ESTIMATION AND INTERPRETATION OF 

CAPITAL GAINS REALIZATION BEHAYIOR: 

EVIDENCE FROM PANEL DATA 

Gerald E. Auten* 

Leonard E. Burman** 

William C. Randolph*** 

OTA Paper 67 May 1989 

OTA Papers and Briefs are circulated so that the preliminary findings of tax research conducted 

by staff members and others associated with the Office of Tax Analysis may reach a wider 

audience. The views expressed are those of the authors. and do not reflect Treasury policy.

Additional copies of this publication may be purchased from the National Technical Information 

Service 5285 Port Royal Road. Springfield, VA 221 161. Phone (703) 487-4660. 

Office of Tax Analysis 

U.S. Treasury Department, Room 4040 

Washington, D. C. 20220 

* Bowling Green State University and Office of Tax Analysis, U.S.Treasury Department

** U .S. Congressional Budget Office 

1. ***Office of Tax Analysis, U.S.Treasury Department 

1 We are grateful to David Joulfaian and Gordon Wilson for extensive technical assistance and 

advice and to Thomas Barthold. Joseph Cordes. Robert Gillingham. John Greenlees. 

Rosemary Marcuss. Thomas Neubig. James R. Nunns. Larry Ozanne, and participants in 

OTA seminars for comments on earlier drafts. The views expressed in this paper do not 

necessarily represent the policies, methodology, or views of the Congressional Budget Office 

or the Office of Tax Analysis, All access to confidential tax return data was performed by 

staff of the Office of Tax Analysis. 
I. 1ntroduction 

The revenue effects of capital gains taxation have important implications for the extent to 

which capital gains taxes can be modified to achieve policy objectives. But the existing economic 

evidence on capital gains taxation is so imprecise that there is widespread disagreement ill>oLlt 

whether past changes in the taxation of capital gains raised or lost revenue and about what the 

direction and magnitude of the revenue effect of proposals to cut the tax rate on capital pins 

m i gh t be. 

There are three primary reasons why economists can’t answer policymakers questions abut 

the revenue implications of capital gains tax changes with more certainty. First, the econometric 

analysis of capital gains realization behavior has only weak theoretical economic foundations. 

Alxent a clear behavioral model, econometric analysis is as much art as science and artistic 

interpretations clearly vary on this subject. 

Second, it is unclear what kind of data set is adequate for answering policymakers’ 

citiestions. It is possible that cross-section and time series data sets answer different kincls of 

questions. However, there is considerable confusion and dissent among economists about which 

kind of data are appropriate. Moreover, previous studies have lacked important explanatory 

wriahles, such 21s state tax rates and accrued capital gains, that may have added to the uncertainty 

of their analyses. 

Third, previous studies have been hampered by econometric problems. Most notably, wIi ile 

virtually all studies have recognized that the marginal tax rate on capital gains is determinecl 

sit7iult;ineously with the level of capital gains, these studies have ignored the endogeneity of other 

kinds of income and deductions. In addition, the simultaneity of income and tax rates means that 

econometric results cannot answer policy questions about revenue without simulating to find 

equililxium. Another important econometric problem in most previous studies is the selectivity bias 

that arises because individuals simultaneously choose the level of capital gains and whether or not 

to realize a capital gain at all. Furthermore, cross-section studies are unable to account tor the 

dynamics of capital gains responses, Le., that individuals respond to tax changes with a lag. And 

time-series studies are subject to aggregation biases and small samples that reduce the I~rccision 

of statistical estimates. 

This paper focusses attention on the latter two problems. First, we attempts to clarifii some 

ot the issues related to the choice of data set. Then we present the results of ;I panel-chta study 

in which the model and methods have been designed to correct several of the most important 

weaknzsses of previous micro-data studies of the effect of taxes on capital &?ins realizations. To 

1 
correct for the simultaneity problem in estimation, the model treats, in addition to capital gains, 

several other components of capital income and deductions as endogenous choice variables. To 

correct for the simultaneity problem in interpretation of estimated equations, we developed a microsimulation model to examine the effects of changing the inclusion rate for long-term capital gains 

income. To correct for selection bias, assumptions of the Tobit model used by Treasury (19SS) and 

Auten and Clotfelter (1982) were relaxed to allow separate criterion and income level 

In addition, our study incorporates an appropriate exogenous measure of wealth and it is the first 

to include the effect of state income taxes. 

I I. Choice of Data Set 

A. Determinants of Individual Capital Gains Realizations 

We start with a model of how capital gains realizations respond to income tax treatment that 

is similar to the models used in previous research. As in that literature, we do not model the 

choice decision of realizing capital gains because theoretical models, such as Stiglitz ( 19S3), do not 

yield interesting testable hypo these^.^ We simply follow other authors in positing that realizing 

capital gains has some economic value as compared to holding assets with capital gains and so, the 

decision to realize a capital gain depends on whether the value of realizing the gain is at least as 

great ;ISthe cost, which is primarily the capital gains tax.' 

The value to an individual of realizing a capital gain depends on the individual's stock ot 

Linre;ilized gains. The more capital gains in the individual's portfolio, the more gains are likely to 

be candidates for realization. Individuals may realize capital gains to finance consumption, ;ind so 

permanent and transitory income may be important determinants of realizations. And inclivicluiils 

m;iy have different attitudes toward asset trading and risk, and have different discount rii tes. We 

assume that these taste parameters depend on observable demographic variables such as marital 

status, age, and family size. 

We also allow for the possibility that individuals engage in tax planning so that their tax rate 

itself is ;I choice variable. Most of the earlier studies have made a similar assumption, but with the 

'Tlic criterion equation is a Probit rcgression that explains taxpayer decisions of whether or not to rcalizc c:ipi[al gains. 

TI12 incollie level equations exTlaiii taxpayer decisions of how much to realize of capital gains and other c:ipiial iticonic. 

3Siigli[z recognizes tliat his model has limited empirical relevance insofar as it predicts that capital gains tas rc\'ciitics 

\vc>tiItl bc zero tinder any tax regime. 

'Kicfer (19SS) develops a particularly cogent exposition of capital gains behavior under this simple inodcl. 

2 
exception of Cook and O'Hare (1987), their estimation methodology requires that tax planning be 

limited to the choice of the level of capital gains. Our model assumes that other capital inconie 

items, such as dividends and interest, and deductions, such as charitable contributions, may be 

determined endogeno~sly.~ 

There are two components of capital gains decisions that may respond to tax rates. First, 

taxpayers may adjust their level of gains in response to different tax rates. Second, some individuals 

may defer realizations altogether in years when their tax rates are high. For example, in our panel 

of taxpayers, 35% of capital gains were realized by taxpayers with capital gains in only one year. 

Our model explicitly accounts for the decision whether or not to realize capital income (or make 

a charitable contribution) distinct from the level of income or deductions. While Auten and 

Clotfelter (1982) also accounted for this so-called self-selection, the present study models the 

decision to realize separately from the level of realization.6 

B. Why are cross-section and time-series elasticities so different? 

Table 1 summarizes the results of previous studies of capital gains realization responses to 

tax rates. The results are characterized by an elasticity, which represents the approximate change 

in capital gains realizations in response to a one percent change in tax rates (e.g., from a rate of 

20% to 20.2%). As a rough approximation, a capital gains tax cut will increase capital gains 

revenues if the aggregate elasticity is greater than 1 in absolute value and will reduce capital gains 

tax revenues if the elasticity is less than 1.' Table 1 shows that these elasticity estimates range 

widely from a low of essentially 0 (Auerbach, 1988) to a high of almost -4.0 (Feldstein, Slemrod, 

and Yitzhaki (FSY), 1980). Notwithstanding this large variation, there seems to be a clear division 

'The possible cndogeneity of other income and deductions was recognized by Feldstein, Slemrod, and Yitzlinki ( IOSO). 

In ;I rootnote, they acknowledge that thcir tax rate instrument (discussed in section 3 of this pqm) would not l)c csogciiotis 

if oilier inconic responds to tax rates. They suggested the development of a "more elaborate behavioral iiioclcl" as ;I stiI>,iccr 

1.01. I'tiiurc research. 

6

Atitcn and Clotfelter estimated a Tobit capital gains equation. While the Tobit model allows for self-sclcctioii, it 

restricts [he decision function to be the sanie as the level equation. The practical implication of this rcstricrion is i11;lt 

iiiclivirltials who do not realize a gain in a year would realize, at most, only a small gain under the most favorable of tiis 

circuiiistatices. This rules out the possibility that a taxpayer may be waiting to sell a large block of stock or a family btisincss iiiiiil [:is conditions are favorable. 

Gillingliam, Greenlees, and Zieschang (1989) estimate a logistic version of a model similar to ours. 

7

This is only an approximation because it does not account for how an individual's increased realizations might result 

in n change in the marginal t;LY bracket. The effect on capital gains revenues does not directly translate into incrcascd or 

ilccrcascd total tax receipts because the tas change can affect levels of other income and deduction items as discussed bclo\v. 

may affect prices and rates of return in financial markets, and might have macroeconomic feedbacks that would affect total 

receipts. 

3 
- 

between the estimates based on time series and the estimates based on micro data (cross-section 

or panel data). Although there are exceptions, the time series estimates are generally lower in 

alxolute value than the estimates based on micro data. 

