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Distinguishing Limited Commitment from Moral Hazard in Models of Growth with Inequality∗ Anna L. Paulson Federal Reserve Bank of Chicago Robert Townsend University of Chicago Federal Reserve Bank of Chicago This version: February, 2003

Abstract We use non-parametric, reduced form and structural techniques to distinguish the micro-economic foundations of two models of growth with increasing inequality using new data from rural and semi-urban households in Thailand. We estimate a limited commitment model that is similar to Evans and Jovanovic (1989) and a moral hazard model that is an extension of Aghion and Bolton (1996). Both models emphasize the role of occupational choice and financial constraints. While the models share many implications, they are distinguished by their assumptions about the nature of financial market imperfections. We provide structural and reduced form evidence that the dominant source of credit market imperfections varies with wealth. For poorer households limited commitment is the dominant concern. However, as wealth increases moral hazard gains importance. These findings provide a rationale for important characteristics of the financial environment in Thailand. ∗

Comments from Daron Acemoglu, Patrick Bolton, Lars Hansen, Simon Johnson, Boyan Jovanovic, Andreas Lehnert, Peter Murrell, Bernard Salanié, Chris Udry and from conference and seminar participants at the University of Chicago, Federal Reserve Bank of Chicago, DELTA, IUPUI, MIT, UCLA, the University of Toulouse, Stanford and Yale are gratefully acknowledged. We also thank Francisco Buera, Xavier Giné and Alexander Karaivanov for excellent research assistance as well as the National Institute of Health and the National Science Foundation for funding. We are much indebted to Sombat Sakuntasathien for collaboration and for making the data collection possible. The views expressed in this paper are those of the authors and do not necessarily represent those of the Federal Reserve Bank of Chicago or the Federal Reserve System.

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1

Introduction

Financial market imperfections are at the heart of a variety of models, including models of economic development where economic growth comes at the expense of increasing inequality. Most papers posit a particular financial market imperfection and exclude the possibility of alternative sources of imperfections. Our goal in this paper is to identify the source of financial constraints. We use structural, non-parametric and reduced form techniques to distinguish the source of financial market imperfections using microeconomic data from a country that has experienced growth with increasing inequality. In the work of Banerjee and Newman (1993), the financial constraint is due to limited commitment. Agents can supplement their personal stake in entrepreneurial activities by borrowing. Wealth plays the role of collateral and limits default. Thus low-wealth entrepreneurs may be constrained in investment and some potential entrepreneurs may be unable to borrow to finance entrepreneurial projects. More specifically, the limited commitment model that we estimate is a widely used empirical specification that is featured in Evans and Jovanovic (1989), as well as in a variety of other studies of occupation choice (Magnac and Robin (1996), and Holtz-Eakin, Joulfian and Rosen (1994), for example). In contrast, Aghion and Bolton (1996) focus on financial constraints that arise from moral hazard problems. Since effort is unobserved and repayment is only feasible if the project is successful, poor borrowers will face little incentive to be diligent, increasing the likelihood of project failure and default. In order to break-even, lenders charge higher interest rates to low-wealth borrowers. Thus some low-wealth potential entrepreneurs will be unable, or unwilling at such high interest rates, to start businesses at any scale. Low-wealth entrepreneurs who do succeed in getting loans will be subject to a binding incentive compatibility constraint that ensures that they exert the appropriate level of effort, and this limits credit for investment. Conversely as wealth increases, entrepreneurs self-finance and borrowing diminishes. The Aghion and Bolton model is the starting point for the moral hazard model that we estimate. We make a number of substantive modifications that facilitate estimation and add richness to the model. For example, we create a role for entrepreneurial talent, allow investment to be divisible, and consider the possibility that agents are riskaverse. Because we allow investment to vary, the positive relationship between wealth and borrowing is not driven by indivisibilities. One contribution of our paper is to construct and estimate this moral hazard version of an occupational choice model with fully endogenous contracts, using linear programming techniques from the mechanism design literature (see Phelan and Townsend (1991)). The two models share many predictions. Both models imply that entrepreneurship will be positively related to pre-existing wealth. In both models the long-run impact of financial constraints may be alleviated through savings and growth. However, in both model economies the initial distribution of wealth will have long run effects. In addition, both models imply that economic growth will be accompanied by increases 2

in inequality. In addition to wealth, the returns to education and entrepreneurial talent are also allowed to influence the choice of occupation. We also allow observed education and unobserved talent to be correlated with wealth. Despite these shared predictions, the two models differ in their implications for how the behavior of constrained entrepreneurs will vary with wealth. In the limited commitment model, constrained entrepreneurs will borrow more when wealth increases and in the moral hazard model, as noted above, the opposite will occur. In addition, because of their particular assumptions about financial market imperfections, policy recommendations for improving welfare will vary across the two models. The goal of this paper is to see if we can distinguish the limited commitment model from the moral hazard model using cross-sectional data. We use both structural and reduced form techniques. When we use structural maximum likelihood estimation, we naturally limit ourselves to relatively simple versions of the limited commitment and moral hazard models. Because the models that we estimate are deliberately drawn from the literature, they are not nested and so we use the appropriate Vuong (1989) model comparison test. When we use less restrictive reduced form estimation, and even less restrictive non-parametric estimates, we make use of additional multi-variate controls. This paper is related to work that tries to identify the underlying source of market imperfections. For example, Abbring, Chiappori, Heckman and Pinquet (2002) use dynamic data to distinguish moral hazard from adverse selection in the insurance context. We focus on the distinction between financial market imperfections arising from moral hazard and those arising from limited commitment. The Vuong tests that we use to distinguish non-nested models are also featured Wolak’s (1994) work on water regulation in California. He tests whether the data offer more support for a model where the principle observes the characteristics of the agents or a model where these characteristics are unobserved. We chose to compare the models using data from Thailand because it has experienced with growth with increasing inequality. From 1981 to 1995 real per capita GDP grew 8% per year, and from 1987 to 1992 Thailand’s growth rate was the fastest in the world. Yet within Thailand, this period of rapid income growth was accompanied by substantial increases in inequality. From 1981 to 1992, the Thai Gini coefficient increased by 22%, approaching the level of inequality of many Latin American countries.1 Both the Banerjee and Newman (1993) and the Aghion and Bolton (1996) models can deliver this phenomenon. However, as we emphasize, these models differ in their assumptions about the source of financial market imperfections. Our earlier work demonstrates that financial constraints have an important effect on who starts businesses and on how existing businesses are run in Thailand (see Paulson and Townsend, in press). A symptom of financial constraints is that wealth will be positively correlated with the probability of starting a business. A positive correlation between becoming an entrepreneur and beginning-of-period wealth can be seen very 1

After 1992, inequality appears to have decreased somewhat, and the 1996 Gini coefficient is 0.50.

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dramatically in the non-parametric regression displayed in Figure 1.2 In Paulson and Townsend (in press), we provide additional evidence that financial constraints are important in Thailand and document the statistical significance and robustness of our findings. In this paper, we explore the source of these financial constraints. The Thai data come from our own large socioeconomic survey that was fielded in March - May of 1997 to 2,880 households, approximately 21% of whom run their own businesses. The sample focuses on households living in two distinct regions of the country: rural and semi-urban households living in the central region, close to Bangkok, and more obviously rural households living in the semi arid and much poorer northeastern region.3 We designed the survey instruments that were used to collect the data with economic theory very much in mind. This focus dictated collecting current and retrospective information on wealth (household, agricultural, business and financial), occupational history (transitions to and from farm work, wage work and entrepreneurship), access and use of a wide variety of formal and informal financial institutions (commercial banks, agricultural banks, village lending institutions, money lenders, as well as friends, family and business associates). The data also provide detailed information on household demographics, education and entrepreneurial activities. Because these data provide rich and detailed information about both the firm and the household as well as information on financial intermediaries, they are particularly well designed for studying theories of entrepreneurship and the financial system. Theory emphasizes that both firm and household characteristics are important in determining the supply and the demand for credit. In many studies, the available data force a focus on either the firm or the household as potential entrepreneur, but do not allow for both to be treated with equal thoroughness.4 In sum the challenge of this paper is to confront the models with these data. We conclude that progress can be made in distinguishing models and in identifying the nature of financial constraints. Overall, and especially in the Central region and among wealthier households, the moral hazard model does a better job of explaining the data. In contrast, in the Northeast and among lower wealth households, the limited 2

For each observation in Figure 1, a weighted regression is performed using 80% (bandwidth = 0.8) of the data around that point. The data are weighted using a tri-cube weighting procedure that puts more weight on the points closest to the observation in question. The weighted regression results are used to produce a predicted value for each observation. Because the graphs can be fairly sensitive to outliers, we have dropped the wealthiest 1% of the sample. 3 See Binford, Lee and Townsend (2001) for more details on the sampling methodology. 4 For example, Evans and Jovanovic (1989) use data from the National Longitudinal Study of Young Men, which has detailed information on the self-employed, but very sparse information about the businesses they run. In their studies of banking relationships and access to credit in small businesses, Petersen and Rajan (1994 and 1995) analyze data collected by the Small Business Administration (SBA). The SBA data provide a wealth of detail about the firm, but very little information about the entrepreneur. Holtz-Eakin, Joulfian and Rosen (1994) use data from U.S. individual tax returns. These data provide detailed information about inheritances and some information about both the entrepreneur and the firm; however they do not include important firm and household variables, such as the nature of the business and the education of the entrepreneur, for example.

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commitment model does a better job. For these households, the possibility of default seems to govern lending and repayment. We emphasize that these findings are robust to the choice of statistical technique. That is, the conclusions are based both on the formal model comparison tests from the structural estimation, as well as on findings from reduced form and non-parametric estimation. The rest of the paper is organized as follows. In the next section we discuss the models and their implications in detail. In that section we also outline how the structural maximum likelihood estimation of each model will proceed. Detailed descriptions of the maximum likelihood estimation are relegated to an Appendix that is available from the authors. Section three describes the data. Section four reports on the structural maximum likelihood estimation of each model. In section five, we compare the overall fit of the models using structural, reduced form and non-parametric techniques. In the final section we discuss how the findings might explain important features of the financial environment in Thailand and suggest directions for future research.

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Models and Implications

In this section, we describe the models whose empirical implications we are interested in evaluating, and we provide an outline of how the structural maximum likelihood estimation of each model will proceed. The model descriptions below concentrate on describing the key features that are necessary for developing the implications that we evaluate in the empirical section. Each of the models come from papers that include a much richer descriptions of the model economies than we can do justice to here. Our emphasis in this paper is on describing and evaluating the micro economic implications of the models. That is, the emphasis on empirical work guides the level of detail we provide in describing the models. In the model descriptions, the same symbols are used to label variables that are common across models. For example, the variable A always stands for wealth, k∗ always denotes the optimal amount of capital to invest when households are unconstrained, and the parameter θ stands for entrepreneurial talent.

2.1

Description of the Models

2.1.1

Limited Commitment Model

The first model that we estimate comes from Evans and Jovanovic (1989). Evans and Jovanovic (1989) is a static model of occupational choice where households decide whether to work in the wage sector or to become entrepreneurs. Evans and Jovanovic use this model to provide structural estimates of the choice between wage work and entrepreneurship using U.S. data. Magnac and Robin (1996) use data from France to do the same thing. Evans and Jovanovic assume that credit is exogenously limited to be less than some fixed multiple of wealth. We use the possibility that borrowers will default to endogenize the financial constraint and come up with a lending contract 5

with the same feature: the amount borrowed must be less than or equal to a fixed multiple of beginning-of period wealth. In a dynamic environment with the same financial market imperfection, but different assumptions about production, Banerjee and Newman (1993) find economic growth is likely to be accompanied by increases in inequality. Evans and Jovanovic (1989) Ignoring for the moment the wealth-associated financing constraint, the amount of capital that an entrepreneurial household would like to invest is determined by entrepreneurial skill θ, interest rate r, and a productivity parameter α. The production function is y = f (k) = εθkα

(1)

where ε is a log normal independent and identically distributed productivity shock whose logarithm has variance σ 2ε .5 Entrepreneurial talent, θ, is determined ex ante and is known to the household. We follow Evans and Jovanovic and imagine that talent is log normally distributed. Specifically we assume that: ln θ = ¯θ + η,

(2)

where η is normally distributed with mean zero and variance σ η . In order to avoid the spurious inference that wealth rather than talent is the source of constraints, we follow the literature and allow an individual’s expected talent to be correlated with wealth.6 We also generalize the Evans and Jovanovic slightly and allow talent to be correlated with formal education: ¯θ = δ 0 + δ 1 ln (A) + δ 2 (education)

(3)

Since households are risk neutral, the problem of a would be entrepreneur is to maximize expected profits: MaxE[f (k) − r(k − A)] k

(4)

The solution to the maximization problem delivers the optimal amount of capital to invest: ∗

k =

µ

θα r

5

¶1/(1−α)

(5)

Like Evans and Jovanovic (1989), we assume that E(ε) = 1 so that E[log(ε)] = −σ 2ε /2. Like Evans and Jovanovic (1989), we assume that entrepreneurial talent is unrelated to wage income. This assumption is also made in the moral hazard model. Evans and Jovanovic experimented with allowing wages to depend on entrepreneurial talent, but found that this led to models that were analytically intractable. Effectively, the parameter θ captures the comparative advantage in entrepreneurial activities compared to wage labor. 6

