Monthly Archives: April 2014

A GENERAL MODEL OF THE BEHAVIORAL RESPONSE TO TAXATION: Implications for Empirical Analysis

In the framework of the standard model, the estimated response of labor supply to the tax rate, holding income constant, reveals information about the utility function (in particular S, the rate of change of the slope of the indifference curve). The general model of behavioral response makes clear that in fact this response reveals a mixture of information about individual preferences and the avoidance technology.
There are several reasons why it is important to separately identify the structure of preferences and the structure of the avoidance technology. First of all, it is likely that the avoidance technology varies across individuals in systematic and observable ways. This implies that the behavioral response of labor supply to taxation will also vary, and the differential response can potentially be related to observable characteristics. Second, while in the standard model the labor supply response to a change in the pre-tax wage rate is identical (except for a multiplicative constant) to the response to a change in a proportional tax rate, that connection breaks down in the general model. Thus, estimates of the wage elasticity of labor supply do not necessarily carry over to estimates of the tax elasticity of labor supply, and vice versa. Separate identification of the structure of preferences and of the avoidance technology is required to nail down the relationship between these two elasticities. Thus, this model forces a reinterpretation of the results of, for example, Rosen (1976), who stimates a labor supply function of the formw6582-9
and interprets the estimated value of (qi-q2) as a measure of “tax illusion,” or the tendency of taxpayers to be more aware of the pre-tax wage rate than the appropriate marginal tax rate. In the general theory of behavioral response presented here, the value of qf- q2 has a structural
interpretation that is unrelated to tax illusion.

A GENERAL MODEL OF THE BEHAVIORAL RESPONSE TO TAXATION: Some Examples

A concrete example nicely illustrates the important points.
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A GENERAL MODEL OF THE BEHAVIORAL RESPONSE TO TAXATION: Proportional Labor Income Taxation 4

The more negative is С , the more damped is the negative response of reported income to an increased tax rate, both because it scales down the labor supply response (which is zero if CJ2 = -C22) and because it reduces the positive avoidance response (the higher is 1C I, the more any labor supply decreases the attractiveness of avoidance). The reported income response is increased, though, because of the avoidance response itself, which is larger, ceteris paribus, the larger is 1/C • The net change is of ambiguous sign. The response of reported income to wage rate changes is, however, always lower than in the standard model, as long as Cl2/C22 is negative and D/S is non-negative, as I maintain is the usual case. To the extent that C12/C22 is negative, an increased wage rate makes avoidance more attractive, offsetting to some extent the induced increase in true income. As discussed above, more negative D (recall that S
One fascinating special case obtains when the cost of avoidance depends only on the taxpayer’s reported income (wL – A), which I will denote R. In this circumstance Ci = -C2, and
5L
С = С = -С = С. This has the startling result of making — equal precisely to zero.
3L
As it also makes — into exactly its value in the absence of taxes, taxation has no
(compensated) effect on labor supply. Furthermore, the compensated response of reported income (wL-А) to a change in w is always zero, because the increase in actual labor income will be exactly offset by an increase in avoidance. This occurs because, at the optimal amount of avoidance, С equals t. But if only reported income affects the cost of avoidance, increasing actual income will be as effective in reducing cost as reducing avoidance itself, so that = -C^.
This implies that С = -t or, in other words, there is an implicit subsidy to working equal to wt, which exactly offsets the explicit tax rate. Thus a (compensated) reduction in t reduces avoidance but leaves labor supply unchanged, and increases reported income concomitantly. credit

A GENERAL MODEL OF THE BEHAVIORAL RESPONSE TO TAXATION: Proportional Labor Income Taxation 3

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When CJ2 < 0, increased avoidance raises the avoidance-facilitating value of labor supply, and thus makes it more attractive. The reverse holds true as well—increased labor supply, by lowering the marginal cost of avoidance, makes avoidance more attractive. As Cj2 rises in absolute value, the compensated decline in labor supply that would otherwise occur when t increases is somewhat mitigated because the increased avoidance that accompanies the higher tax rate increases the avoidance-facilitating value of labor supply. A higher absolute value of С increases the positive effect on labor supply of a wage rate increase, because any labor supply increase that occurs also increases the attractiveness of avoidance; as above, increased avoidance increases the avoidance-facilitating value of labor supply. Thus, to the extent that C(2 < 0, a (compensated) increase in w will be more effective at increasing labor supply than an equal percentage (compensated) increase in (1 -1): an increase in pre-tax wage rates is more effective at increasing labor supply than a concomitant decline in the marginal tax rate. The latter will decrease avoidance and reduce the avoidance-facilitating value of labor income.

A GENERAL MODEL OF THE BEHAVIORAL RESPONSE TO TAXATION: Proportional Labor Income Taxation 2

The first-order conditions for this problem are:
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Expression (4b) states that avoidance should be increased until its marginal cost, С , equals its marginal return of t. The first-order condition (4a) is the usual one that labor supply is optimal when the marginal rate of substitution of labor for income equals the net-of-tax wage rate. The critical aspect of the general model is that the net-of-tax wage rate includes an implicit subsidy to working equal to wC(, due to the fact that earning more income lowers the marginal cost of avoiding taxes bv that amount. The implications of this can be drawn out by examining the Slutsky equations for the response of labor supply and avoidance to the tax rate and wage rate, which are summarized in Table l:

A GENERAL MODEL OF THE BEHAVIORAL RESPONSE TO TAXATION: Proportional Labor Income Taxation

In the standard textbook model of the effect of income taxation on labor supply,1 the individual maximizes utility, which is a function of income, or consumption of goods, and labor supply, subject to a budget constraint affected by taxes:
w6582-1
where Y is income, L is labor supply, t is a proportional tax rate, w is the wage rate, and M is non-labor income, presumed for simplicity to be untaxed.

A GENERAL MODEL OF THE BEHAVIORAL RESPONSE TO TAXATION: Introduction 2

There are many possible explanations of the small observed real substitution response. Perhaps not enough time elapsed after the tax changes for individuals and firms to exhibit their long-term reaction to the changed environment. It may be that the tax changes, particularly the Tax Reform Act of 1986, were so complicated that it is difficult to accurately measure how the relevant relative prices changed. Of course, another possibility is simply that the relevant elasticities of real substitution are close to zero, so that a correctly measured elasticity is also quite low.

A GENERAL MODEL OF THE BEHAVIORAL RESPONSE TO TAXATION: Introduction

taxes2
Legal responses to taxation can usefully be divided into two categories: real substitution responses, in which the tax-induced change in relative prices causes individuals to seek a different consumption bundle; and avoidance responses, in which taxpayers undertake a variety of tax planning, renaming, and retiming activities whose goal is to directly reduce tax liability without consuming a different mix of consumption. There is much evidence that suggests that the class of avoidance behaviors is more responsive to tax changes than are real substitution responses. Certainly, the evidence about the behavioral response to the major U.S. tax changes of the 1980s and 1990s suggests such a hierarchy of response (Slemrod, 1992, Auerbach and Slemrod, 1997).