The debate about which, if any, set of estimates is relevant for policy purposes is reminiscent 

of the debate about consumption functions in the 1940s and 1950s. In the case of consumption 

functions, the conundrum was reconciled by explaining that individuals respond differently to 

permanent income than to transitory income. Since cross-section income levels include the 

transitory component that is washed out in the aggregate data, the cross-section consumption 

function estimates were biased downward. A similar analysis might be useful in explaining the 

variation in capital gains elasticity estimates.' 

Suppose that individuals view their marginal tax rate on capital gains as comprising two 

parts. The first is a statutory component that reflects the average tax rate on capital gains under 

current law.' The second is the individual variation from the average statutory rate. The first 

component is exogenous to the individual. The second component has both an exogenous 

component due to uncontrollable temporary changes in taxable income, and an endogenous 

component that reflects tax planning. 

Individuals may respond differently to changes in the statutory marginal tax rate than to 

changes in the individual-specific component. The statutory component is purely exogenous, which 

may mean that it is harder for individuals to plan to either take advantage of a low statutory rate 

or to avoid a high rate. The statutory rate may also be perceived to be more permanent. At 

present, assume that the statutory component is the same for all individuals in ii given year. We 

will consider later what deviations from this assumption might imply. 

The following is a simple linear representation of the model." 

'it - ~TSTAT,+ R(T~,- TSTAT,) + x,r t vi,, 

s

Tlic follo\viiig analysis is largely a formalization of views that have been expressed by otlicr rescarclicrs. For cxirilpic. 

~CCAiicrbiicli (l%S), Gravelle (19S7), Slemrod and Sliobe (19S9), and U.S. Congressional Budgct Orficc (198s). 

9

To keep things simple, assume that individuals respond instantaneously to tax rate changes. We look at the dynamics 

of [:ISrate responses later in this section. 

"We consider the non-linearity of realization responses later. 

4 
where G,, is capital gains realizations by individual i in year t, TSTAT, is the average statutory 

marginal tax rate on gains in year t, which only varies over time, Ti,is individual i's marginal tax 

rate on gains in year t, and Xi," is a vector of other parameters that affect capital gains. 

In this simple model, neither cross-section nor time-series data will permit identification of 

both Q and R. In a time series, the sum of (Tit - TSTAT,) is zero since TSTAT, is the sum over i 

of T,l. Thus, only a can be identified using time series data. In the special case of this linear 

model, the time series estimates can yield accurate information about how capital gains realizations 

and tax revenues respond to changes in tax law. 

Using cross-section data, the situation is reversed. B is identifiable whereas Q is not. In 

a cross-section, TSTAT, is a constant, and its effect is subsumed in the constant term in the S 

matrix.'* The coefficient R may be estimated using T,, as a regressor in an appropriate 

sini 111t ;I neoiis equation estimation technique (see below). 

Panel data are necessary, but not sufficient, to identify both a and 13in a single equ''I t '1011. 

There must be more years in the panel than there are time-varying explanatory variables (such ;IS 

value of the stock market, interest rates, and TSTAT,). If there are lags or fixed effects in the 

model, the minimum number of years of data increases accordingly. Finally, as 21 practical matter, 

the length of the panel would have to be substantially greater than the mininium to achieve 

re;iwnahly precise estimates of Q because significant shifts in TSTAT are infrequent. 

If this simple model were an accurate representation, then we could use cross-xection 

estimates for R and time-series estimates for 0:. Based on this model, we might conclude that cmx+ 

xection elasticities are consistently higher than time-series estimates because individuals ;ire more 

responsive to individual (short-term) variation in marginal tax rates than they are to statutory (longterm) changes. 

However, the division between cross-section and time-series components of marginal ts 

rates is not so clear cut. Individuals face different long-run statutory tax rates becaiise of 

permanent differences in income and wealth. Thus, cross-section tax elasticities in part retlect <I 

response to the peculiarities of current tax law. Moreover, individuals are affected differently hy 

changes in tax laws, This means that time series estimates based on a single summary variable, sLd1 

'I\ ;in average tax rate, are of limited relevance to predict the effects of ;I tax schedLile change thilt 

I' BoldPacc notation represents vectors. 

"Estiniatcs of the intercept term in equation (1)would be biased by an amount equal to (a-b)TSTAT,, but it is iirllikcly 

illat illis \v~iildbe of any practical significance. 

5 
might be significantly different from prior laws.13 In addition, even the average statutory tax rate 

varies across individuals because state tax rates on capital gains vary substantially. 

There are other drawbacks in time series estimates that arise when the simplifying 

assumptions made above are relaxed. There are two kinds of potentially serious aggregation bias. 

First, the relationship between marginal tax rates and realizations is certainly not linear," which 

means that the aggregate response to changes in tax rates would not be the sum of the indivicliiiil 

response^.'^ This implies that (1) time-series estimates of Q will be biased estimates of the 

individual response parameter, and (2) aggregate revenue responses will not in general he the 

product of aggregate realizations and the average tax rate on capital gains. Second, there map be 

a sample-selection bias due to individuals' choosing whether or not to realize a capital gain 

separately from the level of gain.16 While it is possible to correct for this bias in cross-section or 

panel data, it is not possible in the time series data, so it is hard to tell if this bias is important or 

what sign it is likely to have. In addition, there is the obvious problem that time series estimates 

are necessarily imprecise because there are so few degrees of freedom (typically 30 observations 

or so). 

Cross-section estimates of R will accurately predict responses to tax policy changes only if 

individuals treat all components of their marginal tax rate in the same way, Le., CY=& However, 

even under this assumption, cross-section estimates may be flawed. There is evidence tl1:lt 

individuals do not respond instantaneously to tax rate changes." If individuals respond to tax rate 

changes with ii lag, the absence of lagged tax rate variables would bias elasticity estimates in cro\ssection data. 

Panel data estimates based on a short panel are complements to time series estinl'itc\. 

Usins panel data, both sample-selection problems and dynamics may be addressed appropri:itely. 

I3

This is csscntially thc Lucas (1976) critique of econometric policy evaluation. Aucrbach (1989) also iii:idc this poilit. 

For csnmplc, the Congressional Budget Office estimates that the average marginal t&y rate on capital gains was 14',; in L0S-I 

and \votild be nearly the same tinder the Administration's 1989 budget proposal of a top capital gains r:itc of I5'Y. FIo\wrcr, 

iiitlividual tas ratcs varied widely in 1984 whereas they would be nearly uniform (at 15%) undcr the budget propos;il. 

Ftirthcrinorc, opportunities for tax planning were much greater in 1954 (before passagc of the Tax Reform Act of 19S6) th:iii 

ilicy ivotild be in 1989. 

"A lincar relationship would imply that the change in realizations when tax rates change wotild bc the s:Iinc I'or :I 

iiiillioii:iirc as thcywould be for an individual with no assets. While this might be approximately acctiratc for the proportional 

cliarigc, it ccrtainly does not apply to the level. 

15Tlic iinttirc of this bias is eqJlored in Darby, Gillingham, and Greenlees (1388) and US. Congrcssional Bticlgct Ol'l'icc 

( lorn). 

"See Maddala (1983) 

"Scc, for csaniple, Auten and Clotfelter (1952) and Auerbacli (1989). 

6 
Moreover, the panel data do not suffer from problems of aggregation bias. If tax law changes affect 

indivicluals differently, panel estimates based on a panel that spans at least one tax law change will 

reflect that variation in their elasticity estimates, as well as the individual-specific response to 

marginal tax rates. 

The time series estimates under the most optimistic of assumptions reflect a good estimate 

of CY, the average effect of statutory tax changes. The panel estimates capture how a particular tax 

law change affects individuals differentially, as well as individuals' responses to other sources of 

variation in tax rates. It seems reasonable to conjecture that the "correct" elasticity might be 

between these two sets of estimates. 

C. Other advantages of panel data 

There are other advantages of panel data over cross-section data sets. First, panel data 

allow estimation of the dynamics of individual response to capital gains tax changes because lagged 

diitit ;ire available. The possible importance of dynamics has been stressed by Auerbach ( 1988) iInd 

Kiefer (19SS). Second, panel data provide information to proxy permanent income based on 

itveritge income over a number of years. Third, the presence of lagged income and deduction items 

provides useful instruments for two-stage estimation of the simultaneous system of equations and 

to create exogenous proxies for permanent income and wealth. Fourth, panel data allows for tixecl 

effects such as unobservable taste parameters or components of household wealth.Is 

Ill. Econometric problems in cross-section studies 

Aside from the identification problem discussed in the last section, there is sLlbsti1ntitll 

\lariat ion in cross-section estimates. Some of the variation in results across previous rnicro-d:it,i 

stirdie5 can he explained by their failure to model the simultaneous nature of the deixndency 

Iwt\veen marginal tax rates, capital gains income, and other forms of income and clecluctions. 111 

the construction of estimation procedures, most of the studies have accounted in some way tor 

simultaneity of long-term capital gains and marginal tax rates on long-term capital gains. Ho\sevrr, 

none ot' the micro-diita studies has accounted for potential simultaneity of capital gains and otI1t.i 

forms of income and deductions. 

I?r 111 cur model, we choose to focus on the issues of simultaneity and self-selection, which coniplicatcs thc cs[iiiialiciri 

of l'iscd cl'fects models. Slemrod and Shobe (1989) examined the role of fixed effects in a simpler model of capit:il gains 

rc:ilizatiotw and found them to be statistically insignificant. 

