LABOR SUPPLY RESPONSES TO TAXES AND TRANSFERS: PART I (BASIC APPROACHES) Henrik Jacobsen Kleven London School of Economics

LABOR SUPPLY RESPONSES TO TAXES AND TRANSFERS: PART I (BASIC APPROACHES) Henrik Jacobsen Kleven London School of Economics Lecture Notes for MSc Public Finance (EC426): Lent 2013

AGENDA Efficiency cost of labor supply responses to taxes and transfers. Theoretical models of labor supply. Empirical approaches and methodological issues in labor supply estimation. Quasi-experiments and difference-in-differences. Key findings and consensuses.

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 =,where is the utility loss from taxation (in monetary units) and is collected tax revenue. The marginal DWL is given by =. We have = + where is the mechanical revenue effect and is the behavioral revenue effect. Wehave = using the envelope theorem. = ( + ) =. 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 = = = (1 ) (1 ) where to the net-of-tax rate. 1 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 = ( x) st. = + where is the wage rate, is non-labor income, and x is a vector of individual characteristics. Optimal labor supply satisfies 0 0 = along with a non-negativity constraint labor supply function = ( 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 = or negative. Income elasticity =. Can be either positive. Negative if leisure is normal. Compensated wage elasticity captures the response at a constant utility level. This elasticity is always positive. The Slutsky Equation links elasticities: = where is the income effect.

BASIC CROSS-SECTIONAL ESTIMATION Based on the model above, early work considered a regression specification such as = 0 + 1 + 2 + 3 x + where x is a vector of observable controls and is the error term. OLS is consistent if explanatory variables and are uncorrelated. Results: Male labor supply (see Pencavel, 1986): ' 0 and ' 0 1 ' 0 1. Female labor supply (Heckman-Killingsworth, 1986): Much larger elasticities on average, but enormous variation across studies.

PROBLEMS WITH BASIC APPROACH 1. Identification: may be positively correlated with taste for work, which is unobserved and captured by positive correlation between and upward bias [omitted variable bias]. 2. Measurement error as 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 0, because otherwise no wage rate is observed. Extensive responses ignored.

ACCOUNTING FOR (NON-LINEAR) TAXES -bracket piecewise linear schedule ( ) with marginal tax rates 1 The budget constraint: = ( )+ =(1 ) + where ( )+ is virtual income in bracket. Within each bracket, optimal labor supply can be written on the form = ((1 ) ). 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 = 0 + 1 (1 ) + 2 + 3 x + which can be estimated by e.g. OLS. Problems with this approach: 1. Identification: (a) is correlated with [omitted variable bias] (b) are endogenous to and hence correlated with [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 working due to child care, commuting, etc. Fixed costs of employing due to hiring costs, technological constraints, etc. Means-tested transfers creating higher marginal tax rates at the bottom than further up the distribution. 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

MODERN LABOR SUPPLY LITERATURE Early phase (around 1990s): Focus on the evaluation problem in previous work Search for identification takes center stage Focus on experimental evidence Later phase (2000s onwards): Sharper identification and graphical evidence Shift from survey data to large administrative datasets Sufficient statistics approach as a bridge between reducedform and structural estimation

SOURCES OF EXPERIMENTAL VARIATION Randomized experiments Truly exogenous variation Relatively uncommon in public finance Quasi-experiments [variation created by actual policy] Tax-transfer reforms and difference-in-differences Discontinuities in tax-transfer schedules and bunching approaches Regression Discontinuity Design

THE EVALUATION PROBLEM Counterfactual question: what would person s labor supply be if taxes were different? = person s labor supply if taxes are high ( treatment ), = person s labor supply if taxes are low ( control ). We don t observe both and at the same time. What we do observe is [ ] [ ] = [ {z } ] + ³ [ ] ] [ {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 and controls. Group is treated by a policy while group is not. The treatment effect on outcome is measured by [ ] [ ]. Random assignment [ ] = [ ]. Then, [ ] [ ] = [ ]=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).

