absolute changes in the rental price of capital equal the absolute changes in the real interest rate and reflect the same
57
GRAPH 5.6
Change in output over time when the wage tax rate increases from 20% to 30% 1.06
Output
1.04 1.02 1 0.98 0.96 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 Year Number
economic mechanisms. See Graph 5.7. There is no value for the rental price of capital until year 3. From year 3 to year 80, the changes in the rental price of capital mirror the changes in the real interest rate. The economy’s discounter is defined by the Euler equation as an inverse function of the real interest rate, so that when the real interest rate increases, the economy’s discounter decreases. The Euler equation is 1
,
1.
The discounter is only defined between years 2 to 79. It decreases asymptotically toward a steady state as the real interest rate increases over that period. See Graph 5.8. 5.3.2. Decreasing the Tax Rate from 20% to 10% The economic explanation of the changes in the parameters when the tax rate is lowered is simply the inverse of that of the changes when the tax rate is raised. For example, when the tax rate decreases in the baseline case, economic intuition suggests that hours worked should
58
GRAPH 5.7
Change in the rental price of capital over time when the wage tax rate increases from 20% to 30% Rental Price of Capital
0.154 0.152 0.15 0.148 0.146 0.144 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60 63 66 69 72 75 78 Year Number
Value of the Economy's Discounter
GRAPH 5.8
Change in the value of economy's discounter over time when the wage tax rate increases from 20% to 30% 0.958 0.956 0.954 0.952 0.95 0.948 2 5 8 11 14 17 20 23 26 29 32 35 38 41 44 47 50 53 56 59 62 65 68 71 74 77 Year Number
59
TABLE 5.2 RESULTS FROM THE TAX DECREASE FROM 20% TO 10%
Parameter
Interpretation
Percentage Change from Year 1 to Year 80
Percentage Change from Year 2 to Year 80
y h r w c k m b
Output Hours worked Real Interest Rate Pre-Tax Wage Consumption Capital Economy's Discounter Rental Price of Capital
+5.6% +5.6% 0.0% 0.0% +5.6% +5.6% n/a* n/a*
+0.5% –1.7% –11.1% +2.2% +1.3% +4.7% +0.6% –4.2%
*There is no value for m or b for year 1.
increase because there is more incentive to work. Given the same pre-tax wage, the after-tax wage rises. The increase in after-tax wage raises the marginal utility of work. Consider, for example, the case in which the tax rate decreases from 20% in year 1 to 10% in year 2 and remains at 10% through year 80. Table 5.2 presents a summary of the results while Results Spreadsheet 2, presented in the Appendix B, gives these results in detail. The pre-tax wage decreases slightly from year 1 to year 2 from 0.935 to 0.915 because, assuming diminishing returns to labor, an increase in hours worked from 0.781 to 0.839 results in a decrease the marginal product of labor. See Graphs 5.9 and 5.10. This decrease in the pre-tax wage, however, does not even come close to compensating for the increase in the after-tax wage caused by decrease in the tax rate. After the large increase hours worked from year 1 to year 2 (from 0.781 to 0.839), hours worked gradually decreases to asymptotically approach the steady state value of 0.825. This small decrease in hours worked slightly raises the pre-tax wage. In fact, the pre-tax wage increases asymptotically back to its steady state value of 0.935 in year 80. The after-tax wage is thus much higher due to the lower taxes. Similarly, the changes in other parameters
60
GRAPH 5.9
Change in the pre‐tax wage over time when the wage tax rate decreases from 20% to 10% Pre‐Tax Wage
0.94 0.935 0.93 0.925 0.92 0.915 0.91 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 Year Number
GRAPH 5.10
Change in hours worked over time when the wage tax rate decreases from 20% to 10% Hours Worked
0.86 0.84 0.82 0.8 0.78 0.76 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 Year Number
61
TABLE 5.3 RESULTS FROM THE CHANGING THE TAX RATE BY VARIOUS AMOUNTS
Parameter
Interpretation
y h r w c k
Output Hours worked Real Interest Rate Pre-Tax Wage Consumption Capital
Percentage Change from Year 1 to Year 80* Rate = 0%
Rate = 10%
Rate = 20%
Rate = 30%
Rate = 40%
+10.1% +10.1% 0.0% 0.0% +10.1% +10.1%
+5.6% +5.6% 0.0% 0.0% +5.6% +5.6%
0.0% 0.0% 0.0% 0.0% 0.0% 0.0%
–6.0% –6.0% 0.0% 0.0% –6.0% –6.0%
–12.6% –12.6% 0.0% 0.0% –12.6% –12.6%
*These columns present the percentage change for each parameter given an initial tax rate of 20% and a final tax rate indicated by each column heading.
Parameter
Interpretation
y h r w c k
Output Hours worked Real Interest Rate Pre-wage Wage Consumption Capital
Percentage Change from Year 1 to Year 80* Rate = 50%
Rate = 60%
Rate = 70%
Rate = 80%
Rate = 90%
–19.7% –19.7% 0.0% 0.0% –19.7% –19.7%
–27.8% –27.8% 0.0% 0.0% –27.8% –27.8%
–37.0% –37.0% 0.0% 0.0% –37.0% –37.0%
–48.3% –48.3% 0.0% 0.0% –48.3% –48.3%
–63.6% –63.6% 0.0% 0.0% –63.6% –63.6%
*These columns present the percentage change for each parameter given an initial tax rate of 20% and a final tax rate indicated by each column heading.
parallel those in the case of the tax increase with the obvious reversal of sign. The Graphs of those changes are the mirror image of those for the tax increase. Compare, for example, Graph 5.1 to 5.9 or Graph 5.2 to 5.10. 5.3.3. Varying the Magnitude of the Change in the Tax Rate It is also interesting to examine how much the parameters are affected by tax changes of varying magnitudes. I have analyzed data for the cases in which the initial tax rate is 20% and
62
GRAPH 5.11
Percentage Change in Output
Changes in output from year 1 to year 80 given an initial tax rate of 20% and various final tax rates 20.0% 0.0% ‐20.0% ‐40.0% ‐60.0% ‐80.0% 0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
Final Tax Rate
Percentage Change in Hours Worked
GRAPH 5.12
Changes in hours worked from year 1 to year 80 given an initial tax rate of 20% and various final tax rates 20.0% 0.0% ‐20.0% ‐40.0% ‐60.0% ‐80.0% 0%
10%
20%
30%
40%
50%
Final Tax Rate
60%
70%
80%
90%
63
Percentage Change in Consumption
GRAPH 5.13
Changes in consumptionfrom year 1 to year 80 given an initial tax rate of 20% and various final tax rates 20.0% 0.0% ‐20.0% ‐40.0% ‐60.0% ‐80.0% 0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
Final Tax Rate
Percentage Change in the Capital Stock
GRAPH 5.14
Changes in the capital stock from year 1 to year 80 given an initial tax rate of 20% and various final tax rates 20.0% 0.0% ‐20.0% ‐40.0% ‐60.0% ‐80.0% 0%
10%
20%
30%
40%
50%
Final Tax Rate
60%
70%
80%
90%
64
the final tax rate is 0%, 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, and 90%. See Table 5.3. A few results stand out. First, after 80 years the real interest rate and the pre-tax wage are in all cases unchanged. Second, output, hours worked, consumption, and the capital stock all increase when the tax rate is decreased and decrease when the tax rate is increased. Finally, each 10% increase in the final tax rate from 0% to 90% has an increasingly large effect on the magnitude of the resulting changes in output, hours worked, consumption, and the capital stock. In other words, the marginal loss in output, hours worked, consumption, and the capital stock between year 1 to year 80 is smallest when the final tax rate goes from 0% to 10%, larger when the final tax rate goes from 10% to 20%, and so on in an increasing fashion until the greatest marginal loss occurs largest when the final tax rate goes from 80% to 90%. See Graphs 5.11-5.14. This demonstrates that the disincentives of higher tax rates become more and more pronounced as those rates increase because individuals have less and less incentive to work as the government takes more and more of their income. For example, when the tax rate goes from 0% to 10%, individuals keep only 90% of their pre-tax wage instead of 100%. When the final tax rate is changed from 80% to 90%, individuals go from keeping 20% of their pre-tax wage to keeping only 10%, a much larger relative decrease. Thus, an increase in the final tax rate of a given percentage of income will have less of a negative effect on output, hours worked, consumption, and the capital stock when the tax rate is low than the same increase in terms of percentage of income when the tax rate is already high. 5.4. Removing the Assumption of Consumption-Work Complementarity One of the assumptions of my dynamic general equilibrium model is that there is a complementarity between consumption and work. This complementarity is reflected in
65
equation (4.1) /
1
/
/
/
1/
1
1/
where χ signifies the magnitude of the complementarity. I assume consumption-work complementarity in my baseline case because empirical evidence suggests that an individual’s consumption of goods and services in the market economy will indeed rise when he works more hours, holding marginal utility constant. If an individual works more, he will have less time for home production and will rely more on purchases in the market. The existence of consumptionwork complementarity is reflected, for example, in the data regarding the “retirement consumption puzzle.” Consumption of goods and services in the market decreases when individuals retire as retirees apparently devote more time to home production. Although it is logical to assume consumption-work complementarity, one can alter my model to remove this assumption. This yields a new utility function /
1
1/
/
1
1/
.