7 
Yet more of the variation across micro-data results may be explained by their fa ilure to 

account correctly for simultaneity when interpreting estimation results. If capital gains income and 

marginal tax rates are determined simultaneously, then analysis of the effects of changing statutory 

tax rates on capital gains must account for the fact that actual marginal tax rates would not 

necessarily change by as much after accounting fully for implied behavioral responses. Ignoring 

such simultaneity when interpreting the results may cause the impression that capital gains are more 

sensitive to tax rates than they actually are. 

As an additional possible cause of variation in results, all but two studies, Treasury (1985) 

and Auten and Clotfelter (1982), have failed to correct for sample-selection bias in their parameter 

estimates. In a sample of primarily upper-income taxpayers, such as the panel-data sample used 

for this study, less than 50% of the taxpayers realize long-term capital gains income in any one year. 

Many taxpayers may not realize capital gains simply because they have little wealth. On the other 

hand, wealthier taxpayers may choose not to realize capital gains either by choosing not to sell 

appreciated assets or by choosing not to hold their wealth in the form of assets on which capital 

crrains would be realized. For the wealthier group of taxpayers, the decision of whether or not to 

realize capital gains income may be distinct from the decision of how much capital gains income 

to realize. Failure to model such a distinction may have led to biased estimation results in previous 

ni icr o-cl ;I t a stud ies. 

Another issue that arose in the exchange between FSY (1980) and Minarik( 1984) W:IS 

\vhether weighting was appropriate for estimation. Minarik argued that weighting was essential 

because the cross-section individual income tax returns in the FSY study were drawn from a 

strat itiecl sample that oversampled the rich. However, the validity of Minarik's weighting procedure 

depends on very strong assumptions about unobservable model characteristic^.'^ In fact, given that 

the weights are endogenous (capital gains are an important component of the stratification variable) 

and the other complexities of the capital gains model, the correct weighting procedure would be 

very complex. 

"Thcse assumptions are explored in the case of: exogenous sample strata by Duncan and Duhloucl1cl (lN3). They 

dcrivc :I test statistic for estimating whether weighting matters, but conclude that weighting is generally not an issuc il' 3 

iiiodcl is propcrly specified. 

8 
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IV. A Simple Model of Capital Gains and Income Shifting 

Some essential features of our model are represented by the following three equation 

system.20 

- 'it a, + a, Tit + a, X, + e, , 

Oit - bo + b, Ti, + b, Zit + uit , 

Tit = f(Git, Oit, Yit), 

where i = I,...,N, are individuals in the panel and t = 1,...,S are years. G, is realized long-term 

capital gains, 0, represents endogenous components of other taxable income and deductions, Ti, 

is the marginal tax rate on ordinary income, Xi, and Zitrepresent other exogenous or predetermined 

fiictors affecting Gitand Oi,. Yit represents exogenous components of taxable income iis ivtjll iis 

Other t'ilctors that determine tax liability. 

The marginal tax rate, T, is endogenous so that the parameters in equation (la) cannot be 

consistently estimated using least squares. In fact, it can be shown that, under weak assumptions, 

orclinary least squares estimates of tax elasticities would be biased toward zero (Auten, Burman. 

and Randolph 1988). Fortunately, the simple model suggests several options for estimating the 

capital gins equation (la). First, the equation could be estimated by two-stage least sqiiares, using 

Xil, Z,,, and Yit as exogenous variables. This method assumes that the tax rate function, (IC), is 

linear. Since (IC) is non-linear, and the non-linearities serve to aid identification, we aclopt ;in 

alternative that is similar to the approach taken by other authors. We construct ;I tax riitt: 

instrument by computing the marginal tax rate after setting the endogenous components of taxalde 

income, G,, and Oit,equal to zero. This is f(O,O,Yit). This variable preserves the information alxliit 

the non-linear relationship between Titand Yit, while purging Titof its endogenous components. 

The tax rate instrument used in previous studies has been either f(O,Oit,Yil)or f(Gi,,Oil,Yi,), 

\vhere Git is some variant of a reduced form estimate of G,,. Such tax rates are only exogenous it 

hth 17, and the covariance between the equation errors, e,,and ui,, are zero. While this possil>ility 

c:innot be ruled out with certainty, it is inappropriate to impose such ;I restriction ;I priori. 

Moreover, if these strong assumptions are not satisfied, estimates of the responsiveness of ci\l>itLll 

20 For simplicity, Oit, Xit, Yit, and Zit are treated as scalars here although they are vectors in our estimatcd modcl 01' 

inconic deterinination. It is also assumed for this exposition that the marginal ta rate on long-term capital gains is a fiscd 

fraction of the tax rate on ordinary income (Le., the ordinary income tax rate multiplied by the incliidcd fraction of longterm capital gains). The estimated model does not impose this restriction, which would not hold when there arc carried ovcr 

Ic)sscs, for example. In addition, we defer consideration of sample selection until later in this section. 

9 
gains to tax rates (al) as well as other parameters may be biased and inconsistent, and the sign of 

the bias is indeterminate a priori.21 

Wealth, as an indicator of accrued capital gains, may be an important determinant of the 

level of capital gains, but tax return data do not provide a direct measure of wealth. In 

consequence, previous studies have had to use current endogenous variables such as diviclends, 

interest, and rent as proxies for wealth. For example, FSY (1980), used dividends as ii proxy and 

argued that, while this measure might bias parameter estimates because the relationship lxtween 

dividends and stock may vary consistently with income, and thus tax rates, the hias would he to\\jarcl 

zero. Since FSY were interested in showing that taxes were important in determining the level of 

capital gains, they argued that this bias would simply mean that the strength of their positive 

conclusions was, if anything, understated. 

However, with both dividends and capital gains endogenously determined, the FSY 

conclusions about bias are not necessarily correct. If dividends are negatively related to tax rates 

(and positively related to wealth), the bias from using dividends instead of wealth would likely be 

negative (Le., estimated tax elasticities would be overstated).22 

On the other hand, the FSY hypothesis suggests that there might be a spurious correlation 

hetween wealth and income and tax rates that could cause estimates of al to be biased toward zero. 

The net effect of these factors is ambiguous. 

This paper avoids the hazards of using an endogenous proxy for wealth by estimating ii 

rediicecf form wealth equation using the Office of Tax Analysis (OTA) estate match file, which 

matched the prior year income tax returns to estate tax returns for estate tax filers in lOS2. This 

1 1r oced 11re y ielcls a fu nct iona1 rela ti onsh ip between observed wealth a n d p red eter in i iied (I ;I gged ) 

income items and demographic variables. We use this estimated variable as a proxy for wealth in 

our equation estimation. While we have not guaranteed that there is not ii problem of errors in 

wriables (the error in the wealth equation may be correlated with the error in the income 

equation), this wealth measure is purged of the obviously endogenous components in current 

cliviclencls, etc. 

"See Autcn, Burman, and Randolph (19SS) for a discussion of the circiinistanccs iindcr which the bias ~votildbc positive 

or 1cg;itivc. 

? > --This is fairly simple to sce if we look at the substitution of dividends for wealth as an errors in variables problciii 

(ignoring, for siniplicity, the endogeneity of tax rates). The bias in the tax rate coefficient in (1) would be cqtial 10 flit 

coCl.liciciit on wcaltli in equation (I) multiplied by the coefficient on tax ratcs in equation (2) dividcd by thc iiicIubi(lii r;iLc 

for capil:il gains. Since the effcct of taxes on dividends is likely to be nCgative and wealth is positively rclatcd to gains 1hc 

bi:rs is probably negative. 

10 
Our model explicitly accounts for the censoring of the observed income and deduction items 

at zero. The system of equations in (la) and (lb) is extended to include a criterion function for 

each of income item. Each criterion function is essentially a Probit model of the decision of 

whether or not to realize a non-zero amount of the corresponding income. These criterion 

functions are of the form, 

(21) 

(217) 

where GT, and O;, are unmeasured indices such that Gi, in (la) is only observed if G;, > 0 and Oil 

in (lL7) is only observed if O;, > 0. X;, and Z;, are vectors of exogenous variables that are not 

necessarily identical to Xi, and Zit. The error terms are standard normally distributed. 

V. Data 

The data are from ii panel of Federal income tax returns compiled by the US. Ti.e;ihiii.> 

Department for approximately 12,000 taxpayers for 1979 through 1983. One advantage of the clata 

is the availability of detailed tax data over a time period in which tax laws changed. Another 

iiclvantage is the availability of the ages and other characteristics of taxpayers in the sample. The 

sample was stratified to oversample high-income taxpayers, for whom capital gains were more likely 

to be an important component of income. For estimation, we used a random, though still stratified, 

suIxample of about 5,000 taxpayers, for which four years of data were included for each tn~payer.'~ 

For simulation we increased the sample size by adding randomly sampled data on about S,OOO 

tiispayers. Sample weights, used for simulation, reflect the number of taxpayers represented by each 

of the taxpayers included in the sample. Unlike previous studies which limited their samples to 

taxpayers with some amount of dividend or rental income or losses, we included all taxpayers in 

the sample who filed returns in two consecutive 

Marginal - Tax Rates: Marginal tax rates were calculated by increasing the appropriate type

of income, e.g., long-term capital gains for the marginal tax rate on long-term capital gains, by the 

ni:iuiniuni of either $1,000 or the square root of estimated wealth. The total tax liability WIS then 

23.A subsaiiiple \vas iiscd for esriniation due to computer and software liniitations. Four years wwc iiicludc'cl so tli;ll 

laggcd \:~~lucsof some variables, such as the tax rate, could be used. 