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Thus, in the absence of financial constraints, the optimal amount of level of investment, k∗ , is not influenced by wealth. However, the optimal investment level does depend on entrepreneurial talent, θ. The interest rate, r, is fixed exogenously. We set the gross interest rate equal to 1.25, which is the average interest rate in the data. However, suppose that borrowers may strategically default. If they do so they keep the revenues from running the business, but they lose their collateral and the accumulated interest on it. There is also some possibility they will be caught and punished. Assume that π represents the probability of being caught times the fraction of wealth that is forfeited if a defaulting entrepreneur is caught. In this setting, a borrowers who chooses to repay will receive the following payoff: εθkα + r(A − k)

(6)

εθkα − πA

(7)

Borrowers who choose to default will receive:

Since lenders will only be willing to lend to borrowers who will choose to repay, it must be the case that the return to borrowing and repaying is at least equal to the return to borrowing and defaulting: εθkα + r(A − k) ≥ εθkα − πA

(8)

Solving the equation (8) for wealth, we see that lenders will only lend to households if wealth is sufficiently high: rk (9) r+π It follows that the maximum amount of capital that can be invested will be a linear function of wealth: A≥

π k ≤ (1 + )A (10) r Let λ = 1 + πr . Equation (10) implies that the highest possible value for λ would be two, or that the maximum a household can borrow is equal to its wealth. Note that in equilibrium no one will default, so the interest rate will be the one for risk-free debt. Since households can borrow up to some fixed multiple of their total wealth, but no more, the maximum amount that can be invested in a firm is equal to λA and the maximum amount that a household can borrow is given by (λ − 1)A. Of course more talented entrepreneurs will want to invest more capital, as can be seen in equation (5). This means that the borrowing constraints are more likely to bind for higher skilled households, since business skill and capital are complements. Holding household wealth constant, more talented households are more likely to want to invest amounts of capital that exceed λA.7 Put the other way around, from equation (5), we see that for a given 7

While the demand for credit will clearly depend on entrepreneurial talent, the supply of credit will respond only to wealth.

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level of wealth, entrepreneurs will be unconstrained only if their talent is low enough. Specifically, they will be unconstrained if talent satisfies: r (λA)1−α (11) α This curve is plotted in Figure 2, and it defines the boundary between constrained and unconstrained entrepreneurs as a function of wealth, A, and talent, θ. Not everyone need be an entrepreneur, of course. We focus on the fundamental decision about whether to become an entrepreneur or to work in the wage/subsistence agriculture sector. If a household works in the wage or subsistence agriculture sector, its earnings will be given by: w = µξ (12) θ
µ(1−α) (1 − α)−(1−α) (13) α The right hand side of equation (13), denoted as c1 in logs below, does not depend on wealth. For wealth levels to the right of A∗ , entrepreneurial talent θ would have to be still higher in order for the firm to move from the unconstrained to the constrained territory. For households with initial wealth that is below the critical value, A∗ , on the other hand, the choice on the margin is between being a wage earner and starting a constrained firm with k = λA. In this case, agents will start a firm if ability satisfies: θ > (λA)−α (µ + rλA)

(14)

Notice that wealth A now appears in the right-hand side of equation (14) above, which is denoted as c3 in logs below. The lower wealth is, the less likely it is that the household 8

Following Evans and Jovanovic we refer to the alternative occupation as “wage-work”, but it could also be subsistence agriculture that requires relatively little capital. In the data, many non-business households grow rice, use relatively little capital, and do not use credit.

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will start a firm. This is the region where credit constraints impact entrepreneurial choice. The curves that partition (A, θ) space into wage workers, constrained firms and unconstrained firms in Figure 2 clearly depend on the parameters of the production function, the interest rate, the wage rate, and the value of λ. In addition, these parameters also determine the critical value of wealth, A∗ . If we assume that talent, θ, is uniformly distributed in the population, then the fraction of the population that is engaged in wage work for a given wealth level would equal the length of a vertical line segment from the x-axis to the lower curve in Figure 2. Equivalently, we can think of the length of this line segment as representing the likelihood that a household with a particular level of wealth will work for wages. This is a simplified version of how the structural maximum likelihood estimation is performed. However, we assume that talent is log normally distributed as is given by equation (2). This assumption about the distribution of talent determines the log likelihood of entrepreneurship, given the parameter vector ψ = [α, λ, δ 0 , δ 1 , δ 2 , µ, σ η , σ ε , σ ξ ] as follows: ( ¶ ¶¶ µ µ µ X 1 c3 − ¯θ c3 − ¯θ + Ei ln 1 − Φ (1 − Ei ) ln Φ Ln (ψ) = n i:A ≤A∗ ση ση i ¶ ¶¶) µ µ µ X c1 − ¯θ c1 − ¯θ + Ei ln 1 − Φ where (15) (1 − Ei ) ln Φ σ σ η η ∗ i:A >A i

c3 = −α ln λ − α ln A + ln(µ + rλA) and r c1 = (1 − α) ln µ + α ln + (α − 1) ln(1 − α) α

n is the number of observations, Ei is equal to one for entrepreneurial households and zero otherwise, and Φ is the cumulative standard normal distribution function.9 Again, recall that the constants c1 and c3 are equal to the log of the right hand side of equations (13) and (14), respectively. For further details see the appendix. 2.1.2

Moral Hazard Model

There is no existing moral hazard model of occupation choice that can be estimated directly. We make a number of substantive modifications to Aghion and Bolton (1996) and Lehnert (1999) to facilitate estimation and add richness to the model. For example, we create a role for entrepreneurial talent, allow investment to be divisible, and consider the possibility that agents are risk averse. Aghion and Bolton (1996) is a dynamic model of occupational choice with limited information and incentives, as in a classic moral hazard problem. Each household has 9

Since income and occupational choice are jointly determined, we can also use income data together with information on the household’s entrepreneurial status to estimate the joint likelihood of observing the household’s entrepreneurial status together with a particular income. See the appendix for further details.

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a technology for producing output q from its own effort z and from capital k. This technology is written P (q|z, k), the probability of achieving output q given effort z and capital k. When we are explicit about the impact of talent on the probability of success we use the notation pe(q|z, k, θ). Effort is unobservable. Aghion and Bolton suppose that entrepreneurs have access to one large indivisible project that requires investment of one unit of capital, k = 1. In our generalization of their model, capital is allowed to take on a variety of values in the unit interval, [0, 1]. Output q can take on two values, namely q = θ¯ q , which corresponds to success and occurs with positive probability, and q = 0, which is equivalent to bankruptcy and occurs with the remaining probability. As above, the parameter θ refers to entrepreneurial talent. Output can be costlessly observed by everyone. We write this technology in terms of the probability of success: P (q = θ¯ q |z, k > 0) = z 1−α kα

(16)

This is a slight generalization of the original Aghion and Bolton (1996) model where α is assumed to be equal to zero, making the probability of success linear in effort, z. More generally, effort z is assumed to lie in the interval [0, 1]. Again, the key feature of the model is that effort, z, is known only to the entrepreneur and cannot be observed by outsiders, leading to a classic moral hazard problem. When k=0, the firm is not capitalized and we interpret this to mean that the household works in the wage sector or in subsistence agriculture. Earnings are assumed to be stochastic and to depend on effort. Earnings, w, are equal to q¯ with probability z and equal to zero with the residual probability. This is a generalization of Aghion and Bolton (1996) and of Lehnert (1999) who assume that wages are equal to zero. In other words, they assume that workers are completely unproductive or “idle”, to use Aghion and Bolton’s phrase. Although the parameter q¯ is common to both workers and firms, talent, θ, can make either entrepreneurship or wage work the more productive occupation. In this model, as in the limited commitment model, talent is the relative ability in entrepreneurship. In the moral hazard model, talent is assumed to be distributed according to the following density function: h(θ) = 2m(θ − κ1 ) + 1 − m (17) with support [κ1 , κ1 + 1], where κ1 will be endogenously determined. When m is equal to zero, talent is uniformly distributed in the population. When m is greater than zero, the talent distribution is skewed toward high talent households and when m is negative, the talent distribution is concentrated among low talent households. We assume that although lenders cannot observe effort, they do observe talent (and wealth) and are able to design contracts that take talent into account. Incorporating talent into the model is another generalization of Aghion and Bolton (1996) and Lehnert (1999) who do not consider a role for entrepreneurial talent. Households are assumed to derive utility from their own consumption and disutility

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from effort:

c1−γ 1 (1 − z)1−γ 2 U(c, z) = +κ 1 − γ1 1 − γ2

(18)

The parameter γ 1 determines the degree of risk aversion and represents a further generalization of Aghion and Bolton and Lehnert who assume risk neutrality. If γ 1 is equal to zero, then households are risk neutral. The parameters κ and γ 2 determine the relative disutility of effort and the degree of aversion to variation in effort. This is a generalization of the quadratic disutility of effort that is used in Aghion and Bolton. Households are assumed to invest their wealth in a bank or in a financial institution, which might lend funds back to the household for investment. The control of the deposit might be interpreted as collateral, as in the limited commitment model, but in the moral hazard model the deposit plays a different role because there is no default, that is agents are committed to carry out the terms of the contract. The portion of the deposit amount net of repayment that will be recovered at the end of the loan period is dictated by incentives. The interest rate that the bank pays for outside funds is the exogenous interest rate, r. Again, we set the gross interest rate equal to 1.25, which is the average interest rate in the data. The return that the bank will earn on these loans is not guaranteed and will depend on the difference between the firm’s revenue θ¯ q and the firm owner’s compensation (or consumption), c. By construction, the firm will be unable to repay anything from production in the event of bankruptcy. However, in our generalized model it is possible that the bank will make a payment to the household in this event, providing some insurance against loss. In the case of success, the transfer from the household to the bank can be interpreted as both a repayment of the loan and an insurance premium. The implicit interest rate will depend on payments made to the bank in the event of success, on the compensation paid to the household in the event of failure, and on the endogenously determined level of effort, z, which will in turn effect the probability of success. Since the bank is required to break-even, there is a sense in which riskier customers repay more in the event of success, but this effect is dampened by insurance. In this model, the bank is assumed to be able to observe the wealth, A, and the talent, θ, of households and will maximize expected profits as a function of customers’ wealth and talent characteristics. However, we assume that competition will force bank profits to zero in equilibrium, so that we can think of the bank as maximizing the expected utility of customers as a function of their wealth and talent, subject to a zeroprofit constraint. In contrast to the limited commitment model, in the moral hazard model the demand and the supply of credit will vary in a potentially interesting way with entrepreneurial talent, and with other parameters of the utility and production functions. The focus of our model is on the credit-compensation contract. In relatively simple notation, we let c(q) denote the consumption of the borrower when observed output is q. Of course, q − c(q) is therefore the repayment to the bank. Thus, the consumption schedule will induce an effort z and investment in the firm k is fully observed and assigned. Thus a contract is a triplet (c(q), z, k). The incentive to take effort z as 11

distinct from some other effort level z 0 , must satisfy the incentive constraint: X X > U[(c(q), z]P (q|z, k) = U[(c(q), z 0 ]P (q|z 0 , k) for all z, z 0 . q

(19)

q

Finally, the bank is required to cover its costs and given our assumption of perfect competition this will mean that the net repayment from the borrower must be equal to the outside cost of borrowed funds, k − A, that is: X [q − c(q)]P (q|z, k) = r(k − A). (20) q

For computational purposes, we write this as the probability that a particular consumption, c, output, q, effort, z, and investment level, k, are assigned as a function of wealth and talent: π(c, q, z, k|A, θ). This allows households to be assigned a particular deterministic level of investment, k, and to be recommended a particular level of effort, z, which will be carried out due to the effect of the incentive constraints. Household consumption, c, will be assigned as a function of output, q. There is no other randomness in consumption. The program to determine whether the household will become an entrepreneur and to determine the form of the incentive-constrained credit/insurance contract involves maximizing household utility (21), subject to the production function (22), a zero profit condition for the bank (23), incentive compatibility for the household (24), bearing in mind the choice object is formulated as a probability measure or lottery (25). Specifically: Program 1: max

π(c,q,z,k|A,θ)

s.t. X c

X

c,q,z,k

X

>

c,q

X

X

c,q,z,k

π(c, q, z, k|A, θ)

c,q

X

π(c, q, z, k|A, θ) for all q, z, k

(22)

c,q

π(c, q, z, k|A, θ)(q − c) = r

π(c, q, z, k|A, θ)U(c, z) =

(21)

π(c, q, z, k|A, θ)U (c, z)

π(c, q, z, k|A, θ) = pe(q|z, k, θ) c,q,z,k

X

X

π(c, q, z, k|A, θ)(k − A)

(23)

pe(q|z 0 , k, θ) U(c, z 0 )∀z, z 0 and k > 0 pe(q|z, k, θ)

(24)

