ECONOMETRIC ISSUES IN ESTIMATING THE BEHAVIORAL RESPONSE TO TAXATION: A NONTECHNICAL INTRODUCTION ROBERT K. TRIEST *

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1 FORUM ON THE BEHAVIORAL RESPONSE TO TAXATION ECONOMETRIC ISSUES IN ESTIMATING THE BEHAVIORAL RESPONSE TO TAXATION: A NONTECHNICAL INTRODUCTION ROBERT K. TRIEST * Abstract - Reliable estimates of how tax incentives affect behavior are an essential input into the formation of tax policy. However, one encounters a number of difficult econometric problems in estimating the magnitude of the behavioral effects. This paper provides a nontechnical introduction to some of the more prominent problems, particularly the endogeneity of marginal tax rates and the problem of identifying tax effects, and discusses two estimation techniques used in recent studies: difference-in-differences and instrumental variables using panel data. INTRODUCTION Understanding how individuals, families, and households adjust their behavior in response to taxation is one of the most important tasks facing public finance economists. Taxation affects many aspects of individual behavior, including * Research Department, Federal Reserve Bank of Boston, Boston, MA the choice between work and leisure, the choice of occupation and fringe benefits, the choice of deferred versus immediate compensation, the decision of how much to save and consume, the decision of how to allocate one s savings across assets, the decison of whether to rent or own a house, and the decision of how much to donate to charity. Both positive and normative analysis of taxation everything from revenue estimation to social welfare evaluation depends critically on the magnitude of the responses. Economic theory provides a framework for modeling behavioral responses and understanding their implications and importance, but tells us little about the expected magnitude of the responses and in some contexts does not even tell us the direction of the response. The magnitude of behavioral responses is inherently a topic for empirical investigation. Unfortunately, econometric analysis of how behavior responds to taxation is much like the tax code itself: complex and often controversial. At any given moment in time, the marginal tax rate that an individual faces depends on her 761

2 NATIONAL TAX JOURNAL VOL. LI NO. 4 taxable income, which in turn depends on her economic status and behavior. So it becomes difficult to disentangle differences in behavior across individuals, which are induced by taxation, from those due to other determinants of behavior. Over time, changes in the tax code provide an exogenous source of variation in marginal tax rates, but in this case, it becomes difficult to disentangle the behavioral effect of tax code changes from those due to other changes in the economic environment occurring at the same time. The purpose of this paper is to provide a nontechnical discussion of these and other econometric issues that arise is estimating behavioral responses. I first provide an overview of the major econometric problems facing researchers investigating the effect of taxation on behavior, and then discuss some of the estimation techniques used in recent studies. The paper ignores many econometric problems encountered by applied researchers in order to focus on the problems that are largely unique to the study of the behavioral response to taxation. A few studies are cited as examples, but this paper is not meant to be a review of the literature and the list of references is far from comprehensive. AN OVERVIEW OF THE ECONOMETRIC PROBLEMS Taxation often lowers the relative price of a tax preferred activity. For example, for someone who itemizes deductions, the price of giving a dollar to charity is one minus the individual s marginal tax rate. 1 For simplicity, initially consider the case where we posit that an individual s annual contributions to charity are a linear function of the tax price (one minus the individual s marginal tax rate) and after-tax income, and suppose we wish to estimate the coefficients of this relationship using a cross section of individual tax return data. Using ordinary least squares (OLS) to estimate a linear regression of contributions on individuals federal marginal tax rates and disposable incomes would likely result in serious econometric problems and would not be an appropriate technique for estimating the coefficients. A Fundamental Identification Problem Perhaps the most serious problem is that the marginal tax rate is a function of taxable income. As Feenberg (1987) points out, identification of the tax effect in this case depends on our being sure of the exact way in which income should enter the econometric specification. If we allow for only a linear income effect in the specification when, in truth, contributions vary with the square (or some other nonlinear function) of income, then the coefficient on the tax price will generally be biased. Because the tax price is a nonlinear function of taxable income, it will likely be correlated with the omitted nonlinear income term, producing classical omittedvariable bias. The tax-price coefficient would be picking up some of the effect of the nonlinear income effect in this case. In addition to income, tax rates are strongly influenced by marital status and the presence of dependent children in the household, but these factors are likely to themselves be determinants of charitable contributions and other taxrelated activities. Feenberg (1987) notes that, as polynomial and interaction terms in income and other variables that determine both charitable contributions and marginal tax rates are added to the specification, the tax price will become nearly collinear with the other variables. It is in this sense that the tax price model is identified only through 762

