NEW ESTIMATES OF 

CAPITAL GAINS REALIZATION BEHAVIOR: 

EVIDENCE FROM POOLED CROSS-SECTION DATA 

by 

Robert Gillingham"

John S. GreenleeP 

Kimberly D. Zieschang** 

OTA Paper 66 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 22161. Phone (703)487-4660. 

Office of Tax Analysis

U.S. Treasury Department. Room 4040 

Washington, D. C. 20220 

* Office of Economic Policy, Department of the Treasury ** Division of Price and Index Number Research. Bureau of Labor Statistics. 

Department of Labor 

Each of the authors was detailed to the Office of Tax Analysis (OTA) for some or all of the 

duration of this project, and OTA staff members did all the analysis of confidential tax 

data for the purposes of this research. This paper is part of a larger OTA project on 

capital gains. We benefited greatly from discussions with OTA staff members. and especially

William Randolph. Gerald Auten and Leonard Burman. Special thanks are also due 

Roy Wyscarver and James Cilke. without whose assistance our analysis of the Individual Tax 

Model data would have been impossible and to Michael Darby who initiated our work on this 

topic. All views expressed are those of the authors and do not necessarily represent the 

policies or views of the Department of the Treawry. 
New Estimates of Ca ita1 Gains Realization Behavior: 

Evidence fromBooled Cross-Section Data 

Summary 

In this paper we develop and estimate a behavioral model of taxpayer response to capital 

gains taxation. This issue is of tremendous current policy interest. In part because of the series of tax 

law changes culminating in the Tax Reform Act of 1986, capital gains realizations have fluctuated 

widely from year to year, with significant implications for federal and state tax revenues. In order to 

properly evaluate the likely revenue impact of the current Bush Administration proposal reducing 

the maximum tax rate to 15 percent, analysts must'have an accurate, reliable measure of the degree 

to which taxpayers would increase the equilibrium flow of realized capital gains. This paper offers 

important new insights into this complex issue. 

The econometric problem facing us is not a new one; numerous prior reports and scholarly 

papers have examined the capital gains response, either at an aggregate level using time-series data 

or at the cross-sectional taxpayer level. The two approaches are ' often viewed as yielding 

contradictory results, although U.S. Treasury Department (1988) argues that a correct interpretation 

of the time-series coefficients implies that they are consistent with the cross-section analyses. In any 

case, there is general agreement that the optimal empirical approach would exploit cross-section data 

from several different years. 

To date, the only published research study combining cross-section data from a number of 

years is the panel analysis in the Treasury Department's Report to Congress on the Capital Gains 

Reductions of1978 (U.S. Treasury Department 1985). Using data on capital gains for a sample of 

taxpayers over the years 1973-75, the study identified a high elasticity of realizations to the marginal 

tax rate on long-term gains. As in that panel study, we employ several years of taxpayer data from 

Internal Revenue Service Statistics of ,Income (SOI) files to estimate our model. The distinction is 

that our pooled cross-section (PCS) data do not represent a series of observations on the same group 
-- -- 

Summary -- 2 

of taxpayers, but rather a set of independent observations from a larger taxpayer sample, extending 

over a wider time span. Since we construct dynamic measures of tax rate change from auxiliary data, 

we overcome the presumed weakness of pooled cross-section data vis-a-vis panel data -- the lack of 

information on last year's tax rate --while retaining the relative strengths. 

We recognize that development of a "non-static" i.e., behaviorally based revenue 

estimate for a hypothetical capital gains tax change requires knowledge of not only the elasticity of 

declared long-term gains, but also whether there are either direct or indirect effects of the long-term 

rate on other categories of income. For this purpose, our basic behavioral model is broader in scope 

than the models used in prior capital gains research. It divides total capital income into five 

categories -- long-term capital gains, interest, dividends, business income, and short-term capital gains 

-- which are viewed as comprising a seemingly-unrelated system of income-determination equations 

at the individual level. 

This research is also more ambitious than earlier studies in its econometric approach. The 

endogeneity of so-called "last-dollar" marginal tax rates, the importance of the entire progressive tax 

schedule, dynamic "unlocking" of long-term capital gains, and the censored (i.e., clustered at zero) 

nature of the realizations variable are handled in a more sophisticated fashion. Using a multinomial 

logit model, we estimate behavioral parameters explaining long-term losses as well as gains within a 

consistent, mutually exclusive framework. As noted above, capital gains are recognized as being part 

of a system of jointly-determined capital income categories, thus allowing for Yncome switching" 

effects. Finally, and perhaps most importantly, our data base extends over the period 1977-85, 

thereby including three significantly different regimes of capital gains taxation. 

As have prior researchers, we find strong evidence of responsiveness to capital gains tax 

rates. The coefficients in our tables show that the marginal tax rate on long-term gains has a 

significant and powerful negative impact both on the proportion of taxpayers realizing gains and on 

the value of capital gains declared by realizers. That is, despite the theoretical misgivings that many 

analysts have expressed, the data continue to imply that the realizations response would be sufficient 
Summary -- 3 

to yield revenue increases from capital gains rate reductions. Employing a measure of the year-toyear change in the rate schedule to allow for unlocking effects, we find that inclusion of the variable 

in no way negates the long-run tax impact. 

Our other primary result is that income switching in response to capital gains tax changes was 

not evident in our data. Whereas the own tax rates were generally valuable explanatory variables in 

equations for all capital income categories, the long-term gains tax rate was usually either 

insignificant or entered with a counterintuitive sign when added to the other income models and the 

business tax rate was similarly uninformative when added to the capital gains equation. Identifying 

the degree to which income switching does in fact take place is a potential area for further research. 

In the process of estimating our model we have recognized and addressed most limitations for 

which earlier studies have been criticized. We specifically analyzed capital losses as well as gains. We 

developed an instrumental variable procedure for measuring the impact of the marginal tax rate, and 

relaxed prior maintained restrictions in the modeling of the censored and clustered nature of the 

capital gains dependent variable. We employed the rate structure premium concept to recognize the 

progressivity of the tax schedule. We used sample survey weights in our estimation procedures to 

correct for sample selection bias. We tested the use of the business, or "ordinary," tax rate as well as 

the long-term gains tax rate in our capital gains equations to allow for the possibility that the rate 

differential might be the critical price variable. Finally, we estimated equations for other capital 

income components to test for the presence of income switching. 

The review of time-series evidence in U.S. Treasury Department (1988) concludes: 

We do not argue that our time-series regressions provide conclusive evidence on 

taxpayer responsiveness to capital gains tax laws. In fact, we believe that crosssection regressions, with their large sample sizes and detailed wealth and 

demographic detail, are the most reliable basis for inferences. 

Neither this nor any other single paper can constitute definitive proof regarding the revenue impact 

of capital gains taxes. However, despite the reluctance on the part of many policy analysts to accept 
Summary -- 4 

the possibility of such elastic taxpayer behavior, we believe that it should now be possible to reach 

consensus regarding what data and econometrics tell’us about the historical evidence. First, the 

panel analysis in U. S.Department of the Treasury (1985) implied that the capital gains tax cuts of 

1978 and 1981 were both revenue-enhancing. Second, Auten, Burman, and Randolph (1989) 

obtained similar results in a recent study that also used panel data. That study, using different data 

and a different statistical model from ours, identifies a high realizations response and simulates 

substantial revenue gains from hypothetical capital gains rate reductions in 1982. Thus, all three 

recent econometric analyses using microdata from multiple years have reached essentially the same 

conclusion. 

It is our view that the theoretical models of taxpayer behavior are not really in conflict with 

the econometric evidence. It has often been argued that the realizations response can only be a 

temporary, stock adjustment effect, since the equilibrium flow of realized gains is necessarily limited 

by the flow of accruals. However, Gravelle and Lindsey (1988) point out that the vast majority of 

capital gains are never realized for tax purposes. On average, according to their estimates, only 3.1 

percent of the stock of accrued gains was realized in any given year during the 1960-84 period. The 

existence of a large flow of unrealized gains should provide ample theoretical plausibility to the 

strong behavioral response we and others have identified. 
New Estimates of Ca ita1 Gains Realization Behavior: 

Evidence fromBooled Cross-Section Data 

I. Introduction 

In this paper we develop and estimate a behavioral model of taxpayer response to capital 

gains taxation. This issue is of tremendous current policy interest. In part because of the series 

of tax law changes culminating in the Tax Reform Act of 1986, capital gains realizations have 

fluctuated widely from year to year, with significant implications for federal and state tax 

revenues. In order to properly evaluate the likely revenue impact of the current Bush 

Administration proposal reducing the maximum tax rate to 15 percent, analysts must have an 

accurate, reliable measure of the degree to which taxpayers would increase the equilibrium flow 

of realized capital gains. This paper offers important new insights into this complex issue. 

The econometric problem facing us is not a new one; numerous prior reports and 

scholarly papers have examined the capital gains response, either at an aggregate level using 

time-series data or at the cross-sectional taxpayer level. The two approaches are often viewed as 

yielding contradictory results, although U.S. Treasury Department (1988) argues that a correct 

interpretation of the time-series coefficients implies that they are consistent with the crosssection analyses. In any case, there is general agreement that the optimal empirical approach 

would exploit cross-section data from several different years. 