>

π(c, q, z, k|A, θ) = 1 and each π(c, q, z, k|A, θ) = 0,

c,q,z,k

12

(25)

where the first constraint ensures that pe() is embedded in the contract π(), and that pe() is allowed to vary depending on whether k = 0 (wage-workers) or k > 0 (entrepreneurs), the second constraint is the zero profit condition for the bank, the third is the incentive compatibility constraint for entrepreneurs and the fourth is a constraint that guarantees that probabilities sum to one and are positive. Even if talent were observed by the econometrician, this mechanism design setup generates a potentially nontrivial probability of becoming an entrepreneur as a function of wealth, A, and talent, θ. For example, as in Lehnert (1999), indivisibilities in investment levels and the moral hazard problem can make indirect utility a convex function of wealth. Given talent, θ, one can solve the above program and determine the ex ante utility of becoming an entrepreneur, at various levels of investment, k, and effort, z, and the ex ante utility of working for wages at various levels of effort, all for various levels of wealth, subject to the constraint that the bank breaks even. The outer envelope of the ex ante utility determined by this choice between entrepreneurship and wage work is not concave in wealth, even when effort can take on a continuum of values. However, an ex ante lottery in wealth can restore concavity. In a simplified moral hazard model, where investment is assumed to be indivisible and all firms are capitalized at k = 1, the likelihood of starting a firm is zero for households with low wealth and low talent. For high wealth, high talent households, the probability of starting a firm is virtually one. All entrepreneurs who have wealth, A, less than one must borrow. However, as wealth increases, the need for borrowed funds will decrease, and it is possible that effort will be monotonically increasing in wealth, as it is in Aghion and Bolton and Lehnert. Indeed, in Aghion and Bolton and Lehnert, households who have wealth in excess of one will invest all of their surplus funds in the market. These households will not rely on borrowed funds at all. When there is no risk aversion, and therefore no demand for insurance, these households will experience no disincentive effect from the incomplete credit market. These high wealth households will chose their own effort level optimally and run firms that are not credit constrained. Although this is a simplification of the model that we estimate, it delivers the key intuition for the general model. Low wealth borrowers have little incentive to work because the bank would take so much of their project returns when the project is successful. The only way the bank can make up for this is by raising the effective interest rate and at sufficiently low wealth levels the market will clear with no borrowing at all. A firm will be constrained by the moral hazard effect in credit markets when the incentive constraint on effort is binding. In other words, firms will be constrained if they have an incentive to shirk, and this incentive in turn influences the informationconstrained credit contract. In our model, where agents are risk averse and will value insurance, the incentive constraint will generally be binding.10 Note in particular that if effort is equal to zero, then the firm will be completely unproductive. Therefore effort 10

Recall that in Aghion and Bolton (1996) and in Lehnert (1999) agents are risk neutral.

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will be assigned (or induced) to be greater than zero, and this is what makes it likely that the incentive constraint will bind. Figure 3 describes an example solution for our moral hazard model. Figure 3 shows the probability of starting a firm as a function of wealth, A, and talent, θ.11 At relatively low levels of wealth, the probability of becoming an entrepreneur is increasing in wealth and talent. Other things equal, however, high wealth households would prefer to exert little effort. Since wealthy households prefer to enjoy more leisure, the probability of becoming an entrepreneur can actually decline with wealth. In most examples, however, the probability of being an entrepreneur does not decline with wealth, though entrepreneurial effort will decline with wealth. Investment levels typically decline with wealth as well, since investment and effort are complements in affecting the probability of project success. When investment declines, the demand for borrowed funds tends to go to zero relatively quickly. Moreover, since wealthy entrepreneurs do not have to work as hard, the incentive constraint is less binding for them. In the general moral hazard model, therefore, the wealth effect may enhance the tendency for self-financing to increase with wealth and for complaints of financial constraints to decline with wealth. At very low levels of wealth, on the other hand, an entrepreneurial household would have to pay back so much of the proceeds of a successful project that it has little incentive to take effort. As wealth increases, effort can increase and because capital and effort are complementary, the demand for investment could grow at a rate exceeding wealth, and thus it is possible for credit to increase with wealth as well. This can happen in numerical examples, but only infrequently and only over a relatively narrow range at the very low end of the wealth distribution.12 We can evaluate the empirical relevance of the moral hazard model by maximizing the following log likelihood equation which describes the probability that a household will become an entrepreneur as a function of wealth and the parameters of the model, where the parameter vector, ψ, is equal to (γ 1 , γ 2 , κ, q, α, m, κ1 ). 1X Ei ln H(Ai |ψ) + (1 − Ei ) ln(1 − H(Ai |ψ)) Ln (ψ) = n i=1 n

The variable Ai is the wealth of agent i and H(Ai |ψ) is the probability of being an entrepreneur generated by the model for an agent with wealth Ai integrated over the talent distribution. The algorithm for computing solutions is to fix the parameters of preferences and technology (γ 1 , γ 2, κ, q,α), compute the solution to the linear code for fixed A and θ, derive the endogenous likelihood of entrepreneurship, π(k >)|A, θ), integrate via Gauss 11

This figure shows the probability of becoming an entrepreneur as a function of wealth and talent for the sub-sample of households that report that they have used financial institutions in the past. The domain is restricted to the region where there is a positive probability of becoming an entrepreneur. 12 In the various stratifications of the Thai data that we study, investment tends to be invariant with wealth and so credit always declines with wealth.

14

Legendre approximation over a supposed distribution of talent (recall that the distribution of θ depends on parameters (m, κ1 ) and is unobserved by the econometrician), and then specify the likelihood that the econometrician will see the transition from wage work to entrepreneurship at observed beginning of period wealth, A. In practice, the space of possible wealths is approximated by a log grid with a sparse number of points, and cubic spline interpolation delivers the value at all wealths. The overall likelihood is then maximized by choice of parameters.

3

Data and Background Information

In this section we briefly describe some of the salient features of the data. The reader who is interested in more details is referred to Paulson and Townsend (2002). The data we analyze cover four provinces in Thailand. Two of the provinces are in the Central region and are relatively close to Bangkok. The other two provinces are much further from Bangkok and are located in the relatively poor northeastern region. The contrast between the survey areas is deliberate and has obvious advantages. Within each province a stratified random sample of twelve geographic areas (tambons) was selected.13 The stratification ensured that the sample was ecologically diverse. In each tambon, four villages were selected at random. In each village, a random sample of fifteen households was interviewed.

3.1

Characteristics of the Data

The businesses we study are quite varied and include shops and restaurants, trading activities, raising shrimp or livestock and the provision of construction or transportation services.14 While there are many different types of businesses, shrimp and/or fish raising, shops and trade account for 70% of the businesses in the whole sample and make up a similar percentage of the businesses in each region. Median initial investment in the households business varies substantially with business type. Despite this variation, the median initial investment appears to be relatively similar across regions for the same type of business, particularly for the most common business types. For example, the median investment in a shop is 16,000 baht in both the Northeast and the central region. In the Northeast, the median initial investment in trade is 21,000 baht compared to 23,000 baht in the central region.15 For future reference, note that the average annual income in Thailand in 1996 is 105,125 baht, or roughly $4,200. 13

A tambon typically includes 10 - 12 villages. We are aware that some farms are run like businesses and that the dividing line between businesses and farms is not always clear. However, farming, particularly of rice and other crops, can be thought of as a “default” career choice. An active decision to do something else has been taken by the households that we define to be business households. We experimented with different alternative categorizations and found that the one we use has content. See the discussion of the structural estimation of the limited commitment section for more details. 15 Median investment in shrimp and/or fish does differ depending on the region: in the Northeast it is 9,000 baht compared to 51,000 baht in the central region. This is because shrimp farming, which 14

15

Most business households run only a single business and rely very heavily on family workers. Only 10% of the businesses paid anyone for work during the year prior to the survey.16 More than 60% of the businesses were established in the past five years. In the empirical work we restrict our attention to these businesses.17 Households rely heavily on savings (either in the form of cash or through asset sales) to fund initial investment in their businesses. Approximately 60% of the total initial investment in household businesses comes from savings. Loans from commercial banks account for about 9% of total business investment and the Bank for Agriculture and Agricultural Cooperatives (BAAC) accounts for another 7%. In the Northeast, the BAAC plays a larger role compared to commercial banks, and in the central region the opposite is true. Compared to non-business households, entrepreneurial households are a bit younger and more educated. In addition, their current median income is about twice that of nonbusiness households. Business households are wealthier both at the time of the survey as well as prior to starting a business compared to their non-business counterparts. In addition, business households are more likely to be customers of commercial banks and the BAAC, and to participate in village financial institutions. Table 1summarizes the data that are used in the structural maximum likelihood estimates (wealth six years prior to the survey, whether the household has started a business in the past five years and, for the limited commitment model only, the years of schooling of the household head) for the whole sample and for each of the sub-samples that are analyzed. The wealth variable that we use is the value six years prior to the survey of the household, agricultural and land assets that the household owned then. This corresponds to beginning of period wealth, that is, wealth prior to choosing an occupation. We do not include the value of business assets that the household may have owned six years ago. Table 1 also summarizes the data that are used in the reduced form and nonparametric analysis below. In addition to using data on past wealth and entrepreneurial status, this analysis makes use of data on the demographic characteristics of the head of the household (age, age-squared, years of schooling) and on characteristics of the household (the number of adult males, adult females and children in the household). All of these variables are measured at the time of the survey. We also use data on net financial savings at the time of the survey. Net financial savings is equal to the financial savings of the household plus the value of loans that are owed to requires substantial initial investment, is concentrated in the central region, while fish farms are more important in the Northeast. 16 This means that the set of entrepreneurial firms is unlikely to be very affected by the case where wealthy, but untalented, households hire poor, but talented, managers to run their firms. 17 Although these results are not presented in the paper, we have also looked at businesses that were established in the past 10 years. This group includes 83% of the businesses in the sample. None of the results are sensitive to which group of businesses we examine. The decision to focus on businesses that were started in the past 5 years was the result of weighing the benefit of having more accurate measures of beginning of period wealth against the cost of eliminating the 224 households that start businesses more than five years ago.

16

them minus current debt. We also examine the impact of credit market availability by including measures of whether or not the household was a member or a customer of various financial institutions in the past.

4

Structural Maximum Likelihood Estimation

In this section we take the structure of the models literally and see how well each model can fit the observed pattern of who becomes an entrepreneur as a function of wealth and imputed distribution of entrepreneurial talent in the Thai data.18 Each structural maximum likelihood estimation produces a measure of the likelihood that a given model could have generated the patterns observed in the Thai data. In addition, the estimation delivers the maximized values of the model parameters. In this section, we also report on how these parameters vary across subsets of the data. This allows us to explore whether some of the restrictions that the models put on the data are reasonable. For example, we consider whether there is evidence that the parameters of the talent distribution are similar across regions. One advantage of the structural models is that they do not require us to come up with a proxy for entrepreneurial talent. Instead, the structural estimation produces parameters that describe the underlying distribution of talent in the data, given the assumptions of the model and information on who starts a business, wealth and, in the case of the limited commitment model, education.

4.1

Structural Estimation of the Limited Commitment Model

Structural maximum likelihood estimates of the limited commitment model are summarized in Tables 2A and B. The model comparison tests use the estimates that do not rely on income data (Table 2A), since the moral hazard model does not make use of these data either. The estimates with income data (Table 2B) allow us to compare the parameter estimates for Thailand with the ones that Evans and Jovanovic find using U.S. data. These results are discussed below. 4.1.1

Estimates without Income Data

Although some parameters have rather large standard errors, the structural estimates of the limited commitment model produce fairly reasonable parameter values. For example, the production parameter α is estimated to be 0.68 for the whole sample. 18 In the estimates of the limited commitment model, the talent distribution is also allowed to depend on the distribution of wealth and the correlation of wealth and education. The estimation of the moral hazard model does not use data on education. Instead the distribution of talent in the data is inferred from the pattern of who becomes an entrepreneur by wealth. We also study how the talent parameters vary with wealth by examining how they change when we estimate the model for sub-samples of the data that are stratified by wealth and/or region.

17

This means that a 10% increase in business investment would lead to a 6.8% increase in revenue. The productivity parameter, α, is higher among low wealth households.19 The average of log talent, as captured by δ 0 , is estimated to be 2.33 for the whole sample. Average talent tends to be higher in the central region compared to northeastern and poorer households, although the standard errors are quite large. In addition, average talent tends to increase with stratifications which are increasing in wealth. Average talent does not vary significantly, however, when we stratify by wealth within a region. Related, the parameter estimates for δ 1 also indicate that there is some correlation between talent and wealth. This parameter is estimated to be 0.05 for the whole sample, so a 10% increase in wealth would be associated with an increase in average talent of 0.5 percent. However the relationship between wealth and talent is not necessarily uniform across wealth levels. The point estimates of δ 1 increase across wealth stratifications (and are even negative for low wealth households), although again the estimates are imprecise, especially for low wealth households. The parameter that relates years of schooling to entrepreneurial talent, δ 2 , is also estimated to be 0.05. This means that each additional year of schooling is associated with an increase in average talent of 5 percent. This suggests that education may be a reasonable indicator of entrepreneurial talent in Thailand. Entrepreneurial talent appears to be more sensitive to formal education in the Northeast compared to the central region, though the difference is only marginally significant. An additional year of schooling in the Northeast raises average talent by 7 percent, while the same increase in education in the central region leads to close to a 3 percent increase in entrepreneurial talent.20 Interestingly, the model delivers the same relationship between talent and education when we stratify by wealth. Within a region, δ 2 does not appear to vary significantly when we also stratify by wealth. The model implies that the parameter that measures the degree of financing constraints, λ, should lie between one and two. For the whole sample, this parameter is not precisely estimated. This is because λ is pinned down by entrepreneurial households who have wealth below A∗ , approximately 20 households in the whole sample. However, for higher wealth stratifications λ is measured more precisely and the parameter values are quite reasonable. In the stratifications that restrict attention to households with wealth greater than the median for the whole sample, the Northeast and the central region, the maximized value of the parameter λ ranges from 1.5 to 3.0, which means that the maximum that can be borrowed ranges from one-half to twice the value of household wealth. The empirical counterpart to λ would be the ratio of debt to wealth for constrained 19

This does not necessarily mean that the production function itself varies with wealth. Rather, it suggests that, in general, constrained credit keeps these businesses operating at a small scale with high marginal returns. 20 This is consistent with the reduced form estimates that indicate that years of schooling has a significant impact on whether a household will start a business in the Northeast, but not in the central region.

