Labor Supplyg Static Model
Labor Supply— Static Model Simon Chang China Center for Human Capital and Labor Market Research Central University of Finance and Economics
Fall 2010
Simon Chang (Institute)
Labor Supply— Static Model
Fall 2010
1 / 29
Static Model of Labor Supply We begin with a neo-classical model of labor supply. Consider the following assumptions: 1
An individual seeks maximization of utility
2
Competitive labor market; wage is exogenously determined
3
Time is used for either work or leisure
4
One’s own labor decision is independent from others’
5
Planning horizon: only one period, e.g. one month or one year (thus no savings)
6
No uncertainty
We will relax assumption 4, 5 and 6 when we introduce more ‡exible models.
Simon Chang (Institute)
Labor Supply— Static Model
Fall 2010
2 / 29
A Simple Static Model of Labor Supply -Presentation follows Blundell and MaCurdy (1999) -A Quasi-Concave utility function U (C , L, X ) C : consumption; L: leisure time; X : personal attributes -Utility is maximized subject to a budget constraint C + WL = Y + WT W : hourly wage; Y : non-labor income; T : total time -Full income: M Y + WT -First order conditions (FOCs): UC = λ; UL = λW λ: marginal utility of income Simon Chang (Institute)
Labor Supply— Static Model
Fall 2010
3 / 29
A Simple Static Model of Labor Supply -Marginal Rate of Substitution (MRS) equals to wage rate: MRS
UL =W UC
-Solving the FOCs yields the Marshallian (uncompensated) demand funtions:
= C (W , M, X ) L = L (W , M, X )
C
-De…ne hours of work as H = T
T
L:
H = H (W , M, X )
Simon Chang (Institute)
Labor Supply— Static Model
Fall 2010
4 / 29
A Graphical Illustration of the Static Model
Simon Chang (Institute)
Labor Supply— Static Model
Fall 2010
5 / 29
Review of Properties of Indi¤erence Curve
Every bundle point along the curve yields the same level of satis…cation Downward sloping The further away from the origin, the higher the utility No two ind¤erence curves cross Convex to the origin Shape depends on personal taste toward consumption and leisure
Simon Chang (Institute)
Labor Supply— Static Model
Fall 2010
6 / 29
Changes in Non-labor Income
Simon Chang (Institute)
Labor Supply— Static Model
Fall 2010
7 / 29
Changes in Non-labor Income
Simon Chang (Institute)
Labor Supply— Static Model
Fall 2010
8 / 29
Let’s Pause and Think
Will winning the lottery change your life? Read Imbens, Rubin and Scerdote (2001) How will government transfer payment a¤ect labor supply? (More later)
Simon Chang (Institute)
Labor Supply— Static Model
Fall 2010
9 / 29
Changes in Wage Rate
Simon Chang (Institute)
Labor Supply— Static Model
Fall 2010
10 / 29
Changes in Wage Rate
Simon Chang (Institute)
Labor Supply— Static Model
Fall 2010
11 / 29
Let’s Pause and Think
What does the theory predict about hours of work as wage increases? Who would sleep more, a poor graduate student or Bill Gates? Read Biddle and Hamermesh (1990)
Simon Chang (Institute)
Labor Supply— Static Model
Fall 2010
12 / 29
To Work or Not To Work: Reservation Wage
Simon Chang (Institute)
Labor Supply— Static Model
Fall 2010
13 / 29
Let’s Pause and Think whether to work is sometimes called a decision at the "extensive margin", while how many hours to work is called at the "intensive margin" the theory says that one decides whether to work by comparing the market wage and one’s own reservation wage What does the theoy predict about labor force participation as wage increases? How does that compare to the e¤ect on hours of work? Why is there a di¤erence? What explains the rise of women’s labor force participation in the past few decades? How does that correlate with economic development? Read Mammen and Paxson (2000) Assume leisure is a normal good, what happens to reservation wage as nonlabor income increases? Simon Chang (Institute)
Labor Supply— Static Model
Fall 2010
14 / 29
Backward Bending Labor Supply Curve
Simon Chang (Institute)
Labor Supply— Static Model
Fall 2010
15 / 29
Derivation of Aggregate Labor Supply Curve
Simon Chang (Institute)
Labor Supply— Static Model
Fall 2010
16 / 29
Wage Elasticity of Labor Supply Empirical studies generally estimate the wage elasticity of Marshallian/ Hicksian labor supply - Marshallian (uncompensated) elasticity: Ku =
∂ ln H ∂ ln W
- Hicksian (compensated) elasticity : (by Slutsky equation) Ku = K c +
WH ∂ ln H Y ∂ ln Y
On the right hand side, …rst term is the substitution e¤ect, second term is the income e¤ect. Assume leisure is a normal good, Kc > Ku . Simon Chang (Institute)
Labor Supply— Static Model
Fall 2010
17 / 29
Empirical Speci…cation of the Static Model A prototype empirical speci…cation (linear model): ln H = β0 + β1 ln W + β2 Y + BX + ε where ε is an unobserved error term; other notations are the same as before. -ln H is sometimes replaced with H when dealing with non-participation -Various formulations of wage, e.g. after-tax wages, non-linear functions of wages -If the static model is correct, β1 measures the uncompensated wage elasticity conditional on Y and X . (more discussions later) -Typically, instrumental variable (IV) method is used to account for the unobservables that a¤ect both H and W (endogeneity problem) or measurement error (usually in W )
