TAXES, TRANSFERS, AND LABOR SUPPLY Henrik Jacobsen Kleven London School of Economics Lecture Notes for PhD Public Finance (EC426): Lent Term 2012
AGENDA Why care about labor supply responses to taxes and transfers? Theoretical models of labor supply. Empirical strategies in labor supply estimation (and associated problems). Key findings and consensuses for labor supply responses to taxes and transfers.
WHY CARE ABOUT LABOR SUPPLY RESPONSES? When the government levies income taxes to finance transfer programs and public goods, individuals respond by changing labor supply. By revealed preference, each individual prefers the new labor supply to the old one at the tax-inclusive prices. So, everyone is better off because of the labor supply adjustments? No, the revealed preference argument applies to each individual separately, not to the population as a whole. Behavioral responses affect gov t revenue and create a fiscal externality the deadweight loss of taxation.
THE TOTAL DEADWEIGHT LOSS OF TAXATION net-of-tax wage rate tax revenue labor supply function τ w w T DWL A (1- τ)w deadweight loss B CS consumer surplus h* B h* A hours worked
THE MARGINAL DEADWEIGHT LOSS OF TAXATION net-of-tax wage rate Behavioral a revenue e effect db ( ddwl) labor supply function τ w w T DWL (1- τ)w CS C B Mechanical revenue effect dm hours worked
THE DEADWEIGHT LOSS OF TAXATION The deadweight loss is given by DWL = W T,whereW is the utility loss from taxation (in monetary units) and T is collected tax revenue. The marginal DWL is given by ddw L = dw dt. We have dt = dm +db where dm is the mechanical revenue effect and db is the behavioral revenue effect. WehavedW = dm using the envelope theorem. ddw L = dm (dm + db) = db. General insight: In a model with efficient markets, the marginal efficiency cost of taxation is given by the behavioral revenue loss.
We have DWL FROM LABOR SUPPLY RESPONSES ddw L = db = τ w dh = dh/h d(1 τ)/(1 τ) where ε to the net-of-tax rate. τ 1 τ ε dτ wh, is the elasticity of hours worked with respect Compensated vs uncompensated elasticity? For DWL, we want the compensated elasticity (see Auerbach, 1985, for a rigorous treatment). Empirical literature estimates compensated and uncompensated elasticities.
DIMENSIONS OF LABOR SUPPLY RESPONSE 1. Quantitative dimensions: (a) Hours worked for those who are working (intensive margin) (b) Labor force participation (extensive margin) 2. Qualitative dimensions: (a) Effort on the job (b) Type of job (occupation, industry, etc.) (c) Education and on-the-job training (d) Location and migration
THE BASIC STATIC MODEL WITHOUT TAXES Utility maximization: max c,h u = u (c, h, x) st. c = wh + y, where w is the wage rate, y is non-labor income, and x is a vector of individual characteristics. Optimal labor supply satisfies u 0 h /u0 c = w along with a non-negativity constraint labor supply function h = h (w, y, x) 0.
INCOME AND SUBSTITUTION EFFECTS u 0 consumption c substitution effect slope w 0 income effect u 1 slope w 1 y hours worked h
ELASTICITIES AND SLUTSKY DECOMPOSITION Uncompensated wage elasticity ε u = h or negative. Income elasticity η = h y y h w w h. Can be either positive. Negative if leisure is normal. Compensated wage elasticity ε c captures the response at a constant utility level. This elasticity is always positive. The Slutsky Equation links elasticities: ε u = ε c θ, where θ wh y η is the income effect.
BASIC CROSS-SECTIONAL ESTIMATION Based on the model above, early work considered a regression specification such as h i = β 0 + β 1 w i + β 2 y i + β 3 x i + ν i, where x i is a vector of observable controls and ν i is the error term. OLS is consistent if explanatory variables and ν i are uncorrelated. Results: Males labor supply (see Pencavel, 1986): ε u ' 0 and θ ' 0.1 ε c ' 0.1. Female labor supply (Heckman-Killingsworth, 1986): Much larger elasticities on average, but enormous variation across studies.
PROBLEMS WITH BASIC APPROACH 1. Identification: w i may be positively correlated with taste for work, which is unobserved and captured by ν i positive correlation between w i and ν i upward bias [omitted variable bias]. 2. Measurement error as w i is measured as earnings/hours from surveys. 3. Functional form sensitivity. 4. Ignores the impact of taxes on the central explanatory variables. 5. Non-participation: sample is selected so that h i > 0, because otherwise no wage rate is observed. Extensive responses ignored.