18

households. In practice, we can examine the loan to collateral ratio for outstanding loans. These values are typically quite low and very often the value of the loan is significantly less than the value of the collateral used to secure it.21 This would suggest that λ is less than one. On the other hand, there are also many unsecured loans in the data. That is, there are many loans where λ would appear to be infinite. The data suggest that the lower bound for the empirical counterpart to λ lies between 0.37 and 0.48. We interpret this as a lower bound, because it takes into account all loans in the data, not just loans made to households who reported that they were constrained.22 To further address this issue, we have also estimated versions of the limited commitment model where the value of λ is fixed at 2 (i.e. assuming households can borrow an amount equal to their own wealth). In these runs, the other parameter values are similar to the values that are obtained when λ is also estimated.23 Across the stratifications, the limited commitment model fits the data better in the Northeast and among low wealth households. 4.1.2

Robustness Checks

Comparison of Thai Results with U.S. Results When we follow the literature and use income data to estimate the model as well, standard errors are reduced and we can compare the parameter values for Thailand with those that Evans and Jovanovic (1989) found in their study of occupation choice in the U.S., which used data from the National Longitudinal Survey of Youth The results for Thailand that make use of income data are reported in Table 2B. Evans and Jovanovic produce estimates of α that range from 0.22 to 0.39. The estimate of α for Thailand is within this range at 0.31. For Thailand, the point estimate of λ for the whole sample is 7.22, with a standard error of 24.52. This means that households would be able to borrow an amount equal to approximately six times the value of their wealth. Evans and Jovanovic (1989) estimate λ to be between 1.4 and 1.7. If we use data only from households with wealth above the median, the estimate of λ falls to 2.0, and it is measured quite precisely. 21

Land is the most important source of collateral (and wealth) and indivisibilities in land may account for some of the very low loan to collateral ratios that we see. For example, if a household wishes to borrow 10,000 baht and has a plot of land worth 100,000 baht that they use as collateral, the loan to collateral ratio will be 0.1. 22 The empirical counterpart to λ was found by calculating the median collateral to loan value for secured loans by each type of lender. By using collateral to loan values rather than loan to collateral values we avoid the problem of infinite loan to collateral values for unsecured loans. For each lender type, the percentage of funds lent without collateral was then calculated. The collateral to loan figure for each lender type was found by multiplying the median collateral to loan figure for secured loans by the percentage of funds that were lent with collateral. The collateral to loan figure for the whole sample was found by weighting the figures for each type of lender by the percentage of funds lent by that lender type. This figure was then inverted to arrive at the empirical counterpart to λ. 23 These estimates are available from the authors.

19

The Thai talent parameters are not directly comparable with the U.S. estimates because the model we estimate allows talent to be correlated with education and Evans and Jovanovic do not. Nonetheless, Evans and Jovanovic find that δ 0 is equal to 2.34, while we estimated this parameter to be 5.98. The parameter that relates wealth to talent, δ 1 , is estimated to be -0.12 in Evans and Jovanovic. For whole sample, we estimate that δ 1 is 0.06, although we also get negative values for some stratifications. Identification of Business Households We return finally to the issue of whether our assignment of entrepreneurial and non-entrepreneurial status to the sample households has content. We evaluate this using simulations of the limited commitment model, because this model is relatively speedy to estimate numerically. We construct 100 samples of the Thai data where entrepreneurial status is randomly assigned, ignoring the actual occupation of the household. The overall fraction of randomly assigned entrepreneurs is fixed at the proportion of business households actually observed in the original data. The overall fit of the limited commitment model deteriorates substantially when it is estimated using the simulated data.

4.2

Structural Estimation of the Moral Hazard Model

We estimate two versions of the moral hazard model. The first version allows households to be risk averse. The results of this estimation are summarized in Table 2C. The second version assumes that households are risk neutral. The results of this estimation can be found in Table 2D. The risk-neutral version of the moral hazard model is estimated as a check to make sure that the results of the model comparison exercises are not driven by the fact that the moral hazard model allows households to be risk averse while the limited commitment model assumes that households are risk neutral. The risk-neutral estimates also provide a check on the stability of the parameter estimates. 4.2.1

Estimates with Risk Aversion

Looking first at the estimates of the model which allow for risk aversion (Table 2C), we see that relative risk aversion moves around depending on the stratification.24 In the Central region, γ 1 is close to zero, suggesting that households are close to risk neutral. In the Northeast, utility over consumption is close to the log case as γ 1 is 1.06. For the whole sample, γ 1 takes on the intermediate value of 0.49. There is no significant difference in risk aversion when we compare households with below median wealth to households with above median wealth. The disutility of effort, κ, is measured at 0.92 for the whole sample and the curvature parameter on effort, γ 2 , is estimated to be 1.51. The curvature parameter is higher in the relatively wealthy central region compared to the poorer Northeast but the reverse is true for the disutility of effort parameter. 24

Recall that for any given stratification of the data, the model imposes constant relative risk aversion and hence decreasing absolute risk aversion with wealth.

20

The variation in preference parameters with wealth and with region make it clear that wealth effects have the potential to alter the demand for credit. Since entrepreneurs need to work particularly hard when effort and investment are complements and in addition they need to assume risks because of the binding nature of the incentive constraint, entrepreneurship may be distasteful for wealthy households. This can lead to the demand for credit declining when wealth is increased. In principal the demand for credit might increase with wealth at the low end of the wealth distribution, as is predicted by the limited commitment model. However, this does not happen at the estimated parameter values for the samples we study. In the estimates of the moral hazard model that are highlighted in Table 2C, wealth is constrained to lie between 0 and 1, as is investment. The results are not driven by the assumption that maximum investment is equal to maximum wealth. In other estimates (not included here), we have constrained wealth to lie between 0 and 1/2 and let investment range from 0 to 1. Optimal investment is invariant to wealth in these estimates as well. The productivity parameter, α, is similar in the Northeast and the central regions. In general, stratifications with high wealth households deliver high α’s, especially in the Central region. By comparison, the productivity parameter in the limited commitment model was highest for low wealth households. However, in the moral hazard model the standard errors on the productivity parameter are fairly large, so the differences across wealth levels are not statistically significant. We can use the parameter estimates for α together with the predicted values for effort and investment to calculate the probability that a business will be successful. The probability of business success for the whole sample is 64%. This seems like a reasonable value given a four-year success rate for a relatively wealthy group of U.S. entrepreneurs of 72% (see Holtz-Eakin, Joulfian and Rosen, 1994). The value of output in the event of success, q, is also not very precisely measured. Moral hazard is important when there is disutility from effort and when production requires effort. These conditions are met when κ is not equal to zero and when α is not equal to one. The parameter estimates clearly indicate that κ is significantly different from zero for all of the subsamples except households with wealth below the median overall and for the Central region. While the point estimates for α suggest that effort is an important component of output, the large standard errors mean we cannot reject the possibility that α is in fact one and that effort is not an important component in production. However, the small businesses we study use relatively little capital and output is very dependent on labor effort. In the moral hazard model, two parameters are relevant for describing the distribution of talent in the economy, m and κ1 . The parameter m describes the skewness of the talent distribution and κ1 describes the lower limit of the range of the talent distribution. For the whole sample and the northeast, m is maximized at 0.00, which means that the talent distribution is virtually uniform. In contrast the parameter m is 2.45 for the central region, indicating a substantial tilt towards talented households. The moral hazard model fits the data best for low wealth households in the North21

east. It also does well for all households in the Northeast. 4.2.2

Estimates with Risk Neutrality

The standard errors on the parameter which measures the disutility of effort, κ, are much higher when risk neutrality is assumed (see Table 2D). For the whole sample, the point estimate of this parameter has a value of 0.37, somewhat lower than when risk aversion was allowed. The curvature parameter on effort, γ 2 , is estimated to be 0.70, also somewhat lower than in the risk aversion case. Given the large standard errors, the risk neutral results provide no evidence that these parameters vary systematically with region or with wealth. Estimates of the productivity parameter, α, range from 0.06 in the Northeast to 0.84 for the whole sample. However, as was the case for the estimates with risk aversion, the standard errors are quite large. Similarly, the value of output in the event of success, q, is not very precisely measured, although its point estimates are lower when we assume risk neutrality. The skewness parameter, m, is estimated to be 3.8 for the risk neutral case, which indicates a substantial tilt toward talented households for this model. In contrast, the distribution of talent was practically uniform in the estimates that allow for risk aversion. However the estimates of m for the regional stratifications are not statistically different across the risk specifications. The parameter that pins down the support of the talent distribution, κ1 , varies substantially across the two models. However, the standard errors are quite large and we cannot reject the possibility that κ1 is the same across the risk averse and the risk neutral versions of the model. Like the estimates that allow for risk aversion, the risk neutral estimates fit the data best for poor households in the Northeast.

5

Comparison of the Models

In this section we compare the models using two complementary techniques. First we try to distinguish between the models using formal comparisons based on the structural estimates discussed above. Next, we return to non-parametric and reduced form techniques to evaluate the implications that separate the models. It is important to keep in mind that while the structural estimation imposes a number of restrictions on the data, it relies only on a very limited subset of the available data: past wealth, the entrepreneurial status of the household, and, in the case of the limited commitment model, the years of schooling of the household head. In contrast, the non-parametric estimates impose almost no structure on relationships between the key variables of interest. The non-parametric and reduced form estimates also make use of the detailed information about the households and the businesses from the survey data. While the reduced form estimates impose a particular functional form on the relationship between the dependent and independent variables, the functional form assumptions are 22

more flexible than those imposed in the structural estimation. In particular, they are independent of the assumptions made in the structural models regarding production functions, utility functions and the nature of the financial constraint. In addition, they are also completely independent of the parameter estimates generated by the structural models. We use non-parametric and reduced form techniques to examine the implications of the models for relationships between variables that were not explicitly considered in the structural estimation, namely the relationship between credit and wealth.

5.1

Structural Evidence

In this sub-section, we provide formal tests of which of the candidate models best fit the whole sample and the various sub-samples of the data that were described earlier. The models are compared using the Vuong likelihood ratio test for strictly non-nested models (see Vuong 1989). One advantage of the Vuong test is that it does not require either model to be correctly specified. This feature is appealing given the necessity of studying models that are much simpler than reality. The null hypothesis is that the two models are equally near the actual data generating process and the Vuong test delivers an asymptotic test statistic that measures the weight of the evidence in favor of one model or the other.25 The likelihood ratio test statistic that Vuong proposes is appropriate regardless of whether the two models are completely non-nested, overlapping or nested. However, the asymptotic distribution of the test statistic depends on the relationship between the models. The models that we study are all non-nested except in the extreme case of parameter values which lead to degenerate distributions, i.e. all households start businesses or no households start businesses regardless of wealth. When the models are strictly non-nested, Vuong’s likelihood ratio test statistic is normally distributed. The results of the model comparison tests are provided in Table 3. We base our main conclusions on a comparison of the limited commitment model with the version of the moral hazard model that allows for risk aversion. We also consider whether the findings are robust to assuming households are risk neutral instead. In what appears to be an anomaly, all of the models fit the data better when there are very few businesses in the sub-sample under consideration: low wealth households, the Northeast, and low wealth households in the Northeast. This is a statistical result, however. When there is very little variation in the data, the structural estimates can produce parameter values that will lead to very few business without penalty. In any case, our main concern is the relative performance of the models for a given sample. 25

One could use the same procedure where the null hypothesis was that one model was closer to the actual data generating process. The test statistic would remain the same, however, the critical values for rejecting the null would of course change.

23

5.1.1

Limited Commitment v. Moral Hazard with Risk Aversion

In the top panel of Table 3, we compare the limited commitment model with the moral hazard model with risk aversion. An examination of the bilateral model comparisons allows us to determine which of the models does the best job overall and for various subsamples of the data. The findings are summarized in the following table. Sample Model That Fits the Data Best Whole Sample Moral Hazard Central Moral Hazard Central, Wealth > Median Moral Hazard Wealth < Median Limited Commitment Overall, the moral hazard model fits the data best. Specifically, this model is closer to the actual process generating the wealth and occupation-choice data than the limited commitment model for the whole sample. The moral hazard model also fits the data best in the central region, and more specifically in the higher-than-median wealth category of the central region. However, for households with wealth below the median for the whole sample, the limited commitment model dominates.26 It is in precisely this subsample that the parameter estimates from the moral hazard model suggest that moral hazard may not be important because effort may not be costly to households, in the sense that κ, the disutility of effort parameter, cannot be significantly distinguished from zero. Figures 4A - C compare the likelihood of starting a business as a function of wealth at the maximized parameter values produced by each model. These graphs also include non-parametric estimates of the likelihood of starting a business as a function of wealth. The non-parametric estimates were produced using the same techniques as Figure 1 (see footnote 5 for details). Figure 4A reports the results for the whole sample and figures B and C report the findings for households with wealth below the median and for households with wealth greater than the median, respectively. These graphs are useful for gaining a visual understanding of why one model out-performs another. For the whole sample, the estimates produced by the moral hazard models come closest to the non-parametric estimates (see Figure 4A). The limited commitment model underestimates the fraction of business households over the bulk of the wealth distribution. The moral hazard models also underpredict the fraction of business households, but only at high wealth levels. For households with wealth below the median, the limited commitment model and the non-parametric estimates are virtually identical over the vast majority of the wealth distribution (see Figure 4B). In contrast, the moral hazard model with risk aversion overstates the fraction of business households at low wealth levels and understates at higher wealth levels. The risk neutral version of the moral hazard model predicts a higher percentage of business households compared to the non-parametric estimates. 26

The limited commitment model also fits the data best in the Northeast when per-capita wealth rather than total household wealth is used.