(5.1)
If the consumption-work complementarity is removed, the magnitude of the decreases in output, hours worked, consumption, and the capital stock caused by higher tax rates is smaller. This is because when higher tax rates induce individuals to works less, the consumption-work complementarity implies that they would decrease their market consumption by a larger amount because they would have more time for home production. If there were no complementarity, individuals would not reduce their market consumption as much. Larger decreases in consumption would result in larger decreases in output, hours worked, and the capital stock, so if
66
the complementarity is not assumed, these parameters will not decrease as much. For example, consider an increase in the tax rate from 20% to 30%. If the complementarity is assumed, the decrease in output, hours worked, consumption, and the capital stock is 6.0%. If the complementarity is not assumed, this decrease is 5.1%. Conversely, if there is a tax decrease and the consumption-work complementarity does not exist, the increase in output, hours worked, consumption, and the capital stock will be smaller. These results are summarized in Tables 5.4 and 5.5. 5.5. Assuming a Lower Wage Elasticity of Labor Supply Another key assumption of my model in the baseline case is that the wage elasticity of labor supply is 1.9. Labor supply elasticity is defined as the elasticity of hours worked with respect to the wage rate, given a constant marginal utility of consumption. Economists disagree about the actual magnitude of the labor supply elasticity. Empirical household data suggests that it may be between 0.2 and 1.0. Macroeconomic models, however, yield higher estimates. Hall (2009a) used an employment function which takes into account both the elasticity resulting from choices by workers about how much to work and from sticky wage compensation in the searchand-matching setup of Mortensen and Pissarides (1994). Hall found the labor supply elasticity to be 1.9. I have chosen to use that value in my baseline case rather than the value of 2.97 which I derived in chapter 3 with a less sophisticated static model, especially because 2.97 is at the extreme upper end of estimates of the labor supply elasticity found in the literature. If I had chosen to use a labor supply elasticity of 0.5, the changes in output, hours worked, consumption, and the capital stock for a given change in the tax rate would have been smaller because, although the same increase in the tax rate would cause the same change in the
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TABLE 5.4 RESULTS FROM THE TAX INCREASE UNDER DIFFERENT ASSUMPTIONS Percentage Change from Year 1 to Year 80* Parameter
Interpretation
y h r w c k
Output Hours worked Real Interest Rate Pre-Tax Wage Consumption Capital
Base Case
No Complementarity
Less Elastic Labor Supply
–6.0% –6.0% 0.0% 0.0% –6.0% –6.0%
–5.1% –5.1% 0.0% 0.0% –5.1% –5.1%
–4.6% –4.6% 0.0% 0.0% –4.6% –4.6%
*These columns indicate the percentage change for each parameter given an initial tax rate of 20% and a final tax rate of 30%.
TABLE 5.5 RESULTS FROM THE TAX DECREASE UNDER DIFFERENT ASSUMPTIONS
Parameter
Interpretation
y h r w c k
Output Hours worked Real Interest Rate Pre-Tax Wage Consumption Capital
Percentage Change from Year 1 to Year 80* Base Case +5.6% +5.6% 0.0% 0.0% +5.6% +5.6%
No Complementarity +4.8% +4.8% 0.0% 0.0% +4.8% +4.8%
Less Elastic Labor Supply +4.3% +4.3% 0.0% 0.0% +4.3% +4.3%
*These columns indicate the percentage change for each parameter given an initial tax rate of 20% and a final tax rate of 10%.
after-tax wage, this would have caused in a smaller decrease in hours worked. If hours worked decreases by a smaller amount, output, consumption, and capital stock also decrease by smaller amounts. By the same logic, if a higher wage elasticity of labor supply is assumed, a given tax increase would decrease hours worked by a larger amount. Individuals will produce less, consume less, and require less capital. If the tax rate rises from 20% to 30%, assuming a wage
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elasticity of labor supply of 1.9, the decrease in output, hours worked, consumption, and the capital stock is 6.0%. If the wage elasticity of labor supply is 0.5, the decline in those parameters is 4.6%. Conversely, if there is a tax decrease, a lower labor supply elasticity results in smaller increases in the parameters. These results are summarized in Tables 5.4 and 5.5.
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Chapter 6: Alternative Scenarios for Government Spending In the previous chapter, I analyzed the results generated by my dynamic general equilibrium model assuming that all tax revenue was spent on lump sum transfers to individuals regardless of hours worked. In this chapter, I examine other possibilities. First, I consider the extreme case in which all tax revenue is spent on projects which do not affect the individual’s marginal utility of consumption. Next, I consider the case in which a certain fraction (μ) of tax revenue is spent on programs corresponding to individuals’ consumption preferences and the remainder (1– μ) is spent on projects that do not affect the individual’s marginal utility of consumption. This scenario reflects the fact that individuals usually do not value government spending as much as their own consumption, but rather value it less than their disposable income. 6.1. Government Spending on Wasteful Projects When all tax revenue is returned to individuals in the form of lump sum transfers regardless of hours worked, tax changes do not produce an income effect because in the model all individuals make the same wage and thus the lump sum transfer exactly equals the taxes paid. Tax changes only produce a substitution effect because individuals are not made richer or poorer by the changes. All the money paid to the government in taxes returns to individuals to spend as they please. Tax rate changes still have a substitution effect, however, because they change the after-tax wage from (1 – τi)w to (1 – τf)w, where τi is the initial tax rate and τf is the final tax rate. When the after-tax wage changes, the marginal utility of work changes, inducing individuals to work more if their after-tax wage is higher and to work less if their after-tax wage is lower.
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Suppose, however, that all tax revenue is spent on projects which do not affect the individual’s marginal utility of consumption. A tax change will now have both an income effect and a substitution effect. Consider the base case of a tax increase from 20% to 30%. The tax increase will make individuals poorer. They will now only keep 70% of their wage instead of 80% of it. The remainder of their wage will be used by the government in ways that provide them no utility. The tax increase clearly makes them poorer. Since my model assumes diminishing returns to consumption, the poorer the individual is, the more he values a given unit of consumption. The income effect of the tax increase induces an individual to work more hours because his marginal utility of consumption increases when his income decreases. The substitution effect is also present with the tax increase. If the marginal utility of consumption were held constant, the individual making 70% of his wage after the tax increase instead of 80% would have less incentive to work. Each additional hour he spent working under the higher tax rate would produce less additional ability to consume. This is clearly true if the marginal utility of consumption is held constant, but when the income effect is present, the marginal utility of consumption changes. A lower after-tax wage does not necessarily result in less incentive to work. In fact, economic theory is ambiguous about the potential effect of an increase in the tax rate on labor supply in this case because it is ambiguous about whether the income effect or substitution effect will dominate (Kalemli-Ozcan and Weil 2010). The results from my model, presented in the right hand column in Table 6.1 (μ = 0), indicate that an increase in the tax rate from 20% to 30% increases labor supply (and output and the capital stock) when government revenue is assumed to be spent on projects which do not affect the individual’s marginal utility of consumption. Consumption is the economic parameter which still falls when the tax rate increases. This is because while individuals work more when the tax rate increases
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TABLE 6.1 RESULTS FOR A TAX INCREASE FROM 20% TO 30% WITH DIFFERENT VALUES OF μ
Parameter
Interpretation
Percentage Change from Year 1 to Year 80 (μ = 1)
Percentage Change from Year 1 to Year 80 (μ = 0.75)
Percentage Change from Year 1 to Year 80 (μ = 0.50)
Percentage Change from Year 1 to Year 80 (μ = 0.25)
Percentage Change from Year 1 to Year 80 (μ = 0)
y h r w c k
Output Hours worked Real Interest Rate Pre-Tax Wage Consumption Capital
–6.0% –6.0% 0.0% 0.0% –6.0% –6.0%
–4.2% –4.2% 0.0% 0.0% –6.3% –4.2%
–2.0% –2.0% 0.0% 0.0% –6.6% –2.0%
+0.7% +0.7% 0.0% 0.0% –6.9% +0.7%
+3.9% +3.9% 0.0% 0.0% –7.1% +3.9%
*Assuming consumption-work complementarity and an elastic labor supply.
TABLE 6.2 RESULTS FOR A TAX DECREASE FROM 20% TO 10% WITH DIFFERENT VALUES OF μ
Parameter
Interpretation
Percentage Change from Year 1 to Year 80 (μ = 1)
Percentage Change from Year 1 to Year 80 (μ = 0.75)
Percentage Change from Year 1 to Year 80 (μ = 0.50)
Percentage Change from Year 1 to Year 80 (μ = 0.25)
Percentage Change from Year 1 to Year 80 (μ = 0)
y h r w c k
Output Hours worked Real Interest Rate Pre-Tax Wage Consumption Capital
+5.6% +5.6% 0.0% 0.0% +5.6% +5.6%
+3.6% +3.6% 0.0% 0.0% +5.9% +3.6%
+1.4% +1.4% 0.0% 0.0% +6.2% +1.4%
–1.0% –1.0% 0.0% 0.0% +6.4% –1.0%
–3.5% –3.5% 0.0% 0.0% +6.6% –3.5%
*Assuming consumption-work complementarity and an elastic labor supply.