3 FORUM ON THE BEHAVIORAL RESPONSE TO TAXATION functional form assumptions. In practice, of course, researchers have little a priori information about what the functional form of the specification should be, so this is a serious problem. Separately identifying the income and tax price effects requires that there be some source of variation in tax rates that is independent of other explanatory variables that are in the regression (or should be in the regression). One source of variation in tax prices that is plausibly not a direct determinant of charitable contributions or other tax-related activities is state of residence, and this is the source of Feenberg s (1987) solution to the identification problem. States differ considerably in the structure of their income taxes, and in whether they impose an income tax at all, so this provides the needed independent variation in tax prices. As Feenberg (1987) notes, two key assumptions underlie the use of state taxes for identification: (1) that individuals respond to state taxes in the same way that they respond to federal taxes, and (2) that state tax laws are independent of other determinants of the taxpayers behavior being modeled. The latter assumption might be problematic in some contexts. State policies are not set purely randomly, but instead reflect the values and circumstances of voters in each state. These values and circumstances may also directly influence taxpayers behavior and need to be controlled for in the econometric analysis. One can do so by introducing a set of state-specific dummy variables into the regression, but doing so effectively destroys the ability of the state tax variation to identify the tax price effect. However, if one does not control for the state varying factors that are correlated with their tax policies, then the estimated tax price effect will be biased due to the influence of the omitted state effects. The importance of controlling for the determinants of state policy formation depends on the type of policy being analyzed. In the charitable contributions case considered by Feenberg (1987), it seems reasonable that variation over states in the tax treatment of contributions is largely independent of other determinants of contributions. However, in other contexts, this assumption may be less innocuous. For example, state variation in welfare program generosity has been used to identify the effects of welfare programs on family structure. Moffitt (1994) and Hoynes (1997) find that econometric estimates of the effect of welfare programs on female headship decisions are very sensitive to controlling for unobserved state varying determinants of headship decisions, suggesting that state welfare program generosity is a function of factors that also affect headship decisions. Another potential solution to the identification problem is to use data spanning a period of time over which the tax code changed. In this case, the tax reforms provide the needed variation in tax prices. However, some of the problems involved in using state tax variation to identify tax effects also apply in this case. Changes in the economic environment occurring as the tax reforms are implemented may influence the behavior being modeled and will bias the estimated tax effects unless controlled for in the regression. The difference-in-differences methodology discussed later in this paper is designed to control for nontax effects that coincide with tax reforms. When investigating the effect of taxation on hours of work, identification of the tax effects may be a less severe 763

4 NATIONAL TAX JOURNAL VOL. LI NO. 4 problem than it is in other cases. Taxation affects the incentive to work by reducing taxpayers after-tax wage and nonearned income. As long as one is willing to maintain the assumption that taxation affects hours of work only through these channels, and does not affect pretax wages, then one can use the variation over taxpayers in pretax wages to identify the tax effects. However, these assumptions may be questionable. Remuneration for work effort comes in the form of current earnings, fringe benefits, and deferred compensation, but only current earnings are typically used in computing the wage rate used in labor supply regressions. The desired mix of current taxable earnings and other forms of remuneration is influenced by the structure of the tax system, and so tax reforms may affect the observed pretax wage rate. Partly because of this, some researchers have elected not to rely on the traditional labor supply specification in examining how taxation affects hours of work. 2 Another reason for caution in assuming that taxation affects hours of work only through the traditional wage and income effects is that this ignores the way in which tax avoidance affects labor supply decisions. Triest (1992) estimates a labor supply model in which the tax price of deductible expenditures (one minus the marginal tax rate) directly enters the labor supply specification for those who itemize deductions and finds that deductibility has a potentially important effect on labor supply. Heckman (1983) and Slemrod (1998a) provide theoretical models of the labor/ leisure choice that incorporate more comprehensive forms of tax avoidance. As Slemrod (1998b) also points out, behavioral responses to taxation will generally depend on the avoidance opportunities permitted under the tax code. Tax reforms that change avoidance opportunities may change the way in which behavior responds to marginal tax rates. The ways in that avoidance opportunities affect real behavioral responses to taxation are little understood at present and provide an important area for future research. Endogeneity of Marginal Tax Rates A second important econometric problem faced by researchers investigating the behavioral effects of taxation is that the marginal tax rates faced by taxpayers depend on their own behavior. For example, as a worker s hours of work increase, taxable income will also increase, and eventually the worker will shift into a bracket with a higher marginal tax rate (in the case of a progressive tax system where marginal tax rates increase with income). Workers who work more hours than are typical of others with the same wage rate, unearned income, and other characteristics that influence labor supply will also face higher marginal tax rates than are typical. As a result, the additive error term in a labor supply regression will be positively correlated with the marginal tax rate, and OLS is a biased estimator of the coefficients of the regression. Similar problems result in other taxrelated analyses. For example, as an individual s charitable contributions increase, taxable income decreases, and the individual will eventually drop into a bracket with a lower marginal tax rate. A commonly adopted solution to the tax rate endogeneity problem is to use an instrumental variables estimator. One or more suitable instruments must be found that are correlated with the marginal tax rate, but not correlated with unobserved determinants of the behavior being analyzed (the error term of the regression). In studies of chari- 764

5 FORUM ON THE BEHAVIORAL RESPONSE TO TAXATION table contributions, the marginal tax rate applying to the first dollar of contributions is often used as an instrument for the tax price. Because the rate applying to the first dollar of contributions does not depend on the amount that an individual decides to contribute, it does not bear the same obvious link to the the value of the regression error term that the finaldollar tax rate does. However, more subtle endogeneity problems may still remain. The first-dollar tax rate depends on all of the components of taxable income except the charitable contributions deduction. If the unobserved determinants of contributions are correlated with other deductions or income sources, for example, then the first-dollar tax rate may itself be correlated with the unobserved determinants of contributions. Recognizing this possibility, Feenberg (1987) uses the tax subsidy rate on contributions (evaluated over a fixed sample of returns) in the taxpayer s state as an instrument for the tax price of charitable contributions. This solves both the endogeneity and identification problems. Researchers need to be concerned with how strongly correlated their instruments are with the tax price. Bound, Jaeger, and Baker (1995) show that, when instruments are only weakly correlated with an endogenous explanatory variable, even a small correlation between the instruments and the error term of the regression can induce a serious bias in the direction of OLS. In practice, there is often reason to suspect some correlation, although perhaps small, between potential instruments for the tax price and the regression error term. If the instruments also explain little of the variation in the tax price, then we may need to worry about bias. Staiger and Stock (1997) suggest using a limited information maximum likelihood estimator rather than two-stage least squares to reduce the degree of bias, and also develop methods appropriate for the construction of confidence intervals when instruments are weak. Behavior of Taxpayers Facing Nonlinear Budget Constraints Complex tax schedules sometimes create unusual incentives for taxpayer behavior, which estimation strategies must take into account. For example, consider the case of a progressive income tax with a marginal tax rate which increases with income in discrete jumps (as the U.S. system does over much of its range). A worker who is at a point where an extra hour of work will push him into a bracket with a higher marginal tax rate faces a lower after-tax wage for that additional hour than he did for the previous hour. Some workers who wish to work additional hours at the higher after-tax wage may not be willing to work additional hours at the lower after-tax wage rate. This will tend to lead to desired hours of work being more heavily concentrated at the kink points between tax brackets than they are elsewhere on workers budget constraints. A clear example of this is provided by Burtless and Moffitt (1984), who show that there was a sharp spike in the distribution of earnings of Social Security recipients in the late 1960s near the amount exempt under the earnings test. Social Security benefits were reduced by 50 cents for every dollar beyond the exempt amount, resulting in a sharp drop in the after-tax wage rate at that point. In some cases, taxation results in the price of a good decreasing as consumption of it increases. For example, as consumption of a tax deductible good increases (starting from a point of no deductible expenditures), at some point 765