To date, the only published research study combining cross-section data from a number 

of years is the panel analysis in the Treasury Department’s Report to Congress on the Capital 

Gains Reductions of1978 (U.S. Treasury Department 1985). Using data on capital gains for a 

sample of taxpayers over the years 1973-75, the study identified a high elasticity of realizations to 

the marginal tax rate on long-term gains. As in that panel study, we employ several years of 

taxpayer data from Internal Revenue Service Statistics of Income (SOI) files to estimate our 

model. The distinction is that our pooled cross-section (PCS)data do not represent a series of 

observations on the same group of taxpayers, but rather a set of independent observations from a 
-- 

larger taxpayer sample, extending over a wider time span. Since we construct dynamic measures 

of tax rate change from am'liary data, we overcome the presumed weakness of pooled crosssection data vis-a-vis panel data -- the lack of information on last year's tax rate -- while retaining 

the relative strengths. 

We recognize that development of a "non-static" -- i.e., behaviorally based -- revenue 

estimate for a hypothetical capital gains tax change requires knowledge of not only the elasticity 

of declared long-term gains, but also whether there are either direct or indirect effects of the 

long-term rate on other categories of income. For this purpose, our basic behavioral model is 

broader in scope than the models used in prior capital gains research. It divides capital income 

into five categories -- long-term capital gains, interest, dividends, business income, and short-term 

capital gains which are viewed as comprising a seemingly-unrelated system of incomedetermination equations at the individual level. 

This research is also more ambitious than earlier studies in its econometric approach. 

The endogeneity of so-called "last-dollar" marginal tax rates, the importance of the entire 

progressive tax schedule, dynamic "unlocking" of long-term capital gains, and the censored (Le., 

clustered at zero) nature of the realizations variable are handled in a more sophisticated fashion. 

Using a multinomial logit model, we estimate behavioral parameters explaining long-term losses 

as well as gains within a consistent, mutually exclusive framework. As noted above, capital gains 

are recognized as being part of a system of jointly-determined capital income categories, thus 

allowing for "income switching" effects. Finally, and perhaps most importantly, our data base 

extends over the period 1977-85, thereby including three significantly different regimes of capital 

gains taxation. 

The remainder of this paper is divided into six sections. Section I1 discusses our 

behavioral model and the econometric procedures used to estimate it. Section I11 describes the 

PCS data base, while Section IV describes exploratory analysis on a subsample of the data to 

determine functional form. Sections V and VI present the results of the two-step estimation of 

-2-
the behavioral model on four additional subsamples of the data. Section VI1presents simulations 

of the model to measure the overall responsiveness of taxpayers to tax policy and Section VI11 

summarizes our results. 

11. Methodological Approach 

In this section we briefly discuss the essential aspects of our behavioral model, of the 

special problems in speciwng the equations in the system, and of the econometric procedures we 

use to estimate the parameters of the equations. 

The System of Capital Income Equations. We model capital income as accruing from five 

sources -- interest, dividends, business income, and short and long term capital gains (including all 

capital gains distributions). The behavioral equations determining the amount of declared gross 

income from each source are assumed, in principle, to comprise a seemingly-unrelated fiveequation system at the taxpayer level. The explanatory variables in each equation would include 

total income, the marginal tax rates on each capital income source, and a vector of demographic 

and locational variables. (For estimation purposes we restrict each of our equations to include at 

most two marginal tax rates, as discussed in Section IV below.) 

This specification permits the relationship between total income and its components to 

be non-homogeneous. That is, the predicted share of interest in total capital income may decline 

as total income rises. More importantly, we test for "income-switching" behavior. We 

hypothesize, for example, that the coefficient of the capital gains tax rate in the dividends 

equation should be positive if taxpayers adjust their portfolios in response to changes in relative 

tax rates. With the exception of the time-series study by Cook and O'Hare (1987), previous 

studies of capital gains behavior have been single-equation models, estimating only the own-price 

effect of the long-term gains tax rate on total realized gains. It has often been suggested that the 

cross-price effect on other income categories would have an important offsetting effect on tax 

revenues. As we show below, our analysis does not support this contention. 

-3-
Despite its similarity to theoretically-derived specifications for systems of production or 

consumer demand functions, our empirical model reflects a number of compromises between the 

requirements of theory and data. Ideally, we would like to model the portfolio asset choices of 

taxpayers, employing user costs and total wealth as determining variables. Under suitable 

assumptions, an underlying portfolio allocation model could be transformed to yield equations 

for income flows. However, like prior cross-section or panel researchers we have data only on 

capital income flows, not asset portfolios. Another difficulty is that the opportunity cost of 

capital, nominal rates of return on specific financial assets, and rate of price appreciation for 

equity assets are unobserved as well. Moreover, the problem is complicated considerably by the 

fact that capital gains are only observed when realized, not as they are accrued. 

Given these data constraints, we prefer to view the income variable on the right hand side 

of our equations as a proxy for total wealth or permanent income, rather than as a total income 

constraint with accompanying adding-up restrictions for the parameters of the individual 

equations. In accord with this view, we will measure total income below, not as the explicit sum 

of the modeled components, but as the sum of positive values of the lower-level income items in 

our data set. This follows in the spirit of the Treasury Department's "Total Positive Income" 

concept. 

The Logit Model of Gains and Losses. Previous researchers have had to confront the 

problem that capital gains realizations are heavily clustered at zero. This suggests a violation of 

the usual distributional assumptions underlying ordinary least square (OLS) estimation. One 

potential solution, employed in the 1985 Treasury report, was to employ Tobit estimation. The 

Tobit method is designed to estimate linear equations when the dependent variable is bounded at 

zero. While this procedure corrects for the violation of the OLS assumptions, it precludes the 

modeling of capital losses, which are excluded or recoded to zero for Tobit estimation. It also 

imposes a specific, and in our view arbitrary, parameter restriction on the relationship between 

the choice of whether or not to declare gains and the level of gains given that they are declared. 

-4-
We employ a more general approach in'which the i-th individual is presumed to choose 

among three mutually exclusive alternatives. In our case, alternative 1is the declaration of net 

capital gains, alternative 2 is the declaration of net losses, and alternative 3 is the declaration of 

neither losses nor gains. Let us define the variable wi, equal to j when alternative j is chosen, and 

let Pijindicate the corresponding probability. 

Corresponding to each alternative j we also have a level equation explaining the value of 

a continuous variable Y..: 1J 

(1) Yj = xisj+ uij 

where Xi and p. are vectors of explanatory variable values and parameters, respectively, and uij is J 

a disturbance term. The value of Yijis observed only when wi=j. In our application, Yil is the 

level of net capital gains (or the logarithm of gains) and Y, the value (or logarithm) of net losses. 

We thus assume separate coefficient vectors for the impacts of our explanatory variables on 

capital gains and capital losses, while the third level equation is degenerate: the value Yi3and 

vector p3 corresponding to the "no realization" alternative are normalized at zero, with no loss of 

generality. 

The observed sample of the model is {wi,Yij},and the likelihood function is given by 

(2) Li = Pilflyi, I wi=ll for wi=l 

for wi=2 

Pi3 for wi=3. 

Implementation of this model requires first, the determination of a probability rule for choice 

among the three alternatives, and second, the specification of the conditional density functions f 

in equation (2). These decisions imply the form of the relationship between the choice among 

alternatives and the levels of the continuous variables. In the Tobit model, for example, the P 

-5-
and f distributions are not distinguished from each other. The observed values of Yi, are 

assumed to follow a normal distribution, truncated from below at zero, while Pi, is the mass of 

that same distribution. (Since the Tobit is a binary choice model, we also must have P,=O and 

pi3=bPi1.) 

A recent paper by Hay (1985) presents an alternate estimation technique based on 

multinomial logit estimation that we modify and adopt in Sections V and VI to obtain our 

behavioral parameters. The Hay model was designed for situations such as physician specialty 

choice, where each specialty is characterized by its own income equation. Estimation of the 

income function parameters is complicated by the self-selection of the samples; those physicians 

choosing a specialty are likely to be the ones most adept at earning income in that specialty. This 

implies that the income function must be estimated in conjunction with the estimation of a 

specialty choice model in order to obtain consistent coefficients. (Hay was also interested in the 

corollary problem of estimating the impact of specialty income on specialty choice, an aspect that 

is not directly relevant to our case. See also the similar model discussed by Dubin and McFadden 

(1984)J 

Our estimation procedure is based on the familiar multinomial logit probability model, in 

which the probability that an individual will choose the j-th of J available alternatives is given by: 

where Zi is a vector of explanatory variable values specific to the i-th individual and the ~~'s are 

vectors of parameters specific to each alternative. An equivalent way of specifying this 

probability model is to assume that the j-th alternative is chosen if the condition 

(4) vij e zisj 

is met, where vij is a (J-1) element vector of independent standardized logistic random variables 

and the k-th element of Sj is equal to ~ ~ - 7 ~ 

-6-
The jointness of the level equation (1) and the choice equation (4) is implemented by 

assuming that u and v are correlated random variables. Without presenting the specific 

derivation here, we note that u.. is assumed to have a conditional expectation equal to a linear

B 

weighted sum of the elements of vij. This yields an expression for the expectation of uij given that 

condition (4) above holds, Le., given that alternative j is chosen and Y..'J is observed. In turn, this 

enables us to define a term A.. which is proportional to that conditional expectation and which 11 

can be computed from the estimated probabilities Pij. 

Our model can be estimated in two steps. First, the standard logit maximum likelihood 

procedure is used to estimate the parameters 7

j' Second, the subsamples of individuals choosing 

each alternative are used to estimate the corresponding level equation parameters pj. In this 

second step, the value of A.. is used in the j-th equation to correct for the nonzero conditional 

11 

expectation of the disturbances. This process can be thought of as an extension of the 

generalized Tobit models described by Amemiya (1984), modified to allow for the multialternative model and based on a logit rather than probit assumption regarding the probability 

densities. 