24 Fcldstcin, Slcinrod, and Yitzhaki (1980) and Minarik (1981) limited their samples to taspaycrs with at IC;I~L S3,OOO 01' 

dividciicls. Auten and Cloifelter (19S2) and Treasury (1385) limited their samples to ta?cpaycrs with at least 5200 in cillicr 

dividends or rcnlal income or loss. 

11 
divideci by the change in income. To calculate the total tax liability, a Federal income tax 

calculator was adapted for the panel years from a tax calculator developed by the U.S. Treasury, 

Office of Tax Analysis (Cilke and Wyscarver, 1987). In addition, state tax calculators were 

developed for all years of the panel. 

Wealth: Although the wealth of each taxpayer should be an important determinant of the 

ability to realize capital gains and other forms of capital income, deductions, and losses, no direct 

information about taxpayer wealth is reported on income tax returns. Because wealth is important, 

we developed a proxy variable for wealth by using the U.S. Treasury’s Estate-Income Tax Match 

Study for 1981-82, which included a sample of estate tax returns, matched with corresponding 

income tax returns for the last full year prior to death. These data were used to compute total 

wealth, net of life insurance payments, and total stock holdings. The logarithm of total wealth 

reported on the estate tax returns, net of life insurance payments, was regressed on lagged c;ipital 

income items, lagged losses, and demographic variables such as age. Because there was a $300,000 

exemption for filing estate tax returns, truncated-regression methods were used to estimate 

parameters of the imputation regressions. The estimated regressions were then used to impute 

level.\ of weolth and stock holdings for each taxpayer in the panel sample, conditional on the 

appropriate lagged values of income and demographic variables. 

Permanent Income: The permanent income variable is the predicted value fr-om an 

estimated regression which had the logarithm of a 5-year average of total positive incoiiie iIS ;I 

dependent variable and exogenous income and demographic variables as right-hand-side variables, 

evaluated at their 1979 levels. Total positive income is the sum of all positive components of 

income, including capital gains, i.e., gross income before losses. It is a measure of income used 

by the IRS and several previous studies as a measure of economic income. This measure of 

permanent income can be interpreted as a measure of expected permanent income. 

VI. Eclwition Specification and Estimation Method 

The capital gains level equation and criterion function capture six aspects of inciivicluals’ 

decisions to realize capital gains. There is the decision whether to realize any capital gains at all 

or to defer realization to another year. This decision is reflected in the criterion function, similar 

to (?;I), discussed in section IV. There is the dynamic response to tax rates. We model this 

response as a first-order difference equation, where lagged tax rates are :issumeci to he 

predetermined. Permanent and transitory income variables are included to reflect the consumption 

motive for capital gains realizations as well as to control for different attitudes toward risk that niay 

12 
be related to income. Wealth is included as a proxy for accrued capital gains. Lagged business and 

rental income and lagged rental losses control for previous investments that may be expected to 

result in capital gains. We also include available demographic variables-marriage dummies, family 

size, age brackets, and regional dummies--to try to control for different tastes that might affect 

trading strategies. The age brackets also reflect the benefit of holding capital assets until death, 

which increases with agez. Finally, time dummies reflect the impact of macroeconomic variables 

that affect individual asset values as well as the constant component of the 1981 tax law change ;IS 

discussed in section 11. 

The equations were estimated in two-steps. First, the criterion function parameters were 

estimated by Probit maximum likelihood. Estimated criterion function parameters were then used 

to construct Mill's ratios, which were added to the income level equations to correct for sampleselection bias. As the second estimation step, income level equations were estimated by least 

sqiiares, using only the observations for which non-zero levels of income were realized. 

Because the marginal tax-rates are endogenous right-hand-side variables, the two estinin tion 

steps were preceded by an instrumental-variables procedure. Before the Probit step, actual 

niarginal tax rates were regressed, using least squares, on all exogenous variables in the criterion 

function and the tax rate instrument discussed in Section 3. Probit estimates and the resulting 

Mill's ratios were then obtained using fitted tax rates in place of actual tax rates. Actual tax rates 

were then regressed, using least squares on the sample of realizers only, on all exogenous variables 

in the level equation, the tax rate instrument, and the Mill's ratio. Fitted tax val~iest'or this 

suhsample were then used in place of actual tax rates in the second step of estimation.26 

VII. Estimation Results 

Estimation results for the capital gains equations appear in Table 2. The first two columns 

contain parameter estimates for the equations that explain the levels of long- and short-term 

realizations, respectively. The last two columns are the corresponding parameter estimates t'or the 

criterion functions, which explain taxpayers' decisions whether or not to realize capital gains. 

25 Scc Holt and Slielton (1962). 

25 Undcr assumptions of our model, resulting parameter estimates are consistent. Asymptotic standard crrors l'or the 

paranicrcr estimates were derived by Lee, Maddala, and Trost (1980). Results were obtained by use of the LIhlDEP progr:iiii 

(wc Grccne 1x3s). 

13 
For the level equations, the dependent variable is the natural logarithm of the net-positive 

amount of capital gains before loss carryovers.27 Each coefficient implies a directional effect of 

c1i:inges in the corresponding right-hand-side (RHS) variable on the dependent variable. For 

example, wealth was estimated to have a positive effect on the levels of both short- and long-term 

capital gains. 

For the criterion functions, the dependent variables are unobserved indexes that determine 

whether a taxpayer realizes capital gains income. Capital gains income is realized only if the index 

is positive. A positive estimate of a criterion-function coefficient implies that an increase in the 

corresponding RHS variable would increase the likelihood that capital gains are realized. 

For two reasons, however, individual coefficients provide only first-order approximations 

to the full effects of changing RHS variables. First, the current year marginal tax rate is 21 function 

of the dependent variable, so that a complete characterization of the effect of any RHS vari:ilde 

must account for all feedback effects on the current year tax variable. Second, complete 

characterization of the effects of RHS variables must simultaneously consider effects on the level 

of capital gains and the likelihood of realizing a nonzero amount of capital gains, as implied by the 

estiinated parameters of the criterion functions. 

Although complete interpretation of the coefficients requires simulation of the model. ;IS 

descritxd in Appendix I, examination of individual coefficients and other parameters is inform:itive. 

For this purpose, the coefficients can be divided into three groups: tax-rate variables, wealth ancl 

income variables, and age and other variables. 

The tax variables are -Ln( 100-t),where "Ln" is the natural logarithm and t is the appropriate 

nxirginal tax rate, either current or lagged, short- or long-term. Because the tax price term is 

negiited, the negative coefficients of the current-year tax variables in the level equations imply that 

increasing the tax rate decreases capital gains income. Similarly, coefficient estimates for the 

criterion functions imply that increasing the own tax rate decreases the likelihood of realization. 

In :ill four equations, the own lagged tax coefficients are positive, which implies that ;I higher las!gecl 

ni;irginal tax increases both the level of capital gains income and the likelihood thL1t capital gains 

are realized. 

Opposite signs on the coefficients of current and lagged tax-rate variables suggest that 

t;isp;iyers time capital gains realizations so that they occur in relatively low marginal tax rate years. 

For esample, if the previous year's marginal tax rate was higher, then capital giiins \voirIJ he 

realized in the current year rather than the previous year. The sums of the current and hggeil tiis 

27Equ3tions were also estimated for net negative capital gains and other typs of capital income hnd cli>iritable 

tlccluctions. Results are reported in Tables 5 and 6. 

14 
rate coefficients, i.e., the long-run effects, are negative in all four equations but smaller than the 

current year tax rate coefficients, i.e., the short-run effects. 

As a first-order approximation to the importance of timing relative to the long-run effects 

of changes in the marginal tax rates, the size of the lagged tax coefficients can be compared to the 

sum of the current and lagged tax coefficients. For the level equations, timing is about 15% of the 

tax effect for long-term gains and about 25% of the tax effect for short-term gains. For the 

criterion functions, timing is about 67% for the long-term gains equation and about 48% for the 

short-term gains equation. For both types of gains, timing appears to be more important for the 

likelihood of a sale than it is for the level of a sale. This may reflect the fact that appreciated 

assets are often indivisible when taxpayers consider which assets to sell, how much, and when. If 

not all assets are divisible and not all taxpayers have access to a means, such as installment sales, 

by which they can spread out the sales of indivisible assets over several years, then the relative 

timing effect would be larger for the sell/don’t sell decision than for the how-much-to-sell decision. 

The wealth variable coefficients are positive in all four equations, implying that wealthier 

tiispayers are more likely to realize capital gains and they realize larger amounts of capital gains. 

Likewise, taxpayers with higher permanent income tend to realize higher levels of short and longterm capital gains. 

The transitory income variable seems to be uniformly unimportant. This could be because 

the important source of transitory variations is reflected in the current and lagged tax rates or 

because of errors in measurement of transitory and permanent income. 

Higher levels of wage and salary income lead to lower levels of short-term capital gains. 

Because permanent income is held constant, the negative coefficient of wage and salary income 

implies that higher transitory levels of wages and salaries cause lower levels of short-term capital 

gains. Taxpayers with higher lagged business losses are more likely to realize each type of capital 

g;i ins income. Surprisingly, however, the coefficient of the lagged business loss variable is negative 

;ind significant in the long-term capital gains equation. 