ACCOUNTING FOR (NON-LINEAR) TAXES N-bracket piecewise linear schedule T (wh) with marginal tax rates τ 1,..., τ N The budget constraint: c = wh T (wh)+y =(1 τ n ) wh + R n, where R n τ n wh T (wh)+y is virtual income in bracket n. Within each bracket, optimal labor supply can be written on the form h = h ((1 τ n ) w, R n ). We must deal explicitly with the possibility of a kink solution at the threshold between two brackets.
BUDGET SET AND VIRTUAL INCOME WITH A 2-BRACKET NONLINEAR TAX SCHEDULE consumption c u slope (1-2 ) w kink R 2 slope (1-1 ) w R 1 h hours worked h
ESTIMATION WITH NONLINEAR TAXES Based on the model, consider an empirical specification such as h i = β 0 + β 1 (1 τ i ) w i + β 2 R i + β 3 x i + ν i, which can be estimated by e.g. OLS. Problems with this approach: 1. Identification: (a) w i is correlated with ν i [omitted variable bias] (b) τ i,r i are endogenous to h i and hence correlated with ν i [reverse causality]. 2. Bunching: the model predicts bunching at kink points, but we typically do not observe much bunching in the data.
THE CONVEXITY ASSUMPTION So far, we have assumed that workers supply labor where the indifference curve is tangent to the budget set. If this point of tangency occurred at negative hours, a non-negativity constraint implied a corner solution at zero hours (non-participation). In this model, marginal changes in taxes lead to marginal changes in hours worked. Even participation responses are smooth in this way. This analysis is fine as long as the budget and preferences are convex.
THE CONVEX MODEL: INTENSIVE VS EXTENSIVE LABOR SUPPLY RESPONSES consumption c u B u A slope w 0 y h A h B hours worked h
THE CONVEX MODEL: INTENSIVE VS EXTENSIVE LABOR SUPPLY RESPONSES consumption c u B u A slope w 1 slope w 0 y h A h B hours worked h
THE REAL WORLD IS NON-CONVEX Fixed costs of work due to child care and to commuting. Means-tested income transfers creating higher marginal tax rates at the bottom than further up the distribution. A transfer system with work tests so that transfers are lost completely at the point of labor market entry. Non-convexities bring discrete participation responses into play even with small changes in wages or taxes.
A MODEL WITH FIXED WORK COSTS: INTENSIVE VS EXTENSIVE LABOR SUPPLY RESPONSES consumption c slope w 0 y F y h F hours worked h
A MODEL WITH FIXED WORK COSTS: INTENSIVE VS EXTENSIVE LABOR SUPPLY RESPONSES consumption c slope w 1 slope w 0 y F y small intensive response large extensive response hours worked h h F
BUDGET SET WITH MEANS-TESTED TRANSFERS consumption c Indifference Curve Nonconvex Budget High-Tax Bracket Low-Tax Bracket Transfer Phase-Out hours worked h
RECENT WORK ON TAX AND LABOR SUPPLY Distinguishes clearly between hours worked and participation. Accounts for discrete participation responses and nonconvexities. The search for identification takes centre stage. Uses experimental evidence to estimate labor supply: Randomized experiments (the ideal) Natural experiments (variation created by tax policy): Regression Discontinuity Design: close to the ideal Tax reforms and dif-in-dif Bunching around kink points
THE EVALUATION PROBLEM Counterfactual question: what would person i s labor supply be if taxes were different? L T i = person i s labor supply if taxes are high ( treatment ), L C i = person i s labor supply if taxes are low ( control ). We don t observe both L T i and L C i at the same time. What we do observe is E[L T i T ] E[LC i C] =E[LT i {z LC i T } ] + ³E[L C] C i T ] E[LC i {z } treatment effect selection bias The selection bias reflects systematic differences between treatments and controls. Randomized experiments solve this problem.
RANDOMIZED EXPERIMENTS A sample of agents is divided randomly into treatments T and controls C. GroupT is treated by a policy X while group C is not. The treatment effect on outcome L is measured by E[L T T ] E[L C C]. Random assignment E[L C C] =E[L C T ]. Then, E[L T T ] E[L C C] =E[L T L C T ]=true treatment effect. Applications: 1. NIT experiments in the U.S. in the 60s and 70s. Many studies (e.g., Ashenfelter-Plant, JLE 1990). 2. Canadian Self Sufficiency Programme (SSP) in the 90s. Michalopoulos-Robins-Card (JPubE 2005).
