Triest Econometric Issues in Estimationg the Behavioral Response to Taxation

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ECONOMETRIC ISSUES

IN ESTIMATING THE

BEHAVIORAL RESPONSE

TO TAXATION:

A NONTECHNICAL

INTRODUCTIONROBERT K. TRIEST *

Abstract - Reliable estimates of how tax incentives affect behavior are anessential input into the formation of tax

policy. However, one encounters anumber of difficult econometric

problems in estimating the magnitudeof 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 estimationtechniques used in recent studies:difference-in-differences and instrumen-tal variables using panel data.

INTRODUCTION

Understanding how individuals, families,and households adjust their behavior inresponse to taxation is one of the mostimportant tasks facing public finance

economists. Taxation affects manyaspects of individual behavior, including

the choice between work and leisure,the choice of occupation and fringebenefits, the choice of deferred versusimmediate compensation, the decisionof how much to save and consume, thedecision of how to allocate one’s savingsacross assets, the decison of whether torent or own a house, and the decisionof how much to donate to charity. Bothpositive and normative analysis oftaxation—everything from revenue

estimation to social welfare evaluation—depends critically on the magnitudeof the responses. Economic theoryprovides a framework for modelingbehavioral responses and understandingtheir implications and importance, buttells us little about the expectedmagnitude of the responses and insome contexts does not even tell us thedirection of the response. The magni-tude of behavioral responses is inher-ently a topic for empirical investigation.

Unfortunately, econometric analysis of

how behavior responds to taxation ismuch like the tax code itself: complexand often controversial. At any givenmoment in time, the marginal tax ratethat an individual faces depends on her

*Research Department, Federal Reserve Bank of Boston,Boston, MA 02106-2076.

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taxable income, which in turn dependson her economic status and behavior. Soit becomes difficult to disentangledifferences in behavior across individu-als, which are induced by taxation, fromthose due to other determinants ofbehavior. Over time, changes in the taxcode provide an exogenous source ofvariation in marginal tax rates, but inthis case, it becomes difficult to disen-tangle the behavioral effect of tax codechanges from those due to otherchanges in the economic environmentoccurring at the same time. The purposeof this paper is to provide a non-technical discussion of these and other

econometric issues that arise is estimat-ing behavioral responses. I first providean overview of the major econometricproblems facing researchers investigat-ing the effect of taxation on behavior,and then discuss some of the estimationtechniques used in recent studies. Thepaper ignores many econometricproblems encountered by appliedresearchers in order to focus on theproblems that are largely unique to thestudy of the behavioral response totaxation. A few studies are cited asexamples, but this paper is not meant to

be a review of the literature and the listof references is far from comprehensive.

AN OVERVIEW OF THE ECONOMETRIC

PROBLEMS

Taxation often lowers the relative“price” of a tax preferred activity. Forexample, for someone who itemizesdeductions, the price of giving a dollarto charity is one minus the individual’smarginal tax rate. 1 For simplicity, initiallyconsider the case where we posit thatan individual’s annual contributions to

charity are a linear function of the taxprice (one minus the individual’smarginal tax rate) and after-tax income,and suppose we wish to estimate thecoefficients of this relationship using a

cross section of individual tax returndata. Using ordinary least squares (OLS)to estimate a linear regression ofcontributions on individuals’ federalmarginal tax rates and disposableincomes would likely result in seriouseconometric problems and would notbe an appropriate technique forestimating the coefficients.

A Fundamental Identification Problem

Perhaps the most serious problem is thatthe marginal tax rate is a function oftaxable income. As Feenberg (1987)points out, identification of the tax

effect in this case depends on our beingsure of the exact way in which incomeshould enter the econometric specifica-tion. If we allow for only a linear incomeeffect in the specification when, intruth, contributions vary with the square(or some other nonlinear function) ofincome, then the coefficient on the taxprice will generally be biased. Becausethe tax price is a nonlinear function oftaxable income, it will likely be corre-lated with the omitted nonlinear incometerm, producing classical omitted-variable bias. The tax-price coefficient

would be picking up some of the effectof the nonlinear income effect in thiscase.