Age has opposite effects on the level and likelihood of realizing capital gains. Older 

taspayers ;ire more likely to realize capital gains income but they realize less than j’ounger 

tayxiyers. One possible explanation for such a sign reversal is that wealth is not perfectly n1e:isured 

by other RHS variables. If the distribution of wealth is more highly skewed for young than for 

older populations of taxpayers, then a smaller fraction of young taxpayers would have capital gains 

that Ciin be realized, thus causing the younger taxpayers to be less likely to realize capital gains. 

However, the young taxpayers who realize capital gains may be relatively wealthier than older 

individuals who realize capital gains. 

15 
The estimates of the covariance between the errors in the level equation and criterion 

function are negative and statistically significant in both the long- and short-term capital gains 

equations. This suggests that the failure to correct for sample selection may have resulted in 

important biases in previous research?8 The negativity of the covariance estimate implies that the 

Tobit model is inappropriate for modelling selectivity because the covariance is constrained to be 

1.0, which is 16 standard deviations away from the estimated covariance of -4.36 in the long-term 

gains equation. It also suggests that there may be some unobserved variables that are missing from 

both equations that result in a spurious correlation between the equation errors. For example, 

inclivicluals with a large amount of capital losses may have small net gains but be especially likely 

to realize. Another explanation is that some individuals may be "buy and hold" types whereas 

others trade actively. Those who trade more than expected would then be observed to have lower 

t hati average gains.29 

VIII. Simulation 

We developed a simulation method so that the estimated econometric model coulcl be used 

to examine the effect of changes in the individual income tax code on aggregate capital gains 

income and Federal tax receipts. A simulation model is necessary for several reasons. 

The first and most important reason is simultaneity. The econometric model was 

constructed so that capital gains income depends upon the marginal tax rate for capital gains. The 

niarginal tax rate also depends upon the level of capital gains income. Estimated coefficients from 

TaI~le2 imply that an increase in statutory marginal tax rates on long-term capital gains would also 

decrease long-term capital gains income. The decrease in capital pins income woulcl, in turn, 

decrease the tax rate for some taxpayers, etc., until an equilibrium is reached. Simulation is 

necessary to find the policy effect on the equilibrium solution for each taxpayer. 

Second, simulation is necessary so that the individual behavioral effects of tax policy changes 

;ire aggregated properly to derive implied effects on aggregate capital gains income and aggregate 

Federal tax receipts. Behavioral effects must be evaluated on an individual basis and then 

a3greg;ited because the econometric model implies that each behavioral response depends on the 

level of the marginal tax from which the evaluation starts, Le., it is a non-constant tax elasticity 

model. 

2s Wc discuss this issue more in Section X. 

29This type of behavior might be modelled as a fixed effect. See Slemrod and Shobe (1989). 

16 
The tax calculator provides the third reason. In the econometric model, capital gains income 

only depends on the tax code through the marginal tax rate on capital gains. Simulation is the only 

way to examine the effect of changing the complex tax code in a way that changes the marginal tax 

rate differently for different taxpayers, depending on their other levels of income items, credits, and 

deductions. In addition, because state tax codes are included in our calculations, changes in the 

Federal income tax code would affect marginal tax rates differentially across states. 

The fourth reason is statistical. For a standard self-selection model with no endogenous 

right-hand-side variables, the effects of changing RHS variables can be examined by solving for the 

expected value of the dependent variable. However, the marginal tax rate in our model is 

endogenous and it is on the right hand side of the criterion and level equations. The marginal tax 

rate is also a complicated function of the dependent variable. It is therefore not possible to solve 

for a closed form for the expected level of capital gains income. 

1X. Simulation Experiments 

We conducted several simulation experiments. PLLl involved changing the inclusion rate on 

long-term capital gains, using data and a tax calculator for 1982, when the inclusion rate was 40%. 

In general, ii 5% change (for example, from 40% to 38%) would produce a 5% change in all 

Federal statutory marginal tax rates3' The simulation experiments were therefore designed to 

esamine the effects of changing all statutory marginal tax rates on capital gains income. Jt slio~~lcl 

Iw noted that the results reported below may not accurately reflect Federal revenue responses to 

htatiitory tax changes because of the concerns raised in section 11. 

Results of the simulations appear in Tables 3 and 4. For all but the last several lines of 

Tahle 3, the simulations reflect the effect of small changes around the actual inclusion rate for 1982. 

The long-run elasticity of long-term capital gains with respect to the tax rate is 1.63 whereas the 

short-run elasticity is not much greater, Le., 1.98. Part of the long-term elasticity, 1.33, is due to 

changes in the levels of capital gains income for taxpayers who realize capital gains in the base and 

3"11\n esccption would be if a taxpayer was subject to the alternative minimum tax in the base case. Because the c:ipitnl 

gins csclusion was treated as a tax preference and therefore not allowed under the alternative niinimum tax in 1082, such 

t:isp:i).crs would csperience no change in statutory marginal tax rates as a result of a small change in the inclusion rate. Also. 

the inclusion rate was changed for Federal taxes only, except for states that automatically used the Federal iiiclusion rate. 

Tn tlic cstent that states varied in their treatment of capital gains tqes, a percentage change in the Federal inclusion rate 

' docs no( necessarily result in an equal percentage change in the combined marginal tax rates. 

17 
comparison simulation^.^' The remainder of the response, .30, is due to taxpayers who switch 

between realizing and not realizing as a result of a change in the inclusion rate. 

Simulation results in Table 3 also demonstrate that actual marginal tax rates do not change 

as much as statutory marginal tax rates when the inclusion rate is changed. The responsiveness of 

the actual marginal tax rate is represented by the elasticity of the actual (capital gains weighted 

average) marginal tax rate on capital gains with respect to a change in the inclusion rate. If there 

were no state taxes, no alternative minimum tax, and no behavioral feedback effect, then the 

elasticity would be 1.0. However, the average elasticity is only 0.61 because (aside from the other 

two factors) there is a behavioral feedback effect for many taxpayers. When the statutory marginal 

tax rate is decreased, for example, taxpayers respond by increasing their capital gains income, which 

may push them into higher marginal tax brackets, to which they may respond by not increasing 

their capital gains income by as much as they, otherwise, would have. The full effect on the xtual 

marginal tax rate would, in such cases, be less than the change in the statutory tax rate. 

Table 4 presents another view of the simulation process. Before simulation, capital gains 

increase from $83.0 billion to $94.3 billion. Of this change, $7.6 billion is due to increased 

realizations by individuals who realized gains before and after the tax change and the remainder 

is clue to realizations by the additional returns with capital gains. 

However, these additional realizations increase individuals' tax rates because of the 

progessivity of the tax code, especially for those who did not realize capital gains in the baseline 

case. Simulation adjusts gains (and other income and deductions) until individuals are in 

equilibrium in the sense that the components of their income solve the estimated equations at the 

tax rate that is consistent with that their income level. After simulation, most of the induced 

realizations evaporate when taxpayers figure out that if they realized a big capital gain in response 

to ;i lower tax rate, they would be pushed up into a higher tax bracket. The resultant ecluililx-ium 

shows induced realizations of $2.2 billion, or 2.2% of the total. Increased levels of realizations by 

inclividuals with gains in the baseline amount to $5.4 billion. 

Under this scenario, tax receipts increase by 0.6% from the baseline because the 9.2% 

increase in equilibrium realizations more than offsets the 2.7% decrease in average equilibrium tax 

Kites. 

3'0thcr capital income equations, discussed in Section 11, such as those for interest income, dividends, and short-run 

capital gains, were included in the simulation. The effect of changes in the inclusion rate, however, had almost 110 effcct oil 

1hc oLlicr income lcvcls because the other equations contained either the marginal tax rate on ordinary income or that on 

short-term capital gains. Such tax rates were not effected much by the change in the inclusion rate nor by the resulting

changes in levels of long-term capital gains income. The simulated effects on other income items are thcrcforc 

ii pprox i ma t ely zero. 

18 
We also examined the effect of larger changes in the inclusion rate on long-term capital 

gains income. The inclusion rate was increased by 50%, Le., from 40% to 60%. Elasticities 

averaged over the range of inclusion rates are reported in the last five rows of Table 3. The longrun capital gains elasticity is larger, 1.67, than the elasticity derived for a small change in the 

inclusion rate for two reasons. First, the average marginal tax rate, and therefore the individual 

taxpayer elasticities are larger over the range between the 40% and 60% inclusion rates than they 

are in a neighborhood of the 40% inclusion rate. Second, relative to the simulation of a small 

change, a large change results in a larger fraction of switching between realizing and not realizing 

capital gains income. The part due to switchers is .47, which is about 28% of the total response. 

Though it was only used to simulate the effects of changing the inclusion rate, the model 

ciin he used to simulate the effects of any other tax code change that may affect marginal tax rates. 

X. Sensitivity Analysis 

A sensitivity analysis was conducted for the long-term capital gains equations to examine 

the effects of varying the assumptions on which the econometric model was specified and to 

esamine the effect of improvements in the econometric model relative to the models used in 

previous studies of capital gains taxation. Changes were made to the model, one change at a time. 

Results for some of these alternative specifications appear in Table 5.32 The second column was 

copied from Table 2 for comparison to the results of the sensitivity experiments, which are 

presented in columns 3 through 9. 