6 NATIONAL TAX JOURNAL VOL. LI NO. 4 it becomes optimal to itemize deductions rather than take the standard deduction, and the tax price of the good drops from one to one minus the marginal tax rate. More familiar examples come from analysis of how taxation affects the price of leisure time, the after-tax wage rate. The Earned Income Tax Credit results in the effective marginal tax rate dropping, and the after-tax wage increasing, as one exits the claw back region where the credit is reduced as income increases. So, as a worker s leisure time increases (and hours of work decrease) just enough so that he goes from being ineligible for the credit to being in the claw back region, the price of leisure decreases. Economic theory implies that taxpayers will not find it optimal to locate at such points. If the taxpayer is at a point where he or she has willingly bought the good at a given price, but can now buy additional units at a lower price, it is always optimal to do so. This implies that there will be some region around such kink points in the budget constraint that individuals will avoid. As Moffitt (1990) demonstrates, small changes in tax rates may result in large changes in individuals behavior in this case, because taxpayers may be induced to jump from one side of the nonconvex kink to the other. If one does not take this possibility into account in investigating the behavioral effects of taxation, one might incorrectly infer that the jump in behavior is the result of a large tax price elasticity rather than the nonconvexity in the budget set. Burtless and Hausman (1978) pioneered econometric methodology that cleanly accounts for utility maximization of taxpayers subject to complex nonlinear tax schedules. 3 This methodology also takes into account the possibility of measurement error in tax rates induced when taxpayers are observed in tax brackets that differ from their utility maximizing positions. Moreover, by making explicit the assumptions regarding the preferences underlying the behavioral response to taxation, the methodology allows precise predictions to be made regarding the changes in excess burden and behavior that would result from potential tax reforms. However, the methodogy has been criticized for its complexity and strong assumptions. Heckman (1983) has criticized it for making overly strong assumptions regarding researchers knowledge of the budget constraints and choice problems facing taxpayers, and MaCurdy, Green, and Paarsch (1990) criticize the restrictions on possible estimated behavioral responses that it imposes. Recent research has tended to use less structural methods to investigate behavioral responses to taxation, but it is still important to take into account the nonlinear nature of the budget constraint in interpreting results and simulating the effects of potential tax reforms. Timing Issues Slemrod (1995) argues that the behavioral response to taxation can be divided into three tiers according to the sensitivity of the response. The three levels of the hierarchy, ranked from most to least responsive, are timing responses, avoidance responses, and real responses. Real responses have a direct impact on individuals well being, but the timing of transactions can often be easily modified in such a way as to reduce taxes paid without having a large impact on the benefit ultimately derived from the transactions. An important task facing researchers is to determine how much of the observed behavioral response is due to a shift in the timing of activities in response to tax incentives 766

7 FORUM ON THE BEHAVIORAL RESPONSE TO TAXATION and how much is due to a more permanent change in the level of the activities. The behavioral response of taxpayers to changes in the marginal tax rate that they face is likely to depend on whether the change in the marginal rate they face is temporary or permanent. Marginal tax rate changes might be temporary due either to the change in the tax law being temporary or due to transitory movements in the taxpayer s income. The latter possibility has especially disturbing implications for the use of cross-sectional data in measuring behavioral responses. Taxpayers with transitorily high incomes will tend to face temporarily high marginal tax rates, while taxpayers with transitorily low incomes will tend to face temporarily low marginal rates. Taxpayers facing temporarily high marginal tax rates have an incentive to shift income receipts to years in which they face lower marginal tax rates and to shift deductions to the current year, when the value of the deduction is temporarily high. Conversely, taxpayers facing temporarily low marginal rates have an incentive to concentrate income receipts in the current year, when they are taxed less heavily, and to defer deductions to years in which they face higher marginal tax rates. Even if a taxpayer s behavior would be unchanged if there were a permanent change in the marginal rate she faces, there might still be a sizable transitory response to a temporary change in tax rates. More generally, the behavioral response to a temporary tax change is likely to be greater than the behavioral response to a permanent change. Unfortunately, using crosssectional data, it is generally impossible to tell to what degree variation in marginal rates across taxpayers is due to