In addition to income, tax rates arestrongly influenced by marital status andthe presence of dependent children inthe household, but these factors arelikely to themselves be determinants ofcharitable contributions and other tax-related activities. Feenberg (1987) notesthat, as polynomial and interactionterms in income and other variables thatdetermine both charitable contributions

and marginal tax rates are added to thespecification, the tax price will becomenearly collinear with the other variables.It is in this sense that the tax pricemodel is identified only through



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problem than it is in other cases.Taxation affects the incentive to work byreducing taxpayers’ after-tax wage andnonearned income. As long as one iswilling to maintain the assumption thattaxation affects hours of work onlythrough these channels, and does notaffect pretax wages, then one can usethe variation over taxpayers in pretaxwages to identify the tax effects.However, these assumptions may bequestionable. Remuneration for workeffort comes in the form of currentearnings, fringe benefits, and deferredcompensation, but only current earningsare typically used in computing the

wage rate used in labor supply regres-sions. The desired mix of current taxableearnings and other forms of remunera-tion is influenced by the structure of thetax system, and so tax reforms mayaffect the observed pretax wage rate.Partly because of this, some researchershave elected not to rely on the tradi-tional labor supply specification inexamining how taxation affects hours ofwork. 2

Another reason for caution in assumingthat taxation affects hours of work only

through the traditional wage andincome effects is that this ignores theway in which tax avoidance affects laborsupply decisions. Triest (1992) estimatesa labor supply model in which the taxprice of deductible expenditures (oneminus the marginal tax rate) directlyenters the labor supply specification forthose who itemize deductions and findsthat deductibility has a potentiallyimportant 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 willgenerally depend on the avoidanceopportunities permitted under the tax

code. Tax reforms that change avoid-ance opportunities may change the wayin which behavior responds to marginaltax rates. The ways in that avoidanceopportunities affect real behavioralresponses to taxation are little under-stood at present and provide animportant area for future research.

Endogeneity of Marginal Tax Rates

A second important econometricproblem faced by researchers investigat-ing the behavioral effects of taxation isthat the marginal tax rates faced bytaxpayers depend on their own behav-

ior. For example, as a worker’s hours ofwork increase, taxable income will alsoincrease, and eventually the worker willshift into a bracket with a highermarginal tax rate (in the case of aprogressive tax system where marginaltax rates increase with income). Workerswho work more hours than are typicalof others with the same wage rate,unearned income, and other character-istics that influence labor supply will alsoface higher marginal tax rates than aretypical. As a result, the additive errorterm in a labor supply regression will be

positively correlated with the marginaltax rate, and OLS is a biased estimatorof the coefficients of the regression.Similar problems result in other tax-related analyses. For example, as anindividual’s charitable contributionsincrease, taxable income decreases, andthe individual will eventually drop into abracket with a lower marginal tax rate.

A commonly adopted solution to the taxrate endogeneity problem is to use aninstrumental variables estimator. One ormore suitable instruments must be

found that are correlated with themarginal tax rate, but not correlatedwith unobserved determinants of thebehavior being analyzed (the error termof the regression). In studies of chari-



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table contributions, the marginal taxrate applying to the first dollar ofcontributions is often used as aninstrument for the tax price. Becausethe rate applying to the first dollar ofcontributions does not depend on theamount that an individual decides tocontribute, it does not bear the sameobvious link to the the value of theregression error term that the final-dollar tax rate does. However, moresubtle endogeneity problems may stillremain. The first-dollar tax rate dependson all of the components of taxableincome except the charitable contribu-tions deduction. If the unobserved

determinants of contributions arecorrelated with other deductions orincome sources, for example, then thefirst-dollar tax rate may itself becorrelated with the unobserved determi-nants of contributions. Recognizing thispossibility, Feenberg (1987) uses the taxsubsidy rate on contributions (evaluatedover a fixed sample of returns) in thetaxpayer’s state as an instrument for thetax price of charitable contributions.This solves both the endogeneity andidentification problems.

Researchers need to be concerned withhow strongly correlated their instru-ments are with the tax price. Bound,Jaeger, and Baker (1995) show that,when instruments are only weaklycorrelated with an endogenous explana-tory variable, even a small correlationbetween the instruments and the errorterm of the regression can induce aserious bias in the direction of OLS. Inpractice, there is often reason to suspectsome correlation, although perhapssmall, between potential instruments forthe tax price and the regression error

term. If the instruments also explainlittle of the variation in the tax price,then we may need to worry about bias.Staiger and Stock (1997) suggest usinga limited information maximum likeli-

hood estimator rather than two-stageleast squares to reduce the degree ofbias, and also develop methods appro-priate for the construction of confidenceintervals when instruments are weak.