The first experiment examined the effects of simultaneity bias. For the experiment, instead 

of an instrumental variables procedure, the actual tax rate was used. Results reported in column 

3 clemonstrate that simultaneity bias is an important issue. The tax variable coefficients reverse 

signs because higher actual capital gains realization levels cause higher marginal tax rates. The 

resulting bias is large enough to more than offset the negative effect of marginal tax rates on 

capital gains realizations. Other estimated coefficients are also apparently biased by simultaneity 

when the actual tax rate is used. For example, the estimated coefficients of the age dummy 

\Iariables change considerably relative to the coefficient estimates reported in column 2.33 

32 Wc mi a number of other sensitivity tests that are not reported here. For example, we tested sonic alternative 

functional rclationsliips between marginal rax rates and realizations and found preliminary evidence that our results arc robust 

with rcspcct to functional form. We intend to expand on these results in future research. 

33Tcchnically,the differences from estimates in column 2 are not actually the bias but may be caused by bias. Diffcrcriccs 

arc suggestive of the sign and size of the bias. 

19 
Columns 4 and 5 of Table 5 demonstrate the effect of selection bias in estimation of the 

model parameters. In each case, self-selection was ignored and the capital gains level equation was 

estimated by an instrumental variables method with no correction for selection bias, Le., there MJ~S 

no criterion function and there was no Mill’s ratio included as a RHS variable. Column 4 used 

all data, realizers and non-realizers, whereas column 5 used realizers only. In both cases, there is 

apparently a large bias for the coefficients of the marginal tax rates. The estimated coefficients 

on wealth increased by an order of magnitude and the coefficients of the age-group duiiiiiiy 

variables actually change signs. The results of this experiment suggest that previous capital gains 

micro-data studies that have ignored selection bias may have overestimated the response of longterm capital gains income to changes in the marginal tax rate. 

Results of three other sensitivity experiments are also reported in Table 5. When wealth 

\viis omitted, the tax rate coefficients did not change much because other variables, such as iige. 

control for wealth variation. The criterion function and the resulting Mill’s-ratio correction variable 

also control for some wealth variation because the likelihood of realizing capital gains is highly 

correlated with wealth. 

The lagged tax rate variable was omitted as an explanatory variable in the equation 

summarized in column 7. The estimated coefficient on the current-year marginal tax rate almost 

exactly equals the sum of the coefficients on current and lagged rates in column 2 and coefficients 

on other variables are virtually unchanged. This result suggests that the primary value of adjusting 

for dynamics is that it permits estimation of the short-run response to tax rate changes. 

Column 8 suggests that estimates of the response of capital gains realizations to tax rate 

changes may be biased upward when state taxes are ignored, although the difference in the tax rate 

coefficient is not statistically significant. The other noticeable difference in column 8 is that the 

coefficients on regional dummies vary from column 2. 

Table 6 reports estimates from weighted and unweighted equations under several different 

specifications. The effect of weighting on the long-run marginal tax rate does not appear to be 

significant in our level equation. The unweighted long-run response is -1 1.6 where as the estimated 

response in the weighted equation is -10.9, There are significant differences in the wealth and 

income coefficients, which is not too surprising since the weights are highly correlated with these 

m e:i s ii res, 

In the criterion equation, the weighted profit estimate of the long-run tax rate effect ch;inges 

sign from -2.7 in the unweighted equation to +0.7 in the weighted equation. The net effect on 

simulation of weighing in the two equations would be to slightly reduce the simulated change in 

realizations resulting from a change in tax rate. 

20 
The level equation is much less robust when sample-selection bias is ignored. Using all data 

(realizers and non-realizers), the long-run tax estimate is roughly halved from -13.7 in the 

unweighted equation to -7.0 in the weighted equation. However, this result is reversed if only 

realizers are considered. The weighted equation in the case results in an estimated long-run 

response of -26.8 whereas the unweighted equation estimate is -17.5. 

This almost four-fold discrepancy between the weighted estimates in the all-data and 

realizers-only equations roughly parallels the discrepancies between FSY (1982) and Minarik ( 19S4). 

Most of the difference between the estimates in these studies appears to be due to their failure to 

appropriately adjust for sample-selection bias. 

XI. Conclusion 

This study has attempted to shed light on why empirical capital gains realization equations 

have produced such widely varying results and to explore the relevance of panel data to resolve 

some of those questions. Our results suggest that a substantial part of the past variance in 

realization elasticities may have been due to the simultaneity between marginal tax rates and capital 

-rrains realizations and to the failure of previous studies to correctly deal with sample-selection bins. 

111addition, the failure to deal with these sources of biases has resulted in discrepancies that have 

been blamed on other causes. For example, much of the discrepancy between FSY and Minarik 

was prohably due to the failure of both authors to adjust for the self-selection in their data sets 

rather than because of weighting, as Minarik concluded. 

We also find that simulation is important for estimating the equilibrium response of 

individual taxpayers to changes in tax law under a progressive income tax. Previous studies that 

treated the marginal tax rate as fixed with respect to induced changes in capital gains realizations 

probably overstated the response of taxpayers to changes in tax rates. On the other hand, the 

failure to simulate the induced changes in the number of realizers may have resulted in 

iinderstatements of individual responsiveness. 

We found some other factors to be surprisingly unimportant. Income shifting, which wi~s 

;I key subject of this study, does not substantially affect either the estimated parameters in capital 

gains realization equations or the simulated results of a change in tax regimes. However, because 

ot' the limitations of a short panel (for example, because there was no change in the proportional 

clitferential between tax rates on capital gains and other income), this negative finding must be 

viewed as very tentative. 

21 
Incorporating dynamics (i,e., lagged tax rates), an exogenous wealth instrument, and state 

tax rates did not substantially change the estimated long-run response of capital gains realizations 

to tax rates. However, the lag term did detect a short-term capital gains response that was 

significantly greater than the long-run response. In addition, the exclusion of wealth seems to bias 

estimates of the effects of other variables, such as income and age, on capital gains. We also 

found some evidence that our results are relatively robust with respect to the chosen functional 

form. 

We argue that data from a long panel are essential to fully unravelling the components of 

capital gains realization responses that are due to Federal policy and the part that is due to 

individual-specific factors. The panel we used is probably not long enough at present. First, it 

cannot identify the effects of a differential between capital gains tax rates and other income. 

Second, it cannot distinguish the aggregate effects of ERTA from other time-series data, such as 

interest rates and aggregate activity. Since the results are not significantly different in the panel 

from the results based on separate years, our elasticity estimates probably include the inctividuiilspecific response with some part of the aggregate response. More definitive results must await a 

longer panel. 

There are some deficiencies that will not be remedied in any data set, however. First, 

interpretation of empirical capital gains models will always be subject to debate until there is 21 firm 

theoretical foundation for such research. Developing testable theories should be a priority in future 

research. Second, focussing on individual capital gains realization behavior may ignore some 

important determinants of the aggregate revenue effects of capital gains tax changes. There shoulcl 

he more research on the effects of capital gains tax policies on rates of return in financial markets 

and on growth. Without understanding the effects of capital gains tax policies on GNP, interest 

r;i te:,, dividend payouts, and asset values, predictions about revenue consequences must be viewed 

;IS ten LI ous. 

22 
Appendix 1. Simulation Method 

Using the estimated econometric model, the effect of a change in the inclusion rate on 

capital gains income was simulated for each taxpayer in the sample for 1982 tax law and income 

levels. Using sample weights for the number of taxpayers represented by each taxpayer in the 

sample, the individual simulated effects were then aggregated to derive the effects on aggregate 

capital gains income and Federal tax receipts. 

Simulation consists of four steps: calibration, equilibrium solution for il base cabe, 

equilibrium solution for a comparison case, and aggregation. The calibration step generates 

residuals for the criterion and level equations. Using the structure of the self-selection model and 

the estimated parameters, regression residuals are drawn in a way that insures that the model, 

including the residuals, predicts levels of capital gains income that equal the levels actuaUy realized 

by each taxpayer in the sample for 1982.w 

Calibration is necessary not only to correctly model the distribution of capital gains income 

and tax payments, but also to insure realistic results. Because the model implies that the behavioral 

effect of a change in the capital gains tax depends upon level of the marginal tax rate, calihration 

is necessary to insure that the model will not systematically over- or underpredict income levels 

in ;I manner that would push taxpayers into unrealistically high or low tax brackets. Otherwise. the 

simulation would predict inaccurate aggregate income and tax-receipt levels. 

In the second major step of simulation, iterative numerical methods are used to solve for 

bise ci16e equilibrium levels of capital gains income. An equilibrium is defined as the level of 

income md marginal tax rates that simultaneously solve the criterion, income level, and marginal 

tax rate functions. To simulate a steady state with respect to the marginal tax rate in the base 

cabe, the equilibrium is solved under the condition that current and lagged marginal tax rates are 

eq11a I. 

The base-case simulation is constructed so that, in the third simulation step, the comparison 

case can be used to examine either the short- or long-run effect of changes in the tax code. In the 

comparison case, a new equilibrium solution is found after a change is made in the tax calculator 

to change the inclusion rate on capital gains income.35 A short run, or first-year-after-the-c~l~in~~ 

simulation solves for a new equilibrium solution, holding the lagged tax rate fixed at its buse-case 

3'C:ilibration is a niontc-carlo method by which sample information is combined with a pscudo-randoin iniinitxr gciicrnior 

Lind csriniatcd parameters in order to provide a distribution of regression errors consistent with the samplc. 

3-iTheeffects of other changes to the tax code can also be simulated. 

23 
level. A long-run simulation solves for a new steady-state equilibrium, by again equating the current 

and lagged marginal tax rate. 