Since the presence of positive, negative, and zero capital gains are three mutually 

exclusive alternatives, we estimate the impact of income, tax rates, and other variables on the 

probability of each outcome using the multinomial logit model. The results of this procedure are 

discussed in Section V. We then estimate capital gains level equations for "gainers" and "losers", 

including the A variables computed from the logit parameters to correct for least-squares bias in 

each equation. These results are presented in Section VI. Joint treatment of gainers and losers 

is important to obtain a theoretically consistent behavioral model and enable us to evaluate the 

total response to changes in tax policy. The simulations of taxpayer response which we present in 

Section VI1 explicitly recognize the impact of tax policy on both gain and loss behavior at the 

individual taxpayer level to yield meaningful estimates of total taxpayer response. 

-7-
Since other capital income sources also are clustered at zero, we use the same technique 

for these categories as for capital gains. In the cases of interest and dividends, we need only 

model a binary choice model, with a single level equation, since negative values are not observed. 

Tax:Progressivdy. We hypothesize that the declaration of capital gains is a function of, 

inter alia, a taxpayer’s total income and his last-dollar tax rate -- the tax liability on the marginal 

dollar of capital gains. Under a proportional income tax system, this would be a relatively 

straightforward model. Tax progressivity, however, creates two distinct problems for 

characterizing the determination of long-term gains and other capital income levels. First, the 

measure of income must reflect the fact that under a progressive tax schedule the taxpayer is 

better off than if all income were taxed at the last-dollar rate. Second, the marginal tax rate 

depends on the amount of capital gains declared and so cannot be treated as an exogenous righthand-side variable in our equations. 

Prior researchers have recognized the problems created by tax schedule progressivity in 

the context of modeling the demand for certain tax-deductible items such as charitable 

contributions. These problems are also faced in other areas, such as medical care or electricity 

demand, where consumers face piecewise-linear rate schedules. Hausman (1985) and Moffitt 

(1986) provide recent reviews of the econometric literature on the issue. Various empirical 

techniques have been proposed, ranging widely in complexity and sophistication, to deal with the 

two problems mentioned in the previous paragraph. We discuss our approaches to these two 

problems in turn below. 

The concept oE what Barnes et aZ(1981) call the rate structure premium (RSP) forms the 

basis for our treatment of the income effects of tax schedule progressivity. In general, the 

marginal tax rate on the last dollar of income will be higher than the rate on the first dollar, and 

the econometric model used to estimate capital income declarations should incorporate this 

incentive aspect. Holding constant the level of a taxpayer’s total income and the marginal tax 

rate on each capital income category, the taxpayer benefits by the lower tax rates on 

-8-
" 

inframarginal income. Previous authors, beginning with Nordin (1976) in the consumer demand 

context, have shown that a variable measuring this benefit should have a coefficient in the 

behavioral equation equal to the coefficient on income. 

In our application, the RSP is computed as the product of the level of income and the 

marginal tax rate on that income, summed over all capital income sources (i.e. the total tax paid 

on capital income if all capital incomes were taxed at the last-dollar rate), less the actual total tax 

liability. We add the RSP to total positive before-tax income in our model equations, thus 

imposing the theoretical parameter constraint in the definition of what Burtless and Hausman 

(1978) have termed '%irtual income." Note that labor income is not included in the first term of 

the RSP, since it is assumed to be exogenous; the marginal tax rate on labor income plays no role 

in our model. By the same token, the RSP nets out in the second term the taxes paid on labor 

income as well as capital income, reflecting the fact that all income variables have been measured 

on a before-tax basis. A derivation of the rate structure premium used in this study is presented 

in Appendix A. 

The endogeneity of the marginal tax rate is the problem which has received most 

attention in prior studies of capital gains realizations. With a progressive tax schedule, taxpayers 

who declare large capital gains will face higher marginal tax rates completely aside from any 

behavioral incentive effect. In an econometric sense, the last-dollar marginal tax rate is 

correlated with the disturbance term of the equation, so that OLS estimation will yield biased 

coefficients. Several approaches have been taken to deal with this problem, including the 

replacement of the last-dollar rate with the first-dollar rate or the marginal rate evaluated at 

some "typical" level of capital gains for similar taxpayers. By construction, virtual income is also 

an endogenous variable, for two reasons. First, and most obviously, it includes the dependent 

capital income variables as components. Second, it is adjusted for tax schedule progressivity 

using the RSP computed with endogenous tax rates. 

-9-
Recently, sophisticated econometric procedures have been designed to estimate models 

in which the equation disturbance is decomposed into two components. The first component 

reflects heterogeneity of behavior across individuals, for example due to unobserved determining 

factors. The second disturbance component represents random variation, or measurement error, 

of the dependent variable around the value chosen by the individual. Within this framework, 

behavior is a function of the entire vectors oftax rates and corresponding virtual income levels, 

and the observed marginal rate bracket need not even be the bracket in which the taxpayer is 

assumed to find equilibrium. An example of this approach is found in Reece and Zieschang 

(1985). Although it permits a theoretically richer specification of behavior, it is impractical in our 

application given the other econometric difficulties discussed in this section. 

In our analysis we follow an instrumental variables approach. We compute an alternative 

total income level implied by the taxpayer’s known characteristics but independent of his actual 

declared capital income. As detailed in Appendix B, we derive an exogenous measure of annual 

income by imputing the predictions from regressions of actual capital income components on a 

number of exogenous explanatory variables. We then calculate marginal tax rates and virtual 

income corresponding to the alternative income level. As in Feldstein et a1 (1980), we employ 

these as instruments for the observed values, rather than as proxy variables, in our behavioral 

equations. This procedure corrects for endogeneity while retaining the assumption that the lastdollar rate is in fact the incentive variable to which the individual taxpayer responds, rather than 

a first-dollar or average rate. 

WeightingforSample Selection Bias. A final complication in estimating our model derives 

from the design of the Internal Revenue Service SO1 samples used in our estimation. As 

described more fully below, high-income taxpayers are heavily oversampled, giving us good 

coverage of those individuals most likely to declare capital gains. Unfortunately, when the 

dependent variable is a component of income, this sampling procedure imparts a sample 

selectivity bias to estimated regression parameters. 

- 10-
-- 

Truncating a sample by eliminating observations on the dependent variable below a 

specified cutoff leads to bias in much the same way that censoring at zero creates the bias 

addressed by the Tobit procedure (see Hausman and Wise 1977). In the SO1 data, the sampling 

rates vary widely with income class. The sampling probability for a typical taxpayer might be 

roughly 1 in 1O00, but if that taxpayer declared $2,oaO,000in capital gains he would be sampled 

with certainty. This issue was pointed out in the capital gains context by Minarik (1984), who 

recommended weighted regression to correct the bias. Weighting by the inverse of the sampling 

probability does not fully resolve the problem in particular, computed standard errors of 

coefficients remain incorrect. However, since we will not rely on parametric estimates of 

sampling variance, it does provide a viable correction for us. We therefore use the SO1 sampling 

weights in all the regressions reported below. 

With respect to our logit equations, the SO1 data make up a "choice-based sample," in the 

sense of Manski and Lerman (1977). The likelihood that a given choice will be observed depends 

upon the alternative chosen. Again, we follow the appropriate correction by weighting individual 

likelihood values by the SO1sample weights. 

Nonparametric Standard Errors. Several aspects of our econometric specification call into 

question the computed standard errors yielded by the estimation programs we employ. In the 

logit step, the information matrix does not reflect the fact that some of the explanatory variables 

are generated by auxiliary regressions on tax rate and income instruments. The level equations 

yield consistent parameter estimates, but the disturbance terms are heteroskedastic by 

construction. Finally, as noted above, the use of sample weights to correct for selection bias is 

not reflected in the equation standard errors. Fortunately, however, our data base is sufficiently 

large that we can estimate our entire model separately on four independent subsamples. The 

means of the four sets of coefficient vectors can be used as our final parameter estimates, and 

one-half the standard deviations in the estimates provide nonparametric estimates of their 

accuracy. 

- 11 -
III. The Pooled-Cross-SectionData Base 

Taxpayer Files. The data base available for this research is an aggregate of four large 

cross-sectional taxpayer samples drawn from Internal Revenue Service SO1 files. The 

construction and attributes of the annual SO1 files are described in Internal Revenue Service 

(1986). The Office of Tax Analysis maintains subsamples of the SO1 files for analytical use, and 

we employed four of these "production" files here. 

For present purposes, the primary characteristic of this data set is its intensive coverage 

of high-income filing units. The files are drawn as stratified samples, with a sampling rate of unity 

for taxpayers with incomes above specified cutoffs (typically $2,000,000) and/or who file 

particular forms (such as Schedule C, for proprietorship income). As a result, we have unusual 

potential for accurate modeling of the types of individuals who are most likely to accrue and 

declare long-term capital gains and other types of capital income. 

Because the data come from income tax returns, we have detailed information on the 

composition of both labor and, most importantly, capital income. We can therefore identify the 

determinants of tax liability, and marginal tax rates, much more accurately than would be possible 

with most other household survey data bases. On the other hand, SO1 data provide little direct 

demographic information other than that which can be inferred from filing status and exemptions 

taken. That is, we can identify married, blind, and over-65 taxpayers, along with the number of 

dependents, but we have no information on education, work experience, or asset holdings. 

The principal weakness of a cross-sectional file, for the purpose of capital gains modeling, 

is that virtually the only variation in tax rate is across taxpayers facing the same rate schedule. 