transitory rather than permanent factors. To the extent that the marginal rate variation is due to transitory factors, estimated behavioral responses will likely overstate the behavioral response to a permanent change in tax rates. The degree to which timing matters will differ across the type of behavior being analyzed. Making substantial changes in one s hours of work might require a change of jobs, and so this likely responds fairly slowly to changes in tax law. Capital gains realizations, on the other hand, are often cited as a form of behavior that can respond very quickly to tax changes. Individuals may be able to reduce the present value of their expected tax burden by realizing gains during a period in which they face a temporarily low marginal tax rate with relatively little change in the composition of their asset portfolio. RECENT APPROACHES TO ESTIMATION Recent research on the behavioral effects of taxation has tended to use either panel data or several cross sections of data spanning a period of time encompassing a tax reform. Changes in tax law provide an exogenous source of variation in tax rates, which can be used to help solve the identification problem discussed above. However, the researcher needs to be able to distinguish between changes in behavior caused by the change in tax law and changes in behavior induced by other changes in the economic environment that coincide with the tax reform. The key to sorting out the tax effects from other factors is that tax reforms generally do not treat all groups of individuals in the same way. Some groups experience larger marginal rate changes than do others, and sometimes marginal tax rates increase for some groups while they decrease for others. Two closely related methods for using the variation in tax rates generated by 767

8 NATIONAL TAX JOURNAL VOL. LI NO. 4 reforms to estimate the behavioral effects of taxation, difference-indifferences and instrumental variables, are discussed below. Difference-in-Differences The difference-in-differences estimation technique has increasingly been used in work examining the ways in which taxation and other government policies affect behavior. This methodology treats tax reforms as natural experiments that can be used to identify the effect of taxation on behavior. Because some taxpayer groups experience larger changes in marginal tax rates than do other groups, those who are subject to relatively small changes in marginal rates can serve as a quasicontrol group and those who experience larger changes function as a treatment group. The change in the behavior of the control group can be used as a measure of how underlying nontax factors affected behavior. Comparison of the change in behavior of the group experiencing the large tax rate change with the change in behavior of the group experiencing the smaller change can then be used as an indicator of how the tax reform affects behavior. This methodology is perhaps best explained by working through a concrete example of its use. Eissa (1995) investigates how the Tax Reform Act of 1986 (TRA 86) affected the labor supply of married women using repeated crosssectional data from the Current Population Survey (CPS). Her estimate of the effect of TRA 86 is based on comparisons of the average hours of work of four different groups of married women: high-income women in years before TRA 86 (H tb ), high-income women in years after TRA 86 (H ta ), lowincome women in years before TRA 86 (H cb ), and low-income women in years after TRA 86 (H ca ). Eissa assumes that the nontax factors affected both the high- and low-income women in the same way, so that the effect of the nontax factors on labor supply can be removed by taking the difference between the pre TRA 86 ( ) and post TRA 86 ( ) values of hours of work. Women are classified as high or low income on the basis of household income excluding their own earnings. High-income women, defined as those at the 99th percentile of the income distribution, on average experienced a drop in their marginal tax rate of 14 percentage points as a result of TRA 86 and are the treatment group. Lowincome women, defined as those at the 90th percentile of the income distribution, on average experienced a drop in their marginal tax rate of only seven percentage points and are the control group. 4 Under the assumption that women treat their asset income and husbands earnings as given, the classification of women to the treatment and control groups is exogenous. Eissa (1995) takes the difference between hours of work post TRA 86 and pre TRA 86 for each group to eliminate nontax related changes, which affect labor supply during the period being analyzed. An important assumption underlying this step is that the nontax factors affected both groups equally. The difference in the change in hours of work between the two groups, the difference-in-differences (H ta H tb ) (H ca H cb ), then indicates the degree to which the larger cut in marginal tax rates applying to high-income women affected their hours of work. If the tax reform had no effect on hours of work, the difference-in-differences would be zero, while a positive value of the difference-in-differences indicates that the tax reform resulted in increased work hours by high-income women. 768

