ESTIMATION AND INTERPRETATION OF CAPITAL GAINS REALIZATION BEHAVIOR: EVIDENCE FROM PANEL DATA' GERALD E. AUTEN,* LEONARD E. BURMAN** AND WILLIAM C. RANDOLPH*** 1. Introduction capital gains is determined simulta- neously with the level of capital gains, T HE revenue effects of capital gains these studies have ignored the endogene- taxation have important implications ity of other kinds of income and deduc- for the extent to which capital gains taxes tions. In addition, because income and tax can be modified to achieve policy objec- rates are simultaneously determined, tives. But the existing economic evidence econometric results cannot answer policy on capital gains taxation is so imprecise questions about revenue without careful that there is widespread disagreement microsimulation. Another important about whether past changes in the taxa- econometric problem that most previous tion of capital gains raised or lost reve- studies ignore is the selectivity bias that nue and about what the direction and arises because individuals simulta- magnitude of the revenue effect of pro- neously choose the level of capital gains posals to cut the tax rate on capital gains and whether or not to realize a capital gain might be. at all. Furthermore, cross-section studies There are three primary reasons why have been unable to account for the dy- economists can't answer policymakers' namics of capital gains responses. Time- questions about the revenue implications series studies suffer from aggregation of capital gains tax changes with more biases and small samples that reduce the certainty. First, the econometric analysis precision of statistical estimates. of capital gains realization behavior has This paper focuses attention on the lat- only weak theoretical economic founda- ter two problems. First, we clarify some tions. Absent a clear behavioral model, issues regarding the choice of data set. We econometric analysis is as much art as then present an econometric analysis of science and artistic interpretations clearly panel data. Our model and methods were vary on this subject. designed to correct several of the most Second, it is unclear what kind of data important weaknesses of previous micro- are adequate for answering policymakers' data studies of the effect of taxes on cap- questions. It is possible that cross-section ital gains realizations. To correct for the and time series data answer different kinds simultaneity problem in estimation, our of questions. However, there is consider- model treats, in addition to capital gains, able confusion and dissent among econo- several other components of capital in- mists about which kind of data are ap- come and deductions as endogenous choice propriate. Moreover, previous studies have variables. To correct for the simultaneity lacked important explanatory variables, problem in interpretation of estimated such as state tax rates and accrued capi- equations, we developed a micro-simula- tal gains, that may have added to the un- tion model. In addition, unlike previous certainty of their analyses. studies, our study corrects for selection Third, previous studies have been ham- bias, incorporates an appropriate exoge- pered by econometric problems. Most no- nous measure of wealth, and includes state tably, while virtually all studies have income taxes. recognized that the marginal tax rate on II. Choice of Data Set *Bowling Green State University, Bowling Green, OH 43403 and Office of Tax Analysis, U.S. Treasury Department, Washington, DC 20220. A. Determinants of Individual Capital **U.S. Congressional Budget Office, Washington, Gains Realizations DC 20515. ***Office of Tax Analysis, U.S. Treasury Depart- We start with a model of how capital ment, Washington, DC 20220. gains realizations respond to income tax 353
Transcript
ESTIMATION AND INTERPRETATION OF CAPITAL GAINSREALIZATION BEHAVIOR: EVIDENCE FROM PANEL DATA'
GERALD E. AUTEN,* LEONARD E. BURMAN** AND WILLIAM C. RANDOLPH***
1. Introduction capital gains is determined simulta-neously with the level of capital gains,
THE revenue effects of capital gains these studies have ignored the endogene-taxation have important implications ity of other kinds of income and deduc-
for the extent to which capital gains taxes tions. In addition, because income and taxcan be modified to achieve policy objec- rates are simultaneously determined,tives. But the existing economic evidence econometric results cannot answer policyon capital gains taxation is so imprecise questions about revenue without carefulthat there is widespread disagreement microsimulation. Another importantabout whether past changes in the taxa- econometric problem that most previoustion of capital gains raised or lost reve- studies ignore is the selectivity bias thatnue and about what the direction and arises because individuals simulta-magnitude of the revenue effect of pro- neously choose the level of capital gainsposals to cut the tax rate on capital gains and whether or not to realize a capital gainmight be. at all. Furthermore, cross-section studies
There are three primary reasons why have been unable to account for the dy-economists can't answer policymakers' namics of capital gains responses. Time-questions about the revenue implications series studies suffer from aggregationof capital gains tax changes with more biases and small samples that reduce thecertainty. First, the econometric analysis precision of statistical estimates.of capital gains realization behavior has This paper focuses attention on the lat-only weak theoretical economic founda- ter two problems. First, we clarify sometions. Absent a clear behavioral model, issues regarding the choice of data set. Weeconometric analysis is as much art as then present an econometric analysis ofscience and artistic interpretations clearly panel data. Our model and methods werevary on this subject. designed to correct several of the most
Second, it is unclear what kind of data important weaknesses of previous micro-are adequate for answering policymakers' data studies of the effect of taxes on cap-questions. It is possible that cross-section ital gains realizations. To correct for theand time series data answer different kinds simultaneity problem in estimation, ourof questions. However, there is consider- model treats, in addition to capital gains,able confusion and dissent among econo- several other components of capital in-mists about which kind of data are ap- come and deductions as endogenous choicepropriate. Moreover, previous studies have variables. To correct for the simultaneitylacked important explanatory variables, problem in interpretation of estimatedsuch as state tax rates and accrued capi- equations, we developed a micro-simula-tal gains, that may have added to the un- tion model. In addition, unlike previouscertainty of their analyses. studies, our study corrects for selection
Third, previous studies have been ham- bias, incorporates an appropriate exoge-pered by econometric problems. Most no- nous measure of wealth, and includes statetably, while virtually all studies have income taxes.recognized that the marginal tax rate on
II. Choice of Data Set*Bowling Green State University, Bowling Green,
OH 43403 and Office of Tax Analysis, U.S. TreasuryDepartment, Washington, DC 20220. A. Determinants of Individual Capital
***Office of Tax Analysis, U.S. Treasury Depart- We start with a model of how capital
ment, Washington, DC 20220. gains realizations respond to income tax
353
354 NATIONAL TAX JOURNAL [Vol. XLII
treatment similar to the models used in table contribution) distinct from the levelprevious research. As in that literature, of income or deductions. While Auten andwe do not have an explicit theoretical Clotfelter (1982) and Treasury (1985) alsomodel of capital gains because theoretical accounted for this self-selection in a Tobitmodels, such as Stiglitz (1983), do not yield model, we take that analysis a step fur-interesting testable hypotheses.' We sim- ther by modelling the decision to realizeply follow other authors in positing that separately from the level of realization.'realizing capital gains has some economicvalue as compared to holding assets with B. Why are Cross-Section and Time-capital gains and so, the decision to re- Series Elasticities so Different?alize a capital gain depends on whetherthe value of realizing the gain is at least Table 1 summarizes the regults of pre-as great as the cost, which is primarily vious studies of capital gains realizationthe capital gains tax.' responses to tax rates. The results are
The amount of capital gains depends on characterized by an elasticity, which rep-the individual's stock of unrealized gains. resents the approximate change in capi-The more unrealized capital gains in the tal gains realizations in response to a oneindividual's portfolio, the more gains are percent change in tax rates (e.g., from alikely to be candidates for realization. In- rate of 20 percent to 20.2 percent). As adividuals may realize capital gains to fi- rough approximation, a capital gains taxnance consumption, and so permanent and cut will increase capital gains revenues iftransitory income may be important de- the aggregate elasticity is greater than 1terininants of realizations. In addition, in absolute value and will reduce capitalindividuals may have different attitudes gains tax revenues if the elasticity is lesstoward asset trading and risk, and have than 1.6 Table 1 shows that these elastic-different discount rates. We assume that ity estimates range widely from a low ofthese taste parameters depend on observ- essentially zero (Auerbach, 1988) to a highable demographic variables such as mar- of almost -4.0 (Feldstein, Slemrod, andital status, age, and family size. Yitzhaki (FSY), 1980). Notwithstanding
We also allow for the possibility that this large variation, there seems to be aindividuals engage in tax planning so that clear division between the estimates basedtheir tax rate itself is a choice variable. on time series and the estimates based onMost of the earlier studies have made a micro data (cross-section or panel data).similar assumption, but with the excep- Although there are exceptions, the timetion of Cook and O'Hare (1987), their es- series estimates are generally lower intimation methodology requires that tax absolute value than the estimates basedplanning be limited to the choice of the on micro data.level of capital gains. Our model assumes The debate about which, if any, set ofthat other capital income items, such as estimates is relevant for policy purposesdividends and interest, and deductions, is reminiscent of the debate about con-such as charitable contributions, may be sumption fimctions in the 1940s and 1950s.determined endogenously.' In the case of consumption functions, the