24

For households with wealth greater than the median (see Figure 4C), the Vuong model comparison test revealed that the limited commitment and the moral hazard models were equally close to the underlying process generating the data, and the figure reveals that the predicted probability of starting a business from the various structural estimates and the non-parametric estimates are very close to one another, particularly at relatively low levels of wealth. It is important to keep in mind in that the probability of starting a business as a function of wealth produced by the structural estimates also includes the impact of integrating out over the talent distribution. This effect accounts for the "wiggles" that appear in the graphs for the moral hazard model with risk aversion in Figure 4B and C. 5.1.2

Robustness

Even when we penalize the moral hazard model by setting risk aversion equal to zero, allowing the financial contract to take into account incentives but not risk sharing, we see that the moral hazard model is closer to the data in the central region and does marginally better than the limited commitment model for the whole sample (significance level of 16% for a two-sided test). However, the limited commitment model continues to do better for some subsamples of the data: households with wealth below the median and low wealth households in the central region. For households in the Northeast and households with below median wealth in the Northeast, the limited commitment model does marginally better than the moral hazard model with risk neutrality. The significance levels range from 13% to 15% for a two-sided test. The following table summarizes our findings: Sample Model That Fits the Data Best Whole Sample Moral Hazard* Central Moral Hazard Central: Wealth < Median Limited Commitment Northeast Limited Commitment* Northeast: Wealth < Median Limited Commitment* Wealth < Median Limited Commitment ∗significant at 90% or better for a one-sided test The overall findings are thus very similar. This conclusion is reinforced by a direct comparison of the two versions of the moral hazard models, which reveals that the performance of the models cannot be statistically distinguished for most of the stratifications we consider, with the exception of the whole sample and low-wealth households in the central region.27 The conclusion that we draw from this exercise is that the financial market imperfection varies with wealth. For low wealth households and households in the Northeast, 27

These results are available from the authors.

25

the dominant problem is limited commitment, that is, lenders tend to design financial contracts that relate the maximum amount that can be borrowed to a fixed multiple of total household wealth. For wealthier households and households in the central region, the main problem is designing financial contracts that provide appropriate incentives to the borrower when effort is unobservable.

5.2

Non-parametric and Reduced Form Evidence

In addition to comparing the models based on the structural evidence about who will start a business as a function of wealth and talent, we can also use non-parametric and reduced form techniques which make use of additional variables to try to distinguish the models. While none of the findings presented here is definitive on its own, taken together they reinforce the findings from the structural model comparisons: at low levels of wealth, the limited commitment model seems to fit best and at higher levels of wealth the implications of the moral hazard model are favored. The limited commitment and the moral hazard models make different predictions about how borrowing will change with wealth, particularly for constrained business owners. In the limited commitment model, constrained business owners have borrowed up to the maximum multiple of wealth allowed, so increases in wealth will necessarily lead to increased borrowing for these businesses. In the standard moral hazard model, the opposite is true: borrowing will decrease with wealth for constrained business owners. Business owners can relax the incentive compatibility constraint by borrowing less. The parameter values resulting from the structural maximum likelihood estimation of our version of the moral hazard model indicate that the same is generally true for this model as well.28 If investment increases at the same rate or more slowly than wealth does, then borrowing will decrease with wealth. This effect is reinforced if investment and effort are complements so that decreases in effort as wealth increases lead to decreases in investment as well. 5.2.1

Non-parametric Evidence

We use non-parametric estimates to investigate the relationship between current net savings and past wealth in Figure 5 for the central region (top panel) and the Northeast (bottom panel). Figure 5 was produced using the same non-parametric techniques that were used to create Figure 1. In the central region, net savings decreases slightly with past wealth at low levels of wealth for business households. However at higher levels of wealth, net savings increases with past wealth. This is what we would expect to happen if moral hazard were the key financial market imperfection, especially at high wealth levels. While the point estimates are quite striking, the standard errors are non-trivial. In the 28

For some sub-samples of the data, investment increases with wealth at very low levels of wealth. However, investment does not increase faster than wealth, so there is no tendency for borrowing to increase with wealth for these households.

26

Northeast, the standard error bands are especially large so none of the patterns for this region are observed with any degree of precision.29 The emerging view that wealthier households reduce debt when wealth increases, as predicted by the moral hazard model, and that poorer households increase debt when wealth increases, as predicted by the limited commitment model, is bolstered by a direct comparison of the wealth levels of households with and without debt in the Northeast and the central regions. In the Northeast, among debt-free business households, median wealth is 218,000 baht while for business households with debt, median wealth is more than twice as high, at 453,000 baht. This difference in median wealth between indebted business households and debt-free business households in the Northeast is significant at the 8.1% level. That Northeastern business households with no debt are significantly poorer than their counterparts who borrow contradicts the predictions of the moral hazard model. However, the evidence from the relatively wealthy central region is in favor of the moral hazard model. In the Central region, the median debt-free business household is wealthy (1,364,000) compared to the median business household who borrows (1,037,000) and the difference is significant at a 15% level. The same pattern is repeated with greater statistical significance in both regions when we restrict attention to constrained businesses. In addition, the evidence shows that household reports of being constrained are strongly associated with borrowing in the central region.30 In the moral hazard model borrowing is associated with a binding incentive compatibility constraint. In the Northeast, household reports of constraints do not have a strong association with borrowing. In the limited commitment model, only some households who borrow are at the credit limit. Specifically, in the central region, 73% of constrained businesses have outstanding debts compared with only 54% of unconstrained businesses. This difference is statis29

One might also be interested in the relationship between net savings and wealth for non-business households because, although the models assume that the alternative to starting a business is to use no capital and work for wages, in the data many non-business households do use capital in their farm activities and so they may be subject to the same financial market imperfections that are important for business households. We observe the same patterns in the data for non-business households. 30 Each respondent with a household business was asked, “If you could increase the size of your business, do you think it would be more profitable?”. We call the households who answered yes to this question “constrained”. The respondents appear to consider the availability of capital an important factor in whether their business is operating at an optimal scale. Sixty-four percent of the household businesses in the Northeast and 50% of the households in the Central region answered yes to this question. Those who answered yes were asked to name the main barriers to expanding the business. The most common answer, especially in the Northeast, was “not enough money to expand”. Seventy-two percent of the constrained businesses in the Northeast gave this answer, compared with 47% in the Central region. Scarce land and labor were also important reasons for not expanding, particularly in the Central region. Thirteen percent of constrained businesses in the Central region reported that they did not have enough land to expand and 15% reported that they did not have enough labor.

27

tically significant. Constrained businesses in the central region also have significantly more debt than unconstrained businesses (median of 50,000 baht v. median of 30,000 baht). This evidence favors the moral hazard model which predicts that everyone who borrows will be constrained. In the Northeast, roughly the same percentage of constrained and unconstrained businesses borrow, and borrowing levels are roughly the same across the two groups as well. 5.2.2

Parametric Evidence

Regression estimates of net savings for business households as function of various demographic controls and past wealth reveal that for the whole sample and for the central region, but not the Northeast, a 1,000,000 baht increase in wealth for a constrained business would increase net savings (equivalently decrease borrowing) by 48,000 baht (see Table 4A). This finding is consistent with the moral hazard model qualitatively if not quantitatively and echoes our findings that the moral hazard model outperforms the limited commitment model for the whole sample and the central region. Table 4B reports on probit estimates of whether an entrepreneurial household is a net borrower as a function of demographic controls, past use of various financial institutions, past wealth and whether or not the household reports being constrained. These results suggest that the limited commitment effect may dominate in the poorer northeastern region and that the moral hazard effect is prevalent in the central region. According to these estimates, being constrained has no significant effect on whether or not northeastern business households borrow. However, in the central region, households who report that they are constrained are 13% more likely to be net borrowers, as we might expect if private information problems dictated financial contracts. We have emphasized the different assumptions that the models make regarding the constraints on financial contracting. The models also differ somewhat in their assumptions about production, the distribution of talent and error terms. However, we do not think that these differences can explain the findings. While the results of the formal comparisons of the models do incorporate these auxiliary assumptions, all the non-parametric and reduced form evidence that we have just described are independent of the model assumptions regarding production functions, talent and errors, and these results also point to the nature of the financial market imperfection varying with wealth.

6

Conclusions and Discussion

The parametric, non-parametric, reduced form and structural evidence all indicate that both limited commitment and moral hazard are important. However, they operate at different wealth levels. For low wealth households, limited commitment is the major problem, and for high wealth households the dominant concern is moral hazard.31 31

We have emphasized the different assumptions that the models make regarding the constraints on financial contracting. The models also differ somewhat in their assumptions about production,

28

The finding that the limited commitment model fits better for relatively poor households, like the bulk of the households in the Northeast, and that the moral hazard model fits better among wealthier households, like those living in the central region, leads us to consider whether these findings are consistent with other differences in the financial environment across the two regions. For example, our results offer a rationale for differences in the concentration of the lending market across the two regions. When limited commitment is the key financial market imperfection, lending will be easier if there is a single dominant lender. In this case, a defaulting borrower’s credit history will be taken into account in the future, since the defaulting borrower will have to face the same lender. Likewise, the financial institution will not have to worry about losing customers to competitors. This is what we observe in the Northeast where the limited commitment model fits the data best. The percentage of total funds lent is very concentrated compared to the Central region. The BAAC accounts for 39% of all funds lent. Other formal lenders account for only 11% of lending. In the central region lending is much more dispersed. The BAAC accounts for 24% of lending. However, commercial banks and relatives account for another 21% and 17% of lending, respectively. We are not suggesting, however, that the concentration of lending in the Northeast can fully overcome the default problem. In the model and in the data, very low wealth households simply do not borrow. When the key financial market imperfection is moral hazard, and especially when borrowers are risk averse, simple debt contracts are not optimal. Optimal contracts will provide insurance along with incentives to exert effort. These contracts will necessarily have more contingencies, although credit will only be available for those households who are sufficiently wealthy. Lenient repayment terms are one way to introduce contingencies for these higher wealth households. A dispersed credit market, with a variety of lenders, is another way to introduce contingencies, borrowing from one source to repay another, for example. Commercial banks may be reluctant to seize collateral in the event of default or late payment,32 and, again, they are most prevalent in the Central region, where our findings suggest loans with contingencies are optimal. The fact that lending is dispersed in the central region is also likely to affect the BAAC’s behavior in the central region compared to the Northeast. The BAAC may be more willing to seize collateral and otherwise enforce loan contracts in the Central region. The BAAC is particularly reluctant to lose customers who borrow large sums because at the time of the survey they paid higher interest rates than households who borrowed smaller sums. Finally, loans from relatives are rarely collateralized, so the importance of relatives in the central region also helps to weaken the relationship between borrowing and wealth). Loans from the distribution of talent and error terms. However, we do not think that these differences can explain the findings. While the results of the formal comparisons of the models do incorporate these auxiliary assumptions, all the non-parametric and reduced form evidence that we have just described are independent of the model assumptions regarding production functions, talent and errors, and these results also point to the nature of the financial market imperfection varying with wealth. 32 The Thai financial crisis and its aftermath provide ample evidence of this phenomenon.

29

relatives may also provide exactly the kind of contingencies that are featured in the moral hazard model and may be missing from commercial bank and BAAC loans. Indeed, the work of Ahlin and Townsend (2002) on the repayment behavior of joint liability lending groups in Thailand comes to a surprisingly similar conclusion. In the Northeast, a limited commitment model best explains patterns of repayment. As would be expected from the model, repayment is higher when local enforcement is more severe. In contrast, a moral hazard model can better explain repayment patterns in the Central region. These findings reinforce our conclusions that the financial market imperfections vary with region and wealth. This paper contributes to the discussion of the desirability of policy interventions that are intended to alleviate financial constraints. In particular, the paper highlights the fact that the presence of financial constraints does not establish grounds for a policy intervention. In both models, the existing set of contracts are the optimal ones, given the financial market imperfections. Nonetheless, the findings suggest fruitful directions for policy discussions. For example, a program to establish secure property rights in land (so that it could serve as collateral) would be a higher priority in the Northeast compared to the central region. The findings also suggest that requiring commercial banks to lend to rural households in the Northeast, as has been proposed in Thailand, could actually be counter productive. Currently the BAAC emphasizes joint liability lending groups for poor farmers. Our findings suggest that these groups, which may use the superior information that villagers have about one another to mitigate the moral hazard problem, could be usefully extended to wealthier households. Indeed, we find some evidence that wealthier households who participate in BAAC borrowing groups may be less constrained in the Central region (see Paulson and Townsend 2002), as though the BAAC were using these groups as a screening mechanism and channeling larger loans to individuals who are deemed acceptable group member by their peers. The key to a successful policy intervention is that it address the underlying financial market imperfection, rather than its symptoms.