That is, it is difficult to establish a tax rate effect independent of the impact of taxable income or 

other variables correlated with income. We avoid this problem in two ways. First and most 

important, we use several independent cross-sections, each characterized by a different set of 

rate schedules. Second, we incorporate state income tax rates into the analysis. 

- 12-
-- 

Two milestones in the recent history of capital gains taxation were the Revenue Act of 

1978 and the Economic Recovery Tax Act of 1981 (ERTA). The former law, by increasing the 

long-term gains exclusion from 50 to 60 percent, sharply reduced the tax rate on gains relative to 

other income for most taxpayers. In particular, the maximum statutory rate on gains dropped 

from 35 to 28 percent. ERTA reduced this maximum further, by lowering the top rate on all 

income to 50 percent. After 1981, the general federal tax rate schedules continued to move 

downward each year through 1984, although the top rate remained at 50 percent (20 percent for 

long-term gains). Indexation of schedules by the Consumer Price Index began in 1985, the last 

year of our sample. 

Our PCS data base was designed to span the three general tax regimes indicated above, 

by analyzing the years 1977, 1979 (following the effective date of the 1978 Revenue Act), 1983 

(following ERTA), and 1985. The remaining odd-numbered year, 1981, was characterized by an 

ambiguous incentive structure: the maximum effective tax rate changed in the middle of the year, 

and it is unclear when the rate change was fully anticipated by taxpayers for planning purposes. 

(See Slemrod and Shobe (1989) for one attempt’to construct a marginal tax rate variable for 1981 

taxpayers.) Further, with the passage of ERTA many taxpayers -- though not those with very 

high incomes knew with certainty that rate schedules would fall sharply again in 1982, 

potentially affecting their realizations behavior in a way that would be difficult to model. With 

1981 therefore excluded from study, our taxpayer sample sizes by year are: 

1977 - 74,763 

1979 - 72,035 

1983 - 81,806 

1985 - 88,725 

Our model focuses on the relationship between permanent income and the current 

realization of capital income. If the representative taxpayer’s transitory income fluctuates widely 

from year to year, he or she may pursue an aggressive strategy of declaring gains only when 

taxable income and hence marginal rates are low. Without carefully designed estimation 

- 13 -
procedures, coefficients might tend to exaggerate the long-run response of realizations to tax 

rates. 

Our instrumental variable procedure, however, specifically addresses this problem. Our 

income instrument includes the measured level only of labor income, and transitory fluctuations 

in labor income are presumably not sufficiently important to be of major concern. For the capital 

components, we use predicted values of income which are independent of year-to-year 

fluctuations at the individual level. Although ideally we could observe and use the level of 

transitory income, it should not be correlated with any of our included variables, and so its 

absence should not bias our results. 

The other dynamic issue often raised in the context of capital gains behavior is the 

"unlocking" effect. If we observe a sample of taxpayers in the years immediately preceding and 

following a tax reduction, for example, we may overestimate the long-run realizations response if 

there is a one-time unlocking of a backlog of accrued gains at the new, lower rate. There is clear 

theoretical plausibility to this scenario, and there is obvious evidence of anticipatory unlocking 

behavior in particular episodes such as in the months just prior to the effective date of the Tax 

Reform Act of 1986. Surprisingly, econometric time series studies have yielded surprisingly little 

evidence of a systematic effect of lagged tax rates on current realizations (cf. Congressional 

Budget Office (1988) and U. S. Department of Treasury (1988)). 

We also address this issue directly, by constructing a measure of the degree to which the 

capital gains rate changed from the previous sample year. This variable is constructed from 

unpublished annual data on effective marginal tax rate by AGI class developed for Congressional 

Budget Office (1988) and graciously provided by Larry Ozanne. We compute for each sample 

taxpayer the absolute difference between the current-year effective rate for his AGI class and the 

prior-year effective rate corresponding to the same level of real AGI. For example, this 

procedure yields a rate change of -7.03 percentage points for a taxpayer with an AGI of $150,000 

- 14-
in 1979, the year folIowing the Revenue Act. This compares to no change in tax rate in 1985 for 

a taxpayer at $SOO,OOO, who continued to face the ceiling 20 percent rate. 

We thereby obtain a quantitative measure of the unlocking incentive without the need 

for multiple observations on the same taxpayer. Because the change in effective rate is specific 

to AGI class, and because AGI is an endogenous variable in our model, we compute a second 

rate change variable based on our exogenous measure of AGI described earlier and in Appendix 

B. The exogenous estimate of effective tax rate change is then used as an instrument in 

estimation. 

It is often contended that panel data are necessary to adequately treat the dynamics of 

capital gains realizations behavior. Our treatment of behavioral dynamics allows us to obtain the 

same richness of model using pooled cross sections and, at the same time, frees us to examine a 

time period with a far more varied history of tax policy than that For which panel data are 

currently available. 

Tax CalculatorPrograms. We computed federal marginal tax rates and total tax payments 

for our sample taxpayers using the OTA's Individual Income Tax Simulation Models (Cilke and 

Wyscarver 1987). A separate simulation model is available for each OF our Four sample years. 

The programs are ordinarily used to compute taxable incomes and liabilities under hypothetical 

tax regimes. In this application, we incremented each OF the various categories of capital income 

in turn to determine marginal effective tax rates For each sample taxpayer. This process is more 

precise than the simple capture of the statutory marginal rate at a particular taxable income level. 

Obviously, the long-term gains rate differs from the statutory rate because of the 50 or 60percent 

exclusion. Just as important, the true effective rate may lie below the statutov rate due to, for 

example, tax credits or the alternative minimum tax rules. Alternatively, the effective rate may 

exceed the statutory rate because of such factors as the taxation of social security income or 

income-dependent floors on Schedule A deduction items. With respect to long-term gains, the 

effective rate will depend also on the presence or absence of short-term capital gains or losses. 

- 15 -
In a similar, though somewhat more rudimentary fashion, we calculated state marginal tax 

rates and tax liabilities using a set of state tax calculators based on programs developed by the 

Office of Tax Analysis. State systems differ in many ways besides having unique income tax rate 

schedules. Most obviously, several states have no income tax at all. Others tax only interest and 

dividends, and some states granted no exclusion for long-term capital gains during our period of 

study. The state tax calculators reflect these and other special treatments of income and/or 

deductions. 

Both the federal and state programs determined the additional tax generated by 

successive increments of $100 in dividends, interest, business income, short-term capital gains, 

and long-term gains. To avoid having the dividend exclusion distort the marginal rates, we 

assumed that taxable dividends are incremented by $100. The interest, dividend, and business 

calculations all yield the same result at the federal level, roughly what would be considered the 

"ordinary" capital income tax rate. (Personal services income was taxed at a special maximum 

rate of 50 percent prior to 1981.) 

The first panel of Table 1presents mean last-dollar federal and state marginal tax rates by 

year and capital income category, with the rates for sample taxpayers weighted by the SO1 

sampling weights (but not by dollars of income). The table shows the decline in the long-term 

capital gains rate following the Revenue Act of 1978,while the tax rate on, for example, business 

income was rising due to bracket creep. In 1983 and 1985, following ERTA, the Federal rates on 

both capital gains and business income were both somewhat lower than in 1979. 

In the second panel of the table, we display the rates applicable to taxpayers with actual 

Adjusted Gross Income levels above $200,000. For this group of taxpayers the decline in the lastdollar long-term capital gains rate was matched by large reductions in federal marginal rates For 

the other capital income categories, due to ERTA's reduction in the top statutory rate from 70 to 

50 percent. Interestingly, no such trend is evident at the state level. 

- 16-
We combined the federal and state rates into a total effective tax rate recognizing that for 

taxpayers who itemize deductions on their federal returns, the deductibility of state taxes implies 

that the total effective rate is less than the sum of the two components. Our procedure also 

accounts for the different rules regarding deductibility of federal taxes on state tax returns. 

IV. Exploratory Analysis 

We estimated our model in two stages. First, we used a 10 percent subsample of our data 

to address a number of functional form questions. (The full four-year subsample has 30,791 

observations, including 12,668 with capital gains after carryover and 2,517 with losses.) This 

approach allowed us to make decisions on which variables to include in our analysis without 

"mining" the data actually used to estimate our model. In the second stage, we estimated the 

model selected in our exploratory analysis on Four additional 10 percent subsamples. The use of 

four subsamples allows us to estimate nonparametric standard errors for the parameters of our 

model, as well as our simulated measures OF taxpayer response. 

Our exploratory analysis focused on three questions: (1) is the realization of a particular 

type of capital income sensitive to the tax rate on other types of capital income; (2) what is the 

best tax rate measure to use in the model; and (3) is the model sensitive to the inclusion of 

dummy variables for tax year. 

The first question addresses the theoretical "income-switching" issue discussed in section 

I1 above. In the only previous study to address this question, Cook and O'Hare (1987) included 

the differential between the maximum capital gains and ordinary tax rates as an additional 

regressor in time-series equations explaining long-term capital gains and the sum of interest and 

dividends. The coefficient on this variable was insignificant and of the a priori wrong sign in the 

gains equation, but significant in the dividends and interest equation. However, Jones (1989) 

recently discovered that this latter result was an artifact of the errors in computing the dependent 

variable and the exclusion of a price deflator. Thus, prior analyses have not found evidence of 

income-switching behavior. 