There are two components of capital conundrum was reconciled by explaininggains decisions that may respond to tax that individuals respond differently torates. First, taxpayers may adjust their permanent income than to transitory in-level of gains in response to different tax come. Because cross-section income levelsrates. Second, some individuals may defer include the transitory component that isrealizations in years when their tax rates washed out in the aggregate data, theare high. For example, in our panel of cross-section consumption function esti-taxpayers, 35 percent of capital gains were mates were biased downward. A similarrealized by taxpayers with capital gains analysis might be useful in explaining thein only one year. Our model explicitly ac- variation in capital gains elasticity esti-
7counts for the decision whether or not to mates.realize capital income (or make a chari- Suppose that individuals view their
No. 31 G. E. AUTEN, L. E. BURMAN, AND W. C. RANDOLPH 355
Table I
Ranges of Point Estimates From Previous Studies:Long-Term Capital Gains Realization Elasticities
Capital Gains RealizationStudies Data Type Type Elasticity
Minarik Cross-Section Corporate Stocks Range from -.44(1981) High-Income to -.79
Sample, 1973
Auten and Clotfelter Panel Data, All Capital Assets Short-Run Range:(1982) Middle-Income -.91 to -3.46,
Sample, Long-Run Range:1967 to 1973 -.36 to -1.45
U.S. Treasury Panel Data, All Capital Assets Long-Run Range:(1985) 1971 to 1975 - 1. 16 to -2.20
Corporate Stocks Long Run: -2.07
U.S. Treasury Time Series, All Capital Assets Short Run: -1.3(1985) 1954-1985, Long Run: -0.8
All Taxpayers
Lindsey Pooled Cross- All Capital Assets *Short Run: -2.14(1987) Section and *Long Run: -1.37
Time Series,1965-1982
Darby, Gillingham, Time Series, All Capital Assets *Long-Run Range:and Greenlees 1954 to 1985, -.62 to -1.51(1988) All Taxpayers
Congressional Time Series, All Capital Assets *Range from -.79Budget Office 1954 to 1985, to -.99(1988) All Taxpayers
Auerbach Time Series, All Capital Assets *Long-Run Range:
(1988) 1954 to 1986, -.06 to -1.09All Taxpayers
Derived at 25.4% average tax.
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marginal tax rate on capital gains as sumed in the constant term in the Xit vec-comprising two parts. The first is a stat- tor." The coefficient p may be estimatedutory component that reflects the aver- using Tit as a regressor in an appropriateage tax rate on capital gains under cur- simultaneous equation estimation tech-rent law.' The second is the individual nique.variation from the average statutory rate. Panel data are necessary, but not suf-The first component is exogenous to the ficient, to identify both ot and p in a sin-individual. The second component has both gle equation. There must be more yearsan exogenous component due to uncon- in the panel than there are time-varyingtrollable temporary -changes in taxable explanatory variables (such as value of theincome, and an endogenous component stock market, interest rates, and TSTATT).that reflects tax planning. If there are lags or fixed effects in the
Individuals may respond differently to model, the minimum number of years ofchanges in the statutory marginal tax rate data increases accordingly. Finally, as athan to changes in the individual-specific practical matter, the length of the panelcomponent. The statutory component is would have to be substantially greaterpurely exogenous, which may mean that than the minimum to achieve reasonablyit is harder for individuals to plan to either precise estimates of cLbecause significanttake advantage of a low statutory rate or shifts in TSTAT are infrequent.to avoid a high rate. The statutory rate If this simple model were an accuratemay also be perceived to be more per- representation, then we could use cross-manent. For now, assume that the stat- section estimates for p and time-series es-utory component is the same for all in- timates for a. Based on this model, wedividuals in a given year. We consider later might conclude that cross-section elastic-the implications of deviations from this ities are consistently higher than time-se-assumption. ries estimates because individuals are
The following is a simple linear repre- more responsive to individual (short-term)sentation of the model.' variation in marginal tax rates than they
are to statutory (long-term) changes.Git = oLTSTATt + p(Tit - TSTATT) However, the division between cross-
section and time-series components of+ xitr + vit, marginal tax rates is not so clear cut.
Individuals face different long-run statu-where Git is capital gains realizations by tory tax rates because of permanent dif-individual i in year t, TSTATT is the av- ferences in income and wealth. Thus, cross-erage stat;utory marginal tax rate on gains section tax elasticities in part reflect a re-in year t, which only varies over time, Tit sponse to the peculiarities of current taxis individual i's marginal tax rate on gains law. Moreover, individuals are affectedin year t, and Xit is a vector of other pa- differently by changes in tax laws. Thisrameters that affect capital gains.10 means that time series estimates based
In this simple model, neither cross-sec- on a single summary variable, such as antion nor time-series data permit identifi- average tax rate, are of limited relevancecation of both a and p. In aggregate time to predicting the effects of a tax scheduleseries, the sum of (Tit - TSTATT) is zero change that might be significantly differ-since TSTATT is the sum over i of Tit. Thus, ent from prior laws. 12 In addition, even theonly ot can be identified using aggregate average statutory tax rate varies acrosstime series data. In the special case of this individuals because state tax rates onlinear model, time series estimates can capital gains vary substantially.provide information about how capital There are other drawbacks in time se-gains realizations and tax revenues re- ries estimates that arise when the sim-spond to changes in tax law. plifying assumptions made above are re-
Using cross-section data, the situation laxed. There are two kinds of potentiallyis reversed, i.e., 0 is identifiable whereas serious aggregation bias. First, the rela-a is not. In a cross-section, TSTATT is sub- tionship between marginal tax rates and
No. 31 G. E. AUTEN, L. E. BURMAN, AND W. C. RANDOLPH 357
realizations is certainly not linear,13 Which C. Other Advantages of Panel Datameans that the aggregate response tochanges in tax rates would not be the sum There are other advantages of panel
14 - data over cross-section data. First, panelof the individual responses. This imdata allow estimation of the dynamics ofplies that (1) time-series estimates of a willindividual response to capital gains taxbe biased estimates of the individual re-changes because lagged data are avail-sponse parameter, and (2) aggregate rev-able. The possible importance of dynam-enue responses will not in general be theics has been stressed by Auerbach (1988)product of aggregate realizations and theand Kiefer (1989). Second, panel dataaverage tax rate on capital gains. Second,provide information about permanent in-there may be a sample-selection bias duecome. Third, lagged income and deduc-to individuals' choosing whether or not totion items are useful as instruments forrealize a capital gain separately from the
level of gain. 15 While it is possible to cor- two-stage estimation of the simultaneousrect for this bias in cross-section or panel system of equations and to create exoge-data, it is not possible in the time series nous proxies for permanent income anddata, so it is hard to tell if this bias is wealth. Fourth, panel data allow correc-important or what sign it is likely to have. tion for individual-specific fixed effectsIn addition, there is the obvious problem such as unobservable taste parameters orthat time series estimates are necessarily components of household wealth.'8imprecise because there are so few de-grees of freedom (typically 30 observa- 111. Econometric Problems in Cross-tions or so). Section Studies
Cross-section estimates of Pwill accu-rately predict responses to tax policy In addition to the identification prob-changes only if individuals treat all com- lem discussed in section II, there is sub-ponents of their marginal tax rate in the stantial variation in the results from pre-same way, i.e., ot = P. However, even un- vious cross-section studies. Some of theder this assumption, cross-section esti- variation can be explained by the failuremates may be flawed. There is evidence to model the simultaneous nature of thethat the response of individuals to tax dependency between marginal tax rates,changes is dynamic." Therefore, the ab- capital gains income, and other forms ofsence of lagged tax rate variables may bias income and deductions. In the construc-elasticity estimates in cross-section data." tion of estimation procedures, most of the
Panel data can be used to address both studies have accounted in some way forsample-selection problems and dynamics. simultaneity of long-term capital gainsMorever, panel data do not suffer from and marginal tax rates on long-term cap-problems of aggregation bias. If tax law ital gains. However, none of the micro-datachanges affect individuals differently, studies has accounted for potential si-elasticity estimates based on a panel that multaneity of capital gains and otherspans at least one tax law change will re- forms of income and deductions.flect that variation, as well as the indi- Yet more of the variation in micro-datavidual-specific response to marginal tax results can be explained by the failure torates. account for simultaneity when interpret-
The time series estimates under the ing estimation results. If capital gains in-most optimistic of assumptions reflect a come and marginal tax rates are deter-good estimate of ot, the average effect of niined simultaneously, then analysis of thestatutory tax changes. The panel esti- effects of changing statutory tax rates onmates capture how a particular tax law capital gains must account for the fact thatchange affects individuals differentially, actual marginal tax rates would not nec-as well as individuals' responses to other essarily change by as much after account-sources of variation in tax rates. The ing fully for implied behavioral re-t,correct" elasticity might be between these sponses. Ignoring such simultaneity whentwo sets of estimates, interpreting the results may cause the
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impression that capital gains are more to use current endogenous variables suchsensitive to tax rates than they actually as dividends, interest, and rent as proxiesare. for wealth.