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30

[4] Banerjee, Abhijit and Andrew Newman. “Occupational Choice and the Process of Development.” Journal of Political Economy 101 (1993): 274 - 298. [5] Binford, Michael, Tae Jeong Lee and Robert Townsend. “Sampling Design for an Integrated Socioeconomic and Ecologic Survey Using Satellite Remote Sensing and Ordination.” Manuscript. Chicago: University of Chicago, 2001. [6] Blanchflower, D. and A. Oswald. “What Makes an Entrepreneur?” Journal of Labor Economics, 16(1998): 26-60. [7] Buera, Francisco. “Identification of Occupational Choice Models.” Manuscript. Chicago: University of Chicago, 2002. [8] Buera, Francisco. “A Dynamic Model of Entrepreneurial Choice with Borrowing Constraints.” Manuscript. Chicago: University of Chicago, 2002. [9] Evans, David S. and Boyan Jovanovic. “An Estimated Model of Entrepreneurial Choice under Liquidity Constraints.” Journal of Political Economy 97 (1989): 808 - 827. [10] Feder, Gershon et. al. Land Policies and Farm Productivity in Thailand. Baltimore: Johns Hopkins University Press, 1988. [11] Giné, Xavier and Robert Townsend, “Evaluation of Financial Liberalization: A general equilibrium model with constrained occupation choice”, Manuscript. Chicago: University of Chicago, 2001. [12] Greene, William, “Econometric Analysis”, Prentice Hall, 2000. [13] Greenwood, Jeremy and Boyan Jovanovic. “Financial Development, Growth, and the Distribution of Income.” Journal of Political Economy 98 (1990): 1076 - 1107. [14] Heckman, James and Bo Honore. “The Empirical Content of the Roy Model.” Econometrica 58 (1990): 1121-1149. [15] Holtz-Eakin, Douglas, Joulfian, David and Harvey S. Rosen. “Sticking It Out: Entrepreneurial Survival and Liquidity Constraints.” Journal of Political Economy 102 (1994): 53 - 75. [16] Jeong, Hyeok. “Decomposition of Growth and Inequality in Thailand.” Manuscript. Chicago: University of Chicago, 1998. [17] Jeong, Hyeok and Robert Townsend. “Household Businesses and their Financing in Semi-Urban and Rural Thailand.” Manuscript. Chicago: University of Chicago, 1998. [18] Judd, Kenneth, “Numerical Methods In Economics”, MIT Press, Cambridge, MA, 1998. 31

[19] Kaboski, Joseph and Robert Townsend. “Borrowing and Lending in Semi-Urban and Rural Thailand.” Manuscript. Chicago: University of Chicago, 1998. [20] Karaivanov, Alexander. “Financial Contracts Structure and Occupational Choice.” Manuscript. Chicago: University of Chicago, 2002. [21] Lehnert, Andreas. “Asset Pooling, Credit Rationing and Growth.” Working Paper no. 1998-52. Washington D.C.: Finance and Economics Discussion Series, Federal Reserve Board, 1998. [22] Lerner, Josh. “The Government as Venture Capitalist.” Journal of Business vol.72 num. 3 July, 1999. [23] Lloyd-Ellis, Huw and Dan Bernhardt, “Enterprise, Inequality and Economic Development.” Review of Economic Studies 67 (2000): 147 - 168. [24] Magnac, Thierry and Jean-Marc Robin, “Occupational Choice and Liquidity Constraints.” Richerche Economiche (1996) 50: 105 - 133. [25] Paulson, Anna L. “Financial Intermediation and Inequality: Evidence from Rural Thailand” Manuscript. Evanston, IL: Northwestern University., 1997. [26] Paulson, Anna L. and Robert Townsend “Entrepreneurship and Financial Constraints in Thailand.” (2002) forthcoming Journal of Corporate Finance. [27] Petersen, Mitchell A. and Raghuram G. Rajan. “The Benefits of Lender Relationships: Evidence from Small Business Data.” Journal of Finance 49 (March 1994): 3 -37. [28] Petersen, Mitchell A. and Raghuram G. Rajan. “The Effect of Credit Market Competition on Lending Relationships.” Quarterly Journal of Economics 110 (May 1995): 407-444. [29] Phelan, Christopher and Robert Townsend. “Computing Multi-Period, Information-Constrained Equilibria.” Review of Economic Studies 58 (1991): 853881. [30] Piketty, Thomas. “The Dynamics of the Wealth Distribution and the Interest Rate with Credit Rationing.” Review of Economic Studies 64 (1997): 173 - 189. [31] Seiler, Edward and Robert Townsend. “Assets in Semi-Urban and Rural Thailand.” Manuscript. Chicago: University of Chicago, 1998. [32] Townsend, Robert principal investigator with Anna Paulson, Sombat Sakuntasathien, Tae Jeong Lee and Michael Binford. “Questionnaire design and data collection for NICHD grant ‘Risk, Insurance and the Family’ and NSF grants”, 1997. 32

[33] Townsend, Robert and Jacob Yaron. “The Credit Risk-Contingency System of An Asian Development Bank”, Economic Perspectives, Federal Reserve Bank of Chicago, 2001. [34] Vuong, Quang H. “Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses.” Econometrica, Volume 57, Issue 2, (March 1989): 307-333. [35] Wolak, Frank. “An Econometric Analysis of the Asymmetric Information, Regulator-Utility Interaction”, Annales d’Economie et de Statistiques (1994), 34, 13-69.

33

Probability of Starting a Business

Past Wealth

Figure 1: Non-parametric relationship between Starting a Business and Wealth

Indifference Curve for Occupation Choice θ

Constrained Entrepreneurs

(r/α)(λA) 1 - α

Unconstrained Entrepreneurs E(y) = E(w) W age /Subsistence

A*

A

Figure 2: Limited Commitment Model

Figure 3: Example Solution of the Moral Hazard Model

Figure 4A: Whole Sample Notes to Figures 4A – 4C: These figures depict the likelihood of starting a business as a function of wealth six years prior to the survey. The wealth variable is normalized by dividing household wealth by the maximum value of household wealth in the sample, so that normalized wealth lies in a range from zero to one. For the structural estimates, the likelihood of starting a business is found by calculating the likelihood function for each model at the maximized parameter values as a function of wealth. See footnote 5 for details on how the non-parametric estimates of the likelihood of starting a business were created.

Figure 4B: Wealth < Median

Figure 4C: Wealth > Median

Net Savings

Past Wealth

Net Savings

Business Households, Central Region

Past Wealth

Business Households, Northeastern Region Figure 5: Non-parametric Relationship between Net Savings and Total Wealth

Table 1: Summary Statistics –Households who started Businesses in the past 5 years, Standard Errors in Parentheses Whole Sample Northeast Central % of Business Households All Households 14% 9% 19% Households with wealth < median 12% 8% 17% Households with wealth > median 16% 10% 21% Years of Schooling – Head All Households 4.03 3.97 4.09 2.56 2.45 2.67 Households with wealth < median 3.85 3.87 3.87 2.37 2.31 2.46 Households with wealth > median 4.21 4.08 4.32 2.73 2.58 2.85 Business Households 4.7 5.0 4.5 (2.9) (3.0) (2.8) Wealth Six Years Prior to survey All Households 1,007,166 355,996 1,712,046 (3,929,520) (648,590) (5,545,901) 43,578 Households with wealth < median 43,011 43,140 (46,492) (44,790) (49,881) Households with wealth > median 1,972,048 669,322 3,383,576 (5,388,944) (803,005) (7,484,382) Business Households 2,532,464 428,490 3,614,755 (7,603,877) (558,630) (9,168,505) Constrained Business Households 1,199,500 313,093 1,655,471 (5,770,291) (546,497) (7,051,744) Unconstrained Business Households 1,562,854 137,406 2,296,109 (5,550,756) (343,281) (6,713,852) Characteristics of Business Households Initial Business investment 148,734 81,311 179,349 (339,562) (176,918) (388,312) Net Savings 4,562 -13,680 13,946 (714,701) (410,166) (829,564) % who are net borrowers 55% 61% 51% % who are constrained* 56% 68% 50% Age of Head 49.5 48.4 50.1 (13.9) (13.6) (14.1) # of Adult Females in household

1.6 1.6 (0.9) (0.8) # of Adult Males in household 1.6 1.5 (0.9) (0.9) # of Children (< 18 years) in household 1.5 1.5 (1.2) (1.1) % who were Member/Customer of Organization/Institution Six Years Ago Formal Financial Inst. 23% 16% Village Inst./Org 11% 10% 33% 33% Agricultural Lender BAAC Group 22% 29% 4% 5% Money Lender *Households who reported that their businesses would be more profitable if it were expanded are labeled “constrained”.

1.7 (0.9) 1.7 (0.9) 1.6 (1.3) 27% 12% 33% 18% 4%

Table 2A: Structural Maximum Likelihood Estimation of Limited Commitment Model without Income data # of Obs. Log Likelihood Parameter Values λ δ0 δ1 δ2 Whole Sample 2313 -0.3957 40.37 2.33 0.05 0.05 (12.3733) (0.4092) (0.0180) (0.0113) Northeast 1209 -0.2991 29.34 1.89 0.04 0.07 (10.2049) (0.4369) (0.0315) (0.0221) Central 1104 -0.4911 57.11 3.42 0.06 0.03 (16.2901) (1.0754) (0.0193) (0.0178) Wealth Below median 1157 -0.3713 29.62 0.47 -0.09 0.07 (12.8113) (2.2429) (0.0709) (0.0184) Above median 1156 -0.4003 3.00 1.99 0.31 0.03 (0.7216) (.9476) (0.0409) (0.0158) Region/Wealth Northeast, below median 605 -0.2824 18.41 2.25 0.01 0.08 (7.3431) (0.6211) (0.0646) (0.0341) Northeast, above median 604 -0.3100 3.00 1.98 0.30 0.07 (0.7241) (0.9055) (0.1103) (0.0279) Central, below median 552 -0.4576 3.19 6.35 0.19 0.05 (10.8873) (2.0079) (0.1174) (0.0258) Central, above median 552 -0.4906 1.50 3.00 0.33 0.01 (1.2231) (0.7144) (0.0568) (0.0203) Bootstrap standard errors in parentheses. Sample

α 0.68 (0.0333) 0.69 (0.0333) 0.62 (0.0952) 0.95 (0.1747) 0.41 (0.1095) 0.68 (0.0492) 0.37 (0.1540) 0.58 (0.2014) 0.32 (0.1137)

Sample Whole Sample Northeast Central

Table 2B: Structural Maximum Likelihood Estimation of Limited Commitment Model with Income data # of Obs. Log Likelihood Parameter Values λ δ0 δ1 δ2 α µ ση σε σξ 2313 -1.9046 7.22 5.98 0.06 0.05 0.31 10.88 1.07 0.95 1.08 (24.5168) (0.4459) (0.0309) (0.0214) (0.0996) (0.0222) (0.3420) (0.1073) (0.0210) 1209 -1.6911 10.98 5.80 0.02 0.04 0.42 10.49 0.49 1.04 0.96 (7.3564) (0.6250) (0.0518) (0.0442) (0.1667) (0.0275) (0.5519) (0.1685) (0.0276) 1104 -1.9415 1.00 7.87 0.09 0.05 0.11 11.36 1.48 0.71 1.03 (4.5864) (0.4059) (0.0299) (0.0202) (0.0752) (0.0251) (0.2513) (0.0873) (0.0271)

Wealth Below median

1157

Above median

1156

Region/Wealth Northeast, below median

605

Northeast, above median

604

Central, below median

552

Central, above median

552

Bootstrap standard errors in parentheses.

