Working Paper Series

Congressional Budget Office

Washington, D.C.

Taxable Income Responses to 1990s Tax Acts:

Further Explorations

Seth H. Giertz

Tax Analysis Division

Congressional Budget Office

Washington, D.C.

Seth.Giertz@cbo.gov

September 2008

CBO Working Paper 2008-08

Congressional Budget Office working papers in this series are preliminary and are circulated

to stimulate discussion and critical comment. These papers are not subject to the

Congressional Budget Office’s formal review and editing processes. The analysis and

conclusions expressed in them are those of the authors and should not be interpreted as those

of the Congressional Budget Office. References in publications should be cleared with the

authors. Papers in this series can be obtained at www.cbo.gov. Select “publications” and then

“working papers.”
The Elasticity of Taxable Income during the 1990s: Further Explorations

Abstract

This paper presents applications of variants of a differencing methodology to Internal

Revenue Service tax records in order to estimate taxable income elasticities for the 1990s.

Estimates are systematically examined by applying a number of sensitivity tests. Estimates are

produced after altering the: (1) time interval over which observational-level behavior is

measured; (2) income restrictions on the sample; (3) choice of control variables; and (4)

weighting scheme used in the regressions. In general, estimates are quite sensitive to a

number of different factors. In contrast to some of the literature, estimates are larger when

behavior is measured over 3-year intervals as opposed to over 1-year intervals, suggesting

small transitory responses to tax changes but larger longer-term responses. When including

the richest set of income controls, income-weighted short-term elasticity estimates (based on

1-year differencing) range from 0 to 0.19. Similarly estimated longer-term elasticities (where

data are differenced over 3-year intervals) are about 0.32. When adding adjacent year tax rates

to the model, short-term elasticity estimates range from 0.30 to 0.43 and longer-term

estimates from 0.97 to 1.37. In most cases, estimates from an end-year approach (which

includes only 2 years of data, one well before the tax change and one well after) are not

statistically different from 0. However, even for the approaches that produce statistically

significant results, estimates are sensitive to an array of factors and plausible sensitivity

checks often result in estimates that differ greatly. A major conclusion is that isolating the true

taxable income responses to tax changes is inherently complex and little confidence should be

placed on any single estimate.

JEL Codes: H2, H21, H31, and J22

The author thanks David Weiner, Ed Harris, Bob Dennis, Doug Hamilton, Tom Woodward,

and Emmanuel Saez for comments and for assistance with the construction of the data.
3

I. Introduction

This paper is the third in a series describing estimates of the elasticity of taxable income with a

focus on the sensitivity of these estimates to an array of factors (see Giertz 2006 and 2008). The

paper revisits the 1990s tax increases using panels constructed from Internal Revenue Service tax

return data for 1988–95 from the Statistics of Income (SOI). These data heavily oversample

high-income filers, who, research suggests, play a critical role in determining overall responses

to changes in tax rates (Navratil 1995; Moffitt and Wilhelm 2000; Gruber and Saez 2002; and

Saez 2004).

This paper makes several contributions to the recent literature. It offers estimates of new

elasticities for the 1990s. These estimates are systematically examined by applying a wide array

of sensitivity tests. The estimates are produced using different regression weights (i.e.,

unweighted versus income-weighted) and alternative sample income restrictions. Furthermore, in

order to examine the effect of income controls on estimates, six different specifications are run

using different intervals (1-, 3-, and 6-year differences) for the measurement of (observationlevel) behavior.

In general, income-weighted estimates are larger when behavior is measured over 3-year

rather than 1-year intervals. This is in contrast to some of the literature, which has found large

transitory responses to tax changes but smaller longer-term responses. With the richest set of

income controls, but with no allowance for adjacent-year income shifting, income-weighted ETI

estimates based on 1-year differencing range from 0 to 0.19. Similarly estimated elasticities over

3-year intervals are about 0.32 (and not sensitive to income cutoffs). The inclusion of adjacentyear tax rates (to control for income shifting between years adjacent to each base and subsequent

year) results in much larger estimates, ranging from 0.30 to 0.43 for 1-year differences and from
4

0.97 to 1.37 for 3-year differences. However, among the four specifications that include separate

controls for mean reversion and income divergence, estimates range from 0.41 to 1.37. And

using the specification preferred by Gruber and Saez yields an estimated elasticity of 0.3

(compared to their estimate of 0.4 for the 1980s). In most cases, estimates from the end-year

approach are not statistically different from 0 for the 1990s, in contrast to estimates for the

1980s, where the same approach yields estimates ranging from 0.39 to 0.67.