As an additional possible cause of vari-ation in results, only two studies-Trea- IV. A Model of Capital Gains andsury (1985) and Auten and Clotfelter Endogenous Taxable Income(1982)-corrected for sample-selectionbiasin their parameter estimates. In a sample Some essential features of our model areof primarily upper-income taxpayers, such represented by the following three-equa-
20as the panel-data sample used for our tion system.study, less than 50 percent of the taxpay-ers realize long-term capital gains income Git = ao + atit + a2Xit + eit, (1a)in any one year. Many taxpayers may not Oit = bo + b,Tit + b2Zit + uit, (lb)realize capital gains simply because theyhave little wealth. On the other hand, Tit = f(Git, Oit, Yit), (1c)wealthier taxpayers may choose not to re-alize capital gains either by choosing not where i = 1, N, are individuals in theto sell appreciated assets or by choosing panel and t 1, ..., S are years. Gi, isnot to hold their wealth in the form of as- realized long-term capital gains, Oit rep-sets on which capital gains would be re- resents endogenous components of otheralized. For the wealthier group of taxpay- taxable income and deductions, Tit is theers, the decision of whether or not to marginal tax rate on ordinary income, Xitrealize capital gains income may be dis- and Zit represent other exogenous or pre-tinct from the decision of how much cap- determined factors affecting Git and Oit.ital gains income to realize. Failure to Yit represents exogenous components ofmodel such a distinction may have led to taxable income as well as other factors thatbiased estimation results in previous mi- determine tax liability.cro-data studies. The marginal tax rate, Tit, is endoge-
Another issue that arose in the ex- nous so that the parameters in equationchange between FSY (1980) and Minarik (1a) cannot be consistently estimated -us-(1984) was whether weighting is appro- ing least squares. In fact, it can be shownpriate for estimation. Minarik argued that that, under weak assumptions, ordinaryweighting is essential because the cross- least squares estimates of tax elasticitiessection individual income tax returns in would be biased toward zero (Auten, Bur-the FSY study were drawn from a strat- man, and Randolph, 1988). Fortunately,ified sample that oversampled high-in- the simple model suggests several optionscome taxpayers. However, the validity of for estimating the capital gains equationMinariles weighting procedure depends on (1a). First, the equation could be esti-very strong assumptions about unobserv- mated by two-stage least squares, usingable model characteristics.'9 In fact, given Xit, Zit, and Yit as exogenous variables.that the weights are endogenous (capital This method assumes that the tax rategains are an important component of the function, (1c), is linear. Since (1c) is non-stratification variable) and the other linear, and the non-linearities serve to aidcomplexities of the capital gains model, identification, we adopt an alternative thatthe correct weighting procedure would be is similar to the approach taken by othervery complex. authors. We construct a tax rate instru-
Previous studies may have produced ment by computing the marginal tax ratebiased estimates because they lacked an after setting the endogenous componentsexogenous measure for wealth. Wealth, as of taxable income, Git and Oi,, equal toan indicator of accrued capital gains, may zero, i.e., f(O,O,Yit). This variable pre-be an important determinant of the level serves the information about the non-lin-of capital gains, but tax return data do
-ear relationship between Tit and Yit, while
not provide a direct measure of wealth. In purging Tit of its endogenous components.consequence, previous studies have had The tax rate instrument used in pre-
No. 31 G. E. AUTEN, L. E. BURMAN, AND W. C. RANDOLPH 359
vious studies has been either f(O,O,Yit) or income, For estimation, we used a ran-f(O,it,Oit,Yit), where Git is some variant of dom, though still stratified, subsample ofa reduced form estimate of Git. Such tax about 5,000 taxpayers, for which four yearsrates are only exogenous if both b, and of data were included for each taxpayer .22
the covariance between the equation er- For simulation we increased the samplerors, eit and uit, are zero. While this pos- size by adding randomly sampled data onsibility cannot be ruled out with cer- 'about 8,000 taxpayers. Sample weights,tainty, it is inappropriate to impose such used for simulation, reflect the number ofa restriction a priori. Moreover, if these taxpayers represented by each of the tax-strong assumptions are not satisfied, es- payers included in the sample. Unliketimates of the responsiveness of capital previous studies which limited their sam-gains to tax rates (a,) as well as other pa- ples to taxpayers with some amount oframeters may be biased and inconsistent, dividend or rental income or losses, we in-and the sign of the bias is indeterminate cluded all taxpayers in the sample who
21 23a priori. filed returns in two consecutive years.Our model explicitly accounts for the Marginal Tax Rates: Marginal tax rates
censoring of the observed inconke,, and de- were calculated by increasing the appro-duction items at zero. The system of priate type of income, e.g., long-term cap-equations in (1a) and (lb) is extended to ital gains for the marginal tax rate oninclude a criterion function for each in- long-term capital gains, by the maximumcome item. Each criterion function is es- of either $1,000 or the square root of es-sentially a Probit model of the decision of timated wealth. The total tax liability waswhether or not to realize a non-zero then divided by the change in income. Toamount of the corresponding income. calculate the total tax liability, a FederalThese criterion functions are of the form, income tax calculator was adapted for the
panel years from a tax calculator devel-G* = co + c,Tit (2a)it + C2Xi*t + ei*t oped by the U.S. Treasury, Office of Tax
Oi*t= do + d,Ti*t + d2Zi*t + Ui*t(2b) Analysis (Cilke and Wyscarver, 1987). In
addition, state tax calculators were de-where Gi*t and Oi*t are unmeasured indices veloped for all years of the panel.such that Git in (1a) is only observed if Wealth: Although the wealth of eachGi*t> 0 and Oit in (lb) is only observed if taxpayer should be an important deter-oi*t > 0. Xi*t and Zi*t are vectors of exoge- minant of the ability to realize capitalnous variables that are not necessarily gains and other forms of capital income,identical to Xit and Zit. The error terms in deductions, and losses, no direct infor-(2a) and (2b) are standard normally dis- mation about taxpayer wealth is reportedtributed, and correlated with the corre- on ncome tax returns. Because wealth issponding errors in (1a) and (lb). important, we developed a proxy variable
for wealth by using the U.S. Treasury's
V. DataEstate-Income Tax Match Study for 1981-82, which included a sample of estate tax
The data are from a panel of Federal returns, matched with corresponding in-income tax returns compiled by the U.S. come tax returns for the last full year priorTreasury Department for approximately to death. These data were used to com-12,000 taxpayers for 1979 through 1983. pute total wealth, net of life insuranceOne advantage of the data is the avail- payments, and total stock holdings. Theability of detailed tax data over a time logarithm of total wealth reported on theperiod in which tax laws changed. An- estate tax returns, net of life insuranceother advantage is the availability of the payments, was regressed on lagged capi-ages and other characteristics of taxpay- tal income items, lagged losses, and de-ers in the sample. The sample was strat- mograhic variables such as age. Becauseified to oversample high-income taxpay- there was a $300,000 exemption for filingers, for whom capital gains were more estate tax returns, parameters were es-likely to be an important component of timated by truncated regression. The es-
360 NATIONAL TAX JOURNAL [Vol. XLII
timated parameters were then used to until death, which increases with age."impute levels of wealth and stock hold- Finally, time dummies reflect the impactings for each taxpayer in the panel sam- of macroeconomic variables that affect in-ple, conditional on the appropriate lagged dividual asset values as well as the con-values of income and demographic vari- stant component of the 1981 tax lawables. change as discussed in section 11.