- 17-
We tested for cross-price effects by adding the business income tax rate to the long-term 

capital gains equations (both logit and level) and the long-term gains tax rate to the equations for 

each of the other types of capital income. Although the existence of important income-switching 

effects has great theoretical plausibility, we also found little evidence consistent with this 

hypothesis. The coefficients on the cross price terms had the a priori incorrect sign in more than 

half the cases, and the estimated own price coefficients were very sensitive to the inclusion of the 

cross price term. For instance, in the long-term gains logit equation, the coefficient on the 

business tax rate was -.057 with an asymptotic standard error of .017. The coefficients on the two 

tax rate variables were highly correlated, and the major impact of including both terms was to 

distribute the total tax rate effect between the two coefficients in a manner which had no 

theoretical justification. In what follows we include only the own price term, and feel that it is 

appropriate to interpret the coefficient on this variable as the net effect of the tax change. 

Most previous studies of taxpayer response to capital gains tax rates have used either the 

level of the tax rate or the logarithm of the "you-keep-it" rate, i. e., the logarithm of 100minus the 

tax rate, as the tax rate variable. Each of these choices yields a function in which the elasticity of 

realizations with respect to the tax rate increases with the tax rate, a desirable property on a 

priori grounds. We tested both variables and found that the level of the tax rate had higher 

explanatory power in all cases, although the differences were small and the implications of the 

two models were essentially identical. Because of its slightly better explanatory power, we used 

the level of the tax rate, but this was obviously not a crucial decision. 

One of the benefits of pooled cross-section data is that tax rates vary across tax regimes as 

well as across individuals. Given this fact, we were hesitant to include year dummies in the 

estimated equations, thereby purging the tax variable of its interyear variation. (In addition, 

exclusion of year dummies greatly simplifies estimation of the logit models. In a three-alternative 

model, it reduces the number of parameters by six, and the CPU time required for estimation on 

Treasury's VAX 8800 system by over four hours.) Despite this reluctance, we tested whether 

- 18-
inclusion of year dummies would seriously alter the implications of our analysis. In several of our 

equations, year dummies significantly increased explanatory power, but their only qualitative 

impact on our results was to slightly increase the estimated responsiveness of realizations to the 

tax rate. In order to preserve the interyear tax rate variation in our data and reduce computer 

time requirements, we excluded year dummies from our analysis. 

After making these decisions on model formulation, we proceeded to the next stage of 

our estimation procedure. In section V we will discuss estimation of the logit choice equations, 

and in section VI we discuss estimation of level equations conditional on choice. 

V. Logit Maximum Likelihood Estimation 

We assume that recipiency of long-term capital gains can be analyzed using a multinomial 

logit model, with three alternatives corresponding to the sign of net long-term gains after 

carryover. Using this model we estimate two.parameter vectors p1 and p2 representing the 

effects of several independent variables on the probability of declaring long-term gains and longterm losses, respectively, relative to the third alternative of having neither losses nor gains. 

Numerically, the value of each coefficient in p.J measures the impact of a unit change in the 

associated explanatory variable on the logarithm of the ratio Pij/Pi3,what is termed the log-odds 

of alternative j relative to alternative three. 

For this analysis, we estimated the logit model using four 10 percent subsamples of our 

data. The table on the next page summarizes frequencies of recipiency in the subsamples for 

each of the capital income categories analyzed. (Total sample sizes are not identical because 

within each subsample taxpayers filing For other than the current year were deleted.) In addition 

to a constant term, the independent variables in the model are the logarithm of income and the 

squared logarithm of income, dummy variables for married taxpayers and For taxpayers aged 65 or 

over, number of dependents, and the own marginal tax rates. 

- 19-
The income variable is measured as total virtual income. As discussed in Section II,it can 

be viewed alternatively as a total net income constraint or as a proxy for permanent income. 

Computationally, virtual income consists of the sum of all positive components of income plus 

the value of the rate structure premium. The RSP, in turn, is defined as the inner product of 

income and marginal tax rates for the five capital income categories, less total income tax paid. 

We measure virtual income in thousands of 1982 dollars, using the National Income and Product 

Accounts personal consumption expenditures deflator to derive the constant-dollar figure. 

Sample Sizes and Frequencies of Recipiency 

Sample Partition 

Total Sample 

Long-term Gains 

Long-term Losses 

Business Profits 

Business Losses 

Short-term Gains 

Short-term Losses 

Dividends 

Interest 

Subsample 

1 2 3 4 

30,816 30,837 30,845 30,804 

13,111 13,134 13,090 13,165 

2,514 2,547 2,530 2,492 

13,307 13,369 13,314 13,307 

9,961 9,873 9,890 9,920 

3,840 3,863 3,772 3,793 

4,408 4,534 4,520 4,469 

17,041 17,077 16,930 17,050 

26,386 26,356 26,378 26,299 

We adopted the instrumental variables approach in our logit estimation as well as in the 

subsequent level equation step. We regressed the marginal tax rate variable and the virtual 

income variables, which were defined using actual marginal tax rates and capital income levels, on 

the exogenous explanatory variables in the model and on a set of instruments. One of the 

instruments for each equation was the own tax-rate instrument derived in Appendix B. The 

others were the logarithm and squared logarithm of an exogenous income variable, defined as 

total labor income (including wages, salaries and pensions), plus the regression-based capital 

- 20 -
income imputations described in Appendix B, plus the RSP based on the instrument income and 

tax rate vectors. The predictions from these auxiliary regression equations then became the tax 

and income variables actually used in the logit equations. 

Table 2 presents parameter estimates for the multinomial logit model of long-term capital 

gains recipiency. The coefficients in Table 2 are maximum likelihood estimates, obtained using a 

program developed by Kimberly Zieschang based on the Kalaba-Tesfatsion-Wang table 

algorithm for semi-automatically computing analytical derivatives. The parameter estimates 

reported here are the average of the parameters from the four subsamples. The standard errors 

are simply one-half of the standard deviation of the subsample estimates, i. e., the standard error 

of the mean in a sample of size four. 

The reported parameter results in Table 2 are substantially in line with expectations. 

Capital gains and losses are both significantly more likely for households with taxpayers or 

spouses aged 65 or over, and both probabilities are negatively related to the number of 

dependents. Married taxpayers are more likely to declare gains. Gains and losses are also found 

to be positively related to virtual income over most of the observed income range. 

Turning to the coefficients of most interest, declaration of long-term gains is negatively 

associated with the marginal tax rate on gains, as theory predicts. The estimated tax rate effect is 

important; it implies, for example, that for a typical taxpayer a percentage-point decrease in the 

marginal tax rate would raise the probability of declaring gains from 7.6 percent to 8.9 percent. 

On the other hand, the capital gains tax rate also is estimated to have a significant, though 

smaller, negative effect on declaring losses. We might conclude from this that the tax rate on 

gains works primarily through the incentive to hold capital assets, which can generate either gains 

or losses. 

Table 3 reports on parallel logit model estimation for the four other capital income 

categories. The set of independent variables and instruments is identical. Again, most of the 

- 21 -
coefficients in the table are plausible in sign. All of the own tax rate effects except that for 

interest are negative, and all have t-statistics greater than two. That is, the likelihood of income 

recipiency (and loss declaration in the case of business income and short-term gains) is in all but 

one case found to be negatively related to the marginal tax rate. 

VI. Level Equation Estimation 

The final step in our econometric analysis is instrumental-variables estimation of longterm capital gains and other capital income equations separately for the samples of taxpayers 

with gains and taxpayers with losses. The coefficients in these equations show the effects of 

explanatory variables on the levels of gains and losses conditional on the mix of recipiency. The 

results of the logit equation are used to construct additional regressor variables, which we refer to 

as A and which, under the assumptions of our model, should be proportional to the expected 

value of the equation residuals. The inclusion of these variables is designed to correct for the 

censored nature of the dependent variable in each equation. 

For the three-alternative model used for long- and short-term gains and business income, 

the term A is defined by: 

for gains and 

for losses, where the i subscript refers to the taxpayer and the second subscript indicates the gain, 

loss, and zero alternatives, respectively. When there are only two states, as for interest and 

dividends, we define recipiency as the first state and compute A as: 

- 22 -
Two specifications of the long-term capital gains and losses equations are shown in Table 

4. The explanatory variables, and their associated instruments, are the same as those in the logit 

equations, except for the inclusion of three dummy variables for regional location and, in one of 

the specifications, the disturbance expectation term A. The latter variable is endogenous because 

the probabilities Pij are computed using actual values of the logit explanatory variables. The 

instrument for A uses the same formula evaluated with predictions from the auxiliary tax rate and 

income regressions. 

The dependent variable in the equations reported in Table 4 is the logarithm of (the 

absolute value of) long-term gains after carryover (in thousands of deflated dollars). As discussed 

above, the tax rate on capital gains enters linearly on the right-hand-side. The parameters in the 

gains equation are consistent with expectations: the level of gains increases, at an increasing rate, 

with the level of virtual income and decreases with the level of the tax rate. The coefficient on A 

is insignificant but its inclusion does have an impact on a number of the other coefficients. The 

most notable is the coefficient on the marginal tax rate, which is reduced by more than 25 percent 

when A is included. Including A in the losses equation also has a seemingly important effect on 

the coefficient on the marginal tax rate, which is insignificant and less than half as large with A 

included as it is with A excluded. Comparison of these seemingly inconsistent results 

demonstrates how important it is to recognize that the effects of all these variables, including the 

marginal tax rate, are also incorporated in the coefficient on A. 