9 FORUM ON THE BEHAVIORAL RESPONSE TO TAXATION Eissa (1995) also implements the difference-in-differences technique in a regression framework that allows for changes in the characteristics of the control and treatment groups over time. In this case, an hours of work regression is run, using individual-level observations from the CPS pooled over years, on individual characteristics, a dummy variable for post TRA 86 years, a variable indicating the woman is a member of the high-income group, and a variable interacting the post TRA 86 indicator with the high-income dummy variable. The coefficient on the post TRA 86 dummy variable captures changes over time that affect labor supply of both the control and treatment groups, the coefficient on the high-income dummy variable captures differences in the hours of work of the high-income group relative to the lower income group, and the coefficient on the interaction of the two indicator variables measures the extent to which the high-income group increased its labor supply more than the lower income group as a result of TRA 86. This last coefficient is capturing the same effect as the difference-in-differences. A critical assumption in difference-indifferences studies is that changes in the economic environment over time have the same effect on the behavior of the groups experiencing different changes in tax rates. In practice, this is often a controversial assumption. Because the magnitude of tax rate changes often vary with income, income or income related variables are often used in grouping observations in difference-indifferences studies. But the welldocumented trend of growing income inequality suggests that different income groups may have been affected in different ways by nontax forces. If these differences in the nontax forces across groups affect the behavior being studied, then the estimated tax effect will be biased. Researchers using difference-in-differences techniques are aware of this possibility, and often take steps to address it. Eissa (1995), for example, investigates whether the labor supply of the two income groups she analyzes exhibited different trends in the years prior to TRA 86. Another approach is to add an additional source of variation in tax rates. For example, in a study of the effect of tax incentives on purchases of health insurance, Gruber and Poterba (1994) use differences in tax prices between employed and selfemployed workers as well as differences across workers due to differing marginal tax rates and differences over time due to implementation of TRA 86. Taking account of all three sources of variation simultaneously results in a difference-indifference-in-differences estimator. The difference-in-differences method depends on a suitable variable being available to classify observations into the control and treatment groups. Heckman (1996) criticizes Eissa s (1996) use of income as a grouping variable, noting that although husbands earnings are relatively unresponsive to taxation, this is not true of capital income. Some women may switch groups as a result of the tax reform, leading to biased estimates of the effects of the reform on behavior. Heckman argues in favor of invoking economic theory to link tax effects to changes in the after-tax wage and using variation in wage growth across exogenously defined groups for identification. 5 However, for most other forms of behavior that are affected by taxation, this identification strategy in not an option. Panel data, where the same individuals or households are followed over time, provide an alternative means of identification. Feldstein (1995) uses data from a 769

10 NATIONAL TAX JOURNAL VOL. LI NO. 4 panel of tax returns to estimate the response of taxable income to the TRA Because he observes the same taxpayers both before and after the Act, Feldstein can use pre TRA 86 marginal tax rates in grouping taxpayers into categories experiencing different changes in marginal tax rates. This avoids the problem of the composition of the groups changing over time. Instrumental Variables Using Panel Data Moffitt and Wilhelm (1998) pose the choice of a suitable grouping variable in terms of instrumental variables. The difference-in-differences methodology using panel data is essentially estimating a regression of the change in a behavioral variable (such as hours of work or taxable income) on the change in the taxpayer s marginal rate. The change in the marginal tax rate is partly a function of the taxpayer s behavior and must be instrumented for. A suitable instrument or grouping variable must be correlated with the change in tax rates but uncorrelated with the regression error term (which can be interpreted as the change in the unobserved determinants of the taxpayer s behavior). Moffitt and Wilhelm question whether prereform tax rates or income are suitable instrumental (or grouping) variables. The prereform tax rate or income may be more highly correlated with the unobserved determinants of prereform behavior than it is with the unobserved determinants of postreform behavior, and so may be correlated with the change in the unobserved determinants of behavior. For example, as Carroll (1997) points out, transitory increases in income prior to a tax reform can be expected to be followed by decreases in income following the reform. This regression to the mean effect would lead to correlation between prereform income and the regression error if the unobserved determinants of behavior are also affected by the transitory factor. A similar critique applies to using postreform income or tax rates as instruments. Moffitt and Wilhelm investigate using several