While this paper provides insight into what methods may be more effective in accurately

identifying responses to changes in tax rates, the findings more broadly highlight the inherent

complexities in separating these responses from the myriad of other factors that influence

income. Incorporating more sophisticated controls for mean reversion and income divergence

may improve estimates, but reasonable a priori specification decisions can lead to a wide array of

estimates and thus little confidence should be placed on any single estimate.

II. The Omnibus Budget and Reconciliation Acts of 1990 and 1993

The two major tax changes examined in this paper are the Omnibus Budget and Reconciliation

Acts (OBRA) of 1990 and 1993. Both tax changes generally raised income tax rates on higher

income filers and left them unchanged for those in the lower brackets.

OBRA 90 raised both the marginal tax rate on top incomes (from 28 to 31 percent) and the

cap on wages subject to Social Security’s hospital insurance tax, which funds Medicare and

amounts to 2.9 percent when including both the employee and employer share (from $53,400 to

$125,000). Although OBRA 90 represented a major tax increase, it lowered marginal tax rates
5

for filers in the so-called “bubble bracket” (prior to OBRA 90), who generally saw their marginal

income tax rate decline from 33 to 31 percent.1

OBRA 93 created two new high-income tax brackets, at rates of 36 and 39.6 percent, and

lifted the cap on wages and salaries subject to the Social Security hospital insurance cap. The

new tax brackets were retroactive and applied for 1993; the removal of the hospital insurance cap

took effect in 1994. The bill’s key provisions did not directly affect those in the lower tax

brackets.

III. Data and Methods

Data on individual tax returns for 1984, 1985, and 1988–95 are from the Statistics of Income

(SOI), a large sample of tax returns compiled by the Internal Revenue Service that includes all

information reported on filers’ tax returns as well as additional demographic information.

Constructing Three Samples

The analysis relies on three samples constructed from the SOI so as to conform to the three key

methodological variants. The main distinction between these variants is the time interval over

which individual-level behavior is examined (i.e., over 1-, 3-, or 6-year intervals). The approach

is presented in detail later in this section.

Table 1 presents summary statistics for the three samples, which include only filers with

taxable income greater than $10,000 whose filing status did not change over the sample period.

The sample for the year-to-year analysis comprises 99,421 paired observations (14,203 filers)

and spans years 1989 to 1995. Mean taxable income (in 1992 dollars and adjusted by sampling

1 Before OBRA 90, those with incomes beyond the 33 percent bracket faced marginal tax rates of 28 percent. These

filers were moved to the 31 percent bracket after OBRA 90.
6

weights) is $36,656 and mean gross income is $51,827. The sample is restricted to filers present

in every year from 1989 to 1995,2 but this restriction should not be particularly important as

observations in the regression analysis are weighted by the inverse of their probability of

appearing in the sample.

The other two samples are very similar to each other in their construction. The sample used

to measure responses over 3-year intervals includes base years (i.e., the first year of each

observation) 1989 to 1992, paired with subsequent years 1992 to 1995 (i.e., the second year of

each paired observation). The sample comparing end years examines responses between just

1989 and 1995. Both require that the filer be present only in the base and subsequent year, not

every year from 1989 to 1995. The sample used to measure responses over 3-year intervals

comprises 157,083 paired observations. Mean taxable income is $34,877 and gross income

$55,749 (in 1992 dollars and adjusted by sampling weights). The sample for examining behavior

between end years has 31,142 paired observations, with a mean taxable income of $41,360 and

gross income of $60,047 (in 1992 dollars and adjusted by sampling weights). For comparison,

data for 37,673 filers3 in 1985–89 are used to estimate elasticities of taxable income (ETIs) for

the Tax Reform Act of 1986 (TRA 86).