NATURAL EXPERIMENTS & DIF-IN-DIF Tax reforms create natural experiments that may resemble true experiments. Compare a group affected by the reform (T ) to a group not affected (C). Let B and A denote before and after the reform. The effect on L can be estimated by the difference-in-differences L T L C =[L T A LT B ] [LC A LC B ]. A before-after estimator L T is biased by time effects. A group comparison L T A LC A is biased by group effects. The dif-in-dif removes common (group-invariant) time effects and time-invariant group effects.
CENTRAL ASSUMPTIONS OF DIF-IN-DIF A1: All time effects must be common for T and C (the "parallel trend" assumption). A2: The composition of T -andc-groups must remain stable during the course of the reform When both T and C experience a policy change but of different size, dif-in-dif is still possible. But this requires a third assumption.
EISSA (1995) Never published but well-cited and a great example for teaching. The Tax Reform Act of 1986 (TRA86) cut marginal tax rates at the top much more than further down the distribution. The jointness of the US income tax implies that wives of rich husbands experienced larger tax cuts than wives of not-so-rich husbands. Treatment/control assignment based on (husband s earnings + family non-labor income). T -group = wives at the 99th percentile, C-group = wives at the 75th percentile. Uses a dif-in-dif comparing changes in labor supply for T and C from before the reform (1985) until after the reform (1989).
Source: Eissa (1995) THE TAX REFORM ACT OF 1986
Source: Eissa (1995) MARGINAL TAX RATES FOR TREATMENTS AND CONTROLS
Source: Eissa (1995) DIFFERENCE-IN-DIFFERENCES: LABOR FORCE PARTICIPATION
DIFFERENCE-IN-DIFFERENCES: HOURS WORKED CONDITIONAL ON PARTICIPATION Source: Eissa (1995)
LABOR SUPPLY ELASTICITIES Relate dif-in-dif for labor supply to dif-in-dif for (1- marginal tax rate): L T /L T L C /L C (1 τ T )/(1 τ T ) (1 τ C )/(1 τ C ) Elasticity of labor force participation is 0.5. Elasticity of hours worked is 0.4. Total elasticity is 0.9. Large elasticities but also large standard errors effects not statistically significant.
ISSUES WITH EISSA S APPROACH 1. The parallel trends assumption: (a) T -group starts from a lower level than the C-group C-group less able to absorb an upward trend in female labor supply. (b) Alternative story: trend towards "power couples" in late 80s. 2. T /C assignment is not clean as TRA86 affected both groups dif-in-dif requires homogeneous responsiveness for T and C. 3. Identification strategy requires no cross-substitutability in spousal leisures, which is very strong.
TRANSFERS AND LABOR SUPPLY: IN-WORK BENEFITS In-work benefits are income transfers that are conditional on labor force participation. They are typically means-tested (targeted to low earnings/assets) and categorical (targeted to single mothers). The best known and extensively analyzed in-work benefit program is the Earned Income Tax Credit (EITC) in the U.S. A cash transfer provided through the tax system. The Working Families Tax Credit (WFTC) in the U.K. is modelled broadly after the EITC.
THE EITC PROGRAM The EITC was introduced in 1975 as a small program. It was expanded by tax reform acts passed in 1986, 1990, 1993, and 2001. The EITC is now the largest cash transfer program at the federal level. It implies negative tax liabilities on earnings (including all federal, state, and social security taxes) for the representative single mother. The EITC expansions in combination with the welfare reform law passed in 1996 has fundamentally changed the focus of low-income support in the U.S. from the poor to the working poor.
LABOR SUPPLY RESPONSES TO THE EITC consumption c Non-EITC budget EITC fixed cost phase-in plateau phase-out hours worked h
LABOR SUPPLY RESPONSES TO THE EITC consumption c Non-EITC budget EITC fixed cost phase-in plateau phase-out hours worked h
LABOR SUPPLY RESPONSES TO THE EITC consumption c Non-EITC budget EITC fixed cost phase-in plateau phase-out hours worked h
LABOR SUPPLY RESPONSES TO THE EITC consumption c Non-EITC budget EITC fixed cost phase-in plateau phase-out hours worked h
LABOR SUPPLY RESPONSES TO THE EITC Eissa-Liebman (1996): effect on single mothers using TRA86 as a quasi-experiment. Large participation response, no hours-of-work response. Meyer-Rosenbaum (2001): effect on single mothers using the 86, 90, and 93 reforms as quasi-experiments. More variation than EL96, but also complications due to welfare reform. Large participation response. Eissa-Hoynes (2004): effect on married couples with low earnings. Jointness of EITC discourages participation of married women.
DIFFERENCE-IN-DIFFERENCES: LABOR FORCE PARTICIPATION RATES OF SINGLE WOMEN Source: Eissa and Liebman (1996)