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because the income effect dominates the substitution effect in this case, the increase in consumption which should result from the increase in the labor supply does not fully offset the decrease in consumption which results from the lower after-tax wage since the government is spending its revenue on projects which do not affect the individual’s marginal utility of consumption. My model also demonstrates that, under the same assumptions, a decrease in the tax rate decreases labor supply (and output and the capital stock) but increases consumption. See the right hand column in Table 6.2 (μ = 0). 6.2. The Concept of μ It is clearly unrealistic to assume that all tax revenue would be returned to individuals in the form of lump sum transfers for their own consumption. The government spends only a fraction of its revenue on direct transfers, and even some of that revenue is “lost” due to various inefficiencies. On the other hand, it is equally unrealistic to assume that all tax revenue would be spent on projects which did not in any way affect the individual’s marginal utility of consumption. It is more reasonable to assume that a certain fraction of government spending provides utility to individuals and that government spending increases the ability of individuals to consume to a certain extent, although the amount may be difficult to quantify. For example, if the government uses revenue for programs such as prescription drug coverage, individuals are likely to value such spending, but they would probably value it less than income which they could spend as they wished. Perhaps they would have used their wage in a similar way, but they might have bought different drugs or entirely different products. Prescription drug coverage would be of value to individuals, but it would not be a perfect substitute for personal income. On
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the other hand, there are government programs, such as Social Security, do in fact provide direct income to individuals. To reflect this reality in a simplified form, I have introduced in my model a new variable, μ, which represents the fraction of government expenditures which corresponds to individuals’ consumption preferences. The remaining (1– μ) of tax revenue is presumed to be used for projects which do affect their marginal utility of consumption. Under this assumption, government spending can be thought of as a substitute, but not a perfect substitute, for individual consumption. In my model, however, government expenditures are still considered to benefit all individuals equally independent of hours worked. 6.3. Introducing μ into the Model I will now analyze the effect of varying the value of μ, considering first the case of a tax increase and then the case of a tax decrease. Specifically, I will examine how the variables in the economy react when μ is set as 1, 0.75, 0.50, 0.25, or 0. 6.3.1. Increasing the Tax Rate from 20% to 30% The parameter μ determines the magnitude of the income effect of a tax change. In the lump sum transfer case discussed in chapter 5 where μ = 1, all tax revenue is assumed to be spent in a way which corresponds to the individuals’ consumption preferences since individuals can spend their lump sum transfers as the wish. In this scenario tax changes do not affect the overall wealth of individuals, and there is no income effect. In the wasteful projects case discussed in section 6.1 where μ = 0, all tax revenue is spent on projects which did not affect the individual’s marginal utility of consumption, and tax changes have the largest possible income effect. My model indicates that under this assumption, the income effect dominates the substitution effect,
74
so that tax increases lead to increases in labor supply and tax decreases lead to decreases in labor supply. When 0 < μ < 1, a change in the tax rate will have an income effect equal to 1–
Δ
(6.1)
where Δτ represents the magnitude of the change in the tax rate. This is because a change in the tax rate has two effects. The amount that individuals have to pay in taxes changes by (Δτ)*wh, and the amount that government expenditures increases their consumption changes by μ*(Δτ)*wh. It is important to recognize that the income effect is dependent both on the value of μ and the magnitude of the change in the tax rate, but the substitution effect is dependent only on the magnitude of the tax rate. It is independent of μ. Therefore, when μ is small, the income effect may dominate the substitution effect. When μ is large, the substitution effect will dominate because the income effect is smaller. Table 6.1 presents the impact of a tax increase on various economic parameters given different values of μ. For larger values of μ, an increase in the tax rate reduces labor supply (and output and the capital stock). The decreased incentive to work caused by a lower wage is greater in magnitude than the increased incentive to work caused by the fact that higher tax rates make individuals poorer, so they value each marginal unit of consumption more. Consumption falls both because of reduced labor supply and because the lower after-tax wage decreases the ability to consume. For smaller values of μ, an increase in the tax rate increases labor supply (and output and the capital stock) because the income effect is large enough to dominate the substitution effect. The decreased incentive to work caused by a lower after-tax wage is smaller in magnitude than the increased incentive to work caused by the fact that higher tax rates make
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individuals poorer, so they value each marginal unit of consumption more. Nevertheless, consumption still falls because the increase in labor supply is more than offset by the reduction in the after-tax wage. 6.3.2. Decreasing the Tax Rate from 20% to 10% Table 6.2 presents the impact of a tax decrease on various economic parameters given different values of μ. For larger values of μ, a decrease in the tax rate increases labor supply (and output and the capital stock) because the income effect is small enough so that the substitution effect is dominant. The effect of the increased incentive to work caused by a higher after-tax wage is greater in magnitude than the decreased incentive to work caused by lower tax rates making individuals richer, so they value each marginal unit of consumption less. Consumption rises both because of greater labor supply and because the higher after-tax wage increases the ability to consume. For smaller values of μ, a decrease in the tax rate decreases labor supply (and output and the capital stock) because the income effect is large enough to dominate the substitution effect. The effect of the increased incentive to work caused by a higher after-tax wage in these cases is smaller in magnitude than the decreased incentive to work caused by the fact that lower tax rates make individuals richer, so they value each marginal unit of consumption less. Consumption still rises, however, because the decrease in labor supply is more than offset by the increase in the after-tax wage. 6.4. Implications of μ As is evident from the previous section, the value of μ is critical in determining how a potential tax change will affect important economic parameters. If the value of μ is sufficiently small, increases in the tax rate may actually increase output and labor supply. If μ is higher,
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increases in the tax rate will decrease output and labor supply. For the United States and for the major European countries which want to eliminate or reduce their deficits, the value of μ is critical in the analysis of whether the tax increases will cause major reductions in output and labor supply, or whether they will have little effect on output and labor supply or even increase them. In the discussion of μ, it is also essential, however, to consider the welfare of individuals in the economic analysis. As will be explained in chapter 7, individuals obtain positive utility from consumption and negative utility from working. If a government raises taxes and spends most or all of its revenue on projects which do not affect the individual’s marginal utility of consumption, this will lead to an increase in how much individuals work, but it will decrease their welfare. Consumption will fall despite the fact that individuals work more because the government will be taking income away from individuals which they could have spent as they pleased and spending it on projects that do not make individuals much better off. On the other hand, if a government raises taxes and spends most or all of its revenue in ways which correspond closely to individuals’ consumption preferences, they will work fewer hours, but they will not be so adversely affected. Consumption will fall, but individuals will work less, so the effect of a tax increase on welfare will not be as negative. This issue is examined in greater depth in section 7.4.
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Chapter 7: Welfare Analysis The effects of tax rate changes on the welfare of individuals are at least as important as their effects on output and labor supply. In this chapter, I first analyze the changes in welfare induced by changes in the tax rate over the course of a “lifetime” of 80 years. I then examine the welfare changes between the initial and final steady states. Although the latter examination allows me to investigate the full impact of the tax changes, it does not take into account changes between years 2 and 79, and so it provides an overestimate of the actual welfare changes. Finally, I consider how altering assumptions about consumption-work complementarity, about the elasticity of labor supply, and about how much individuals value government spending would affect welfare changes over the 80 year lifetime. 7.1. Welfare Analysis over a Lifetime in the Baseline Case In examining welfare changes in the dynamic model, it is important to understand the distinction between changes over the course of a lifetime of 80 years and changes between the initial and final steady states. Only the former reflects the level of welfare during the entire period. Suppose, for example, that an initial tax rate of 20% is raised to 30%. The calculation of welfare changes over the course of a lifetime of 80 years takes into account the fact that individuals do not immediately move from one steady state to another. The capital stock is higher when the tax rate is 20% than when it is 30%, but according to the dynamic model, the capital stock changes slowly over the 80 period to reach its new steady state value. Similarly, consumption and hours worked do not immediately reach their ultimate steady state levels. Because it takes about 20 years for them to asymptotically approach those levels, welfare
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changes calculated over the entire course of 80 years will be smaller than the differences between the initial and final steady states might suggest. I express welfare changes in three ways. First, I examine the change in an individual’s utility if an initial tax rate, for example, of 20%, is increased to 30% or decreased to 10%. Second, I examine the consumption change equivalent of that utility change, holding hours worked constant. Third, I examine the hours worked change equivalent of the utility change, holding consumption constant. The consumption and hours worked equivalents provide an intuitive meaning to the magnitude of the utility changes which are otherwise expressed in units whose significance is difficult to grasp. 7.1.1. Utility Changes Caused by Changes in the Tax Rate Addressing the utility change produced when tax rates are changed is relatively straightforward. The utility function in my model is equation (4.1), which is reproduced below /
1
1/
/
/
/
1
1/
.
I can employ Results Spreadsheets 5.1 and 5.2 to find the values of consumption (c) and hours worked (h) for each of the 80 years when the tax rate is held constant at 20%, when it goes from 20% to 30%, and when it goes from 20% to 10%. With these values and the baseline values of other parameters (β = 0.95 σ = 0.4, ψ = 1.9, χ = 0.334, and γ = 1.103), I calculate the lifetime utility for an individual when the tax rate decreases to 10% to be -31.29, when the tax rate remains at 20% to be -31.53, and when the tax rate changes to 30% to be -32.02. Thus, the utility change which results from increasing the tax rate from 20% to 30% is -0.49 while the utility change from decreasing the tax rate from 20% to 10% is +0.24. In subsection 5.3.3, in
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discussing the effects of changing the tax rate by various amounts, I noted that a given increase in the tax rate when the final tax rate is low will have less of an effect on output, hours worked, consumption, and the capital stock than the same change when the final tax rate is high. The welfare results manifest these phenomena. For example, there is a smaller percentage change in utility when the final tax rate increases from 10% to 20% (a decrease of 0.8%) than when the final tax rate is increases from 20% to 30% (a decrease of 1.6%). 7.1.2. Consumption Gain and Loss Equivalents Caused by Changes in the Tax Rate As these calculations have demonstrated, it is clear that individuals gain utility from tax cuts and lose utility from tax increases. It is difficult, however, to intuitively grasp the magnitude of these changes in terms of arbitrary units of utility. An alternative way to present them is to compute their consumption change equivalents. To compute the consumption change equivalent ĉ, it is necessary to perform the follow calculation ĉ ,
,
.
(7.1)
The expanded form of (7.1) is ĉ 1 1/
/
/
ĉ
/
/
1
1/ (7.2)
/
where
1
1/
/
/
/
1
1/
represents consumption at the initial tax rate of 20% in year t,
worked at the initial tax rate of 20% in year t, 10% or 30% in year t, and
represents hours
represents consumption at the final tax rate of
represents hours worked at the final tax rate of 10% or 30% in year
80
t. Since the values of all other variables are known, it is possible using computer software to compute ĉ. The consumption change equivalent ĉ expresses how much more or less consumption an individual would have to have over the course of an 80 year lifetime, if he worked as much as he would at a constant tax rate of 20%, to attain the utility he actually achieves when the tax rate changes to 30% or 10%. If an individual working as much as he would with a tax rate of 20% is to attain only the utility he would attain when the tax rate increases to 30%, he would have to consume less since he enjoys less utility at the 30% tax rate than he does at the 20% tax rate and he would have to attain that lower utility solely by reducing his consumption. Using equation (7.2), I calculate that ĉ = -0.012. This represents a decrease in consumption of 1.5% compared to consumption at the steady state at the 20% tax rate. In other words, the utility, or welfare, loss that individuals would suffer if the tax rate is increased from 20% to 30% is equivalent to a reduction of 1.5% in consumption if hours worked are held constant. Similarly, if an individual works as much as he would when the tax rate is 20% but is to attain the utility he would have when the tax rate decreases to 10%, that individual would have to consume more since he enjoys more utility at the 10% tax rate than he does at the 20% tax rate and would attain that higher utility solely by increasing his consumption. Using equation (7.2), I calculate that ĉ = 0.0060. This gain represents an increase in consumption of 0.7% compared to consumption at the steady state at the 20% tax rate. In other words, the utility, or welfare, gain that individuals would attain if the tax rate decreased from 20% to 10% is equivalent to an increase of 0.7% in consumption when hours worked are held constant. Table 7.1 presents the consumption change equivalents described in this section.