Simon Chang (Institute)
Labor Supply— Static Model
Fall 2010
18 / 29
Common Empirical Issues in Estimating Wage Elasticity
Hours of work over how long? A week, a month or a year? Measurement errors How to calculate hourly wage if paid an annual salary? Self-selection: only wages of workers are observed, non-random sample Unobserved factors: unobserved "strong taste of work" leads to both high non-labor income and long work hours
Simon Chang (Institute)
Labor Supply— Static Model
Fall 2010
19 / 29
Women’s Labor Force Participation
In the past few decades, the world has witnessed a substaintial rise in women’s labor force particiaption. What caused the rise? - increase in real wage - lower fertility v.s. lower reservation wage (causation runs in both ways) - technological improvement in home production - other cultural/ social factors
Simon Chang (Institute)
Labor Supply— Static Model
Fall 2010
20 / 29
Welfare Programs and Work Incentives (I): TANF
Consider a welfare program providing a cash grant to eligible poor people regardless of their work e.g. Temporary Assistance to Needy Families (TANF) Note that recepients of TANF can still work How does such a program a¤ect labor force participation and hours of work of the poor?
Simon Chang (Institute)
Labor Supply— Static Model
Fall 2010
21 / 29
A Case of Take-it-or-leave-it Cash Grant
Simon Chang (Institute)
Labor Supply— Static Model
Fall 2010
22 / 29
Reduce Grant if Work Suppose the gov takes away $ .5 for every dolloar the recipient earns by working
Simon Chang (Institute)
Labor Supply— Static Model
Fall 2010
23 / 29
Welfare Programs and Work Incentives (II): EITC
Earned Income Tax Credit (EITC): for every dollar you earn, the gov matches it with up to a certain percentage of the earned dollar In 2002 - 40 cents matched to each dollar earned if income < $10350, maximum is $4140 - maximum credit is available if $10350
income
$13520
- credit is reduced by 21.06 cents for each dollar earned if income>$13520
Simon Chang (Institute)
Labor Supply— Static Model
Fall 2010
24 / 29
Welfare Programs and Work Incentives (II): EITC Budget constraint
Simon Chang (Institute)
Labor Supply— Static Model
Fall 2010
25 / 29
Welfare Programs and Work Incentives (II): EITC E¤ects on labor force participation and hours of work
Simon Chang (Institute)
Labor Supply— Static Model
Fall 2010
26 / 29
Family Labor Supply: Interpersonal Dependence Often, within a family, one’s labor decision is correlated with another’s decision. For example, whether wife would work depends on husband’s labor decision. The previous one-person static model is inadequate in this multi-person context. Therefore, we need to modify the static model as follows. Consider a family with two working-age individuals whose labor decision are intercorrelated and other dependents. The family is seeking maximization of total family consumption and the leisure of each family member. -Utility function: U = U (C , L1 , L2 , X ) where C is now the total family consumption; Li is leisure of individual i. -Budget constraint: C + W1 L1 + W2 L2 = Y + W1 T + W2 T where Y is total family non-labor income. Simon Chang (Institute)
Labor Supply— Static Model
Fall 2010
27 / 29
Family Labor Supply -Now the full income is: M = Y + W1 T + W2 T -FOCs: UC (C , L1 , L2 , X ) = λ UL1 (C , L1 , L2 , X ) = λW1 UL2 (C , L1 , L2 , X ) = λW2 -Demand functions: C L1 L2 Simon Chang (Institute)
= C (W1 , W2 , M, X ) = L1 (W1 , W2 , M, X ) = L2 (W1 , W2 , M, X ) Labor Supply— Static Model
Fall 2010
28 / 29
Empirical Evidence of Family Labor Supply
Family labor supply model can be estimated in a similar fashion to the single-person labor supply model Empirical evidence from the US suggests a 10% increase in the husband’s wage lowers the participation rate of women by 5.3 percentage points and reduces the hours that working wives allocate to the labor market by 1.7 percent. On the contrary, little evidence shows that wife’s wage a¤ects husband’s labor supply
Simon Chang (Institute)
Labor Supply— Static Model
Fall 2010
29 / 29
Fall 2010
Simon Chang (Institute)
Labor Supply— Static Model
Fall 2010
1 / 29
Static Model of Labor Supply We begin with a neo-classical model of labor supply. Consider the following assumptions: 1
An individual seeks maximization of utility
2
Competitive labor market; wage is exogenously determined
3
Time is used for either work or leisure
4
One’s own labor decision is independent from others’
5
Planning horizon: only one period, e.g. one month or one year (thus no savings)
6
No uncertainty
We will relax assumption 4, 5 and 6 when we introduce more ‡exible models.