Behavior of Taxpayers Facing Nonlinear Budget Constraints

Complex tax schedules sometimescreate unusual incentives for taxpayerbehavior, which estimation strategiesmust take into account. For example,consider the case of a progressiveincome tax with a marginal tax ratewhich increases with income in discrete

jumps (as the U.S. system does overmuch of its range). A worker who is at apoint where an extra hour of work willpush him into a bracket with a highermarginal tax rate faces a lower after-taxwage for that additional hour than hedid for the previous hour. Some workerswho wish to work additional hours atthe higher after-tax wage may not bewilling to work additional hours at thelower after-tax wage rate. This will tendto lead to desired hours of work beingmore heavily concentrated at the kinkpoints between tax brackets than they

are elsewhere on workers’ budgetconstraints. A clear example of this isprovided by Burtless and Moffitt (1984),who show that there was a sharp spikein the distribution of earnings of SocialSecurity recipients in the late 1960s nearthe amount exempt under the earningstest. Social Security benefits werereduced by 50 cents for every dollarbeyond the exempt amount, resulting ina sharp drop in the after-tax wage rateat that point.

In some cases, taxation results in the

price of a good decreasing as consump-tion of it increases. For example, asconsumption of a tax deductible goodincreases (starting from a point of nodeductible expenditures), at some point



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it becomes optimal to itemize deduc-tions rather than take the standarddeduction, and the tax price of thegood drops from one to one minus themarginal tax rate. More familiarexamples come from analysis of howtaxation affects the price of leisure time,the after-tax wage rate. The EarnedIncome Tax Credit results in the effectivemarginal tax rate dropping, and theafter-tax wage increasing, as one exitsthe “claw back” region where the creditis reduced as income increases. So, as aworker’s leisure time increases (andhours of work decrease) just enough sothat he goes from being ineligible for

the credit to being in the claw backregion, the price of leisure decreases.Economic theory implies that taxpayerswill not find it optimal to locate at suchpoints. If the taxpayer is at a pointwhere he or she has willingly boughtthe good at a given price, but can nowbuy additional units at a lower price, it isalways optimal to do so. This impliesthat there will be some region aroundsuch kink points in the budget con-straint that individuals will avoid. AsMoffitt (1990) demonstrates, smallchanges in tax rates may result in large

changes in individuals’ behavior in thiscase, because taxpayers may be inducedto jump from one side of the nonconvexkink to the other. If one does not takethis possibility into account in investigat-ing the behavioral effects of taxation,one might incorrectly infer that the

jump in behavior is the result of a largetax price elasticity rather than thenonconvexity in the budget set.

Burtless and Hausman (1978) pioneeredeconometric methodology that cleanlyaccounts for utility maximization of

taxpayers subject to complex nonlineartax schedules. 3 This methodology alsotakes into account the possibility ofmeasurement error in tax rates inducedwhen taxpayers are observed in tax

brackets that differ from their utilitymaximizing positions. Moreover, bymaking explicit the assumptionsregarding the preferences underlyingthe behavioral response to taxation, themethodology allows precise predictionsto be made regarding the changes inexcess burden and behavior that wouldresult from potential tax reforms.

However, the methodogy has beencriticized for its complexity and strongassumptions. Heckman (1983) hascriticized it for making overly strongassumptions regarding researchers’knowledge of the budget constraints

and choice problems facing taxpayers,and MaCurdy, Green, and Paarsch(1990) criticize the restrictions onpossible estimated behavioral responsesthat it imposes. Recent research hastended to use less structural methods toinvestigate behavioral responses totaxation, but it is still important to takeinto account the nonlinear nature of thebudget constraint in interpreting resultsand simulating the effects of potentialtax reforms.

Timing Issues

Slemrod (1995) argues that the behav-ioral response to taxation can be dividedinto three tiers according to the sensitiv-ity of the response. The three levels ofthe hierarchy, ranked from most to leastresponsive, are timing responses,avoidance responses, and real re-sponses. Real responses have a directimpact on individuals’ well being, butthe timing of transactions can often beeasily modified in such a way as toreduce taxes paid without having a largeimpact on the benefit ultimately derived

from the transactions. An importanttask facing researchers is to determinehow much of the observed behavioralresponse is due to a shift in the timingof activities in response to tax incentives



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and how much is due to a morepermanent change in the level of theactivities.