The last step is aggregation. A simulation is conducted for each taxpayer in the sample. 

Sample weights are then used to calculate aggregate base and comparison case levels of capital 

gains income and Federal tax receipts. 

24 
Appendix 2. Other Income Regressions 

While the focus of our study has been on capital gains, it is useful to examine the results 

for the other income and deduction equations in Table Al. The wealth and permanent income 

variables have positive effects on both the decision to realize and the levels of dividends, interest 

income, and business losses. The effect of transitory income is small in all of the equations and 

insignificant in most of them. 

The age class variables are significant in both the level equations and the criterion functions 

for dividends and interest. The coefficients increase in size at each age class, holding wealth 

constant, which implies that older individuals tend to hold more wealth in the form of currentyield assets. Such a pattern does not appear for business losses, however, for which the coefficient5 

are lower for older age brackets. 

The coefficients on the current tax rates in the level equations for dividends and interest 

are both negative, indicating that taxpayers with higher tax rates realize smaller amounts of these 

types of income. Coefficients on the lagged tax rates, however, are positive and larger than those 

on current tax rates. These estimates imply that, in the long run, higher tax rates are associated 

with higher realizations of dividends and interest. The short-run timing effect is negative. Because 

dividends and interest are expected to be more stable from year to year than capital gains income, 

and less sensitive to timing decisions, these estimation results are counterintuitive. Furthermore, 

the coefficients in the criterion functions for dividends and interest all have unexpected signs. 

Estimated coefficients for the business loss equations suggest that taxpayers who may face 

high marginal tax rates invest more in assets that provide ordinary income losses for tax purposes. 

The combination of such ordinary income losses with long-term capital g.ains was an essential 

feature of many tax shelters before the Tax Reform Act of 1986. The lagged tax rate coefficients 

in the business loss equations are negative, indicating that the long-run effect is smaller than the 

short-r 11n effect. 

In general, the results for the net capital loss equations in Table A2 are less satistactoi.!~rl1;in 

the results for net capital gains in Table 2. The equations poorly explain both the levels of net 

cilpit;ll losses and the decisions to realize net capital losses. Relatively few of the non-tax rate 

coefficients are statistically significant. The tax rate coefficients in the criterion functions, however, 

have the expected signs. The current year coefficients are positive and the lagged tax-rate 

coefficients are negative. This suggests that taxpayers with high tax rates have a greater incentive 

to realize net capital losses and that much of this effect is a short-run timing effect. This result is 

25 
consistent with previous research in Auten (1982) that suggests that taxpayers control the timing 

of their losses. 

There are a number of factors that may help to explain the unsatisfactory results for the 

capital loss equations. First, there are far fewer taxpayers that realize net capital losses than realize 

net capital gains. In a period of inflation, most appreciating assets will yield net nominal capital 

giins, even though their real value may have declined, Furthermore, there is some evidence 

suggesting that many investors prefer to continue holding investments with capital losses until they 

"turn around," even though they would be better off realizing their losses for tax purposes. Second, 

the mix of assets on which losses are reported is different than that for capital gains. While the 

largest proportion of losses are from sales of corporate stock, significant shares also come from 

bonds and commodities (Clark and Paris, 1985). Taxpayers with commodity losses are likely to be 

wealthier, tax sensitive investors who utilize various devices to minimize taxes and thus have low 

marginal tax rates. Capital losses on bonds were unusually high during the sample period because 

loiig-term interest rates were considerably higher than when the bonds were purchased. The high 

interest rates reduced the market values of the bonds. In many cases such losses would have heen 

passive losses realized when the bonds matured. Third, the tax rates used in the loss equations are 

marginal tax rates on long-term or short-term gains. However, due to a $3,000 limitation on the 

cieciuction of' excess capital losses against ordinary income and the presence of loss-carryover 

provisions in the tax code, the "true" marginal tax rate on net losses is likely to he complex. 

Further research on this problem is necessary. 

26 
Table 1 

Ranges of Point Estimates From Previous Studies: 

Long-Term Capital Gains Realization Elasticities 

Studies Data Type 

Capital Gains 

Type 

Realization 

Elasticity 

Feldstein, Slemrod, 

and Yitzhaki 

(1980) 

Cross-Section, 

High-Income

Sample, 1973 

Corporate Stocks -3.75 

Minarik 

(1981) 

Cross-Section 

High-Income

Sample, 1973 

Corporate Stocks Range from -.44 

to -.79 

Auten and Clotfelter 

(1982) 

Panel Data, 

Middle-Income 

Sample,

1967 to 1973 

All Capital Assets Short-Run Range:

-.91 to -3.46, 

Long-Run Range:

-.36 to -1.45 

U.S.Treasury 

(1985) 

Panel Data, 

1971 to 1975 

All Capital Assets Long-Run Range:

-1.16 to -2.20 

Corporate Stocks Long Run: -2.07 

U.S.Treasury

(1985) 

Time Series, 

1954- 1985, 

All Taxpayers 

All Capital Assets Short Run: -1.3 

Long Run: -0.8 

Lindsey

(1987) 

Pooled CrossSection and 

Time Series, 

All Capital Assets *Short Run: -2.14 

*Long Run: -1.37 

1965- 1982 

Darby, Gillingham,

and Greenlees 

Time Series, 

1954 to 1985, 

All Capital Assets *Long-Run Range:

-.62 to -1.51 

(1988) All Taxpayers 

Congressional

Budget Office 

(1988) 

Time Series, 

1954 to 1985, 

All Taxpayers 

All Capital Assets *Range from -.79 

to -.99 

Auerbach 

(1988) 

Time Series, 

1954 to 1986, 

All Taxpayers 

All Capital Assets *Long-Run Range:

-.06 to -1.08 

* Derived at 25.4% average tax. 
Table 2 

Capital Gains Equations 

Right-Had Level Equations Criterion Functions 

Variable Long-Term Short-Term Long-Term Short-Term 

Intercept 

Marginal Tax Rate 

Long-Term Gains 

Marginal Tax Rate 

Lagged, Long-Term Gains 

Marginal Tax Rate 

Short-Term Gains 

Marginal Tax Rate 

Lagged, Short-Term Gains 

Log of Wealth 

Log, Permanent Income 

Log, Transitory Income 

Log, Lagged Business Income 

Log of Wages 

Log, Lagged Rent Losses 

Log, Lagged

Business Losses 

Marriage Dummy 

Family Sue 

Age 30-39 

Age 40-49 

Age 50-59 

(continued) 

-43.43 -2.87 -25.19 -10.51 

(8.21) (0.68) (13.61) (16.12) 

-13.17 ... -4.50 ... (9.42) (9.15) 

1.58 ... 1.81 ... (4.18) (10.55) 

.e. -3.12 -0.65 

(4.87) (3.38) 

... 0.62 ... 0.21 

(2.24) (2.21) 

0.49 0.14 0.75 0.46 

(3.98) (0.61) (27.40) (19.02) 

0.15 0.27 0.13 0.06 

(4.03) (4.53) (7.95) (4.04) 

5.WE-03 7.76E-03 2.10E-03 2.60E-03 

(0.86) (0.83) (0.95) (1.05) 

-0.07 0.03 ... (7.95) (12.64) 

... -0.03 ... -0.01 

(2.18) (5.02) 

7.20E-04 ... 8.20E-03 ... (0.08) (2.42) 

-0.06 -0.02 0.04 0.04 

(4.25) (0.58) (13.29) (14.43) 

0.19 0.41 0.12 0.04 

(1.88) (2.56) (3.71) (0.9 1) 

-0.05 -0.04 -0.01 0.00 

(2.02) (0.98) (1.07) (0.35) 

-0.76 0.08 0.48 0.41 

(3.35) (0.18) (8.47) (5.52) 

-1.46 -0.60 0.69 0.38 

(5.89) (1.42) (12.28) (5.12) 

-1.89 -0.84 0.81 0.31 

(7.26) (2.15) (15.00) (4.33) 

Note: T-ratios are in parentheses 
Table 2 

Capital Gains Equations 

Right-Hand Level Equations Criterion Functions 

Variable Long-Term Short-Term Long-Term Short-Term 

(continued) 

Age 60-69 

Age 70 and Over 

South Dummy 

West Dumy 

Northeast Dummy 

1981 Dumy 

1982 Dummy 

1983 Dummy 

Standard Deduction 

Error Covariance 

Sigma 

Observations: 

-1.76 -0.91 0.77 0.28 

(6.69) (2.36) (13.93) (3.72) 

-1.71 -1.os 0.95 0.23 

(6.05) (2.74) (16.48) (2.93) 

0.11 0.24 0.03 -0.08 

(1.41) 2.05 (1.03) (2.72) 

0.71 0.12 -0.01 -0.13 

(5.53) (0.65) (0.32) (2.71) 

0.52 0.41 -0.02 0.12 

(5.90) (3.18) (0.52) (3.87) 

-0.93 0.23 0.10 -0.17 

(6.34) (1.49) (2.79) (5.07) 

-1.57 -0.87 0.06 -0.18 

(11.13) (5.43) (1.83) (4.24) 

-1.32 -0.87 0.16 -0.02 

(9.64) (5.19) (4.93) (0.46) 

... ... -0.21 -0.35 

(6.65) (9.15) 

-4.36 -2.22 ... ... (12.62) (3.33) 

4.26 3.21 ... ... 