alternative instruments for the change in tax rates, including educational attainment, broad occupational categories, and illiquid asset holdings. Carroll uses a proxy for permanent income, income averaged over several years, as an instrument. These instruments are less likely than prereform income or tax rates to be sensitive to transitory disturbances, and so are more likely to be uncorrelated with the change in the unobserved determinants of behavior. Using panel data, in some instances, one may be able to determine how much of behavioral responses are due to timing effects and how much of the responses are permanent. Recent work by Burman and Randolph (1994) on capital gains realizations and by Randolph (1995) on charitable contributions attempts to do this. Burman and Randolph use a panel of tax returns to estimate a model in which an individual s capital gains realizations depend on both his permanent tax rate and current tax rate. They rely on the maximum combined state and federal marginal tax rate in the individual s state as an instrument to identify the permanent tax effect. Because the maximum tax rate does not vary over individuals within the state, they argue it is unlikely to be correlated with transitory factors. The individual s marginal tax rate on the first dollar of realizations is used as an instrument to identify the transitory tax effect. 6 The first-dollar tax rate does not depend on the individual s capital gains realizations, and so does not suffer from a direct endogeneity problem as the final-dollar marginal tax rate does, but it does vary over time for the individual. 770

11 FORUM ON THE BEHAVIORAL RESPONSE TO TAXATION The strategy of using a first-dollar tax rate would not work in studying the effect of marginal tax rates on taxable income because in that case there is essentially no exogenous income component on which to base the firstdollar calculation. In the case of capital gains realizations, one can argue that some components of income are unlikely to be correlated with the unobserved determinants of gains realizations and can be treated as exogenous. Burman and Randolph and Randolph both find that the transitory effect of tax changes is much larger than the permanent effect. This is very plausible realizing capital gains and giving to charity are two activities in which taxpayers have quite a bit of flexibility in timing. However, it is asking a lot of the data to distinguish between the transitory and permanent effects of tax changes, and more research is needed to investigate the robustness of this strategy for estimation. Conclusions Researchers investigating how taxation affects behavior face a number of challenging problems. No particular econometric strategy is foolproof, and one must be aware of potential problems and sources of bias in evaluating empirical estimates. However, it is important to not become overly jaundiced or cynical. Despite the problems encountered, econometric analysis of how taxation affects behavior has provided estimates that have led to better informed debate on tax policy. Comparison of alternative policies requires that we know the magnitude of the behavioral responses, and without econometric estimates, we would be left with little more than intuitive guesses on which to rely. Further research investigating the behavioral responses is clearly an important and worthwhile endeavor. ENDNOTES The views expressed in this paper are not necessarily shared by the Federal Reserve Bank of Boston or its staff. 1 The tax price can actually be more complex due to the interaction of state and federal income taxes and the tax treatment of gifts of appreciated property. 2 See, for example, Eissa (1995, 1996) and Moffitt and Wilhelm (1998). 3 Technical expositions of this methodology are provided by Hausman (1985) and Moffitt (1986). 4 Eissa (1995) also conducted the analysis using a second control group whose income was at the 75th percentile of the distribution. 5 Blundell, Duncan, and Meghir (1998) estimate a model of how taxation affects labor supply, which takes this approach to identification. 6 In addition to setting capital gains realizations to zero, Burman and Randolph (1994) also set several other potentially endogenous deductions and income sources to zero before calculating the firstdollar marginal tax rate. REFERENCES Blundell, Richard, Alan Duncan, and Costas Meghir. Estimating Labor Supply Responses Using Tax Reforms. Econometrica 66 No. 4 (July, 1998): Bound, John, David A. Jaeger, and Regina M. Baker. Problems with Instrumental Variables Estimation When the Correlation Between the Instruments and the Endogenous Explanatory Variable is Weak. Journal of the American Statistical Association 90 No. 430 (June, 1995): Burman, Leonard E., and William C. Randolph. Measuring Permanent Responses to Capital-Gains Tax Changes in Panel Data. American Economic Review 84 No. 4 (September, 1994): Burtless, Gary, and Jerry Hausman. The Effect of Taxation on Labor Supply: Evaluating the Gary Negative Income Tax Experiments. Journal of Political Economy 86 No. 6 (December, 1978): Burtless, Gary, and Robert Moffitt A. The Effect of Social Security Benefits on the Labor Supply of the Aged. In Retirement and Economic Behavior, edited by Henry J. Aaron and Gary Burtless, Washington, D.C.: The Brookings Institution, Carroll, Robert. Taxes and Household Behavior: New Evidence from the 1993 Tax 771

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