The behavioral response of taxpayers tochanges in the marginal tax rate thatthey face is likely to depend on whetherthe change in the marginal rate theyface is temporary or permanent.Marginal tax rate changes might betemporary due either to the change inthe tax law being temporary or due totransitory movements in the taxpayer’sincome. The latter possibility hasespecially disturbing implications for theuse of cross-sectional data in measuring

behavioral responses. Taxpayers withtransitorily high incomes will tend toface temporarily high marginal tax rates,while taxpayers with transitorily lowincomes will tend to face temporarilylow marginal rates. Taxpayers facingtemporarily high marginal tax rates havean incentive to shift income receipts toyears in which they face lower marginaltax rates and to shift deductions to thecurrent year, when the value of thededuction is temporarily high. Con-versely, taxpayers facing temporarily lowmarginal rates have an incentive to

concentrate income receipts in thecurrent year, when they are taxed lessheavily, and to defer deductions to yearsin which they face higher marginal taxrates. Even if a taxpayer’s behaviorwould be unchanged if there were apermanent change in the marginal rateshe faces, there might still be a sizabletransitory response to a temporarychange in tax rates. More generally, thebehavioral response to a temporary taxchange is likely to be greater than thebehavioral response to a permanentchange. Unfortunately, using cross-

sectional data, it is generally impossibleto tell to what degree variation inmarginal rates across taxpayers is due totransitory rather than permanentfactors. To the extent that the marginal

rate variation is due to transitory factors,estimated behavioral responses willlikely overstate the behavioral responseto a permanent change in tax rates.

The degree to which timing matters willdiffer across the type of behavior beinganalyzed. Making substantial changes inone’s hours of work might require achange of jobs, and so this likelyresponds fairly slowly to changes in taxlaw. Capital gains realizations, on theother hand, are often cited as a form ofbehavior that can respond very quicklyto tax changes. Individuals may be ableto reduce the present value of their

expected tax burden by realizing gainsduring a period in which they face atemporarily low marginal tax rate withrelatively little change in the composi-tion of their asset portfolio.

RECENT APPROACHES TO ESTIMATION

Recent research on the behavioraleffects of taxation has tended to useeither panel data or several crosssections of data spanning a period oftime encompassing a tax reform.Changes in tax law provide an exog-

enous source of variation in tax rates,which can be used to help solve theidentification problem discussed above.However, the researcher needs to beable to distinguish between changes inbehavior caused by the change in taxlaw and changes in behavior induced byother changes in the economic environ-ment that coincide with the tax reform.The key to sorting out the tax effectsfrom other factors is that tax reformsgenerally do not treat all groups ofindividuals in the same way. Somegroups experience larger marginal rate

changes than do others, and sometimesmarginal tax rates increase for somegroups while they decrease for others.Two closely related methods for usingthe variation in tax rates generated by



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reforms to estimate the behavioraleffects of taxation, difference-in-differences and instrumental variables,are discussed below.

Difference-in-Differences

The difference-in-differences estimationtechnique has increasingly been used inwork examining the ways in whichtaxation and other government policiesaffect behavior. This methodology treatstax reforms as natural experiments thatcan be used to identify the effect oftaxation on behavior. Because sometaxpayer groups experience larger

changes in marginal tax rates than doother groups, those who are subject torelatively small changes in marginal ratescan serve as a quasicontrol group andthose who experience larger changesfunction as a treatment group. Thechange in the behavior of the controlgroup can be used as a measure of howunderlying nontax factors affectedbehavior. Comparison of the change inbehavior of the group experiencing thelarge tax rate change with the change inbehavior of the group experiencing thesmaller change can then be used as an

indicator of how the tax reform affectsbehavior.

This methodology is perhaps bestexplained by working through aconcrete example of its use. Eissa (1995)investigates how the Tax Reform Act of1986 (TRA 86) affected the labor supplyof married women using repeated cross-sectional data from the Current Popula-tion Survey (CPS). Her estimate of theeffect of TRA 86 is based on compari-sons of the average hours of work offour different groups of married

women: high-income women in yearsbefore TRA 86 ( H tb ), high-incomewomen in years after TRA 86 ( H ta ), low-income women in years before TRA 86(H cb), and low-income women in years

after TRA 86 ( H ca). Eissa assumes thatthe nontax factors affected both thehigh- and low-income women in thesame way, so that the effect of the non-tax factors on labor supply can beremoved by taking the differencebetween the pre–TRA 86 (1983–85) andpost–TRA 86 (1989–91) values of hoursof work. Women are classified as high orlow income on the basis of householdincome excluding their own earnings.High-income women, defined as thoseat the 99th percentile of the incomedistribution, on average experienced adrop in their marginal tax rate of 14percentage points as a result of TRA 86

and are the “treatment group.” Low-income women, defined as those at the90th percentile of the income distribu-tion, on average experienced a drop intheir marginal tax rate of only sevenpercentage points and are the “controlgroup.” 4 Under the assumption thatwomen treat their asset income andhusbands’ earnings as given, theclassification of women to the treatmentand control groups is exogenous.