It follows from equations (5) and (6) that A is a nonlinear combination of most of the 

other variables in the level equation (the exceptions are the regional dummies, which were 

excluded from the logit equation to reduce computational expense). While the purpose of 

including A was to correct for censoring bias, it may also simply act to permit estimation of a 

nonlinear relationship in the level equation. In any case, the estimated marginal effect of, for 

example, the dummy variable for age 65 or over on the conditional level of gains is a function not 

only of its own coefficient but also of the coefficient on A. 

- 23 -
What appears to be inconsistency between the two specifications disappears when the 

full effect of an independent variable -- through its own coefficient and the coefficient on A -- is 

evaluated. Evaluated at sample means, the elasticity of expected gains (losses) with respect to 

the marginal tax rate, conditional on recipiency status, is -1.62 (-0.43) when evaluated with the 

equation including A and -1.52 (-0.54) when evaluated with the equation excluding A. 

Furthermore, the variation in the elasticity with the level of the marginal tax rate is very similar in 

both equations. 

Whether the coefficient on A represents correlation in the errors of the level and choice 

equations or the fitting of a somewhat more nonlinear relationship between the independent and 

dependent variables is open to question. What is not open to question, however, is that the two 

specifications have similar implications for the relationship between the dependent and 

independent variables, even in those cases where the coefficient on A is large and significant. 

Since the specifications without A are easier for the reader to interpret, we report those 

specifications in the remainder of this section; the specifications with A included are reported in 

Appendix C. 

Table 5 displays level equation estimates for the other income categories. As with capital 

gains, the signs of the coefficients are almost all in line with expectations. All of the own tax rate 

coefficients are negative. Interestingly, however, the coefficients on dividends and interest are 

small relative to the coefficients on long-term gains and business income. This might reflect the 

fact that taxpayers have substantially more discretion over the levels of gains and business income 

realized than they do over either dividends or interest income. The relatively large negative 

coefficient on the marginal tax rate in the short-term losses equation may at first seem 

anomalous. However, this may reflect the fact that short-term losses are more prevalent than 

short-term gains, and they are often written off against long-term gains. 

- 24 -
-- 

VII. Simulations of Realizations Elasticities 

The nonlinear modeling of gains and losses,the interactions between long-term gains and 

other capital income, and the two-step choice-level specification make it difficult to infer the 

aggregate quantitative response of net capital gains to tax rates simply by reference to coefficient 

values. Any specific proposal to alter the tax schedule by way of, for example, a capital gains 

exclusion or rate cap would have a unique immediate impact on each taxpayer's marginal tax rate 

and rate structure premium. These values would be further altered as the taxpayer adjusts his or 

her realizations and moves to a new equilibrium. Our parameter estimates could be used for this 

policy simulation, using a sample of taxpayer records that reflects current levels of incomes and 

tax rates. The time pattern of response would depend on the coefficients both of the 

"permanent" tax rate and the tax rate change from the prior year. 

In this paper we do not attempt such an ambitious task, given the demands for a more 

current simulation. Instead, we provide an heuristic, but quantitative summary of the 

implications of our model by simulating the marginal effect of a small change in the tax treatment 

of long-term gains. For this purpose we employ the four subsamples of taxpayers used to obtain 

our final model estimates. This enables us also to evaluate the sensitivity of our simulation 

results to the data and parameter values used. 

Specifically, we compute the long-run effect of increasing each taxpayer's marginal tax 

rate on long-term gains by one percent for example, from 20 percent to 20.2 percent. For 

convenience, we assume that the taxpayer remains in the same rate bracket and that his 

inframarginal rates are unaffected, so that the rate structure premium remains the same. 

Based on the coefficients from the logit equations, we compute the predicted 

probabilities of declaring capital gains and losses. The predicted level of net long-term gains is 

obtained by multiplying these probabilities by the conditional expected values of gains and losses 

from the level equation estimates, then subtracting the taxpayer's expected losses from expected 

gains. We repeat this process at the alternative tax rate values to yield the predicted proportional 

- 25 -
change in net gains. Finally, we compute the predicted change in gains as the product of the 

predicted proportional change and the taxpayer's base level of actual net gains. (The use of 

actual, rather than predicted, gains in the last step is a convenient means of "calibrating" the 

simulation, given that in this model with nonlinear disturbance terms total expected gains in the 

sample will not equal total actual gains.) 

The impact of a rate change can be decomposed into two parts: the effect on the 

probability of recipiency of gains (losses) and the effect on the level of gains (losses) conditional 

on recipiency. The latter effect can be further decomposed into the component due to the tax 

rate coefficient and the component resulting from the coefficient on A, which is itself affected by 

the change in the tax rate. As we noted in the previous section, our estimated equations with and 

without A included are more similar in their implications than their estimated parameters would 

seem to imply, since the A coefficient reflects impacts which in its absence would be imputed to 

the other included explanatory variables directly. To demonstrate this, we simulated the 

response elasticity using both forms of the level equations �or capital gains and losses on our 

sample of taxpayers for 1985. 

The table on the next page shows the simulated elasticity of net capital gains using the 

four subsamples of data (and the four associated sets of parameter values) and the level 

equations with and without A. All eight simulations imply a very strong realizations response. 

The long-run elasticity of long-term gains, net of carryover, is simulated to be approximately 4.3 

(without A) or 3.8 (with A). 

We emphasize that these are only point estimates. They should not be interpreted as 

implying that long-term gains would actually fall by four percent, �or example, in response to a 

one percent decrease in statutory rates. As realizations increase in reaction to a lowering o�the 

tax schedule, some taxpayers would move into higher marginal rate brackets, damping the 

response implied by our point elasticity estimates. Other taxpayers, subject to the alternative 

minimum tax before and after the tax law change, might remain in equilibrium with both their 

- 26 -
marginal tax rate and realizations unaffected. (This is likely to be especially important for high 

income taxpayers during our sample period.) In general, the impacts on total realizations, 

average effective tax rates, and total capital gains revenues would depend on the complete set of 

provisions of the particular tax policy change. The appropriate conclusion to draw is that, given 

these simulated point elasticities, a more complete policy simulation of our model would certainly 

show capital gains rate reductions to be revenue-enhancing. 

Simulated Realizations Elasticities 

Specification 

Subsample Without A With A 

-3.8 -3.2 

-4.2 -4.6 

-4.0 -2.7 

-5.3 -4.6 

Mean -4.3 -3.8 

(Std. Dev.) (0.7) (1.0) 

VIII. Implications of the Results 

As have prior researchers, we find strong evidence of responsiveness to capital gains tax 

rates. The coefficients in our tables show that the marginal tax rate on long-term gains has a 

significant and powerful negative impact both on the proportion of taxpayers realizing gains and 

on the value of capital gains declared by realizers. That is, despite the theoretical misgivings that 

many analysts have expressed, the data continue to imply that the realizations response would be 

sufficient to yield revenue increases from capital gains rate reductions. Employing a measure of 

the year-to-year change in the rate schedule to allow for unlocking effects, we find that inclusion 

of the variable in no way negates the long-run tax impact. 

- 27 -
Our other primary result is that income switching in response to capital gains tax changes 

was not evident in our data. Whereas the own tax rates were generally valuable explanatory 

variables in equations for all capital income categories, the long-term gains tax rate was usually 

either insignificant or entered with a counterintuitive sign when added to the other income 

models and the business tax rate was similarly uninformative when added to the capital gains 

equation. Identibng the degree to which income switching does in fact take place is a potential 

area for further research. 

In the process of estimating our model we have recognized and addressed most 

limitations for which earlier studies have been criticized. We specifically analyzed capital losses 

as well as gains. We developed an instrumental variable procedure for measuring the impact of 

the marginal tax rate, and relaxed prior maintained restrictions in the modeling of the censored 

and clustered nature of the capital gains dependent variable. We employed the rate structure 

premium concept to recognize the progressivity of the tax schedule. We used sample survey 

weights in our estimation procedures to correct for sample selection bias. We tested the use of 

the'business, or "ordinary," tax rate as well as the long-term gains tax rate in our capital gains 

equations to allow for the possibility that the rate differential might be the critical price variable. 

Finally, we estimated equations for other capital income components to test for the presence of 

income switching. 

The review of time-series evidence in U.S.Treasury Department (1988) concludes: 

We do not argue that our time-series regressions provide conclusive evidence on 

taxpayer responsiveness to capital gains tax laws. In fact, we believe that crosssection regressions, with their large sample sizes and detailed wealth and 

demographic detail, are the most reliable basis for inferences. 

Neither this nor any other single paper can constitute definitive proof regarding the revenue 

impact of capital gains taxes. However, despite the reluctance on the part of many policy analysts 

to accept the possibility of such elastic taxpayer behavior, we believe that it should now be 

possible to reach consensus regarding what data and econometrics tell us about the historical 

- 28 -
evidence. First, the panel analysis in U. S.Department of the Treasury (1985) implied that the 

capital gains tax cuts of 1978 and 1981 were both revenue-enhancing. Second, Auten, Burman, 

and Randolph (1989) obtained similar results in a recent study that also used panel data. That 

study, using different data and a different statistical model from ours, identifies a high realizations 

response and simulates substantial revenue gains from hypothetical capital gains rate reductions 

in 1982. Thus, all three recent econometric analyses using microdata from multiple years have 

' reached essentially the same conclusion. 

It is our view that the theoretical models of taxpayer behavior are not really in conflict 

with the econometric evidence. It has often been argued that the realizations response can only 

be a temporary, stock adjustment effect, since the equilibrium flow of realized gains is necessarily 

limited by the flow of accruals. However, Gravelle and Lindsey (1988) point out that the vast 

majority of capital gains are never realized for tax purposes. On average, according to their 

estimates, only 3.1 percent of the stock of accrued gains was realized in any given year during the 

1960-84 period. The existence of a large flow of unrealized gains should provide ample 

theoretical plausibility to the strong behavioral response we and others have identified. 