Permanent Income: The permanent in- The equations were estimated in two-come variable is the predicted value from steps. First, the criterion function param-an estimated regression which had the eters were estimated by Probit maximumlogarithm of a 5-year average of total likelihood. Estimated criterion functionpositive income as a dependent variable parameters were then used to constructand exogenous income and demographic Mills ratios, which were added to the in-variables as right-hand-side variables, come level equations to correct for sam-evaluated at their 1979 levels. Total pos- ple-selection bias. As the second estima-itive income is the sum of all positive tion step, income level equations werecomponents of income, including capital estimated by least squares, using only thegains, i.e., gross income before losses. It observations for which non-zero levels ofis a measure of income used by the IRS income were realized.and several previous studies as a measure Because the marginal tax rates are en-of economic income. This measure of per- dogenous right-hand-side variables, themanent income can be interpreted as a two estimation steps were preceded by anmeasure of expected permanent income. instrumental-variables procedure. Before
the Probit step, actual marginal tax rates
VI. Equation Specification andwere regressed, using least squares, on all
Estimation Method exogenous variables in the criterion func-tion and the tax rate instrument dis-
The capital gains level equation and cussed in Section IV. Probit estimates andcriterion function capture six aspects of the resulting Mills ratios were then ob-individuals' decisions to realize capital tained using fitted tax rates in place ofgains. There is the decision whether to re- actual tax rates. Actual tax rates werealize any capital gains at all or to defer then regressed, using least squares on therealization to another year. This decision sample of realizers only, on all exogenousis reflected in the criterion function, sim- variables in the level equation, the tax rateilar to (2a), discussed in section IV. There instrument, and the Mills ratio. Fitted taxis the dynamic response to tax rates. We values for this subsample were then usedmodel this response as a first-order dif- in place of actual tax rates in the second
21ference equation, where lagged tax rates step of* estimation.are assumed to be predetermined. Per-manent and transitory income variables VII. Estimation Resultsare included to reflect the consumptionmotive for capital gains realizations as well Estimation results for the capital gainsas to control for different attitudes toward equations appear in Table 2. The first tworisk that may be related to income. Wealth columns contain parameter estimates foris included as a proxy for accrued capital the equations that explain the levels ofgains. Lagged business and rental income long- and short-term realizations, respec-and lagged rental losses control for pre- tively. The last two columns are the cor-vious investments that may be expected responding parameter estimates for theto result in capital gains. We also include criterion functions, which explain taxpay-available demographic variables-mar- ers' decisions whether or not to realizeriage dummies, family size, age brackets, capital gains.and regional dummies-to try to control For the level equations, the dependentfor different tastes that might affect trad- variable is the natural logarithm of theing strategies. The age brackets also re- net-positive amount of capital gains be-flect the benefit of holding capital assets fore loss carryovers." Each coefficient
No. 31 G. E. AUTEN, L. E. BURMAN, AND W. C. RANDOLPH 361
implies a directional effect of changes in function coefficient implies that an in-the corresponding right-hand-side (RHS) crease in the corresponding RHS variablevariable on the dependent variable. For would increase the likelihood that capitalexample, wealth was estimated to have a gains are realized.positive effect on the levels of both short- For two reasons, however, individualand long-term capital gains. coefficients provide only first-order ap-
For the criterion fimctions, the depen- proximations to the full effects of chang-dent variables are unobserved indexes that ing RHS variables. First, the current yeardetermine whether a taxpayer realizes marginal tax rate is a function of the de-capital gains income. Capital gains in- pendent variable, so that a completecome is realized only if the index is pos- characterization of the effect of any RHSitive. A positive estimate of a criterion- variable must account for all feedback ef-
No. 31 G. E. AUTEN, L. E. BURMAN, AND W, C. RANDOLPH 363
fects on the current year tax variable. current and lagged tax coefficients. ForSecond, complete characterization of the the level equations, timing is about 15effects of RHS variables must simulta- percent of the tax effect for long-term gainsneously consider effects on the level of and about 25 percent of the tax effect forcapital gains and the likelihood of real- short-term gains. For the criterion func-izing a nonzero amount of capital gains, tions, timing is about 67 percent for theas implied by the estimated parameters long-term gains equation and about 48of the criterion functions. percent for the short-term gains equation.
Although complete interpretation of the For both types of gains, timing appears tocoefficients requires simulation of the be more important for the likelihood of amodel, as described in Appendix 1, ex- sale than it is for the level of a sale. Thisamination of individual coefficients and may reflect the fact that appreciated as-other parameters is informative. For this sets are often indivisible when taxpayerspurpose, the coefficients can be divided into consider which assets to sell, how much,three groups: tax-rate variables, wealth and when. If not all assets are divisibleand income variables, and age and other and not all taxpayers have access to avariables. means, such as installment sales, by which
The tax variables are -Ln(100 - t), they can spread out the sales of indivisi-where "Ln" is the natural logarithm and ble assets over several years, then the rel-t is the appropriate marginal tax rate, ative timing effect would be larger for theeither current or lagged, short- or long- sell/don't sell decision than for the how-term. Because the tax price terzn is ne- much-to-sell decision.gated, the negative coefficients of the The wealth variable coefficients arecurrent-year tax variables in the level positive in all four equations, implyingequations imply that increasing the tax that wealthier taxpayers are more likelyrate decreases capital gains income. Sim- to realize capital gains and they realizeilarly, coefficient estimates for the crite- larger amounts of capital gains. Like-rion functions imply that increasing the wise, taxpayers with higher permanentown tax rate decreases the likelihood of income tend to realize higher levels ofrealization. In all four equations, the own short- and long-term capital gains.lagged tax coefficients are positive, which The transitory income variable seemsimplies that a higher lagged marginal tax to be uniformly unimportant. This couldincreases both the level of capital gains be because the important source of tran-income and the likelihood that capital sitory variations is reflected in the cur-gains are realized. rent and lagged tax rates or because of
Opposite signs on the coefficients of errors in measurement of transitory andcurrent and lagged tax-rate variables permanent income.suggest that taxpayers time capital gains Higher levels of wage and salary in-realizations so that they occur in rela- come lead to lower levels of short-termtively low marginal tax rate years. For capital gains. Because permanent incomeexample, if the previous year's marginal is held constant, the negative coefficienttax rate was higher, then capital gains of wage and salary income implies thatwould be realized in the current year higher transitory levels of wages and Sal-rather than the previous year. The sums aries cause lower levels of short-termof the current and lagged tax rate coef- capital gains. Taxpayers with higherficients, i.e., the long-run effects, are neg- lagged business losses are more likely toative in all four equations but smaller than realize each type of capital gains income.the current year tax rate coefficients, i.e., Surprisingly, however, the coefficient ofthe short-run effects. the lagged business loss variable is neg-
As a first-order approximation to the ative and significant in the long-termimportance of timing relative to the long- capital gains equation.run effects of changes in the marginal tax Age has opposite effects on the level andrates, the size of the lagged tax coeffi- likelihood of reamng capital gains. Oldercients can be compared to the sum of the taxpayers are more likely to realize cap-
364 NATIONAL TAX JOURNAL [Vol. XLII
ital gains income but they realize less than simultaneity. The econometric model wasyounger taxpayers. One possible expla- constructed so that capital gains incomenation for such a sign reversal is that depends upon the marginal tax rate forwealth is not perfectly measured by other capital gains. The marginal tax rate alsoRHS variables. If the distribution of depends upon the level of capital gainswealth is more highly skewed for young income. Estimated coefficients from Ta-than for older populations of taxpayers, ble 2 imply that an increase in statutorythen a smaller fraction of young taxpay- marginal tax rates on long-term capitalers would have capital gains that can be gains would also decrease long-term cap-realized, thus causing the younger tax- ital gains income. The decrease in capitalpayers to be less likely to realize capital gains income would, in turn, decrease thegains. However, the young taxpayers who tax rate for some taxpayers, etc., until anrealize capital gains may be relatively equilibrium is reached. Simulation is nec-wealthier than older individuals who re- essary to find the policy effect on thealize capital gains. equilibrium solution for each taxpayer.