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TABLE 7.1 CONSUMPTION AND HOURS WORKED EQUIVALENTS OVER AN 80 YEAR LIFETIME
Final Tax Rate
Utility*
Consumption Change Equivalent*
Hours Worked Change Equivalent*
10% 20% 30%
-31.29 -31.53 -32.02
+0.7% 0% –1.5%
–1.0% 0% +2.2%
*Assuming all tax revenue is spent on lump sum transfers regardless of hours worked, an initial tax rate of 20%, the existence of the consumption-work complementarity, and an elastic labor supply.
7.1.3. Hours Worked Gain and Loss Equivalents Caused by Changes in the Tax Rate Another way to express the welfare change resulting from tax rate changes is to compute the hours worked gain or loss equivalent of the change in utility. Individuals value leisure and lose utility when they work more. Hours worked gain represents a loss in utility while an hours worked loss represents a gain in utility. To compute the hours worked gain or loss equivalent ĥ, it is necessary to perform the following calculation ,
ĥ
,
.
(7.3)
The expanded form of (7.3) is /
1
/
1/
ĥ 1 1/
/
ĥ
/
(7.4) /
1
1/
/
/
/
1
1/
82
where
again represents consumption at the initial tax rate of 20% in year t,
worked at the initial tax rate of 20% in year t, 10% or 30% in year t, and
represents hours
represents consumption at the final tax rate of
represents hours worked at the final tax rate of 10% or 30% in year
t. Since the values of all other variables are known, it is possible using computer software to compute ĥ. The hours worked equivalent ĥ expresses how many more or less hours an individual would have to work over the course of an 80 year lifetime, if he consumed as much as he would at a constant tax rate of 20%, to attain the utility he actually achieves when the tax rate changes to 30% or 10%. If an individual consuming as much as he would with a tax rate of 20% is to attain only the utility he would attain when the tax rate is 30%, he would have to work more since he enjoys less utility at the 30% tax rate than he does at the 20% tax rate and he would have to attain that lower utility solely by increasing his hours worked. Using equation (7.4), I calculate that ĥ = 0.016. This “loss” represents an increase of 2.2% in hours worked compared to the steady state at the 20% tax rate. In other words, the utility, or welfare, loss that individuals would attain if the tax rate increased from 20% to 30% is equivalent to an increase of 2.2% in hours worked when consumption is held constant. Similarly, if an individual consumes as much as he would when the tax rate is 20% but is to attain the utility he would have when the tax rate is 10%, that individual would work less since he enjoys more utility at the 10% tax rate than he does at the 20% tax rate and would attain that higher utility solely by decreasing his hours worked. Using equation (7.4), I calculate that ĥ = -0.0080. This “gain” represents a decrease of 1.0% in hours worked compared to the steady state at the 20% tax rate. In other words, the utility, or welfare, gain that individuals would attain if the tax rate decreased from 20% to 10% is equivalent to a decrease of 1.0% in hours worked
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when consumption is held constant. Table 7.1 presents the hours worked change equivalents described in this section. 7.2. Welfare Analysis Between the Steady States in the Baseline Case I now analyze the welfare changes between the initial and final steady states produced by tax changes. Given an initial tax rate of 20%, I determine the change in the individual’s utility when the tax rate is increased to 30% or decreased to 10%. Then, I find the consumption change equivalent of the utility change, holding hours worked constant. Finally, I find the hours worked change equivalent of the utility change, holding consumption constant. 7.2.1. Utility Changes Caused by Changes in the Tax Rate Again the calculation of the utility gain or loss is straightforward. My utility function from equation (4.1) is /
1
/
/
/
1/
1
1/
.
Because I am now only interested in the welfare analysis between steady states, I can simplify the equation by removing the summation across time periods. This yields /
1
1/
/
/
/
1
1/
.
(7.5)
I use Results Spreadsheets 5.1 and 5.2 to determine the values of consumption (c) and hours worked (h) for the tax rates of 10%, 20%, and 30% at their steady state levels. At the tax rate of 10%, c and h are 0.89 and 0.83, respectively. At the tax rate of 20%, c and h are 0.84 and 0.78, respectively. At the tax rate of 30%, c and h are 0.79 and 0.73, respectively. With these values
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and the baseline values for the other parameters (σ = 0.4, ψ = 1.9, χ = 0.334, and γ = 1.103), equation (7.5) allows me to calculate the utility of an individual at the 10% tax rate to be -1.58, at the 20% tax rate to be -1.60, and at the 30% tax rate to be -1.64. Thus, the utility change when the tax rate increases from 20% to 30% is –0.039 and the utility change when tax rate decreases from 20% to 10% is +0.024. As discussed in subsection 5.3.3, a given increase in the final tax rate when that tax rate is low will have a smaller effect on output, hours worked, consumption, and the capital stock than when the final tax rate is high. This phenomenon is reflected in the welfare results. For example, there is a smaller percentage change in utility when the final tax rate increases from 10% to 20% (a decrease of 1.5%) than when the final tax rate is increases from 20% to 30% (a decrease of 2.4%). 7.2.2. Consumption Gain and Loss Equivalents Caused by Changes in the Tax Rate As in subsection 7.1.2, I will now determine the consumption and hours worked change equivalents of the utility changes in order to provide a more intuitive sense of the magnitude of the welfare effects of changes in the tax rate. To compute the consumption change equivalent between steady states, I manipulate equation (7.5) so that consumption (c) is on the left hand side and all other variables and parameters, including utility (U), are on the right hand side. Thus, /
1
/
1/
/
1 /
/
1/ 1
1
/
/
/
1
/
/
/
1/
1 1
1/ /
1 1
1/
85
/
1
1
1
/
/
1
1 1
1
1
1/
/
1
1
/
1
1 1
1
1/ /
/
1
1 1
1
1/ /
.
(7.6)
I can now calculate how much more or less consumption an individual would need in the steady state, when working as much as he would at a constant tax rate of 20%, to attain the utility he actually achieves when the tax rate changes to 30% or 10%. A tax rate increase from 20% to 30% will lower the individual’s utility and produce a consumption loss equivalent. Using the value of h corresponding to the steady state at the 20% tax rate (h = 0.78), the value of U corresponding to the individual’s utility at the 30% tax rate (U = -1.64), and the baseline values for the other parameters in equation (7.6), I calculate c = 0.82. This is less than the value of consumption in the steady state at the 20% tax rate (c = 0.84). Thus, the consumption loss equivalent of the decrease in utility resulting from raising the tax rate from 20% to 30% is 0.019, representing a 2.2% loss in consumption. In other words, the utility, or welfare, loss that individuals would experience if the tax rate increased from 20% to 30% is equivalent to a decrease of 2.2% in consumption when hours worked is held constant. Similarly, a tax rate decrease from 20% to 10% will raise the individual’s utility and produce a consumption gain equivalent. Using the value of h corresponding to the steady state at the 20% tax rate (h = 0.78), the value of U corresponding to the individual’s utility at the 10% tax rate (U = -1.58), and the baseline values for the other parameters in equation (7.6), I calculate
86
TABLE 7.2 CONSUMPTION AND HOURS WORKED EQUIVALENTS BETWEEN STEADY STATES
Final Tax Rate
Utility*
Consumption Change Equivalent*
Hours Worked Change Equivalent*
10% 20% 30%
–1.58 –1.60 –1.64
+1.4% 0% –2.2%
–2.0% 0% +3.2%
*Assuming all tax revenue is spent on lump sum transfers regardless of hours worked, an initial tax rate of 20%, the existence of the consumption-work complementarity, and an elastic labor supply.
c = 0.85. This is greater than the value of consumption in the steady state at the 20% tax rate (c = 0.84). Thus, the consumption gain equivalent of the increase in utility from raising the tax rate from 20% to 10% is 0.012, representing a 1.4% gain in consumption. In other words, the utility, or welfare, gain that individuals would experience if the tax rate decreased from 20% to 10% is equivalent to an increase of 1.4% in their consumption when hours worked is held constant. Table 7.2 presents the consumption change equivalents described in this section. 7.2.3. Hours Worked Gain and Loss Equivalents Caused by Changes in the Tax Rate To compute the hours worked gain or loss equivalent between steady states, I manipulate equation (7.5) so that hours worked (h) is on the left hand side and all other variables and parameters, including utility (U), are on the right hand side. Thus, /
1 /
/
1/ /
/
/
1
/
1
1/
/
1
1/
1/
87
1
1
/
/
1
/
/
1
1
/
/
1
/
1
1/
1
1/
1
/
/
1
1
1/
/
1 1
1 1
1
1
/
1
1 1
1/ /
.