9435 3235 19OOo 19000 

Note: T-ratios are in parentheses 
Table 3 

Simulation Results 

Experiment: Change the Inclusion 

Rate on Long-Term Capital Gains Income 

(1982) 

Experiment: Small changes in the inclusion rate 

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 

Federal individual income tax receipts (1982): 

Short-run elasticity -0.13 

Long-run elasticity -0.11 

Experiment: 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 tax 

receipt elasticity -0.07 
M 

a 2 N 

12

VI 

M 

CI c

3 

.4 

3 
+ F

.5 
v Y 

Y Y 
3 

v 

mm 

Ins: 

v 3 

'?9 

Q", 

ow 

crs : ' 

cl 
I 

.9 m

c E 
Table A.2 

Capital Loss Equations 

Level Equations Criterion Functions 

Long-Term Short-Term Long-Term Short-Term 

Right-Hand

Variable 

Intercept 

Marginal Tax Rate 

Long-Term Gains 

Marginal Tax Rate 

Lagged, Long-Term Gains 

Marginal Tax Rate 

Short-Term Gains 

Marginal Tax Rate 

Lagged, Short-Term Gains 

Log of Wealth 

Log, Permanent Income 

Log, Transitory Income 

Log, Lagged Business Income 

Log of Wages 

Log, Lagged Rent Losses 

Log, Lagged Business Losses 

Marriage Dummy 

Family Sue 

Age 30-39 

Age 40-49 

Age 50-59 

(continued) 

-49.17 -42.26 5.05 -9.35 

(1.70) (2.38) (2.16) (14.42) 

-25.80 ... 2.82 ... (1.32) (4.50) 

8.09 ... -1.12 ... (1.15) (5 25) 

... -21.40 ... 0.30 

(1.76) (1.58) 

... 4.11 ... -0.52 

(1.41) (5.63) 

-0.83 -0.77 0.07 0.45 

(0.69) (0.73) (2.32) (18.28) 

0.13 -0.35 -0.02 0.06 

(0.64) (1.18) (0.76) (3.85) 

-6.50E-03 1S9E-02 -4.10E-03 -1.40E-03 

(0.21) (0.98) (1.41) (0.55) 

0.01 e.. -2.6OE-03 ... (0.31) (0.88) 

... 0.04 ... -3.10E-03 

(0.98) (1.17) 

9.4OE-03 ... -4.18E-03 ... (0.20) (0.98) 

-0.03 -0.14 0.02 0.03 

(0.32) (1.24) (5.11) (10.94) 

0.32 -0.64 -0.11 0.14 

(0.41) (1.02) (2.32) (3.62) 

0.05 -0.03 0.02 -0.01 

(0.38) (0.41) (1.87) (0.52) 

-1.45 -1.17 0.29 0.26 

(0.65) (0.94) (3.13) (3.59) 

-1.59 -1.04 0.42 0.33 

(0.65) (0.87) (4.59) (4.62) 

-1.63 -0.96 0.40 0.29 

(0.69) (0.97) (4.45) (4.20) 

Note: T-ratios are in parentheses 
REFERENCES 

Auerbach, A.J. (1988), "Capital Gains Taxation in the United States: Realizations, Revenue and 

Rhetoric," Brookings - PaDers on Economic Activitv. 

Auten, G.E. (1982), "Estimation of the Effects of Capital Gains Taxes on Realization of Capital 

i Gains," final report to the U.S. Treasury Department, Office of Tax Analysis. 

Auten, G.E., L.E. Burman, and W.C. Randolph (1988), "APanel Data Model of Capital Gains and 

Taxable Income," unpublished manuscript, U.S. Treasury. 

Auten, G.E. and C. Clotfelter (1982), "PermanentVersus Transitory Tax Effects and the Realization 

of Capital Gains," Ouarterlv Journal of Economics. 

Cilke, J.M. and R.A. Wyscarver (1987), "The Treasury Individual Tax Simulation R/Iodel," 

Compendium of Tax Research, Office of Tax Analysis, Department of the Treasury,

Washington, D.C. 

Clark, B. and D. Paris (198S), "Sales of Capital Assets, 1981and 1982,"Statistics of Income Bulletin, 

Vol. 5, No. 3, Winter 1985-86. 

Cook, E.W., and J.F. O'Hare (1987), "Issues Relating to the Taxation of Capital Gains," National 

Tax Journal, Vol. XL, No. 3. 

Darby, M.R., R. Gillingham, and J.S. Greenlees (1988), "The Direct Revenue Effects of Capital 

Gains Taxation: A Reconsideration of the Time-Series Evidence," Treasurv Bulletin, Spring

Issue. 

Duncan, G. and W. DuMouchel (1983), "Using Sample Survey Weights in Multiple Regression 

Analyses of Stratified Samples," Journal of the American Statistical Association 78, No. 381. 

Feldstein, M. and S. Yitzhaki (1978), "The Effects of the Capital Gains Tax on the Selling iincl 

Switching of Common Stock," Journal of Public Economics 9, No. 1. 

Feldstein, M., J. Slemrod, and S. Yitzhaki (1980), "The Effects of Taxation on the Selling of 

Corporate Stock and the Realization of Capital Gains,"Ouarterlv Journal of Economics 94,No. 

4. 

Gillingham, R., J.S. Greenlees, and K.D. Zieschang (l9S9), "New Estimates of Capital Gains 

Realization Behavior: Evidence from Pooled Cross-section Data," OTA working paper

(forthcoming). 

Grwelle, J. (19S7), "A Proposal for Raising Revenue by Reducing Capital Gains Taxes," CRS 

Report S7-562E. 

G reene, W.H. ( 19SS), "LIMDEP Reference Manual," (unpublished manuscript). )* 

Holt, C. and J. Shelton (1962), "TheLock-in Effect of the Capital Gains Tax," National Tax JoLirnaI, 

Vol. XV, No. 4. 

27 
Kiefer, D. (1988), "The Capital Gains Response to a Tax Rate Change: Is it Overestimated?" 

Congressional Research Service Report. 

Lee, L.F., G.S. Maddala, and R.P. Trost (1980), "Asymptotic Covariance Matrices of Two-Stage 

Probit and Two-StageTobit Methods for Simultaneous Models with Selectivity," Econometrica 

48. 

Lindsey, L.B. (1987), "Capital Gains Rates, Realizations, and Revenues," in Martin Feldstein, ed., 

The Effects of Taxation on Cauital Accumulation, Chicago: The University of Chicago Press. 

Lucas, R.E., Jr. (1976),"Econometric Policy Evaluation: A Critique," in The Phillips Curve and 

Labor Markets, in K. Brunner and A.H. Meltzer, eds., Amsterdam: North-Holland. 

Maddala, G.S. (1%3), Limited-DeDendent and Oualitative Variables in Econometrics, Cambridge:

Cambridge University Press. 

Minarik, J.J. (1984), "The Effects of Taxation on the Realization of Capital Gains: Comment," 

Quarterlv Journal of Economics, February. 

(19Sl), "Capital Gains," in H.J. Aaron and J.H. Pechman, eds., How Taxes Affect 

Economic Behavior, Washington D.C.: The Brookings Institution. 

Sletnrod, J. and Shobe, W. (1989), "The Tax Elasticity of Capital Gains Realizations: Evidence 

from a Panel of Taxpayers," (unpublished manuscript). 

Stiglitz,J.E. (1983), "SomeAspects of the Taxation of Capital Gains," Journal of Puhlic Economics. 

US. Congressional Budget Office (19SS), "How Capital Gains Tax Rates Affect Revenues: The 

Historical Evidence." 

(1~89),"Simulatingthe Revenue Effects of Changes in the Taxation of Capital Gains," 

Congressional Budget Office Staff Working Papers. 

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of 1978." 

7 

28 
I 

' 

Recent OTA Papers published by

The Office of Tax Analysis

U.S. Department of the Treasury

Washington, DC 20220 

59. NonCorporate Business Taxation: 

Before and Afrer the Tax RLform Act of I986 

Susan C. Nelson 

May 1988 

60. The Tar Expenditure Budget Before and After tlze 

Tar Reform Act of 1986 

Thomas S. Neubig 

David Joulfaian 

October 1988 

61 . Recent Issues in Transfer Pricirig

Barbara L. Rollinson 

Daniel J. Frisch 

November 1988 

62. Measures of Goodriess of Fit for Extrapolations: 

Initial Results Using the lridividiial Tax Model Database 

Robert E. Gillette 

February 1989 

63. Master Limited Partnerships: 

A Viewfrom Their 1986 Tax Returns 

Susan C. Nelson 

Joann Martens 

May 1989 

64. A History of Federal Tax Depreciation Policy 

David W. Braze11 

Lowell Dworin 

Michael Walsh 

May 1989 

65. An Aizalysis of Aggregate Titne Series 

Capital Gains Equations 

Jonathan D. Jones 

May 1989 

66. New Estimates of Capital Gains Realization Behavior: 

Evidence from Pooled Cross-Section Data 

Robert Gillingham 

John S. Greenlees 

Kimberly D. Zieschang 

May 1989 

67. Estimatiori mid biterpretatiort of Capiral Gairis Behavior: 

Evidence from Pariel Data 

Gerald E. Auten 

Leonard E. Burman 

William C. Randolph 

May 1989 

Copies of these OTA Papers may be purchased from the National Technical Information 

Service, 5285 Port Royal Road, Springfield, VA 22161 (phone: 703-487-4660).