The estimates of the covariance be- Second, simulation is necessary so thattween the errors in the level equation and the individual behavioral effects of taxcriterion function are negative and sta- policy changes are aggregated properly totistically significant in both the long- and derive implied effects on aggregate capi-short-term capital gains equations. This tal gains income and aggregate Federalsuggests that the failure to correct for tax receipts. Behavioral effects must besample selection may have resulted in evaluated on an individual basis and thenimportant biases in previous research." aggregated because the econometric modelThe negativity of the covariance estimate implies that each behavioral response de-implies that the Tobit model is inappro- pends on the level of the marginal tax frompriate for modelling selectivity because the which the evaluation starts, i.e., it is a non-covariance is constrained to be 1.0, which constant tax elasticity model.is 16 standard deviations away from the The tax calculator provides the thirdestimated covariance of -4.36 in the long- reason. In the econometric model, capitalterm gains equation. It also suggests that gains income only depends on the tax codethere may be some unobserved variables through the marginal tax rate on capitalthat are missing from both equations that gains. Simulation is the only way to ex-result in a spurious correlation between amine the effect of changing the complexthe equation errors. For example, individ- tax code in a way that changes the mar-uals with a large amount of capital losses ginal tax rate differently for differentmay have small net gains but be espe- taxpayers, depending on their other lev-cially likely to realize. Another explana- els of income items, credits, and deduc-tion is that some individuals may be "buy tions. In addition, because state tax codesand hold" types whereas others trade ac- are included in our calculations, changestively. Those who trade more than ex- in the Federal income tax code would af-pected would then be observed to have fect marginal tax rates differentially acrosslower than average gains." states.
The fourth reason is statistical. For aVIII. Simulation standard self-selection model with no en-
dogenous right-hand-side variables, theWe developed a simulation method so effects of changing RHS variables can be
that the estimated econometric model examined by solving for the expected valuecould be used to examine the effect of of the dependent variable. However, thechanges in the individual income tax code marginal tax rate in our model is endog-on aggregate capital gains income and enous and it is on the right hand side ofFederal tax receipts. A simulation model the criterion and level equations. Theis necessary for several reasons. marginal tax rate is also a complicated
The first and most important reason is function of the dependent variable. It is
No. 31 G. E. AUTEN, L. E. BURMAN, AND W. C. RANDOLPH 365
therefore not possible to solve for a closed payers respond by increasing their capi-form for the expected level of capital gains tal gains income, which may push themincome. into higher marginal tax brackets, to
which they may respond by increasing
IX. Simulation Experiments their capital gains income by less thanthey would have otherwise. The full effect
We conducted several simulation exper- on the actual marginal tax rate would, iniments." All involved changing the inclu- such cases, be less than the change in thesion rate on long-term capital gains, us- statutory tax rate.ing data and a tax calculator for 1982, Table 4 presents another view of thewhen the inclusion rate war, 40 percent. simulation process. Before simulation,In general, a 5 percent change (for ex- capital gains increase from $83.0 billionample, from 40 percent to 38 percent) to $94.3 billion. Of this change, $7.6 bil-would produce a 5 percent change in all lion is due to increased realizations by in-Federal statutory marginal tax rates.3' The dividuals who realize gains before and af-simulation experiments were therefore ter the tax change and the remainder isdesigned to examine the effects of chang- due to realizations by the additional re-ing all statutory marginal tax rates on turns with capital gains.capital gains income. However, these additional realizations
Results of the simulations appear in increase individuals' tax rates because ofTables 3 and 4 .3' For all but the last sev- the progressivity of the tax code, espe-eral lines of Table 3, the simulations re- cially for those w4w-did not realize capitalflect the effect of small changes around gains in the beg-eline case. Simulation ad-the actual inclusion rate for 1982. The justs gains (and other income and deduc-long-run elasticity of aggregate long-term tions) until individuals are in equilib-capital gains with respect to the inclusion rium in the sense that the components ofrate is 1.63 and the short-run elasticity is their income solve the estimated equa-1.98." Part of the long-run elasticity, 1.33, tions at the tax rate that is consistent withis due to changes in the levels of capital their income level. After simulation, mostgains income for taxpayers who realize of the induced realizations evaporate whencapital gains in the base and comparison taxpayers figure out that if they realizedsimulations.3' The remainder of the re- a big capital gain in response to a lowersponse, 0.30, is due to taxpayers who tax rate, they would be pushed up into aswitch between realizing and not realiz- higher tax bracket. The resultant equilib-ing as a result of a change in the inclu- rium shows induced realizations of $2.2sion rate.31 billion, or 2.2 percent of the total. In-
Simulation results in Table 3 also dem- creased levels of realizations by individ-onstrate that actual marginal tax rates uals with gains in the baseline amount todo not change as much as statutory mar- $5.4 billion.ginal tax rates when the inclusion rate is Under this scenario, tax receipts in-changed. The responsiveness of the ac- crease by 0.6 percent from the baselinetual (capital gains weighted average) because the 9.2 percent increase in equi-marginal tax rate on capital gains is es- librium realizations more than offsets thetimated with respect to a change in the 2.7 percent decrease in average equilib-inclusion rate. If there were no state taxes, rium tax rates.no alternative minimum tax, and no be- We also examined the effect of largerhavioral feedback effect, then the respon- changes in the inclusion rate on long-termsiveness would be 1.0. However, the av- capital gains income. The inclusion rateerage responsiveness is only 0.61 because was increased by 50 percent, i.e., from 40(aside from the other two factors) there is percent to 60 percent, Are elasticities area behavioral feedback effect for many reported in the last five rows of Table 3.taxpayers. When the statutory marginal The long-run capital gains elasticity istax rate is decreased, for example, tax- larger, 1.67, than the elasticity derived
366 NATIONAL TAX JOURNAL [Vol. XLII
Table 3
Simulafion ResultsExperiment: Change the Inclusion
Rate on Long-Term Capital Gains Income*(1982)
Experiment: Small chanp-esin the inclusion rate
Aggregate Long-term gains:
Short-run realization elasticity -1.98
Long-run realization elasticity -1.63
Part due to non-switchers -1.33
Part due to switchers -0.30
Responsiveness of actual,marginal tax 0.61
Total Federal individual income tax receipts (1982):
Short-run elasticity -0.13
Long-run elasticity -0.11
Ext)eriment: Raise the inclusion rate to 60%
Long-run realization elasticity -1.67
Part due to non-switchers -1.20
Part due to switchers -0.47
Responsiveness of actual marginal tax 0.65
Long-run individual income taxreceipt elasticity -0.07
*Elasticities were computed with respect to chanres in the percentage oflong-term capital gains included in Federal AG .