(7.7)
I can now calculate how much more or fewer hours an individual would need to work in the steady state, when consuming as much as he would at a constant tax rate of 20%, to attain the utility he actually achieves when the tax rate changes to 30% or 10%. A tax rate increase from 20% to 30% will lower the individual’s utility and produce an hours worked gain equivalent. Using the value of c corresponding to the steady state at the 20% tax rate (c = 0.84), the value of U corresponding to the individual’s utility at the 30% tax rate (U = -1.64), and the baseline values for the other parameters in equation (7.7), I calculate h = 0.81. This is more than the number of hours worked in the steady state at the 20% tax rate (h = 0.78). Thus, the hours worked gain equivalent of the decrease in utility from raising the tax rate from 20% to 30% is 0.025, representing a 3.2% increase in hours worked. In other words, the utility, or welfare, loss that individuals would experience if the tax rate increased from 20% to 30% is equivalent to an increase of 3.2% in hours worked when consumption worked is held constant. Similarly, a tax rate decrease from 20% to 10% will raise the individual’s utility and produce an hours worked loss equivalent. Using the value of c corresponding to the steady state
88
at the 20% tax rate (c = 0.84), the value of U corresponding to the individual’s utility at the 10% tax rate (U = -1.58), and the baseline values for the other parameters in equation (7.7), I calculate h = 0.77. This is less than the value of hours worked corresponding to the steady state at the 20% tax rate (h = 0.78). Thus, the hours worked loss equivalent to the increase in utility from lowering the tax rate from 20% to 10% is 0.016, representing a 2.0% decrease in hours worked. In other words, the utility, or welfare, gain that individuals would experience if the tax rate decreased from 20% to 10% is equivalent to a decrease of 2.0% in hours worked when consumption worked is held constant. Table 7.2 presents the consumption gain and loss equivalents described in this section. 7.3. Welfare Analysis Assuming No Complementarity or a Less Elastic Labor Supply Although the way in which consumption and hours worked equivalents of utility changes are calculated is not affected by assumptions about the consumption-work complementarity or the elasticity of labor supply, the utility changes caused by changes in the tax rate are indeed affected by these assumptions. As explained in section 5.4, removing the consumption-work complementarity results in tax changes having less of an effect on output, hours worked, consumption, and the capital stock. The resulting changes in utility will therefore also be smaller, and so the consumption and hours worked change equivalents will be smaller. When the consumption-work complementarity assumption is removed, the consumption loss equivalent when the tax rate is raised from 20% to 30% decreases from 1.5% to 1.3%, the consumption gain equivalent when the tax rate is lowered from 20% to 10% decreases from 0.7% to 0.6%, the hours worked gain equivalent when the tax rate is raised from 20% to 30% decreases from 2.2% to 1.8%, and the hours worked loss equivalent when the tax rate is lowered from 20% to 10%
89
TABLE 7.3 EQUIVALENTS FOR VARIOUS ASSUMPTIONS OVER A LIFETIME
Final Tax Rate
Consumption Change Equivalent (Baseline Case)*
Consumption Change Equivalent (No Complementarity)
Consumption Change Equivalent (Less Elastic LS)
10% 20% 30%
+0.7% 0% –1.5%
+0.6% 0% –1.3%
+0.5% 0% –1.0%
*Assuming all tax revenue is spent on lump sum transfers regardless of hours worked, an initial tax rate of 20%, the existence of the consumption-work complementarity, and an elastic labor supply.
Final Tax Rate
Hours Worked Change Equivalent (Baseline Case)*
Hours Worked Change Equivalent (No Complementarity)
Hours Worked Change Equivalent (Less Elastic LS)
10% 20% 30%
–1.0% 0% +2.2%
–0.8% 0% +1.8%
–0.7% 0% +1.5%
*Assuming all tax revenue is spent on lump sum transfers regardless of hours worked, an initial tax rate of 20%, the existence of the consumption-work complementarity, and an elastic labor supply.
decreases from 1.0% to 0.8%. As explained in section 5.5, assuming a lower labor supply elasticity results in tax changes having less of an effect on output, hours worked, consumption, and the capital stock. Therefore, changes in utility are smaller, and so consumption and hours worked change equivalents are smaller. If less elastic labor supply is assumed, the consumption loss equivalent when the tax rate is raised from 20% to 30% decreases from 1.5% to 1.0%, the consumption gain equivalent when the tax rate is lowered from 20% to 10% decreases from 0.7% to 0.5%, the hours worked gain equivalent when the tax rate is raised from 20% to 30% decreases from 2.2%
90
to 1.5%, and the hours worked loss equivalent when the tax rate is lowered from 20% to 10% decreases from 1.0% to 0.7%. Table 7.3 summarizes these results. 7.4. Welfare Analysis Assuming Different Values of μ If individuals value government spending a fraction μ times as much as their own consumption, then, as mentioned in section 6.4, the smaller the value of μ, the greater the impact of that a tax change on welfare. While an increase in the tax rate may lead to an increase in output and labor supply if the value of μ is sufficiently small, individuals will be worse off because they will consume less while working more. On the other hand, higher values of μ imply that individuals value government spending more. An increase in the tax rate may lead them to work and produce less, but their welfare will not be as negatively affected as it is when μ is low. For example, when the tax rate is increased from 20% to 30%, the consumption loss equivalent is 1.5% when μ = 1, 5.2% when μ = 0.50, and 10.6% when μ = 0. When the tax rate is increased from 20% to 30%, the hours worked gain equivalent is 2.2% when μ = 1, 6.8% when μ = 0.50, and 12.3% when μ = 0. This reasoning also applies to a decrease in the tax rate with the obvious reversal of sign. For example, when the tax rate is decreased from 20% to 10%, the consumption gain equivalent is 0.7% when μ = 1, 4.3% when μ = 0.50, and 9.4% when μ = 0. When the tax rate is decreased from 20% to 10%, the hours worked loss equivalent is 1.0% when μ = 1, 5.7% when μ = 0.50, and 11.3% when μ = 0. These results are summarized in Table 7.4.
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TABLE 7.4 EQUIVALENTS FOR VARIOUS VALUES OF μ OVER A LIFETIME Final Tax Rate
Consumption Change Equivalent (μ = 1)
Consumption Change Equivalent (μ = 0.50)
Consumption Change Equivalent (μ = 0)
10% 20% 30%
+0.7% 0.0% –1.5%
+4.3% 0.0% –5.2%
+9.4% 0.0% –10.6%
*Assuming an initial tax rate of 20% as well as consumption-work complementarity, and an elastic labor supply.
Final Tax Rate
Hours Worked Change Equivalent (μ = 1)
Hours Worked Change Equivalent (μ = 0.50)
Hours Worked Change Equivalent (μ = 0)
10% 20% 30%
–1.0% 0% +2.2%
–5.7% 0.0% +6.8%
–11.3% 0.0% +12.3%
*Assuming an initial tax rate of 20% as well as consumption-work complementarity, and an elastic labor supply.
92
Chapter 8: Applying My Model to Real World Scenarios In this chapter, I address by principle research questions by applying my dynamic general equilibrium model to the analysis of real world problems. I use it to predict how much the United States and seven major European countries would have to raise taxes in order to balance their budgets in one year. These countries have budget deficits and substantial debt to GDP ratios, although some face more serious problems than others. I examine various scenarios incorporating different assumptions about government spending to determine how these assumptions would affect predictions about how much taxes would have to increase to eliminate the deficits within one year and assess the expected effects on output and labor supply. In the case of the United States, I pursue this analysis in greater depth. Then I present the Laffer Curves which my model generates for the United States under different assumptions about government spending. Finally, I analyze how much the United States would have to raise taxes in order to balance its budget in the long run, taking into account both the short term and the long term impacts of tax rate increases on output. 8.1. The Economic Situation in the Eight Countries Under Consideration In my analysis of the potential impact of trying to balance the budget within one year on output and hours worked, I consider eight countries: the United States, the four largest European economies (France, Germany, Italy, and the United Kingdom), the two largest European economies with very high deficit to GDP ratios (Greece and Spain) and the largest Scandinavian economy (Sweden). My data comes from the OECD Outlook Database Inventory for the year 2009, the most recent year for which such data is available. In that year, the United States faced a moderate debt to GDP ratio of 0.53 but a high deficit to GDP ratio of 0.11. Germany, Sweden,
93
TABLE 8.1 DEFICIT AND DEBT TO GDP RATIOS AMONG US AND EUROPEAN COUNTRIES
Country*
Deficit to GDP Ratio
Debt to GDP Ratio
France Germany Greece Italy Spain Sweden United Kingdom United States
0.08 0.03 0.14 0.05 0.11 0.01 0.11 0.11
0.61 0.44 1.26 1.07 0.46 0.38 0.75 0.53
*This data comes from the OECD Outlook Database Inventory for the year 2009.
and Spain had lower debt to GDP ratios of 0.44, 0.38, and 0.46 respectively. While the deficit to GDP ratios in Germany and Sweden were moderate at 0.03 and 0.01, respectively, the deficit to GDP ratio in Spain was as large as that of the United States at 0.11. France and the United Kingdom had slightly higher debt to GDP ratios of 0.61 and 0.75, respectively, and also faced considerable deficit to GDP ratios of 0.08 and 0.11, respectively. Italy and Greece had very high debt to GDP ratios of 1.07 and 1.26, although the deficit to GDP ratio in Italy was modest at 0.05 while in Greece it was very high at 0.14. Table 8.1 summarizes these statistics. 8.2. Scenarios for Balancing the Budget in One Year For each country, I will analyze the size of the increase in the tax rate necessary to balance the budget during the following year under each of four possible scenarios. The first is that all government spending consists of lump sum transfers regardless of hours worked and that there is no decrease in government spending. The second is that all government spending consists of lump sum transfers regardless of hours worked and that 50% of the budget fix comes from a decrease in government spending. The third is that individuals value government
94
spending ½ as much as their own consumption (μ = 0.50) and that there is no decrease in government spending. The fourth is that individuals value government spending ½ as much as their own consumption (μ = 0.50) and that 50% of the budget fix comes from a decrease in government spending. For each scenario in each country, I perform a two stage calculation. First, I calculate the tax rate which would be necessary to balance the budget within one year if it were possible to raise the tax rate without affecting output or hours worked. Then I employ my model to recalculate the necessary tax rate taking into account the expected effect of increases in the tax rate on output and hours worked. 8.2.1. Assuming Lump Sum Transfers with No Change in Spending I first create an algorithm to determine the tax rate necessary to balance the budget if the tax rate increases did not affect output. I will illustrate this algorithm using the case of the United States. I start by computing the tax revenue to GDP ratio. In 2009, it was 0.24 for the United States. Because the deficit to GDP ratio in 2009 was 0.11, the tax revenue to GDP ratio at current output necessary to balance the budget would have been 0.24
0.11
0.35.