Simon Chang (Institute)
Labor Supply— Static Model
Fall 2010
2 / 29
A Simple Static Model of Labor Supply -Presentation follows Blundell and MaCurdy (1999) -A Quasi-Concave utility function U (C , L, X ) C : consumption; L: leisure time; X : personal attributes -Utility is maximized subject to a budget constraint C + WL = Y + WT W : hourly wage; Y : non-labor income; T : total time -Full income: M Y + WT -First order conditions (FOCs): UC = λ; UL = λW λ: marginal utility of income Simon Chang (Institute)
Labor Supply— Static Model
Fall 2010
3 / 29
A Simple Static Model of Labor Supply -Marginal Rate of Substitution (MRS) equals to wage rate: MRS
UL =W UC
-Solving the FOCs yields the Marshallian (uncompensated) demand funtions:
= C (W , M, X ) L = L (W , M, X )
C
-De…ne hours of work as H = T
T
L:
H = H (W , M, X )
Simon Chang (Institute)
Labor Supply— Static Model
Fall 2010
4 / 29
A Graphical Illustration of the Static Model
Simon Chang (Institute)
Labor Supply— Static Model
Fall 2010
5 / 29
Review of Properties of Indi¤erence Curve
Every bundle point along the curve yields the same level of satis…cation Downward sloping The further away from the origin, the higher the utility No two ind¤erence curves cross Convex to the origin Shape depends on personal taste toward consumption and leisure
Simon Chang (Institute)
Labor Supply— Static Model
Fall 2010
6 / 29
Changes in Non-labor Income
Simon Chang (Institute)
Labor Supply— Static Model
Fall 2010
7 / 29
Changes in Non-labor Income
Simon Chang (Institute)
Labor Supply— Static Model
Fall 2010
8 / 29
Let’s Pause and Think
Will winning the lottery change your life? Read Imbens, Rubin and Scerdote (2001) How will government transfer payment a¤ect labor supply? (More later)
Simon Chang (Institute)
Labor Supply— Static Model
Fall 2010
9 / 29
Changes in Wage Rate
Simon Chang (Institute)
Labor Supply— Static Model
Fall 2010
10 / 29
Changes in Wage Rate
Simon Chang (Institute)
Labor Supply— Static Model
Fall 2010
11 / 29
Let’s Pause and Think
What does the theory predict about hours of work as wage increases? Who would sleep more, a poor graduate student or Bill Gates? Read Biddle and Hamermesh (1990)
Simon Chang (Institute)
Labor Supply— Static Model
Fall 2010
12 / 29
To Work or Not To Work: Reservation Wage
Simon Chang (Institute)
Labor Supply— Static Model
Fall 2010
13 / 29
Let’s Pause and Think whether to work is sometimes called a decision at the "extensive margin", while how many hours to work is called at the "intensive margin" the theory says that one decides whether to work by comparing the market wage and one’s own reservation wage What does the theoy predict about labor force participation as wage increases? How does that compare to the e¤ect on hours of work? Why is there a di¤erence? What explains the rise of women’s labor force participation in the past few decades? How does that correlate with economic development? Read Mammen and Paxson (2000) Assume leisure is a normal good, what happens to reservation wage as nonlabor income increases? Simon Chang (Institute)
Labor Supply— Static Model
Fall 2010
14 / 29
Backward Bending Labor Supply Curve
Simon Chang (Institute)
Labor Supply— Static Model
Fall 2010
15 / 29
Derivation of Aggregate Labor Supply Curve
Simon Chang (Institute)
Labor Supply— Static Model
Fall 2010
16 / 29
Wage Elasticity of Labor Supply Empirical studies generally estimate the wage elasticity of Marshallian/ Hicksian labor supply - Marshallian (uncompensated) elasticity: Ku =
∂ ln H ∂ ln W
- Hicksian (compensated) elasticity : (by Slutsky equation) Ku = K c +
WH ∂ ln H Y ∂ ln Y
On the right hand side, …rst term is the substitution e¤ect, second term is the income e¤ect. Assume leisure is a normal good, Kc > Ku . Simon Chang (Institute)
Labor Supply— Static Model
Fall 2010
17 / 29
Empirical Speci…cation of the Static Model A prototype empirical speci…cation (linear model): ln H = β0 + β1 ln W + β2 Y + BX + ε where ε is an unobserved error term; other notations are the same as before. -ln H is sometimes replaced with H when dealing with non-participation -Various formulations of wage, e.g. after-tax wages, non-linear functions of wages -If the static model is correct, β1 measures the uncompensated wage elasticity conditional on Y and X . (more discussions later) -Typically, instrumental variable (IV) method is used to account for the unobservables that a¤ect both H and W (endogeneity problem) or measurement error (usually in W )