-1.8314

30.15 4.12 -0.01 0.01 0.68 10.61 0.13 1.05 1.04 (20.7394) (0.7170) (0.0190) (0.0170) (0.0778) (0.0309) (0.2106) (0.0739) (0.0299) -1.8931 2.00 1.27 0.56 0.06 0.03 11.16 1.66 0.93 1.06 (0.2339) (0.8700) (0.0836) (0.0273) (0.0830) (0.0311) (0.2498) (0.1233) (0.0232) -1.6632

14.94 (6.3169) -1.6409 2.00 (0.0002) -1.8262 5.17 (29.2672) 4.00 -1.9684 (0.0000)

4.98 0.00 (0.5842) (0.0254) 3.76 0.29 (1.7931) (0.1490) 7.08 -0.09 (1.5655) (0.0580) 3.09 0.50 (0.6191) (0.0434)

0.02 (0.0346) 0.06 (0.0389) 0.03 (0.0315) 0.03 (0.0311)

0.56 10.24 (0.1250) (0.0379) 0.23 10.75 (0.1370) (0.0429) 0.46 11.13 (0.1571) (0.0431) 0.00 11.59 (0.0060) (0.0443)

0.23 (0.4133) 0.85 (0.3837) 0.61 (0.4808) 1.51 (0.1300)

1.01 (0.1342) 1.02 (0.2066) 0.80 (0.1761) 0.81 (0.1119)

0.96 (0.0390) 0.90 (0.0334) 0.96 (0.0422) 1.04 (0.0353)

Sample

Table 2C: Structural Maximum Likelihood Estimation of Moral Hazard Model with Risk Aversion # of Obs. Log Likelihood Parameter Values

α

q

m

κ1

0.9160 (0.0465) 0.9962 (0.0191) 0.3374 (0.0937)

0.7290 (0.5100) 0.8367 (2.0034) 0.7743 (0.3838)

2.1383 (0.6080) 1.0594 (1.9067) 0.7431 (0.8808)

0.0001 (0.3446) -0.0002 (0.2815) 2.4456 (0.2867)

0.4955 (0.3606) 1.0406 (0.7242) 1.5989 (0.2153)

0.9446 (4.5961) 0.8992 (0.0494)

0.0776 (3.6717) 0.7282 (0.7332)

2.2889 (0.6107) 2.1383 (0.8616)

0.5630 (0.3686) 0.0001 (0.3478)

0.5486 (0.2541) 0.4996 (0.5138)

1.7426 0.4996 0.5351 (0.0000) (0.0000) (0.0000) Northeast, above median 604 -0.3152 2.1006 0.5924 0.3425 (0.0000) (0.0000) (0.0000) Central, below median 552 -0.4599 1.4928 0.2666 0.0391 (.00738) (0.4648) (1.1035) Central, above median 552 -0.4820 0.4951 1.4931 0.9307 (0.0283) (0.0198) (0.1446) Standard errors in parentheses. See appendix for details on how standard errors are estimated.

0.9976 (4.4022) 0.9321 (6.4849) 0.1985 (6.1362) 0.7280 (2.2927)

0.8189 (6.0654) 0.7629 (5.3877) 1.0853 (5.1769) 2.1428 (1.3463)

0.9103 (0.1507) 0.6482 (0.1927) -0.6414 (0.5856) 0.0002 (0.3990)

1.1318 (1.5232) 1.5149 (1.8809) 0.9259 (5.6183) 0.4822 (1.6494)

Whole Sample

2313

-0.3909

Northeast

1209

-0.3033

Central

1104

-0.4760

Wealth Below median

1157

-0.3782

Above median

1156

-0.4025

605

-0.2886

Region/Wealth Northeast, below median

γ1

γ2

0.4937 (0.0367) 1.0647 (0.0116) 0.0004 (0.0420)

1.5062 (0.0222) 0.5095 (0.0027) 0.8836 (0.0940)

0.6712 (4.8309) 0.5109 (0.0392)

2.0512 (3.9497) 1.5011 (0.0951)

κ

Sample

Table2D: Structural Maximum Likelihood Estimation of Moral Hazard Model with Risk Neutrality # of Obs. Log Likelihood Parameter Values

γ2

Whole Sample

2313

-0.3918

Northeast

1209

-0.3039

Central

1104

-0.4760

Wealth Below median

1157

-0.3791

Above median

1156

-0.4028

605

-0.2889

Region/Wealth Northeast, below median

κ

α

q

m

κ1

0.6995 (0.1981) 1.4855 (0.2656) 0.8922 (0.3326)

0.3708 (1.0964) 0.3203 (1.6684) 0.3448 (0.3448)

0.8402 (2.0581) 0.0664 (1.3748) 0.7696 (0.7697)

0.5328 (1.3971) 0.4361 (3.6108) 0.7488 (0.7488)

3.8009 (0.0834) 0.0001 (0.2872) 2.3761 (2.3761)

2.2413 (0.1567) 1.1609 (2.3729) 1.6053 (1.6053)

1.0784 (0.2135) 0.9242 (4.0312)

1.1332 (0.3833) 0.3433 (1.4383)

0.5979 (0.5392) 0.6053 (2.4262)

2.1895 (0.3240) 0.5085 (3.9190)

0.7294 (0.2073) 1.6972 (0.1529)

0.6105 (0.3666) 2.4551 (0.6457)

0.1262 (1.6019) 0.5055 (2.0906) 0.1873 (0.0000) 0.6936 (2.1611)

0.8677 (0.9061) 3.9412 (0.1989) 5.1564 (0.0000) 0.6721 (1.8170)

0.0001 (0.2750) 0.5912 (0.2659) 0.4935 (0.3386) 2.3549 (0.1568)

1.0469 (0.3508) 0.0000 (3.4731) 0.0002 (0.0000) 1.9150 (0.4030)

0.5150 0.9544 (0.3178) (0.6884) Northeast, above median 604 -0.3164 1.0230 0.0964 (0.2708) (5.3708) Central, below median 552 -0.4648 0.1036 0.3008 (0.0000) (0.0000) Central, above median 552 -0.4842 1.1348 0.3828 (0.4189) (2.2237) Standard errors in parentheses. See appendix for details on how standard errors are estimated.

Table 3: Model Comparison Tests Limited Commitment (LC) v. Moral Hazard with Risk Aversion (MH) Limited Moral Hazard Sample Commitment Log likelihood Log likelihood Whole Sample -0.3957 -0.3909 Northeast -0.2991 -0.3033 Central -0.4911 -0.4760 Wealth Below median -0.3713 -0.3782 Above median -0.4003 -0.4025 Region/Wealth Northeast, below median -0.2824 -0.2886 Northeast, above median -0.3100 -0.3152 Central, below median -0.4541 -0.4599 Central, above median -0.4906 -0.4820 Limited Commitment (LC) v. Moral Hazard with Risk Neutrality (MH) Limited Moral Hazard Log likelihood Sample Commitment Log likelihood Whole Sample -0.3957 -0.3918 Northeast -0.2991 -0.3039 Central -0.4911 -0.4760 Wealth Below median -0.3713 -0.3791 Above median -0.4003 -0.4028 Region/Wealth Northeast, below median -0.2824 -0.2889 Northeast, above median -0.3100 -0.3164 Central, below median -0.4541 -0.4648 Central, above median -0.4906 -0.4842

Test of Model Fit z-test -1.74* 1.19 -3.51**

Model that fits best MH MH

1.91* 0.78

LC

1.35 1.12 1.24 -1.73*

Test of Model Fit z-test -1.40 1.43 -3.51**

MH

Model that fits best

2.17** 1.02 1.42 1.22 1.76* -1.16

The model comparison test is from Vuong (1989). Asterisks indicate that the test statistic is significantly large to reject the null. The confidence level used is 90% for one asterisk and 95% for two asterisks.

MH LC

LC

Table 4A: Regression Estimates of Net Savings (Financial Assets + Loans Owed to Household – Debt) for Households who have Started Business in last 5 years Whole Sample Northeast Central Region Coeff. T-statistic Coeff. T-statistic Coeff. T-statistic Age of Head 9592.724 0.52 5639.596 0.29 15814.300 0.60 Age of Head Squared -93.922 -0.56 -71.272 -0.41 -161.393 -0.68 Years of Schooling – Head -23179.890 -1.67 -12283.410 -0.96 -28433.790 -1.35 # of Adult Females in household -105875.200 -2.18 -133223.000 -2.59 -104812.200 -1.56 # of Adult Males in household 108636.700 2.37 60962.520 1.22 140117.500 2.22 # of Children (< 18 years) in household 37710.180 1.21 -60660.900 -1.68 64761.760 1.54 Wealth Six Years ago – Constrained Business† 0.048 4.32 -0.004 0.05 0.048 3.63 Wealth Six Years ago – Unconstrained Business† 0.012 1.42 0.383 3.31 0.012 1.19 Constant -234535.400 -0.48 121595.300 0.25 -461081.300 -0.65 Adjusted R-squared 7.86% 9.94% 8.71% Number of Observations 361 122 239 Dummy variables are marked by an asterisk. †Wealth six years ago is made up of the value of household assets, agricultural assets and land. The sample excludes the top 1% of households by wealth and net savings.

Table 4B: Probit Estimates of Being Net Borrower (Net Savings < 0) For Households who Have Started Business in Last 5 Years Whole Sample Northeast Central Region dF/dx* Z-statistic dF/dx* Z-statistic dF/dx* Z-statistic Constrained (= 1 if constrained, 0 otherwise)* 0.0849 1.55 -0.0491 -0.48 0.1321 1.97 Age of Head -0.0115 -0.82 -0.0149 -0.58 -0.0116 -0.67 Age of Head Squared 0.0001 0.65 0.0001 0.47 0.0001 0.49 Years of Schooling – Head 0.0049 0.47 -0.0027 -0.16 0.0010 0.07 # of Adult Females in household 0.0494 1.37 0.1320 1.81 0.0268 0.62 # of Adult Males in household -0.0701 -2.05 -0.1838 -2.64 -0.0334 -0.82 # of Children (< 18 years) in household 0.0344 1.47 0.1338 2.63 0.0059 0.21 Wealth Six Years ago† -0.0013 -0.24 0.1880 1.75 0.0007 0.12 Member/Customer in Organization/Institution Six Years Ago Formal Financial Inst.* -0.1296 -1.95 -0.1323 -0.94 -0.1181 -1.48 Village Inst./Org* 0.0319 0.35 0.1931 1.04 -0.0303 -0.27 Agricultural Lender * 0.0903 1.22 0.1995 1.46 0.0332 0.37 BAAC Group* 0.1221 1.52 0.0886 0.60 0.1314 1.29 Money Lender* -0.1470 -1.11 -0.0413 -0.18 -0.1562 -0.93 Observed Frequency 0.5457 0.6066 0.5146 Predicted Frequency at mean of X 0.5483 0.6367 0.5153 Log Likelihood -237.02 -70.50 -158.47 Pseudo R-squared 4.70% 13.79% 4.28% Number of Observations 361 122 239 Dummy variables are marked by an asterisk. †Wealth six years ago is made up of the value of household assets, agricultural assets and land. Number in table is estimated coefficient multiplied by 1,000,000. The sample excludes the top 1% of households by wealth.

Appendix: Structural Maximum Likelihood Estimation with Francisco Javier Buera Xavier Giné Alexander Karaivanov Department of Economics University of Chicago December, 2002

1

Limited Commitment Model

1.1

Log-Likelihood Function

An agent will choose to become an entrepreneur if the expected profits, integrating over ε, exceed the expected wage, µ. The expected profits of an entrepreneur will depend on the level of wealth, since this last variable will determine, together with the profitability of the individual project, whether the agent will be constrained. Suppressing for simplicity subscript i for household i, a generic household with relatively high wealth (A ≥ A∗ ) will be an unconstrained entrepreneur when talent θ is high enough, but not so high for it to be constrained.1 That is, comparing expected incomes2 θ(k∗ )α − rk ∗ + rA ≥ µ + rA. Substituting for k∗ and canceling rA from both sides, θ

µ

θα r

α ¶ 1−α

−r

µ

θα r

1 ¶ 1−α

≥ µ.

Taking logs and rearranging, the key selection equation is ln θ ≥ (1 − α) ln µ + α ln

r + (α − 1) ln(1 − α) ≡ c1 . α

(A1)

³ ´ 1 1−α a given wealth level, there is a talent level such that desired capital, k∗ = θα , equals maximun available r capital, λA. Conditional on being an entrepreneur, a firm will be constrained if the desired capital is bigger than the maximun available capital µ ¶ 1 θα 1−α ≥ λA r 1 For

In terms of the talent level, the above corresponds to talent being high enough i.e., r ln θ ≥ (1 − α) ln λA + ln ≡ c2 . α In the model this margin is relevant only for cases with A > A∗ . 2 Like Evans and Jovanovic (1989) we assume that ε and ξ are lognormally distributed shocks whose logartithms have variances σ2ε and σ2ξ respectively. The mean of the log if each shock is given by ¾ ¾ ½ ½ σ2 σ2 σ2 σ2 E[ε] = exp − 2ε + 2ε = 1 and E[ξ] = exp − 2ξ + 2ξ = 1.

1

σ2 ε 2

and -

σ2 ξ . 2

Therefore,

Similarly, for relatively low wealth (A < A∗ ), the choice is between being a worker and being a constrained entrepreneur, and the analog expression comparing ex-ante expected incomes is given by, θ(λA)α + r(A − λA) ≥ µ + rA. Taking logs and rearranging, ln θ ≥ −α ln λ − α ln A + ln[µ + rλA] ≡ c3 .