The fractional increase in the tax rate necessary to balance the budget would therefore have been 0.35 0.24 0.24
0.47.
Next I determine the marginal tax rate in the United States. This is an estimate because there is no single marginal tax rate for all Americans. The income tax system in the United
95
States is progressive, as are the tax systems in all the countries under consideration. In this analysis, I will estimate the marginal tax rate by adding the marginal personal income tax rate and the social security tax rate on gross labor income for workers receiving each country’s average wage. For the United States, this yields a marginal tax rate of 0.34. I calculate the ratio of the marginal tax rate to the average tax rate in the United States (noting rounding errors) to be 0.34 0.24
1.44.
I then determine the marginal tax rate at current output necessary to balance the budget. (“Current” refers to the year 2009 since this is the most recent year for which I have data.) I assume that when the tax rate is raised to balance the budget, the ratio of the marginal tax rate to the average tax rate remains constant. The marginal tax rate at current output necessary in the United States to balance the budget would thus be 1.44 0.35
0.51.
As I have shown, however, an increase in the marginal tax rate would actually lead to a decrease in output when I assume that government revenue is spent on lump sum transfers to individuals regardless of hours worked. Therefore, this marginal tax rate of 0.51 would actually be insufficient to achieve a balanced budget. Using my model, I find that a marginal tax rate of 0.70 would actually have been necessary. This is because the increase of the marginal tax rate from 0.34 to 0.70 would lead to a drop in output of 28% and drop in hours worked of 37%. Such one-year decreases are far greater than those the United States experienced during the worst years of the Great Depression (King 1994). In 2009 if the United States had needed to balance
96
its budget in one year by raising taxes without cutting government spending, the result would have been disastrous. As Table 8.2 demonstrates, the United States was not the only country to be in such a difficult fiscal situation. Table 8.2 implies that it would have been impossible in 2009 for France, Germany, Greece, Italy, and Spain to balance their budgets in one year simply by raising tax rates, assuming that government revenue was used solely for lump sum transfers regardless of hours worked and that government spending did not decrease. France, Greece, Italy, and Spain all had substantial deficit to GDP ratios, so it may not be surprising that it would have been impossible for them to balance their budgets given those assumptions, but it may appear odd that Germany, with its moderate deficit to GDP ratio, could not have balanced its budget. Germany’s problem was that its marginal tax rate was already so high at 0.63 that a further tax increase would have had severe consequences for output. For this reason, Germany could not have simply taxed its way to a balanced budget within one year. The United Kingdom could only have managed to balance its budget in this scenario by raising its marginal tax rate from 0.39 to 0.63. This would have caused its output to fall by 19% and its hours worked to fall by 26%, devastating the country economically. Only Sweden, with its very low deficit to GDP ratio, could have balanced its budget by raising taxes without decreasing spending without facing severe economic repercussions. The increase of its marginal tax rate from 0.48 to 0.50 would have decreased its output and hours worked each by only 2%. 8.2.2. Assuming Lump Sum Transfers with Spending Cuts Constituting 50% of the Budget Fix I will again assume that all government spending consists of lump sum transfers regardless of hours worked, but now I will assume that 50% of the budget fix is derived from
97
TABLE 8.2 BALANCING THE BUDGET WITH LUMP SUM TRANSFERS AND NO CHANGE IN SPENDING
Country*
Deficit to GDP Ratio
Debt to GDP Ratio
Tax Revenue to GDP Ratio
France Germany Greece Italy Spain Sweden United Kingdom United States
0.08 0.03 0.14 0.05 0.11 0.01 0.11 0.11
0.61 0.44 1.26 1.07 0.46 0.38 0.75 0.53
0.42 0.37 0.29 0.44 0.31 0.46 0.34 0.24
Tax Revenue to GDP Ratio at Current Output Necessary to Balance the Budget in 1 Year 0.49 0.40 0.43 0.49 0.42 0.48 0.45 0.35
Fractional Increase in the Tax Rate Necessary to Balance the Budget in 1 Year 0.18 0.08 0.47 0.12 0.36 0.03 0.32 0.47
*This data comes from the OECD Outlook Database Inventory for the year 2009.
Marginal Tax Rate, Marginal Tax Rate Resulting Resulting Accounting for Changes in at Current Output Change in Change in Country Output, Necessary to Necessary to Output³ Hours Worked³ Balance the Budget² Balance the Budget France 0.52 1.24 0.61 Unable4 N/A N/A Germany 0.63 1.71 0.68 Unable4 N/A N/A Greece 0.51 1.73 0.74 Unable4 N/A N/A Italy 0.54 1.23 0.60 Unable4 N/A N/A Spain 0.48 1.57 0.66 Unable4 N/A N/A Sweden 0.48 1.03 0.49 0.50 -0.02 -0.02 United Kingdom 0.39 1.13 0.51 0.63 -0.19 -0.26 United States 0.34 1.44 0.51 0.70 -0.28 -0.37 1. The marginal tax rate is assumed to be the sum of the marginal personal income tax and social security contribution rates on gross labor income for a worker receiving the average wage in the country. 2. Assuming that the ratio of the marginal tax rate to the average tax rate remains constant when the tax revenue to GDP ratio increases by the amount necessary to balance the budget. 3. Assuming government spending as lump sum transfers regardless of hours worked. 4. Unable means that there is no marginal tax rate which would allow the country to balance its budget. Current Marginal Tax Rate¹
Ratio of Marginal Tax Rate to Average Tax Rate
98
TABLE 8.3 BALANCING THE BUDGET WITH LUMP SUM TRANSFERS AND SPENDING CUTS 50% OF BUDGET FIX
Country*
Deficit to GDP Ratio
Debt to GDP Ratio
Tax Revenue to GDP Ratio
France Germany Greece Italy Spain Sweden United Kingdom United States
0.08 0.03 0.14 0.05 0.11 0.01 0.11 0.11
0.61 0.44 1.26 1.07 0.46 0.38 0.75 0.53
0.42 0.37 0.29 0.44 0.31 0.46 0.34 0.24
Tax Revenue to GDP Ratio at Current Output Necessary to Balance the Budget in 1 Year 0.46 0.39 0.36 0.46 0.36 0.47 0.40 0.30
Fractional Increase in the Tax Rate Necessary to Balance the Budget in 1 Year 0.09 0.04 0.23 0.06 0.18 0.01 0.16 0.24
*This data comes from the OECD Outlook Database Inventory for the year 2009.
Marginal Tax Rate, Marginal Tax Rate Resulting Resulting Accounting for Changes in at Current Output Change in Change in Country Output, Necessary to Necessary to Output³ Hours Worked³ Balance the Budget² Balance the Budget 0.52 1.24 0.57 0.63 -0.10 -0.14 France 0.63 1.71 0.66 Unable4 N/A N/A Germany 0.51 1.73 0.63 Unable4 N/A N/A Greece 0.54 1.23 0.57 0.61 -0.07 -0.09 Italy 0.48 1.57 0.57 Unable4 N/A N/A Spain 0.48 1.03 0.49 0.49 -0.01 -0.01 Sweden 0.39 1.13 0.45 0.48 -0.06 -0.09 United Kingdom 0.34 1.44 0.43 0.46 -0.08 -0.11 United States 1. The marginal tax rate is assumed to be the sum of the marginal personal income tax and social security contribution rates on gross labor income for a worker receiving the average wage in the country. 2. Assuming that the ratio of the marginal tax rate to the average tax rate remains constant when the tax revenue to GDP ratio increases by the amount necessary to balance the budget. 3. Assuming government spending as lump sum transfers regardless of hours worked. 4. Unable means that there is no marginal tax rate which would allow the country to balance its budget. Current Marginal Tax Rate¹
Ratio of Marginal Tax Rate to Average Tax Rate
99
decreases in government spending. The other 50% would have to come from an increase in the tax rate. Table 8.3 presents the results. Under these assumptions, it would have been necessary for the United States to raise its marginal tax rate from 0.34 to 0.46. This would have reduced output by 8% and hours worked by 11%. Under similar assumptions, France and Italy would have been able to balance their budgets as well. France would have had to raise its marginal tax rate from 0.52 to 0.63, reducing its output by 10% and hours worked by 14%. Italy would have had to raise its marginal tax rate from 0.54 to 0.61, reducing its output by 7% and its hours worked by 9%. Germany, Greece, and Spain could not have raised enough revenue from taxes to balance their budgets even if spending cuts had accounted for 50% of the budget fix. The United Kingdom would have had to increase its marginal tax rate from 0.39 to 0.48, causing a 6% drop in its output and a 9% drop in its hours worked. Sweden would only have had to increase its marginal tax rate from 0.48 to 0.49. This would have caused only a 1% drop in output and hours worked. 8.2.3. Assuming μ = 0.50 with No Change in Government Spending Next I assume that individuals value government spending ½ as much as their own consumption (μ = 0.50) and that there is no reduction in government spending in the effort to balance the budget. Table 8.4 presents the results. The United States would have needed to raise its marginal tax rate from 0.34 to 0.55. The increase is much smaller than the increase to the 0.70 marginal tax rate necessary if the government had spent its revenue on lump sum transfers regardless of hours worked. Output in the United States would have decreased by 7% and hours worked by 10%. These changes, although large, are smaller than the 28% decrease in output and 37% decrease in hours worked
100
which would have resulted from the tax increase necessary if the government had spent its tax revenue on lump sum transfers regardless of hours worked. Even with μ = 0.50, Greece, Germany, and Spain would not have been able to balance their budgets without a decreases in government spending. All other countries could have done so, but Sweden is the only one which would not have suffered a considerable decrease in output and hours worked. France would have had to raise its marginal tax rate from 0.52 to 0.69, causing an 11% drop in output and a 16% drop in hours worked. Italy would have had to raise its marginal tax rate from 0.54 to 0.65, causing a 7% drop in output and a 10% drop in hours worked. The United Kingdom would have had to raise its marginal tax rate from 0.39 to 0.55, causing an 6% drop in output and an 9% drop in hours worked. Only Sweden, which would only have had to raise its tax rate only from 0.48 to 0.50 to balance its budget, would have endured minimal losses in output and hours worked of 1%. 8.2.4 Assuming μ = 0.50 with Spending Cuts Constituting 50% of the Budget Fix Now I will assume that individuals value government spending ½ as much as their own consumption (μ = 0.50) and that 50% of the budget fix comes from a decrease in government spending. Table 8.5 presents the results. Under these assumptions, all countries under consideration except Greece would have been able to balance their budgets. The United States would have had to increase its marginal tax rate from 0.34 to 0.44, leading to a 3% decrease in output and a 4% decrease in output. France, Italy, Sweden, and the United Kingdom would have faced decreases in output of between 1% and 4% and decreases in hours worked of between 1% and 6%. Germany and Spain would still have suffered greatly from the necessary tax rate increases. With a marginal tax rate
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TABLE 8.4 BALANCING THE BUDGET WITH μ = 0.50 AND NO CHANGE IN GOVERNMENT SPENDING
Country*
Deficit to GDP Ratio
Debt to GDP Ratio
Tax Revenue to GDP Ratio
France Germany Greece Italy Spain Sweden United Kingdom United States
0.08 0.03 0.14 0.05 0.11 0.01 0.11 0.11
0.61 0.44 1.26 1.07 0.46 0.38 0.75 0.53
0.42 0.37 0.29 0.44 0.31 0.46 0.34 0.24
Tax Revenue to GDP Ratio at Current Output Necessary to Balance the Budget in 1 Year 0.49 0.40 0.43 0.49 0.42 0.48 0.45 0.35
Fractional Increase in the Tax Rate Necessary to Balance the Budget in 1 Year 0.18 0.08 0.47 0.12 0.36 0.03 0.32 0.47
*This data comes from the OECD Outlook Database Inventory for the year 2009.