for a small change in the inclusion rate of any other tax code change that may af-because a large change results in a larger fect marginal tax rates.fraction of switching between realizing andnot realizing capital gains income. The X. Sensitivity Analysispart due to switching is 0.47, which isabout 28 percent of the total response. A sensitivity analysis was conducted for
Though it was only used to simulate the the long-term capital gains equations toeffects of changing the inclusion rate, the examine the effects of varying the as-model can be used to simulate the effects sumptions on which the econometric model
Table 4
Simulation Results5% Decreasein the Inclusion Rateon Long-Term Cai
Chanp-es before iterationBaseline Comparison Change
(1) (2) (3)
Average marginal tax rate, 17.8 17.1 -4.2%long-te- capital gains
Total net long-term gains ($ billions) 83.0 94.3 13.6%
Number of returns withact gains or losses (thousands) .6,447 6,595 2.3%
Net long-term gains on returns with gains inbaseline and comparisomi ($ billions) 77.2 94.8 9.9%
Percentage of total net gains 93.0% 89.9% ...
Not long-term gains on returns witk gains inbaseline only ($ billions) 5.8 ... ...
Percentage of total net gains 7.0% ... ...
Not long-term gains on returns with gains incomparison only ($ billions) ... 9.5 ...
Percentage of total net gains ... 10.1% ...
Federal individualincome tax receipts ($ billions) 277.6 280.4 1.0%
368 NATIONAL TAX JOURNAL [Vol. XLII
was specified and to examine the effect of gains income to changes in the marginalimprovements in the econometric model tax rate.relative to the models used in previous Results of three other sensitivity ex-studies of capital gains taxation. Changes perimeilts are also reported in Table 5.were made to the model, one change at a When wealth was omitted, the tax ratetime. Results for some of these altema- coefficients did not change much becausetive specifications appear in Table 5 .35 The other variables, such as age and controlsecond column was copied from Table 2 for wealth variation. The criterion func-for comparison to the results of the sen- tion and the resulting Mills ratio correc-sitivity experiments, which are presented tion variable also control for some wealthin columns 3 through 9. variation because the likelihood of real-
The first experiment examined the ef- izing capital gains is highly correlated withfects of simultaneity bias. For the exper- wealth.iment, instead of an instrumental vari- The lagged tax rate variable was omit-ables procedure, actual tax rates were ted as an explanatory variable in theused. Results reported in column 3 dem- equation summarized in column 7. Theonstrate that simultaneity bias is an im- estimated coefficient on the current-yearportant issue. The tax variable coeffi- marginal tax rate almost exactly equalscients reverse signs because higher actual the sum of the coefficients on current andcapital gains realization levels cause lagged rates in column 2 and coefficientshigher marginal tax rates. The resulting on other variables are virtually un-bias is large enough to more than offset changed. This result suggesta that thethe negative effect of marginal tax rates primary value of adjusting for dynamicson capital gains realizations. Other esti- is that it permits estimation of the short-mated coefficients are also apparently run response to tax rate changes.biased by simultaneity when the actual Coluirm 8 suggests that estimates of thetax rate is used. For example, the esti- response of capital gains realizations tomated coefficients of the age dummy tax rate changes may be biased upwardvariables change considerably relative to when state taxes are ignored, although thethe coefficient estimates reported in col- difference in the tax rate coefficient is notumn 2 .36 statistically significant. The other notice-
Columns 4 and 5 of Table 5 demon- able difference in column 8 is that thestrate the effect of selection bias in esti- coefficients on regional dummies vary frommation of the model parameters. In each column 2.case, self-selection was ignored and the Column 9 reports weighted estimatescapital gains level equation was esti- for the basic model .3' The effect ofmated by an instrumental variables weighting on the long-run marginal taxmethod with no correction for selection rate does not appear to be significant inbias, i.e., there was no criterion function our level equation. The unweighted long-and there was no Mills ratio included as run response is -11.6 whereas the esti-a RHS variable. Column 4 used all data, mated response in the weighted equationrealizers and non-realizers, whereas col- is - 10.9. There are significant differencesumn 5 used realizers only. In both cases, in the wealth and income coefficients,there is apparently a large bias for the which is not too surprising since thecoefficients of the marginal tax rates. The weights are highly correlated with theseestimated coefficients on wealth in- measures.creased by an order of magnitude and thecoefficients of the age-group dummy van- XI. Conclusionables actually change signs. The resultsof this experiment suggest that previous Our study sheds light on why empiricalcapital gains micro-data studies that have capital gains realization equations haveignored selection bias may have overes- produced such widely varying results. Wetimated the response of long-term capital have explored the relevance of panel data
Table 5Sewitivity Analysis, L4)ng-Ter= Capital Gains Level Equa
Right-Hand From Actual Intst Vars Intst Vats WealthVariable Table I Tax Rate AU Data Realizers Omitted
No. 31 G. E. AUTEN, L. E. BURMAN, AND W. C. RANDOLPH 371
to resolve some of those questions. Re- cific factors. The panel we used is prob-sults suggest that a substantial part of the ably not long enough at present. First, itpast variance in realization elasticities cannot identify the effects of a differen-may have been due to the simultaneity tial between capital gains tax rates andbetween marginal tax rates and capital other income. Second, it cannot distin-gains realizations and to the failure of guish the aggregate effects of ERTA fromprevious studies to correctly deal with other time-series data, such as interestsample-selection bias. We also find that rates and aggregate activity.simulation is important for estimating the There are some deficiencies that will notequilibrium response of individual tax- be remedied in any data set, however.payers to changes in tax law under a pro- First, interpretation of empirical capitalgressive income tax. Previous studies that gains models will always be subject to de-treated the marginal tax rate as fixed with bate until there is a firm theoretical foun-respect to induced changes in capital gains dation for such research. Developing tegt-realizations probably overstated the re- able theories should be a priority in futuresponseof taxpayers to changes in tax rates. research. Second, focussing on individualOn the other hand, the failure of previous capital gains realization behavior may ig-studies to simulate the induced changes nore some important determinants of thein the number of realizers may have re- aggregate revenue effects of capital gainssulted in understatements of individual tax changes. There should be more re-responsiveness. search on the effects of capital gains tax
We found some other factors to be sur- policies on rates of return in financialprisingly unimportant. Income shifting, markets and on growth. Without under-which was originally a key subject of our standing the effects of capital gains taxstudy, does not substantially affect either policies on GNP, interest rates, dividendthe estimated parameters in capital gains payouts, and asset values, predictionsrealization equations or the simulated re- about revenue consequences must besults of a change in tax regimes. How- viewed as tenuous.ever, because of the limitations of a shortpanel (for example, because there was nochange in the proportional differential NOTES
between tax rates on capital gains and 'We are grateful to David Joulfaian and Gordonother income), this negative finding must Wilsonfor extensive technical assistance and advicebe viewed as tentative. and to Tom Barthold, Joe Cordes, Robert Gillingham,
Incorporating dynamics (i.e., lagged tax John Greenlees, Rosemary Mam-uss, Tom Neubig, Jim
rates), an exogenous wealth instrument Nunns, Larry Ozanne, and participants in OTA sern-
'inars for comments on earlier drafts. The views ex-
and state tax rates did not substantially pressed in this paper do not necessarily represent thechange the estimated long-run response policies, methodology, or views of the Congressionalof capital gains realizations to tax rater ,. Budget Office or the Office of Tax Analysis. All ac-
However, the lag term did detect a short- e,, to confidential tax return data was performed bystaff of the Office of Tax Analysis.