Simon Chang (Institute)
Labor Supply— Static Model
Fall 2010
18 / 29
Common Empirical Issues in Estimating Wage Elasticity
Hours of work over how long? A week, a month or a year? Measurement errors How to calculate hourly wage if paid an annual salary? Self-selection: only wages of workers are observed, non-random sample Unobserved factors: unobserved "strong taste of work" leads to both high non-labor income and long work hours
Simon Chang (Institute)
Labor Supply— Static Model
Fall 2010
19 / 29
Women’s Labor Force Participation
In the past few decades, the world has witnessed a substaintial rise in women’s labor force particiaption. What caused the rise? - increase in real wage - lower fertility v.s. lower reservation wage (causation runs in both ways) - technological improvement in home production - other cultural/ social factors
Simon Chang (Institute)
Labor Supply— Static Model
Fall 2010
20 / 29
Welfare Programs and Work Incentives (I): TANF
Consider a welfare program providing a cash grant to eligible poor people regardless of their work e.g. Temporary Assistance to Needy Families (TANF) Note that recepients of TANF can still work How does such a program a¤ect labor force participation and hours of work of the poor?
Simon Chang (Institute)
Labor Supply— Static Model
Fall 2010
21 / 29
A Case of Take-it-or-leave-it Cash Grant
Simon Chang (Institute)
Labor Supply— Static Model
Fall 2010
22 / 29
Reduce Grant if Work Suppose the gov takes away $ .5 for every dolloar the recipient earns by working
Simon Chang (Institute)
Labor Supply— Static Model
Fall 2010
23 / 29
Welfare Programs and Work Incentives (II): EITC
Earned Income Tax Credit (EITC): for every dollar you earn, the gov matches it with up to a certain percentage of the earned dollar In 2002 - 40 cents matched to each dollar earned if income < $10350, maximum is $4140 - maximum credit is available if $10350
income
$13520
- credit is reduced by 21.06 cents for each dollar earned if income>$13520
Simon Chang (Institute)
Labor Supply— Static Model
Fall 2010
24 / 29
Welfare Programs and Work Incentives (II): EITC Budget constraint
Simon Chang (Institute)
Labor Supply— Static Model
Fall 2010
25 / 29
Welfare Programs and Work Incentives (II): EITC E¤ects on labor force participation and hours of work
Simon Chang (Institute)
Labor Supply— Static Model
Fall 2010
26 / 29
Family Labor Supply: Interpersonal Dependence Often, within a family, one’s labor decision is correlated with another’s decision. For example, whether wife would work depends on husband’s labor decision. The previous one-person static model is inadequate in this multi-person context. Therefore, we need to modify the static model as follows. Consider a family with two working-age individuals whose labor decision are intercorrelated and other dependents. The family is seeking maximization of total family consumption and the leisure of each family member. -Utility function: U = U (C , L1 , L2 , X ) where C is now the total family consumption; Li is leisure of individual i. -Budget constraint: C + W1 L1 + W2 L2 = Y + W1 T + W2 T where Y is total family non-labor income. Simon Chang (Institute)
Labor Supply— Static Model
Fall 2010
27 / 29
Family Labor Supply -Now the full income is: M = Y + W1 T + W2 T -FOCs: UC (C , L1 , L2 , X ) = λ UL1 (C , L1 , L2 , X ) = λW1 UL2 (C , L1 , L2 , X ) = λW2 -Demand functions: C L1 L2 Simon Chang (Institute)
= C (W1 , W2 , M, X ) = L1 (W1 , W2 , M, X ) = L2 (W1 , W2 , M, X ) Labor Supply— Static Model
Fall 2010
28 / 29
Empirical Evidence of Family Labor Supply
Family labor supply model can be estimated in a similar fashion to the single-person labor supply model Empirical evidence from the US suggests a 10% increase in the husband’s wage lowers the participation rate of women by 5.3 percentage points and reduces the hours that working wives allocate to the labor market by 1.7 percent. On the contrary, little evidence shows that wife’s wage a¤ects husband’s labor supply
Simon Chang (Institute)
Labor Supply— Static Model
Fall 2010
29 / 29