Marginal Tax Rate, Marginal Tax Rate Resulting Resulting Accounting for Changes in at Current Output Change in Change in Country Output, Necessary to Balance Necessary to Output³ Hours Worked³ the Budget² Balance the Budget France 0.52 1.24 0.61 0.69 -0.11 -0.16 Germany 0.63 1.71 0.68 Unable4 N/A N/A Greece 0.51 1.73 0.74 Unable4 N/A N/A Italy 0.54 1.23 0.60 0.65 -0.07 -0.10 Spain 0.48 1.57 0.66 Unable4 N/A N/A Sweden 0.48 1.03 0.49 0.50 -0.01 -0.01 United Kingdom 0.39 1.13 0.51 0.55 -0.06 -0.09 United States 0.34 1.44 0.51 0.55 -0.07 -0.10 1. The marginal tax rate is assumed to be the sum of the marginal personal income tax and social security contribution rates on gross labor income for a worker receiving the average wage in the country. 2. Assuming that the ratio of the marginal tax rate to the average tax rate remains constant when the tax revenue to GDP ratio increases by the amount necessary to balance the budget. 3. Assuming that individuals value government spending ½ as much as their own consumption (μ = 0.50). 4. Unable means that there is no marginal tax rate which would allow the country to balance its budget. Current Marginal Tax Rate¹
Ratio of Marginal Tax Rate to Average Tax Rate
102
TABLE 8.5 BALANCING THE BUDGET ASSUMING μ = 0.50 AND SPENDING CUTS 50% OF BUDGET FIX
Country*
Deficit to GDP Ratio
Debt to GDP Ratio
Tax Revenue to GDP Ratio
France Germany Greece Italy Spain Sweden United Kingdom United States
0.08 0.03 0.14 0.05 0.11 0.01 0.11 0.11
0.61 0.44 1.26 1.07 0.46 0.38 0.75 0.53
0.42 0.37 0.29 0.44 0.31 0.46 0.34 0.24
Tax Revenue to GDP Ratio at Current Output Necessary to Balance the Budget in 1 Year 0.46 0.39 0.36 0.46 0.36 0.47 0.40 0.30
Fractional Increase in the Tax Rate Necessary to Balance the Budget in 1 Year 0.09 0.04 0.23 0.06 0.18 0.01 0.16 0.24
*This data comes from the OECD Outlook Database Inventory for the year 2009.
Marginal Tax Rate, Marginal Tax Rate Resulting Resulting Accounting for Changes in at Current Output Change in Change in Country Output, Necessary to Balance Necessary to Output³ Hours Worked³ the Budget² Balance the Budget France 0.52 1.24 0.57 0.59 -0.04 -0.06 Germany 0.63 1.71 0.66 0.72 -0.09 -0.13 Greece 0.51 1.73 0.63 Unable4 N/A N/A Italy 0.54 1.23 0.57 0.59 -0.03 -0.04 Spain 0.48 1.57 0.57 0.62 -0.08 -0.11 Sweden 0.48 1.03 0.49 0.49 -0.01 -0.01 United Kingdom 0.39 1.13 0.45 0.46 -0.02 -0.03 United States 0.34 1.44 0.43 0.44 -0.03 -0.04 1. The marginal tax rate is assumed to be the sum of the marginal personal income tax and social security contribution rates on gross labor income for a worker receiving the average wage in the country. 2. Assuming that the ratio of the marginal tax rate to the average tax rate remains constant when the tax revenue to GDP ratio increases by the amount necessary to balance the budget. 3. Assuming that individuals value government spending ½ as much as their own consumption (μ = 0.50). 4. Unable means that there is no marginal tax rate which would allow the country to balance its budget. Current Marginal Tax Rate¹
Ratio of Marginal Tax Rate to Average Tax Rate
103
increase from 0.48 to 0.62, Spain’s output would have dropped 8%, and its hours worked would have fallen 11%. With a marginal tax rate increase from 0.63 to 0.72, Germany’s output would have dropped 9%, and its hours worked would have fallen 13%. 8.2.5. The Consequences of Using Tax Increases to Balance the Budget In all these scenarios, all countries except Sweden would have had to endure considerable economic hardship in order to balance their budgets within one year as a consequence of the necessary tax rate increase. Interestingly, under none of the scenarios would Greece have been able to balance its budget, demonstrating the seriousness of its budget crisis. It is important to appreciate that this analysis takes into consideration only the changes in output caused by the increase in the tax rate during the first year after that tax rate increase. My model demonstrates, however, that only about 90% of the decrease in output which occurs in a country over an 80 year lifetime is experienced during the first year. Thus, in the long run, the fall in output would be larger than that which the figures presented in Tables 8.2-8.5 suggest. If these tax increases were implemented, output would continue to fall in succeeding years, so that tax revenues would fall and budgets would again fall into deficit. Thus, even the tax increases I have suggested would not have balanced the budgets in the long run, as will be demonstrated in section 8.5. Larger tax increases would have been necessary to achieve balanced budgets in the long run, causing greater economic harm. 8.3. A Closer Look at the Case of the United States In this section, I will consider additional scenarios for the case of the United States. Again, the goal will be to eliminate the budget deficit within one year. The results are presented in Table 8.6.
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TABLE 8.6 VARIOUS SCENARIOS FOR THE US TO DEAL WITH ITS DEFICIT
Scenario for the United States1
Current Marginal Tax Rate
Marginal Tax Rate, Accounting for Changes in Output, Necessary to Achieve Scenario Goal
Resulting Change in Output
Resulting Change in Hours Worked
Balanced Budget, No Spending Cut
0.34
0.70
-0.28
-0.37
Balanced Budget, No Spending Cut (Prescott Tax Rate)2
0.35
0.71
-0.28
-0.38
Balanced Budget, No Complementarity
0.34
0.63
-0.20
-0.27
Balanced Budget, Less Elastic LS
0.34
0.56
-0.10
-0.14
Balanced Budget, Spending 25% of Budget Fix
0.34
0.54
-0.14
-0.19
Balanced Budget, Spending 50% of Budget Fix
0.34
0.46
-0.08
-0.11
Balanced Budget, Spending 75% of Budget Fix
0.34
0.40
-0.04
-0.06
Balanced Budget, No Spending Cut (μ = 0.25)
0.34
0.51
-0.01
-0.01
Balanced Budget, No Spending Cut (μ = 0.50)
0.34
0.55
-0.07
-0.10
Balanced Budget, No Spending Cut (μ = 0.75)
0.34
0.60
-0.16
-0.21
3% Deficit, No Spending Cut
0.34
0.54
-0.14
-0.19
3% Surplus, No Spending Cut
0.34
Unable3
N/A
N/A
1. Assuming the baseline case of consumption-work complementarity, an elastic labor supply, government spending as lump sum transfers regardless of hours worked, and the marginal tax rate computed in the same manner as in Tables 8.2-8.5 unless otherwise specified. 2. The Prescott tax rate is computed by summing the social security tax rate and 1.6 times the average income tax rate, as discussed in chapter 3. 3. Unable means that there is no marginal tax rate which would allow the United States to balance its budget.