Eissa (1995) takes the differencebetween hours of work post–TRA 86

and pre–TRA 86 for each group toeliminate nontax related changes, whichaffect labor supply during the periodbeing analyzed. An important assump-tion underlying this step is that the non-tax factors affected both groups equally.The difference in the change in hours ofwork between the two groups, thedifference-in-differences ( H ta – H tb )– (H ca – H cb), then indicates the degreeto which the larger cut in marginal taxrates applying to high-income womenaffected their hours of work. If the taxreform had no effect on hours of work,

the difference-in-differences would bezero, while a positive value of thedifference-in-differences indicates thatthe tax reform resulted in increasedwork hours by high-income women.



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Eissa (1995) also implements thedifference-in-differences technique in aregression framework that allows forchanges in the characteristics of thecontrol and treatment groups over time.In this case, an hours of work regressionis run, using individual-level observa-tions from the CPS pooled over years,on individual characteristics, a dummyvariable for post–TRA 86 years, avariable indicating the woman is amember of the high-income group, anda variable interacting the post–TRA 86indicator with the high-income dummyvariable. The coefficient on the post–TRA 86 dummy variable captures

changes over time that affect laborsupply of both the control and treat-ment groups, the coefficient on thehigh-income dummy variable capturesdifferences in the hours of work of thehigh-income group relative to the lowerincome group, and the coefficient onthe interaction of the two indicatorvariables measures the extent to whichthe high-income group increased itslabor supply more than the lowerincome group as a result of TRA 86. Thislast coefficient is capturing the sameeffect as the difference-in-differences.

A critical assumption in difference-in-differences studies is that changes in theeconomic environment over time havethe same effect on the behavior of thegroups experiencing different changesin tax rates. In practice, this is often acontroversial assumption. Because themagnitude of tax rate changes oftenvary with income, income or incomerelated variables are often used ingrouping observations in difference-in-differences studies. But the well-documented trend of growing income

inequality suggests that differentincome groups may have been affectedin different ways by nontax forces. Ifthese differences in the nontax forcesacross groups affect the behavior being

studied, then the estimated tax effectwill be biased. Researchers usingdifference-in-differences techniques areaware of this possibility, and often takesteps to address it. Eissa (1995), forexample, investigates whether the laborsupply of the two income groups sheanalyzes exhibited different trends in theyears prior to TRA 86. Another approachis to add an additional source ofvariation in tax rates. For example, in astudy of the effect of tax incentives onpurchases of health insurance, Gruberand Poterba (1994) use differences intax prices between employed and self-employed workers as well as differences

across workers due to differing marginaltax rates and differences over time dueto implementation of TRA 86. Takingaccount of all three sources of variationsimultaneously results in a difference-in-difference-in-differences estimator.

The difference-in-differences methoddepends on a suitable variable beingavailable to classify observations into thecontrol and treatment groups. Heckman(1996) criticizes Eissa’s (1996) use ofincome as a grouping variable, notingthat although husbands’ earnings are

relatively unresponsive to taxation, thisis not true of capital income. Somewomen may switch groups as a result ofthe tax reform, leading to biasedestimates of the effects of the reform onbehavior. Heckman argues in favor ofinvoking economic theory to link taxeffects to changes in the after-tax wageand using variation in wage growthacross exogenously defined groups foridentification. 5 However, for most otherforms of behavior that are affected bytaxation, this identification strategy innot an option.

Panel data, where the same individualsor households are followed over time,provide an alternative means of identifi-cation. Feldstein (1995) uses data from a



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panel of tax returns to estimate theresponse of taxable income to the TRA1986. Because he observes the sametaxpayers both before and after the Act,Feldstein can use pre–TRA 86 marginaltax rates in grouping taxpayers intocategories experiencing differentchanges in marginal tax rates. Thisavoids the problem of the compositionof the groups changing over time.