(A2)

Again, the agent will become an entrepreneur given that ability is sufficiently high. Evidently the curves c1 and c3 , as displayed in the figures in the text, are functions of the underlying parameters and so at given parameters and our assumption on the distribution of the underlying shocks η determining θ, the likelihood of entrepreneurship choice is determined. Further, suppose we use the data on that choice along with observed income. Then consider the joint probability, for example, that entrepreneurial choice is zero (E = 0 or wage earner) and log earnings are ln y, conditioned on wealth A less than or equal to A∗ , that is,   σ 2ξ ln y − ln µ − 2  Pr(µ ≥ θ(Aλ)α − rλA) f (ln y, E = 0|A ≤ A∗ ) = φ  σξ   µ σ2 ¯¶ ln y − ln µ − 2ξ  Φ c3 − θ = φ σξ ση where f () is the joint density function, φ the normal pdf, Φ the normal cdf, and ¯θ = δ 0 +δ 1 ln A+δ 2 edu. Here the first term is the likelihood of the log wage using the standard log normal distribution (the mean is subtracted and the variable normalized by σ ξ ). The second term is just a statement about log talent, ln θ, being such as to make wage labor the optimal choice. That reduces to a statement about shock η, so again we can use the standard normal distribution, substracting means and normalizing. The derivation of the joint probability of earnings and being a wage earner to the right of A∗ is entirely similar. ¶ µ σ2 ln y − ln µ − 2ξ c1 − ¯θ ∗ )Φ f (ln y, E = 0|A > A ) = φ( σξ ση

More difficult are the cases where the household is an entrepreneur and we also use the data on earnings, because θ determines both. For example, conditioned on A less than A∗ we can express the probability that ln y not exceed a certain level, ln y¯, as a function of talent θ conditioned on being an entrepreneur and conditioned (for the moment) on ln ε. As log income or profits for a constrained entrepreneur is ln θ + α ln λ + α ln A + ln ε, the probability is equivalent to, Pr(ln θ ≤ ln y¯ − α ln λ − α ln A − ln ε| E = 1, ln ε, A ≤ A∗ ). Unfortunately, the conditioning event E = 1 is also a function of the parameter θ, specifically, ln θ ≥ c3 . To proceed we normalize by the probability of the conditioning event, take ratios of standard normal distributions, then integrate with respect to ln ε, and then with much tedious algebra search for a recognizable statistical form. Once found we can multiply by the probability of the original conditioning event, that the household be an entrepreneur. The resulting expression is: Ã ! σ2 ln y − y¯2 − ¯θ − 2ε 1 ∗ f (ln y, E = 1|A ≤ A ) = ¡ ¢1/2 φ ¡ ¢1/2 σ2η + σ 2ε σ 2η + σ 2ε ´ ¡ ¢1/2 ³ σ2 ¡ ¢ ln y − y¯2 − c3 − 2ε σ2η + σ 2ε σ ε ln y − y¯2 − ¯θ − ·Φ  ¡ ¢1/2  ση σε 2 2 ση ση + σε 2

where y¯2 = α ln (λA). For the other branch, when A ≥ A∗ and the household is an entrepreneur, the algebra is similarly tedious: 

 ¯ σ 2ε θ ln y − y ¯ − − 1 1 (1−α) 2   φ ³ f (ln y, E = 1|A > A∗ ) = ³  ´ ´ 1/2 1/2 2 2 ση ση 2 2 2 + σε 2 + σε (1−α) (1−α)  ³ 2 ´ ´ ³ ´ 1/2 ³ 2 ση ¯ σε c1 θ 2 ln y − y ¯ ln y − y ¯ σ + σ − − − 1 ε 1 ε (1−α) 2 (1−α)    (1−α)2 · Φ  − ση ³ ´1/2  2 ση ση 2 (1−α) σ ε + σ ε (1−α) (1−α)2 ³ 2 ´1/2 ³ ´ ³ ´  ση ¯ σ 2ε c2 θ 2 ln y − y ¯ ln y − y ¯ σ − − − 2 + σε 1 ε 1 (1−α) 2 (1−α)   (1−α) −Φ  − ση ³ σ2 ´1/2  σ σ ε η η 2 (1−α) (1−α) (1−α)2 + σ ε Ã ! σ2 ln y − y¯2 − ¯θ − 2ε 1 +¡ ¢1/2 φ ¡ ¢1/2 σ 2η + σ2ε σ 2η + σ 2ε ´ ¡ ¢1/2 ³ σ2 ¡ ¢ ln y − y¯2 − c2 − 2ε σ 2η + σ 2ε σε ln y − y¯2 − ¯θ − ·Φ  ¡ ¢1/2  ση σε σ η σ 2η + σ 2ε

¡ ¢ 1 where y¯1 = (1−α) ln αr and c2 , a function of the underlying parameters and the log of wealth A, define the boundary between constrained and unconstrained firms. The parameters over which we maximize are: (λ, δ 0 , δ 1 , δ 2 , µ, α, ση , σ ε , σ ξ ). These parameters correspond to the proportion of the wealth that can be invested (including outside funds), λ; the mean of the ability distribution, δ 0 ; the interaction between wealth and ability, δ 1 ; the interaction between education and ability, δ 2 ; the mean wage, µ; the curvature of the production function, α; the standard deviation of the ability distribution, σ η ; and the standard deviation of the ex-post shocks to the income of an entrepreneur and worker, σ ε and σ ξ , respectively. Proceeding, we pick a value for the interest rate r = 1.25 from the data. 1.1.1

Identification With Income Data

Here we give an intuitive argument about the identification of the limited commitment model when we observe income and occupational choice. The limited commitment model is very close to the Roy model described in Heckman and Honoré (1990). Heckman and Honoré discussed the identification of the log-normal Roy model. They stated that the log-normal Roy model can be identified from data on the income in each sector and occupational choices (theorem 4 in Heckman and Honoré). This result guarantees the identification of the variant of the limited commitment model with no borrowing constraints and no ex-post heterogeneity. One problem with the maximum likelihood routine relative to the Thai data is the tendency to find that most households lie to the right of A∗ , thus leaving few observations to pin down parameter λ.

1.2

Estimation Without Income

Without data on labor earning the model is not fully identified. We use the mean value for the income of wage earners as our estimate for µ. The probability of being an entrepreneur given A ≤ A∗ and A > A∗ , respectively, is given by

3

Pr (E = 1|A ≤ A∗ ) = Φ(

c3 − ¯θ ) ση

Pr (E = 1|A > A∗ ) = Φ(

c1 − ¯θ ) ση

and

1.2.1

Identification

A particular reparameterization is useful to understand identification. In this case the previous probabilities are Pr (E = 1| log(A) ≤ log(A∗ )) ¶ · µ ¸ α2 − β 2 + log (α3 + β 2 − α2 ) = Φ((α2 − β 2 ) log(α4 ) − log r ¶ µ α3 + β 2 − α2 + β 1 + α2 log(A) − α3 log(1 + α4 rA)) − α3 log α3 and Pr (E = 1| log(A) > log(A∗ )) = Φ(β 1 + β 2 log(A)). where parameters α and β in these equations are related to the underlying parameters by

α2 = α3 = α4 = β1 = β2 = β3 =

α + δ1 , ση 1 , ση λ , µ −(1 − α) log(µ) + α log( αr ) + (1 − α) log(1 − α) + δ 0 ση δ1 ση δ2 . ση

Again, Φ stands for the normal cdf. These probabilities are similar to the ones of a simple probit, particularly for the A > A∗ branch, but with more structure in the A ≤ A∗ branch, and the fact that there is a critical value of wealth, A∗ , which is a function of the underlying parameters of the model and which determines the relevant branch. In principle, there are six parameters (α2 , α3 , α4 , β 1 , β 2 , β 3 ) entering in distinct ways in the probability terms of the two branches. These can be used to identify the underlying six parameters (λ, δ 0 , δ 1 , δ 2 , α, σ η ). When income data are not used, σ ε and σ ξ are not relevant. When we implemented the estimation identification of σ η was numerically difficult. We decided to set σ η = 1 and focus on the estimation of the other five parameters of the model. The parameters to be estimated in this case are ψ = (λ, δ 0 , δ 1 , δ 2 , α). Again, the mean wage, µ, is estimated from income data of the wage earners. 4

1.3

Algorithms and Numerical Issues

In both cases, using income data or without using income data, given expressions for the likelihoods we can proceed to estimate the limited commitment model. The standard errors of the estimated parameters are computed by bootstrap methods using 100 draws of the original sample with replacement. We used the MATLAB 5.3 routine fminunc. The problem is not guaranteed to be concave. Thus, we need to be concerned that solutions could correspond to local maxima instead of the global maxima. We perform the optimization routine starting from eight different initial sets of parameters, and the one yielding the highest overall likelihood is chosen.

2 2.1

Moral Hazard Model Maximum Likelihood Equation

We estimate the moral hazard model by maximum likelihood techniques using the probability of being entrepreneur generated by the model. The likelihood is n

Ln (ψ) =

1X Ei ln H(Ai |ψ) + (1 − Ei ) ln(1 − H(Ai |ψ)) n i=1

In the above equation n is the number of observations, Ei is a binary variable, which takes the value of 1 if agent i is entrepreneur in the data and 0 otherwise, Ai is the wealth of agent i (again from the data), ψ is the vector of model parameters as described below, and H(Ai |ψ) is the (expected) probability of being an entrepreneur generated by the model for an agent with wealth Ai integrated over the talent distribution.

2.2

Parameters to be Estimated

The model-generated probability H(Ai |ψ) is a function of the following parameters (see also the description of the model in the text): γ 1 - the coefficient of risk aversion; γ 2 - a curvature parameter of the disutility of effort; κ - a multiplicative constant governing the relative weight of utility derived from consumption or leisure; q¯ - a parameter determining the higher value of output; α - the investment share in the probability of success function; m - a parameter governing the shape of the talent distribution; κ1 - a parameter determining the support of the talent distribution; r - the interest rate; The first seven parameters are estimated in the moral hazard model with risk aversion. We set the interest rate to 1.25, which is the average gross interest rate observed in the data. In the restricted form of the model we constrain γ 1 = 0 (i.e. assuming risk neutral agents) and estimate only the remaining six parameters.

2.3

Solution and Estimation Techniques

We solve Program 1 in the text for the π(c, q, z, k|A, θ, ψ), where here we make explicit the dependence on the parameter vector, ψ. The aim of the estimation is to find the values for the above parameters which maximize the likelihood that the model could generate the actual observations from the data. The dependent variable is the conditional probability of the binary variable E which equals 1 for entrepreneurs and 5

0 for workers, where as before we drop the subscript i for simplicity of notation. That is, given a wealth level A, the model generates some probability that a person with wealth A is an entrepreneur, E = 1. The wealth levels in the data were normalized to lie on the interval [0, 1], dividing by the biggest observed level. The actual numerical procedure of solving the model takes several steps: (1) For any parameter configuration, ψ and given values for talent, θ and wealth, A, we need to solve the following P linear programming problem for the probability of being entrepreneur, which is π e (θ, A|ψ) = π(c, q, z, k|A, θ, k > 0, ψ) evaluated at the solution. This is the most time c,q,z,k

consuming step. The linear programming Problem 1 is solved using the following numerical procedures:

• Create grids for k, z, c : we use 10 grid points for k on [0, 1], 10 grid points for c on [0, 5] and 5 grid points for z on [0,1]. The somewhat low dimension of the grids was forced by computational time. Notice that even with these seemingly low grid dimensions and the two output levels, we still have 1000 variables (the π 0 s). We can handle a much bigger number of unknowns, but computational time increases quickly. • Construct the matrices of coefficients corresponding to the constraints. We use the single crossing property to eliminate some of the incentive constraints as they do not bind at the solution. • Construct the vector of coefficients on the objective function. • Solve for the optimal π(c, k, z, q|A, θ, ψ) using the Matlab routine linprog and get π e (θ, A|ψ). (2) Since talent θ is assumed unobservable by us as econometricians, we actually need to compute the expected value for π e at A integrating over θ, i.e., e

e

H(A|ψ) = [π (A)|ψ] ≡ Eθ [π (θ, A|ψ)] =

1+κ Z 1

πe (θ, A|ψ)dh(θ, m),

κ1

where h(θ, m) is the density of the talent distribution. The method used is Gauss-Legendre quadrature with 5 nodes for θ (see Judd, ”Numerical Methods in Economics”, p. 260.). It was chosen because it minimizes the number of function evaluations and also because of its nice asymptotic properties. (3) Again, to save on computation time, we do not compute Eθ [π e (θ, A|ψ)] at all data points for A (more than 2,000 observations). We construct a 20-point log-spaced grid (since the wealth data is heavily right skewed) on [0,1] and compute Eθ [πe (θ, A|ψ)] only at these grid points for A. We then use a cubic spline interpolation on the grid, which generates the probability of being entrepreneur, H(A|ψ) predicted by the model for a given wealth level A, for all data points. (4) The actual maximization of the log-likelihood function Ln (ψ) exhibited in the beginning of this section is performed in the following way. First, in order to ensure that a global maximum is reached we do an extensive grid search over the seven parameters (six for the risk neutral version of the model) and pick the parameter configuration which maximizes L. This parameter configuration is then taken as the vector of starting values for the actual optimization procedure. We solve the nonlinear optimization problem of maximizing L by using the MATLAB 5.3 routine fminsearch which represents a generalization of the polytope method using the Nelder-Mead simplex algorithm. The procedure was chosen because of its high reliability, relative insensitivity to initial values, and good performance with low-curvature objective functions (which usually appear in maximum likelihood problems). (5) Finally, we compute the standard errors for the estimated parameters using an approximation of the parameter covariance matrix with the sample second moment matrix of the estimated score vectors, M = SS 0 /n, where S denotes the n × 7 matrix of score vectors with respect to the estimated 6

∂L , j = 1..7. The standard errors of the estimated parameters are then the ∂ψ j square roots of the main diagonal elements of the matrix M (for discussion see Greene, ”Econometric Analysis”, 1990). The score vectors are computed using one-sided numerical differentiation of L around the maximizing parameter values with tolerance of 10−6 . The computationally intensive methods we use precluded us from computing bootstrap standard errors. We follow the same procedure to estimate the risk neutral version of the model, with the exception that γ 1 is fixed at 0 and only the remaining six parameters are estimated. parameters i.e., Sj =

7