- 29 -
-- 

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Hausman, Jerry, and David Wise. "Social Experimentation, Truncated Distributions, and 

Efficient Estimation." Econometrica 45 (May 1977),pp. 919-938. 

Hay, Joel. "Physicians' Specialty Choice and Specialty Wage Structure." Mimeo, 1985. 

Hay, Joel, Robert Leu, and Paul Rohrer. "Ordinary Least Squares and Sample-Selection Models 

of Health-Care Demand." Joumal of Business and Economic Statistics 5 (October 1987), pp.

499-506. 

Internal Revenue Service. Stahtics of Income 1984, Individual Income Tax Retums. 

Washington, D.C.: US.Government Printing Office, 1986, pp.4-6. 

-30-
Jones, Jonathan. "An Analysis of Aggregate Time Series Capital Gains Equations." Office of 

Tax Analysis: mimeo, March 1989. 

Manski, Charles, and Steven Lerman. "The Estimation of Choice Probabilities from ChoiceBased Samples." Econometrics 45 (November 1977), pp. 1977-1988. 

Minarik, Joseph. 'The Effects of Taxation on the Selling of Corporate Stock and the Realization 

of Capital Gains: Comment." QuarterlyJoumal of Economics 99 (February 1984), pp. 93-110. 

Moffitt, Robert. 'The Econometrics of Piecewise-Linear Budget Constraints." Joumal of 

Business and Economic Statz3k.s 4 (July 1986),pp. 317-328. 

Nordin, John. "AProposed Modification of Taylor's Demand Analysis: Comment." Bell Joumal 

of Economics 7 (Autumn 1976), pp. 719-721. 

Reece, William, and Kimberly Zieschang. "Consistent Estimation of the Impact of Tax 

Deductibility on the Level of Charitable Contributions." Econometrics 53 (March 1985), pp.

271-293. 

Slemrod, Joel, and William Shobe. 'The Tax Elasticity of Capital Gains Realizations: Evidence 

from a Panel of Taxpayers." Mimeo, 1989. 

U. S. Department of the Treasury. 'The Direct Revenue Effects of Capital Gains Taxation: A 

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U. S.Department of the Treasury. Report to Congress on the Capital Gains Tax Reductions of 

1978. Office of Tax Analysis, 1985. 

-31-
Table 1 

Marginal Tax Rates by Income Category 

Weighted Means In Percent 

Year Category 

1977 Federal 

State 

1979 Federal 

State 

1983 Federal 

State 

1985 Federal 

State 

1977 Federal 

State 

1979 Federal 

State 

1983 Federal 

State 

1985 Federal 

State 

Long-term Business 

Gains Income 

All Taxpayers 

9.0 18.2 

1.a 3.1 

7.8 19.5 

1.6 3.2 

7.5 18.4 

1.6 3.2 

7.4 18.2 

1.6 3.2 

AGI over $200,000 

28.6 64.1 

2.9 5.0 

25.4 62.1 

2.3 4.8 

19.1 45.1 

2.6 5.2 

19.2 45.4 

2.9 5.4 

Short-term Dividends 

Gains & Interest 

17.7 18.2 

3.0 3.3 

19.2 19.5 

3.1 3.3 

18.1 18.4 

3.2 3.4 

17.8 18.2 

3.2 3.4 

48.7 64.1 

4.2 5.4 

50.3 62.1 

4.2 5.1 

36.7 45.1 

4.5 6.0 

38.1 45.4 

4.9 6.4 
Table 2 

Estimated Choice Equation Parameters 

Long-Term Capital Gains 

Explanatory Variable Gains 

Log of Virtual Income -1.062 

(-7.74) 

Square of Log of Virtual Income 0.501 

Marginal Tax Rate 

MTR Change 

Age 65 or Over 

Married 

Dependents 

Intercept 

(47.46) 

-0.178 

(-10.06) 

0.096 

(3.07) 

1.122 

(11.80) 

0.366 

(4.27) 

-0.138 

(-6.47) 

-2.270 

(-13.48) 

Losses 

-0.749 

(-2.30) 

0.439 

(14.80) 

-0.099 

(-5.32) 

0.194 

(4.86) 

1.289 

(13.27) 

-0.262 

(-1.47) 

-0.101 

(-3.63) 

-4.570 

(-12.50) 

~ ~ ~~~~~~ ~ 

Note: Nonparametric t-statistics in parentheses 
Table 3 

b 

Estimated Choice Equation Parameters 

Other Income Categories 

Business Short-term 

Explanatory Variable Profits Losses Gains Losses Dividends Interest 

Log of Virtual Income -1 341 -1.042 -0.044 -0.099 -1.393 -1.453 

(-1 9.28) (-4.84 (-0.19) (-0.67) (-22.85) (-1 1.44) 

Square of Log of Virtual Income - 0.519 0.432 0.509 0.505 0.502 0.484 

Marginal Tax Rate 

Age 65 or Over 

Married 

Dependents 

Intercept 

(32.55) (30.87) (37.66) (1 24.95) (62.59) (39.99) 

-0.1 19 -0.032 -0.127 -0.124 -0.020 0.020 

(41.75) (-3.34) (-6.38) (-1 1.38) (-3.77) (4.17) 

0.770 0.268 0.193 0.227 1.565 2.420 

(1 6.19) (3.30) (1.74) (3.74) (36.83) (1 5.77) 

1.215 0.635 -0.678 -0.693 -0.064 0.381 

(26.75) (5.23) (-4.85) (-4.72) (-0.97) (12.95) 

-0.043 -0.050 -0.194 -0.209 -0.164 -0.313 

(-8.64) (-2.07) (-1 0.46) (-6.00) (-1 0.29) (-1 2.52) 

-0.450 -2.665 -5.329 -4.928 -1.698 -0.084 

(-5.49) (-1 6.38) (-22.23) (-40.84) (-25.68) (-0.75) 

Note: Nonparametric t-statistics in parentheses 
Table 4 

Estimated Level Equation Parameters 

Long-Term Capital Gains 

Log of Virtual Income -1 333 -1.1 11 -2.400 

(-1.40) (-1.38) (-0.96) 

Square of Log of Virtual Income 0.274 0.311 0.328 

(2.81) (3.18) (1.32) 

Marginal Tax Rate -0.1 16 -0.160 -0.021 

(-2.72) (-10.13) (-0.53) 

MTR Change -0.040 -0.037 4.054 

(-0.91) (-0.63) (-0.68) 

Age 65 or Over 0.001 0.277 0.003 

(0.00) (1.45) (0.01) 

Married 0.035 0.138 0.350 

(0.33) (3.81) (0.90) 

Dependents 0.022 -0.002 0.067 

(0.70) (-0.1 1) (1.19) 

Northeast 0.065 0.070 -0.012 

(0.56) (0.36) (-0.06) 

Midwest 0.027 0.028 -0.577 

(0.60) (0.65) (-1.62) 

West 0.396 0.404 -0.044 

(6.05) (4.14) (-0.33) 

Lambda 0.498 0.484 

(1 (0.72) 

Intercept 3.767 2.151 6.064 

(1.54) (1.44) (0.94) 

Note: Nonparametric t-statistics in parentheses 

-0.973 

(-0.72) 

0.191 

(1.17) 

-0.057 

(-5.98) 

0.019 

(0.28) 

0.244 

(1.91) 

0.061 

(0.41) 

0.046 

(1.24) 

0.044 

(0.26) 

-0.528 

(-1.93) 

-0.015 

(-0.12) 

2.109 

(0.81) 
Table 5 

Estimated Level Equation Parameters 

Other Income Categories 

Business Short-term 

ExplanatoryVariable Profits Losses Gains Losses Dividends Interest 

Log of Virtual Income -0.793 -1.464 2.924 1.547 -1.822 -1.195 

(-3.30) (-1 3.34) (1 -40) (0.68) (-4.94) (-9.99) 

Square of Log of Virtual Income 0.522 0.313 -0.171 -0.094 0.382 0.341 

MarginalTax Rate 

Age 65 or Over 

Married 

Dependents 

Northeast 

Midwest 

West 

Intercept 

(12.06) (19.86) (-0.82) (-0.4) (8.49) (24.86) 

-0.208 -0.001 -0.097 -0.067 -0.019 -0.024 

(-39.06) (-0.41) (-2.95) (-1.66) (-4.13) (-5.77) 

-0.553 -0.549 0.021 -0.441 1.245 2.414 

(-20.79) (-1 5.48) (0.14) (-1.86) (1 1.07) (118.89) 

-0.137 0.079 -0.222 -0.375 -0.274 0.358 

(-1.62) (1.09) (-0.59) (-1 52) (-5.82) (5.93) 

-0.073 -0.021 -0.049 -0.014 -0.148 -0.234 

(-3.53) (-1.20) (-1.77) (-0.47) (-6.06) (-28.05) 

0.208 -0.320 0.218 0.083 0.339 0.339 

(2.86) (-3.92) (1.07) (0.45) (2.28) (9.06) 

0.335 -0.168 0.220 -0.018 -0.033 0.153 

(3.74) (-3.15) (1.19) (-0.10) (-0.43) (3.17) 

0.350 -0.090 0.246 0.230 -0.071 0.205 

(9.41) (-1.01) (1.24) (1 -95) (-0.85) (3.74) 