105
The first scenario considered is that which results from using the method of Prescott (2004) to determine the current marginal tax rate in the United States. Prescott added social security tax rate to 1.6 times the average income tax rate to obtain his estimate. He derived this factor of 1.6 by employing the methodology of Feenberg and Coutts (1993) to estimate the marginal income tax rate in the United States during both 1970-1974 and 1993-1996. This method yields a current marginal tax rate for the United States of 0.35 rather than 0.34, the value used in section 8.2. Using Prescott’s estimate, the marginal tax rate necessary to balance the budget would be 0.71. The resulting fall in output would be 28% and the fall in hours worked would be 38%. As would be expected given the small difference in the estimate of the marginal tax rate, these results are nearly identical to those in the section 8.2. Next I will consider the result of removing the consumption-work complementarity assumption. This would lead to a lower value for the tax rate necessary to balance the budget and smaller decreases in output and hours work because a given increase in the tax rate would have smaller effects on output and hours worked. Similarly, assuming a less elastic labor supply would lead to a lower value for the tax rate necessary to balance the budget since a lower labor supply elasticity implies that given changes in the tax rate would have smaller effects on output and hours worked. Clearly, the greater the share of the budget fix which is made up by decreases in government spending rather than increases in taxes, the smaller the necessary increases in the tax rate and the smaller the consequent decreases in output and hours work, as Table 8.6 demonstrates. Furthermore, the greater the value of μ, the smaller the income effect caused by an increase in the tax rate, and so the more negative the effect of a given tax increase on output
106
and labor supply. Therefore, the greater the value of μ, the larger the tax increase necessary to balance the budget and the larger the resulting decrease in output and hours worked. Even to achieve a deficit to GDP ratio of 3%, the United States would require a marginal tax rate of 0.54 if there were no decrease in government spending. This would induce a 14% decrease in output and a 19% decrease in hours worked. It is striking to note that, despite its relatively low marginal tax rate, the United States simply cannot achieve a budget surplus of 3% by raising tax rates unless it reduces government spending. In 2009, the debt to GDP ratio in the United States was 53%. It will be difficult for the United States to reduce this ratio significantly without cutting government spending. 8.4. The Laffer Curve for the United States In view of the ability of my model to predict the decline in output which results from various tax rate increases, it is interesting to use it to plot the Laffer Curves for the United States. Assuming that the government spends its tax revenue on lump sum transfers regardless of hours worked and that the current marginal tax rate in the United States is 0.34, I obtain the data presented in Table 8.7. To construct my Laffer Curve, I plot the data for final marginal tax rates between 0.00 and 0.80 in increments of 0.05. I stopped at the marginal tax rate of 0.80 because my computer was unable to solve my Matlab program for tax rates greater than 0.80. I compute final average tax rates assuming that the ratio of the marginal tax rate to the average tax rate remains constant. Using the current marginal tax rate, I compute the change in output and the change in hours worked associated with each final marginal tax rate. To determine total tax revenue, I take the product of the final average tax rate and the output for the United States. In Graph 8.1, I assumed that government spends its tax revenue on lump sum transfer payments
107
TABLE 8.7 LAFFER CURVE DATA FOR THE US ASSUMING LUMP SUM TRANSFERS
Current Marginal Tax Rate
Final Marginal Tax Rate
Final Average Tax Rate (τ)*
Change in Output
Change in Hours Worked
Total Tax Revenue (τ*y)
0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80
0.00 0.03 0.07 0.10 0.14 0.17 0.21 0.24 0.28 0.31 0.35 0.38 0.42 0.45 0.49 0.52 0.56
0.19 0.17 0.14 0.11 0.08 0.06 0.03 -0.01 -0.04 -0.07 -0.11 -0.15 -0.19 -0.23 -0.28 -0.33 -0.39
0.29 0.25 0.21 0.17 0.12 0.08 0.04 -0.01 -0.06 -0.10 -0.15 -0.20 -0.26 -0.31 -0.37 -0.43 -0.50
0.000 0.039 0.076 0.111 0.145 0.175 0.204 0.231 0.256 0.277 0.296 0.312 0.325 0.332 0.336 0.335 0.326
*Assuming the ratio of the marginal tax rate to the average tax rate remains constant.
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GRAPH 8.1
Total tax revenue for various marginal tax rates assuming government spending as lump sum transfer payments (μ = 1) 0.4
0.35
Total Tax Revenue
0.3
0.25
0.2
0.15
0.1
0.05
0 0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4 Tax Rate
0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.8
109
regardless of hours worked (the equivalent of μ = 1). This Laffer Curve reaches its peak at a tax rate of about 0.70, implying that the United States government would maximize total tax revenue by implementing a marginal tax rate of about 0.70, corresponding to an average tax rate of about 0.49. Of course, moving to such a high marginal tax rate would have devastating effects on output and hours worked. Output would drop about 30% and hours worked would drop about 40%. If I assume that individuals value government spending ½ as much as their own consumption (μ = 0.50), I obtain the data in Table 8.8. The total tax revenue would be much higher for a given tax rate than in the previous case because there is now an income effect which offsets a considerable amount of the substitution effect of the tax increase. A tax increase will therefore have less of a negative effect on output and labor supply (and a tax decrease will have less of a positive effect on output and labor supply). Graph 8.2 presents the Laffer Curve when μ = 0.50. This Laffer Curve reaches its peak at a tax rate of about 0.75, implying that the United States government would maximize total tax revenue by implementing a marginal tax rate of about 0.75, corresponding to an average tax rate of about 0.52. Moving to such a high marginal tax rate would have devastating effects on output and hours worked. Output would drop about 20% and hours worked would drop about 30%. If I assume that individuals’ marginal utility of consumption is unaffected by government spending (μ = 0), I obtain the data in Table 8.9. The Laffer Curve corresponding to this scenario, (Graph 8.3), is perhaps the most interesting. Because according to my model an increase in the tax rate actually increases labor supply when μ = 0, the Laffer Curve does not reach a peak between marginal tax rates of 0.00 and 0.80. In fact, until the marginal tax rate reaches approximately 0.65, the marginal increase in total tax revenue for each increase in the marginal
110
TABLE 8.8 LAFFER CURVE DATA FOR THE US ASSUMING μ = 0.50
Current Marginal Tax Rate
Final Marginal Tax Rate
Final Average Tax Rate (τ)*
Change in Output
Change in Hours Worked
Total Tax Revenue (τ*y)
0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80
0.00 0.03 0.07 0.10 0.14 0.17 0.21 0.24 0.28 0.31 0.35 0.38 0.42 0.45 0.49 0.52 0.56
0.05 0.05 0.04 0.04 0.03 0.02 0.01 0.00 -0.02 -0.03 -0.05 -0.08 -0.11 -0.14 -0.18 -0.22 -0.28
0.07 0.07 0.06 0.05 0.04 0.03 0.01 0.00 -0.02 -0.05 -0.08 -0.11 -0.15 -0.19 -0.24 -0.31 -0.38
0.000 0.057 0.114 0.171 0.226 0.280 0.333 0.384 0.432 0.478 0.520 0.558 0.590 0.615 0.633 0.639 0.630
*Assuming the ratio of the marginal tax rate to the average tax rate remains constant.
111
GRAPH 8.2
Total tax revenue for various marginal tax rates assuming μ = 0.5 for government spending 0.7
0.6
Total Tax Revenue
0.5
0.4
0.3
0.2
0.1
0 0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4 Tax Rate
0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.8
112
tax rate of 0.05 increases, meaning that, for example, the increase in total tax revenue when the marginal tax rate increases from 0.60 to 0.65 is greater than the increase in total tax revenue when the marginal tax rate increases from 0.55 to 0.60, and so on through the marginal tax increase from 0.00 to 0.05. Even when the marginal tax rate is increased beyond 0.65 to 0.80, total tax revenue continues to increase substantially. Although my computer was unable to solve my Matlab program for marginal tax rates greater than 0.80, it appears that total tax revenue might continue to increase as the marginal tax rate increases at least for some higher marginal tax rates. This implies that when μ = 0, individuals would have a strong incentive to work despite extremely high tax rates. Although the substitution effect would strongly decrease work incentives at such tax rates, the income effect would dominate. 8.5. Balancing the Budget in the Long Run Table 8.10 presents data about how much the United States would have to increase its tax rate to balance its budget, taking into account the resulting changes in output. The top half of the table presents the marginal tax rates necessary to balance the budget in year 80 after all of the effects of the tax rate increase on output have been realized. In contrast, the bottom half of the table presents the marginal tax rates necessary to balance the budget within one year. The data in the bottom half is identical to that presented earlier in Tables 8.2-8.5. As Table 8.10 reveals, the United States would be unable to balance its budget in year 80 when all of the effects of the tax rate increase on output have been realized if there are no cuts in government spending and if government spending consists of lump sum transfers regardless of hours worked. In this scenario, the marginal tax rate of 0.70 necessary to balance the budget in year 2 is actually the tax rate which produces the greatest government revenue, as discussed in section 8.4 and illustrated in Graph 8.1. Output in the United States in year 80, however, would be only about
113
TABLE 8.9 LAFFER CURVE DATA FOR THE US ASSUMING μ = 0
Current Marginal Tax Rate
Final Marginal Tax Rate
Final Average Tax Rate (τ)*
Change in Output
Change in Hours Worked
Total Tax Revenue (τ*y)
0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80
0.00 0.03 0.07 0.10 0.14 0.17 0.21 0.24 0.28 0.31 0.35 0.38 0.42 0.45 0.49 0.52 0.56
-0.11 -0.09 -0.08 -0.06 -0.05 -0.03 -0.01 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.13 0.13 0.11
-0.15 -0.13 -0.11 -0.09 -0.07 -0.05 -0.02 0.01 0.03 0.06 0.09 0.12 0.15 0.17 0.18 0.19 0.16
0.000 0.059 0.120 0.184 0.249 0.317 0.387 0.460 0.536 0.614 0.695 0.779 0.864 0.950 1.032 1.107 1.162
*Assuming the ratio of the marginal tax rate to the average tax rate remains constant.
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GRAPH 8.3
Total tax revenue for various marginal tax rates assuming μ = 0 for government spending 1.4
1.2
Total Tax Revenue
1
0.8
0.6
0.4
0.2
0 0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4 Tax Rate
0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.8
115
TABLE 8.10 VARIOUS SCENARIOS FOR THE US TO DEAL WITH ITS DEFICIT TO BALANCE THE BUDGET IN YEAR 80
Scenario for the United States1
Current Marginal Tax Rate
Marginal Tax Rate, Accounting for Changes in Output in the Long Run, to Balance the Budget
Change in Output
Surplus in Year 22
No Spending Cut, Lump Sum Transfers
0.34
Unable3
N/A
N/A
Spending 50% of Budget Fix, Lump Sum Transfers
0.34
0.47
-0.10
0.01
No Spending Cut, μ = 0.50
0.34
0.56
-0.08
0.01
Spending 50% of Budget Fix, μ = 0.50
0.34
0.44
-0.03
