Emanuel Saez/AEJ-August 2010

Do Taxpayers Bunch at Kink Points?

Emanuel Saez/AEJ-August 2010

Abstract: Using the EITC and US Federal Income tax schedule, the paper analyses the bunching at kink points and estimates the compensated elasticity. It finds evidence of bunching in the first kink point only for self employed,

and no evidence of bunching in other kink points. There is no clear model that explains the behaviour in the Federal Income Tax setting.

Prepared by: José Gabriel CastilloTAMU-2011

The standard model prediction� The standard static model proposes that agents choose labor supply (hours of work) until the marginal disutility of work equals the marginal utility of disposable income (net of taxes).

� The model predicts that if individual preferences are convex and The model predicts that if individual preferences are convex and smoothly distributed in the population we should observe bunching of individuals at convex kink points of the budget set.

� The amount of bunching generated by the budget set at kink points is proportional to the size of the compensated elasticity of income with respect to the net-of-tax rate.

Kink points source� Kink points: are created due to taxes and government transfers. Progressive US individual income tax generates a linear budget set with kinks in every marginal tax rate jump.

� The Earned Income Tax Credit (EITC) creates two large convex kink points: phased-in and phased-out.EITC: It is a tax credit for certain people who work and have earned � EITC: It is a tax credit for certain people who work and have earned income under $48,362. It reduces the amount of tax the taxpayer owes and can also be subject to a refund.(IRS, P-596)

� EITC is a function of family earnings defined as the sum of wages, salaries, self employed income and the number of qualifying children.

� Federal Income Tax also creates kinks due to the tax schedule

Model and methodology� The standard model setting:

� Two goods: � after-tax income c (consumption) ; positively related.� Before-tax income z (earning income effort); negatively related.

� Constant marginal tax rate t.� z is distributed smoothly across the population with density function h(z)h(z)

� Utility function then is described by u(c,z).� Let z* be the point where t changes by dt. Then the slope until z* is (1-t); then, after this point (kink) the slope of the budget line is defined by (1-t-dt).

� The bunching of individuals should be observed between z* and z*+d z*.

� The compensated elasticity of earnings e with respect to (one minus) the marginal tax rate will be:

Model and methodology� The total number of taxpayers bunching at z* is h(z*)dz*.

� h(z*) is the density of income at z*.� dz* comes from the compensated elasticity equation.

� It is worth to note the following:� The larger the behavioral elasticity, the more the bunching.� The larger the behavioral elasticity, the more the bunching.� The size of the jump in marginal tax rates is measured by the change in marginal tax rates relative to the base net-of-tax rate 1-t. (if the jumps are large, income effects might be present and e would be a mixed of compensated and uncompensated elasticity)

� The model assumes that all individuals have the same elasticity.� The results are for the static model but can be extended to a dynamic model in which case bunching is proportional to the Frisch elasticity instead of the compensated elasticity.

Empirical estimation� The maximization problem for the empirical estimation is:

� Max

� st. � n is an ability parameter distributed f(n).Quasi linearity assumption of the utility function implies there � Quasi linearity assumption of the utility function implies there are no income effects, thus compensated and uncompensated elasticities are equal.

� Iso-elastic assumption of the utility function implies the elasticity is constant and equal to e.

� The first order condition of the maximization problems results in:

Empirical estimation� From the FOC’s of the maximization problem one can conclude that individuals behavioral response is to choose z=z* when n is within the range [z*/(1-t0)

e, z*/(1-t1)e],

accounting for the kink created by the change in the marginal tax rate from t0 to t1. tax rate from t0 to t1.

� The generalized equation for the elasticity becomes:

� The fraction of the population bunching is:

EITC-Empirical results

� For the EITC histogram it is evident that the density maximum is exactly at the first kink point.

� “The fact that the location of “The fact that the location of the first kink point differs between recipients with one child vs. two or more children constitutes strong evidence that the clustering is driven by behaviouralreponses as predicted by the standard model”

� Using kernel methods to smooth the density empirical distribution and breaking the sample for taxpayers income type it is easy to observe that bunching happens only for bunching happens only for the self-employed income type, for the families with one child or those with more children.

Elasticity estimation results� Significant elasticities are found around the first kink point for the full sample (1995-2004). (Panel A/Table 2)

� Significant elasticities are driven entirely by the self-employed who show large elasticities of 1.1 and 0.8 for the one child and more than one child, respectively. (Panel A/Table 2)

� Elasticities for the wage earners are small (close to zero) and � Elasticities for the wage earners are small (close to zero) and insignificant; around 0.03 and 0.003 for the one child and more than one child, respectively. (Panel A/Table 2)

� The elasticities increase in time (see differences in the two periods) and remain significant only for the self-employed type whereas labor supply shows to be unresponsive in the margin even in the long run. (Panel C/Table 2)

Interpretation� Wage earners do not response to EITC changes. This might be due to several reasons: low intensive elasticity respect to marginal tax rates; lack of information and understanding of the benefits of the program; lack of flexibility to adjust labor supply; lack of earnings control due to stochastic job opportunities; unable to misreport earnings due to third party reports unable to misreport earnings due to third party reports (employer) making tax evasion difficult.

� Self-employed bunch consistently. Due to private control over the same aspects mentioned and not available for wage earners. The results differ from the standard model in two ways:� Bunching is evident only at the first kink point� Bunching arises only when the EITC subsidy rate is above 15%