QUASI-EXPERIMENTS & DIF-IN-DIF Tax reforms create natural experiments that may resemble true experiments. Compare a group affected by the reform ( ) to a group not affected ( ). Let and denote before and after the reform. The effect on can be estimated by the difference-in-differences =[ ] [ ] A before-after estimator is biased by time effects. A group comparison is biased by group effects. The dif-in-dif removes common (group-invariant) time effects and time-invariant group effects.

REGRESSION FORMULATION OF DIF-IN-DIF Time dummy =1if is after the reform. Treatment dummy =1if individual belongs to the treatment group. Regression framework: = 0 + 1 + 2 + 3 + 4 x + Without covariates x, 3 is the basic dif-in-dif estimate. covariates can improve the basic dif-in-dif. Including

CENTRAL ASSUMPTIONS OF DIF-IN-DIF A1: All time effects must be common for and (the "parallel trend" assumption). A2: The composition of -and -groups must remain stable during the course of the reform When both and 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 a good 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). -group = wives at the 99th percentile, -group = wives at the 75th percentile. Uses a dif-in-dif comparing changes in labor supply for and 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): (1 ) (1 ) (1 ) (1 ) 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) -group starts from a lower level than the -group -group less able to absorb an upward trend in female labor supply. (b) Alternative story: trend towards "power couples" in late 80s. 2. / assignment is not clean as TRA86 affected both groups dif-in-dif requires homogeneous responsiveness for and. 3. Identification strategy requires no cross-substitutability in spousal leisures, which is very strong.

NON-PARALLEL TRENDS? 1. Use data from periods prior and subsequent to the policy change: (a) Do a placebo dif-in-dif for non-reform periods. If it is non-zero, then dif-in-dif is tenuous. (b) Do a triple-dif = dif-in-dif of interest placebo dif-in-dif. (c) Plot longer time series of outcomes for and to see if "something different" happens around the reform. 2. Plotting the time-series from 1979-1998, Liebman and Saez (2006) show that Eissa s results are not robust.

TRANSFERS AND LABOR SUPPLY: IN-WORK BENEFITS Transfers which are conditional on labor force participation. They are typically means-tested [targeted to low earnings/assets] and categorical [targeted to single mothers]. Examples: 1. Earned Income Tax Credit (EITC) in the U.S. A cash transfer provided through the tax system. 2. Working Families Tax Credit (WFTC) in the U.K. is broadly similar to the EITC.

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

EISSA & LIEBMAN (1996) Use a dif-in-dif to estimate the effect of the EITC expansion in TRA86 on labor force participation and hours worked for single mothers. Assignment to treatments and controls: 1. T = single women with children, C = single women without children. 2. T = single women with children and low education, C = single women without children and low education.

EITC BEFORE AND AFTER TRA86 Source: Eissa and Liebman (1996)

DIFFERENCE-IN-DIFFERENCES: LABOR FORCE PARTICIPATION RATES OF SINGLE WOMEN Source: Eissa and Liebman (1996)

PARTICIPATION RATES OF SINGLE WOMEN 1981-1992 All Unmarried Females Source: Eissa and Liebman (1996)

PARTICIPATION RATES OF SINGLE WOMEN 1981-1992 Unmarried Females With Less Than High School Education Source: Eissa and Liebman (1996)

FINDINGS AND ISSUES EL96 find large participation effects, no significant hours-of-work effects. Using single women without children as a control for single women with children is problematic, especially with regards to the parallel trends assumption. Robustness checks: Treatment-control assignment that exploits EITC means-testing: single mothers with low vs. high education no significant effect. Longer time series plot of participation rates across treatment and control groups only moderately convincing.

OVERVIEW OF EITC LABOR SUPPLY STUDIES Eissa-Liebman (1996): effect on single mothers using TRA86 as a quasi-experiment. Large participation effect, no hours-of-work effect. Meyer-Rosenbaum (2001): effect on single mothers using the 86, 90, and 93 reforms as quasi-experiments. More variation than EL96, but complications due to welfare reform. Large participation effect. Eissa-Hoynes (2004): effect on married couples with low earnings. Jointness of EITC discourages participation of married women. early consensus that extensive responses are more important than intensive responses. But this view might need revision in light of more recent work (see subsequent lectures).