term capital gains response that was sig- 'Stiglitz recognizes that his model has limited em-nificantly greater than the long-run re- pirical relevance insofar as it predicts that capital gainssponse. In addition, the exclusion Ofwealth tax revenues would be zero under any tax regime.
seems to bias estimates of the effects of 'Kiefer (1989) develops a particularly cogent ex-position of capital gains behavior under this simple
other variables, such as income and age, model.on capital gains. We also found some evi- 'rhe possible endogeneity of other income and de-dence that our results are relatively ro- ductions was recognized by Feldstein, Slemrod, and
bust with respect to the chosen functional Yitzhaki (1980). In a footnote, they acknowledge thattheir tax rate instrument (discussed in section IV of
form." this paper) would not be exogenous if other incomeWe argue that data from a long panel responds to tax rates. They suggested the develop-
are essential to fully unravelling the ment of a "more elaborate behavioral model" as a
ation subject for future research.components of capital gains realiz 'While the Tobit model allows for self-selection, itresponses that are due to Federal policy restricts the decision function to be the same as theand the part that is due to individual-spe- level equation. The practical implication of this re-
372 NATIONAL TAX JOURNAL [VOI. XLII
striction is that individuals who do not realize a gain (1989) examined the role of fixed effects in a simplerin a year would realize, at most, only a small gain model of capital gains realizations and found no sta-under the most favorable of tax circumstances. This tistieal evidence of their importance.rules out the possibility that a taxpayer may be wait- "These assumptions are explored in the ease of ex-ing to sell a large block of stock or a family business ogenous sample strata by Duncan and DuMoucheluntil tax conditions are favorable. (1983). They derive a test statistic for estimating
Gillingham, Greenlees, and Zieschang (1989) esti- whether weighting matters, but conclude thatmate a logistic version of a model similar to ours. weighting is generally not an issue if a model is prop-
'This is only an approximation because it does not erly specified.account for how an individual's increased realizations 2)For simplicity, Oit, Xit, Yit, and Zit are treated asmight result in a change in the marginal tax bracket. scalars here although they are vectors in our esti-The effect on capital gains revenues does not directly mated model of income determination. It is also as-translate into increased or decreased total tax re- sumed for this exposition that the marginal tax rateceipts because the tax change can affect levels of other on long-term capital gains is a fixed fraction of theincome and deduction items as discussed below, may tax rate on ordinary income (i.e., the ordinary incomeaffect prices and rates of return in financial markets, tax rate multiplied by the included fraction of long-and might have macroeconomic feedbacks that would ter7n capital gains). The estimated model does not im-affect total receipts. pose this restriction, which would not hold when there
'The following analysis is largely a formalization of are carried over losses, for example. In addition, weviews that have been expressed by other researchers. defer consideration of sample selection until later inFor example, see Auerbach (1988), Gravelle (1987), this section.Slemrod and Shobe (1989), and U.S. Congressional "See Auten, Burman, and Randolph (1988) for aBudget Office (1988). discussion of the circumstances under which the bias
'To keep things simple, assume that individuals re- would be positive or negative.spond instantaneously to tax rate changes. We look 'A subsample was used for estimation due to comat the dynamics of tax rate responses later in this sec- puter and software limitations. Four years were in-tion. cluded so that lagged values of some variables, such
'We consider the non-linearity of realization re- as the tax rate, could be used.sponses later. 'Feldstein, Slemrod, and Yitzhaki (1980) and Min-
'OBoldface notation represents vectors. arik (1981) limited their samples to taxpayers with"Estimates of the intercept term in equation (1) at least $3,000 of dividends. Auten and Clotfelter
would bebiased by an amount equal to (a - P)TSTATT, (1982) and Treasury (1985) limited their samples tobut it is unlikely that this would be of any practical taxpayers with at least $200 in either dividends orsignificance. rental income or loss.
12 This is essentially the Lucas (1976) critique of 2See Holt and Shelton (1962).econometric policy evaluation. Auerbach (1988) also 2'Under assumptions of our model, resulting pa-made this point. For example, the Congressional Bud- rameter estimates are consistent. Asymptotic stan-get Office estimates that the average marginal tax dard errors for the parameter estimates were derivedrate on capital gains was 14% in 1984 and would be by Lee, Maddala, and Trost (1980). Results were ob-nearly the same under the Administration's 1989 tained by use of the LIMDEP program (see Greene,budget proposal of a top capital gains rate of 15%. 1988).However, individual tax rates varied widely in 1984 26Equations were also estimated for net negativewhereas they would be nearly unifor7n (at 15%) under capital pins and other types of capital income andthe budget proposal. Furthermore, opportunities for charitable deductions. Results are available from thetax planning were much greater in 1984 (before pas- authors on request.sage of the Tax Reform Act of 1986) than they would 2'We discuss this issue more in Section X.be in 1989. 'Mis type of behavior might be modelled as a fixed
"A linear relationship would imply that the change effect. See Slemrod and Shobe (1989).in realizations when tax rates change would be the 29Appendix 1 describes the simulation methodologysame for a millionaire as they would be for an indi- in detail.vidual with no assets. While this might be approxi- 3'An exception would be if a taxpayer was subjectmately accurate for the proportional change, it cer- to the alternative minimum tax in the base case. Be-tainly does not apply to the level. cause the capital gains exclusion was treated as a tax
"The nature of this bias is explored in Darby, Gil- preference and therefore not allowed under the alter-lingham, and Greenlees (1988) and U.S. Congres- native minimum tax in 1982, such taxpayers wouldsional Budget Office (1989). experience no change in statutory marginal tax rates
"See Maddala (1983). as a result of a small change in the inclusion rate."See, for example, Auten and Clotfelter (1982) and Also, the inclusion rate was changed for Federal taxes
Auerbach (1988). only, except for states that automatically used the"Individuals also may anticipate future tax rate Federal inclusion rate. To the extent that states var-
changes, as happened before the tax rate increase in ied in their treatment of capital gains taxes, a per-1986, when capital gains realizations approximately centage change in the Federal inclusion rate does notdoubled. We do not model future tax rates because of necessarily result in an equal percentage change inlimitations in our data set. the combined marginal tax rates.
"In our model, we choose to focus on the issues of "'The results may not accurately reflect Federalsimultaneity and self-selection, which complicates the revenue responses to statutory tax changes becauseestimation of fixed effects models. Slemrod and Shobe of the concerns raised in section 11.