3.286 2.153 -5.899 -2.666 1.121 -0.691 

(8.08) (26.84) (-1 56) (-0.62) (1.73) (-4.07) 

Note: Nonparametric t-statisticsin parentheses 
Appendix A 

The Rate Structure Premium 

The taxpayer’s total income y is the sum of incomes from different sources which may be 

treated distinctly by the tax laws. Let Y = [yo,Yl, ...,Y,] ‘ denote the array of of the amounts of 

these, say, m + 1 types of income, where y = Ri,ql, ...,, Yr The first category, indexed by 0, will be 

taken by convention as labor income, and we will refer to the vector of the remaining income types as 

Y = Tyl, ...,Ym]’, so that Y = Ty,, Yl’. The income taxes owed by the taxpayer are a function 

T(Y, a) = T(Y, Y,a) of the income array and the characteristics of the taxpayer, a. Total after-tax 

income is thus: 

This identity can be rearranged in terms of marginal tax rates on endogenous income t = 

aT(Y,, Y, a)hY as 

In the analysis in this paper, labor income is taken as exogenous and is used as a conditioning 

variable. Taxpayer behavior determining the sources of nonlabor income is a function of marginal 

tax rates tr since they determine the marginal “tax price” or “you-keep-it-rate”of an income source 

(1- ti). The quantity [t‘Y - T(Y, a)], which is the rate structure premium (RSP) of the tax schedule 

with respect to the endogenous income categories Y, is the difference between what the taxpayer 

would have paid on his endogenous income had it been taxed entirely at marginal rates, and what he 

actually paid on all income. By definition, if the tax system is proportional on endogenous types of 

income the rate structure premium is simply the tax on exogenous income, but it will generally differ 

from this when marginal tax rates vary with income levels. Virtual income is defined as V = y + 

RSP. The taxpayer is indifferent between his current observed situation and an alternative state with 

total income V and T(Y, a) = Xi=l, ... t.Y~ i’ 
Appendix B 

Construction of Instruments 

Our econometric estimation procedure first requires the development of a set of equations 

for the endogenous capital income categories. Exogenous marginal tax rates were then computed at 

the total income level predicted from the regressions. We also measured the rate structure premium 

corresponding to the vectors of predicted capital incomes and marginal tax rates. 

We define components of income for this research as follows. Labor income, which we 

treated as exogenous, consists of wages and salaries, alimony receipts, and fully and partially taxable 

pensions. The five capital income categories are taxable interest, dividends before exclusion, 

business income, short-term capital gains, and long-term gains. Business income comprises those 

sources reported on Schedules C (business income), E (rent, royalty, estate, partnership, and small 

business corporation income), and F (farm income), plus gains from sale of non-capital assets and 

other unspecified income. Capital gains are measured after loss carryovers and before exclusions and 

include all capital gain distributions. 

Simple linear ordinary-least-squares regressions were run on the entire taxpayer sample for 

each of the four years in our data base. The set of explanatory variables was the same in each 

equation: the level of labor income, dummy variables indicating joint filing status and a taxpayer or 

spouse aged 65 years or older, and number of dependents. The squared value OF labor income was 

included to allow for a possible nonlinear relationship. We also included dummy variables for the 

Northeast, Midwest, and West regions. The regressions were weighted by the SO1 sample weights. 

These 20 regressions are not of special interest in themselves and are not described further here. As 

might be expected with large cross-section data sets, the explanatory power was low but the statistical 

significance of the coefficients was generally high. 

The observed distribution of each of the income categories has a clustering of values at zero, 

a characteristic that was not reflected in the predictions from the regression. In addition, dividends 
and interest cannot be negative. To incorporate this constraint, we recoded any negative predicted 

values of these components to zero, and subtracted a corresponding value from predicted business 

income to retain an unbiased prediction of total income. 

In evaluating this unsophisticated procedure for generating income predictions, it should be 

kept in mind that the objective is merely to impute a level and mix of capital income for the purpose 

of obtaining exogenous marginal tax rate instruments. An alternative method would have been to 

impute zero values of capital income, and then compute “first dollar” marginal rates. Our method can 

be thought of as a slight elaboration of the procedure, followed in some earlier studies (e. g., U. S. 

Department of the Treasury (1985) and Congressional Budget Office (1988)) of computing a 

taxpayer’s marginal capital gains rate at the mean level of capital gains for his or her AGI class. 

We also used the income instruments to calculate both federal and state marginal tax rate 

instruments for each taxpayer in our sample. Appendix Table B-1 is analogous to Table 1in the text, 

but displays the instrument tax rates. 
Appendix Table B-1 

Instrumental Marginal Tax Rates by Income Category 

Weighted Means In Percent 

~~~ ~ ~~~ ~ 

Long-term Business Short-term Dividends 

Year Category Gains Income Gains & Interest 

All Taxpayers 

~~ 

1977 Federal 9.4 18.5 12.5 18.5 

State 1.8 3.1 2.4 3.4 

1979 Federal 8.4 19.7 10.5 19.7 

State 1.6 3.2 2.2 3.5 

1 983 Federal 7.9 18.5 9.5 18.5 

State 1.6 3.3 2.1 3.5 

1 985 Federal 7.8 18.3 11.9 18.3 

State 1.6 3.3 2.4 3.5 

AGI over $200,000 

1977 Federal 13.6 25.9 13.5 25.9 

State 1.9 2.9 2.2 3.1 

1979 Federal 12.3 29.2 12.3 29.2 

State 1.5 2.9 1.8 3.1 

1983 Federal 12.5 27.7 12.5 27.7 

State 1.7 3.0 1.9 3.6 

1985 Federal 12.9 28.1 27.6 28.1 

State 1.9 3.4 3.4 4.0 

Note: Actual adjusted gross income used to classify taxpayers. 
Appendix C 

Estimated Level Equation Parameters 

Other Income Categories Including Lambda 

Business Short-term 

Explanatory Variable Profits Losses Gains Losses Dividends Interest 

Log of Virtual income -0.938 -1.572 2.203 37.993 -1567 -1.OS3 

(-2.86) (-3.77) (0.97) (1.OO) (-3.03) (-3.49) 

Square of Log of Virtual Income 0.589 0.331 -0.093 -3.605 0.249 0.247 

MarginalTax Rate 

Age 65 or Over 

Married 

Dependents 

Northeast 

Midwest 

West 

lambda 

Intercept 

(4.22) (4.35) (-0.45) (-0.97) (3.71) (4.16) 

-0.231 0.004 -0.086 -0.954 -0.022 -0.045 

(-3.77) (1.47) (-1.63) (-1.05) (-2.76) (-3.52) 

-0.405 -0.537 0.031 -2.823 0.441 1.424 

(-2.50) (-3.46) (0.18) (-1.18) (1.97) (3.73) 

0.166 0.164 -0.121 -5.158 -0.349 0.062 

(1.13) (2.49) (-0.26) (-1.OS) (-3.01) (0.93) 

-0.077 -0.017 -0.045 -1.172 -0.087 -0.093 

(-2.38) (-0.86) (-0.82) (-1.01) (-1.94) (-3.09) 

0.199 -0.323 0.190 2.733 0.368 0.363 

(2.51) (-2.59) (1.72) (1 *w (2.48) (3.84) 

0.331 -0.174 0.205 2.124 -0.008 0.160 

(2.90) (-2.65) (1.08) (0.97) (-0.83) (2.89) 

0.345 -0.093 0.195 1.719 -0.063 0.225 

(4.90) (-1.16) (2.47) (1.11) (-1.01) (3.45) 

-0.428 -0.144 -0.061 -9.025 0.m 1.046 

(-1.82) (-4.33) (-0.14) (-1-02) (3.20) (3.70) 

2.707 1.824 -4.905 -86.765 3.561 1.531 

(3.10) (3.46) (-0.81) (-1.a) (2.61) (3.02) 

Note: Nonparametrict-statistics in parentheses 
I 

Recent OTA Papers published by

The Office of Tax Analysis

U.S. Department of the Treasury

Washington, DC 20220 

59. NonCorporaie Business Tarntion: 

Before and After the Tax Reform Act of 1986 

Susan C. Nelson 

May 1988 

60. TIie Tax fipenditure Budget Before mid Ajier tlie 

Tax Rejorm Act of 1986 

Thomas S. Neubig

David Joulfaian 

October 1988 

6 1. Receiit Issues iri Transfer Pricing

Barbara L. Rollinson 

Daniel J. Friscli 

November 1988 

62. Measirres of Goodness of Fit for E.rtrnpolatio~is: 

Initial Results Using the Iridividiial Tav Model Database 

Robert E. Gillette 

February 1989 

63. Master Limited Partnersltips: 

A View from Tlieir 1986 Tar Returns 

Susan C. Nelson 

Joann Martens 

May 1989 

64. A History of Federd Tax Dcpreciutiori Policy 

David W. Brazell 

Lowell Dworin 

Michael Walsh 

May 1989 

65. AH Ailalysis of Aggregate Tim? Scries 

Capital Gains Eqirarioiis

Jonathan D. Jones 

May 1989 

66, New Estimates of Capirnl Gains Rcalizatioiz Behavior: 

Evidence ,frorii Pooled Cross-Sec/iori Data 

Robert GiI I in gham 

John S. Greenlees 

Kimberly D. Zieschang 

May 1989 

67. Estitnatiorf and Iiiterpr.etatioir of Capital Gaiiis Behavior: 

Evidence ,from Pailel Data 

Gerald E. Auten 

Leonard E. Burman 

William C. Randolph 

May 1989 

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

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