Instrumental Variables Using Panel Data

Moffitt and Wilhelm (1998) pose thechoice of a suitable grouping variable interms of instrumental variables. The

difference-in-differences methodologyusing panel data is essentially estimatinga regression of the change in a behav-ioral variable (such as hours of work ortaxable income) on the change in thetaxpayer’s marginal rate. The change inthe marginal tax rate is partly a functionof the taxpayer’s behavior and must beinstrumented for. A suitable instrumentor grouping variable must be correlatedwith the change in tax rates butuncorrelated with the regression errorterm (which can be interpreted as thechange in the unobserved determinants

of the taxpayer’s behavior). Moffitt andWilhelm question whether prereformtax rates or income are suitable instru-mental (or grouping) variables. The pre-reform tax rate or income may be morehighly correlated with the unobserveddeterminants of prereform behaviorthan it is with the unobserved determi-nants of postreform behavior, and somay be correlated with the change inthe unobserved determinants ofbehavior. For example, as Carroll (1997)points out, transitory increases inincome prior to a tax reform can be

expected to be followed by decreases inincome following the reform. Thisregression to the mean effect wouldlead to correlation between prereformincome and the regression error if the

unobserved determinants of behaviorare also affected by the transitory factor.A similar critique applies to using post-reform income or tax rates as instru-ments. Moffitt and Wilhelm investigateusing several alternative instruments forthe change in tax rates, includingeducational attainment, broad occupa-tional categories, and illiquid assetholdings. Carroll uses a proxy forpermanent income, income averagedover several years, as an instrument.These instruments are less likely thanprereform income or tax rates to besensitive to transitory disturbances, andso are more likely to be uncorrelated

with the change in the unobserveddeterminants of behavior.

Using panel data, in some instances,one may be able to determine howmuch of behavioral responses are due totiming effects and how much of theresponses are permanent. Recent workby Burman and Randolph (1994) oncapital gains realizations and byRandolph (1995) on charitable contribu-tions attempts to do this. Burman andRandolph use a panel of tax returns toestimate a model in which an

individual’s capital gains realizationsdepend on both his permanent tax rateand current tax rate. They rely on themaximum combined state and federalmarginal tax rate in the individual’s stateas an instrument to identify the perma-nent tax effect. Because the maximumtax rate does not vary over individualswithin the state, they argue it is unlikelyto be correlated with transitory factors.The individual’s marginal tax rate on thefirst dollar of realizations is used as aninstrument to identify the transitory taxeffect. 6 The first-dollar tax rate does not

depend on the individual’s capital gainsrealizations, and so does not suffer froma direct endogeneity problem as thefinal-dollar marginal tax rate does, but itdoes vary over time for the individual.



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The strategy of using a first-dollar taxrate would not work in studying theeffect of marginal tax rates on taxableincome because in that case there isessentially no exogenous incomecomponent on which to base the first-dollar calculation. In the case of capitalgains realizations, one can argue thatsome components of income areunlikely to be correlated with theunobserved determinants of gainsrealizations and can be treated asexogenous. Burman and Randolph andRandolph both find that the transitoryeffect of tax changes is much largerthan the permanent effect. This is very

plausible—realizing capital gains andgiving to charity are two activities inwhich taxpayers have quite a bit offlexibility in timing. However, it is askinga lot of the data to distinguish betweenthe transitory and permanent effects oftax changes, and more research isneeded to investigate the robustness ofthis strategy for estimation.

Conclusions

Researchers investigating how taxationaffects behavior face a number of

challenging problems. No particulareconometric strategy is foolproof, andone must be aware of potential prob-lems and sources of bias in evaluatingempirical estimates. However, it isimportant to not become overly jaun-diced or cynical. Despite the problemsencountered, econometric analysis ofhow taxation affects behavior hasprovided estimates that have led tobetter informed debate on tax policy.Comparison of alternative policiesrequires that we know the magnitude ofthe behavioral responses, and without

econometric estimates, we would be leftwith little more than intuitive guesses onwhich to rely. Further research investigat-ing the behavioral responses is clearly animportant and worthwhile endeavor.

ENDNOTES

The views expressed in this paper are not

necessarily shared by the Federal Reserve Bank ofBoston or its staff.

1 The tax price can actually be more complex due tothe interaction of state and federal income taxesand the tax treatment of gifts o f appreciatedproperty.

2 See, for example, Eissa (1995, 1996) and Moffittand Wilhelm (1998).

3 Technical expositions of this methodology areprovided by Hausman (1985) and Moffitt (1986).

4 Eissa (1995) also conducted the analysis using asecond control group whose income was at the75th percentile of the distribution.

5 Blundell, Duncan, and Meghir (1998) estimate amodel of how taxation affects labor supply, whichtakes this approach to identification.

6 In addition to setting capital gains realizations tozero, Burman and Randolph (1994) also set severalother potentially endogenous deductions andincome sources to zero before calculating the first-dollar marginal tax rate.

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