No. 31 G. E. AUTEN. L. E. BURMAN, AND W. C. RANDOLPH 373
"Note that there is no single elasticity that can be Auten, G. E., L. E. Burman, and W. C. Randolphused to characterize all policy changes. The elastici- (1988), "A Panel Data Model of Capital Gains andties in this paper relate to changes in the inclusion Taxable Income," unpublished manuscript, U.S.rate on long-term capital gains based on 1982 tax law Treasury Department.and levels of income and gains. Elasticities for other Auten, G. E., L. E. Burman, and W. C. Randolphchanges would vary depending on how they affected (1989), "Estimation and Interpretation of Capitaltaxpayers in various income classes and other factors. Gains Realization Behavior: Evidence from Panel
"Other capital income equations, discussed in Au- Data," U.S. Treasury Department, OTA Paper 67.ten, Burman, and Randolph (1989), such as those for Auten, G. E. and C. Clotfelter (1982), "Permanentinterest income, dividends, and short-run capital ganis, Versus Transitory Tax Effects and the Realizationwere included in the simulation. The effect of changes of Capital Gains," Quarterly Journal of Economicsin the inclusion rate, however, had almost no effect 97, No. 4.on the other income levels because the other equa- Cilke, J. M. and R. A. Wyscarver (1987), "The Trea-tions contained either the marginal tax rate on or- sury Individual Tax Simulation Model," Compen-dinary income or that on short-term capital gains. Such dium of Tax Research, Washington: U.S. Govern-tax rates were not affected much by the change in the ment Printing Office.inclusion rate nor by the resulting changes in levels Clark, B. and D. Paris (1985), "Sales of Capital As-of long-term capital gains income. The simulated ef- sets, 1981 and 1982," Statistics of Income Bulletinfects on other income items are therefore approxi- 5, No. 3.mately zero. Cook, E. W., and J. F. O'Hare (1987), "Issues Relating
3'Note that the elasticities in Table 3 are percent- to the Taxation of Capital Gains," National Taxage changes in aggregate capital gains and total Fed- Journal 15, No. 3.eral individual income tax receipts with respect to Darby, M. R., R. Gillingham, and J. S. Greenleespercentage changes in the Federal inclusion rate for (1988), "The Direct Revenue Effects of Capital Gainscapital gains income. As such, the elasticities can not Taxation: A Reconsideration of the Time-Seriesbe compared directly to those summarized in Table 1. Evidence," Treasury Bulletin, Spring Issue.The elasticities reported in previous research are not Duncan, G. and W. DuMouchel (1983), "Using Sam-based on simulation, do not include state taxes, and ple Survey Weights in Multiple Regression Anal-are expressed as elasticities with respect to changes yses of Stratified Samples," Journal of the Ameri-in actual marginal tax rates as if they are the same can Statistical Association 78, No. 383.as changes in statutory marginal tax rates. The es- Feldstein, M. and S. Yitzhaki (1978), "The Effects oftimates from previous studies ignore the progressiv- the Capital Gains Tax on the Selling and Switchingity of marginal tax rates and the simultaneity of in- of Common Stock," Journal of Public Economics 9,come and marginal tax rates. No. 1.
'We ran a number of other sensitivity tests that Feldstein, M., J. Slemrod, and S. Yitzhaki (1960), "Theare not reported here. For example, we tested some Effects of Taxation on the Selling of Corporate Stockalternative functional relationships between mar- and the Realization of Capital Gains," Quarterlyginal tax rates and realizations and found prelimi- Journal of Economics 94, No. 4.nary evidence that our results are robust with respect Gillingham, R., J. S. Greenlees, and K. D. Zieschangto functional form. We intend to expand on these re- (1989), "New Estimates of Capital Gains Realiza-sults in future research. tion Behavior: Evidence from Pooled Cross-Section
'Technically, the differences from estimates in col- Data," U.S. Treasury Department, OTA paper 66.umn 2 are not actually the bias but may be caused Gravelle, J. (1987), "A Proposal for Raising Revenueby bias. Differenres are suggestive of the sign and size by Reducing Capital Gains Taxes," Library of Con-of the bias. gress, CHS Report 87-562E.
17The weighted Probit estimates of the criterion Greene, W. H. (1988), "LIMDEP Reference Manual,"function are discussed in Auten, Burman, and Ran- unpublished manuscript.d I h (1989). Holt, C. and J. Shelton (1962), "The Lock-in Effect of
0;;ee Auten, Burman, and Randolph (1989). the Capital Gains Tax," National Tax Journal 15,"Calibration can be characterized as a monte-carlo No. 4.
method by which sample information is combined with Kiefer, D. (1989), "Lock-In Effect Within a Simplea pseudo-random number generator and estimated Model of Corporate Stock Trading," Library of Con-parameters in order to provide a distribution of gress, CRS report.re as.on errors consistent with the sample. Lee, L. F., G. S. Maddala, and R. P. Trost (1980),
e effects of other changes to the tax code can "Asymptotic Covariance Matrices of Two-Stagealw he simulated. Probit and Two-Stage Tobit Methods for Simulta-
neous Models with Selectivity," Econometrica 48,No. 2.
REFERENCES Lindsey, L. B. (1987), "Capital Gains Rates, Realiza-tions, and Revenues," in Martin Feldstein, ed., The
Auerbach, A. J. (1988), "Capital Gains Taxation in Effects of Taxation on Capital Accumulation, Chi-the United States: Realizations, Revenue and Rhe- cago: The University of Chicago Press.toric," Brookings Papers on Economic Activity. Lucas, R. E., Jr. (1976), "Econometric Policy Evalu-
Auten, G. E. (1982), "Estimation of the Effects of ation: A Critique," in The Phillips Curve and LaborCapital Gains Taxes on Realization of Capital Markets, in K. Brunner and A. H. Meltzer, eds.,Gains," final report to the U.S. Treasury Depart- Amsterdam: North-Holland.ment, Office of Tax Analysis. Maddala, G. S. (1983), Limited-Dependent and Qual-
374 NATIONAL TAX JOURNAL [Vol. XLII
itativeVariablesin Econometrics,Cambridge:Ca-- levels of capital gains income that equal thebridge University Press. levels actually realized by each taxpayer in the
Minarik, J. J. (1984), "The Effects of Taxation on the sample for 1982."Realization of Capital Gains: Comment," Quarterly Calibration is necessary not only to correctlyJournal of Economics,February.Minarik, J. J. (1981), "Capital Gains," in H. J. Aaron model the distribution of capital gains income
and J. H. Pechman, eds.,How Taxes Affect Eco- and tax payments, but also to insure realisticnomic Behavior, Washington D.C.: The Brookings results. Because the model implies that the be-Institution. havioral effect of a change in the capital gains
Slemrod, J. and Shobe, W. (1989), "The Tax Elasticity tax depends upon level of the marginal tax rate,of Capital Gains Realizations: Evidence from a Panel calibration is necessary to insure that the modelof Taxpayer.," published manuscript, University will not systematically over- or underpredietof Michigan. income levels in a manner that would pushStiglitz, J. E. (1983), "Some Aspects of the Taxationof Capital Gains," Journal of Public Economics 21, taxpayers into unrealistically high or low taxNo. 3. brackets. Otherwise, the simulation would pre-
U.S.Congressional BudgetOffice (1988),How Capital dict inaccurate aggregate income and tax-re-Gains Tax Rates Affect Revenues: The Historical ceipt levels.Evidence. In the second major step of simulation, it-
U.S. Congressional Budget Office (1989), "Simulating erative numerical methods are used to solve forthe Revenue Effects of Changes in the Taxation Of base case equilibrium levels of capital gainsCapital Gains," Congressional Budget Office Staff income. An equilibrium is defined as the levelWorking Papers.
U.S. Department of the Treasury (1985), Report to of income and marginal tax rates that simul-Congress on the Capital Gains Tax Reductions of taneously solve the criterion, income level, and1978, marginal tax rate functions. To simulate a
steady state with respect to the marginal taxrate in the base case, the equilibrium is solved
Appendix 1. Simulation Method under the condition that current and laggedmarginal tax rates are equal.
Using the estimated econometric model, the The base-case simulation is constructed soeffect of a change in the inclusion rate on cap- that, in the third simulation step, the compar-ital gains income was simulated for each tax- ison case can be used to examine either thepayer in the sample for 1982 tax law and in- short- or long-run effect of changes in the taxcome levels. Using sample weights for the code. In the comparison case, a new equilib-number of taxpayers represented by each tax- rium solution is found after a change is madepayer in the sample, the individual simulated in the tax calculator to change the inclusioneffects were then aggregated to derive the ef- rate on capital gains income." A short-run, orfects on aggregate capital gains income and fmt-year-after-the-change simulation solves forFederal tax receipts. a new equilibrium solution, holding the lagged
Simulation consists of four steps: calibra- tax rate fixed at its base-case level. A long-runtion, equilibrium solution for a base case, equi- simulation solves for a new steady-state equi-librium solution for a comparison case, and ag- librium, by again equating the current andgregation. The calibration step generates lagged marginal tax rate.residuals for the criterion and level equations. The last step is aggregation. A simulation isUsing the structure of the self-selection model conducted for each taxpayer in the sample.and the estimated parameters, regression re- Sample weights are then used to calculate ag-siduals are drawn in a way that insures that gregate base and comparison case levels ofthe model, including the residuals, predicts capital gains income and Federal tax receipts.