Econometric Approach

The methodology focuses on individual-level changes in income (i.e., first differences) measured

over 1-, 3-, and 6-year intervals. The following equation is estimated via two-stage least squares:

2 Filers in each sample must also be present in 1988 because data from this year are used in constructing the

independent variables.

3 Auten and Carroll (1999 also employ a variation of this approach using similar data for 1985 and 1989. Their

control variables and income restrictions are not the same, however.
7

β β γ ε

τ

τ

α ξ + ⋅ + ⋅ + ⋅ + 















−

− = + ⋅ 















year f income income − X

income

income

t t

t

t

t

t

s s

1 1 2 ( , ) 1

1

ln ln .

4 (1)

The dependent variable is the log of income in a subsequent year ( s ) t income divided by income

in the base year (incomet), where the subsequent year is 1, 3, or 6 years after the base. The key

independent variable equals the log of the net-of-tax rate (NTR) in the same subsequent

year(1 s ) t −τ divided by the NTR in the base year (1 – τt).5 To avoid endogeneity between the tax

rate and income, an instrument is included for the actual log change in the NTR. The coefficient

on that variable, ξ, represents the ETI. In addition the analyses include year fixed-effects plus

demographic information (X), including age, gender, and marital and itemization status.

Functions of income in the base year and the year prior (f(incomet, incomet−1)) are included in

order to control for two of the most vexing obstacles to identification, mean reversion and nontax-related divergence in the income distribution.

Finally, in examinations of year-to-year responses, the explanatory variables include both a

1-year lag and a 1-year lead in the log change in the NTR, in addition to the log change itself.

The lag is intended to account for income shifting resulting from a change in tax rates in the

previous year; such shifting could affect base-year income and, if not accounted for, could bias

elasticities estimates associated with the change in the NTR from the base to subsequent year.6

Analogously, the lead is intended to account for income shifting between the later year of each

paired observation and the year after (recall that in the 1990s, marginal tax rates increased for

some taxpayers in both 1993 and 1994).

4 For simplicity, the equation omits subscripts denoting the individual.

5 In addition, Gruber and Saez (2002) include a variable to separate the income effect from the substitution effect.

They conclude that the income effect is not important and thus exclude it from most of their analysis.

6 This issue should not be a problem with the end-year approach because the two years chosen are either well before

or well after the tax changes. It could however be an issue when examining 3-year differences.
8

The lag is potentially important if the NTR falls from the year prior to the base, as

individuals may shift income from the base year to the preceding year, making base-year income

smaller than otherwise. If rates also change from the base to the subsequent year, this shifting

could overstate the tax response.7

Likewise, the leading rate is potentially important if the NTR falls between the year

subsequent to the base and the following year, inducing individuals to shift income from the year

following the subsequent year to the subsequent year, making income in the subsequent year

larger than otherwise. Additionally, if rates do not change between the base and subsequent year,

exclusion of the leading and lagged rate changes could bias the counterfactual income trend,

which could in turn bias ETI estimates.

Two different income measures are examined. The first measure is gross income, where

gross income = total income – adjustments8 – capital gains – supplemental (Schedule E)

income or loss + dividends excluded from AGI + unemployment compensation not

included in AGI + Keogh and traditional IRA contributions + forfeited interest penalties

+ alimony paid.

The second income measure is taxable income, which equals gross income less exemptions

and the greater of the standard or itemized deductions. As with most of the studies in this

literature, capital gains are excluded from the analysis because they are observed only when they

are realized, not when they accrue. Social Security benefits are excluded because they are not

fully observed in all years.

7 Here and in the following paragraph income shifting is discussed with respect to a falling NTR. The analysis is the

same for an increasing NTR, except that income would be moving (i.e., shifting) in the opposite direction.

8 Adjustments (e.g., certain education expenses, student loan interest, and contributions to traditional IRAs) are

subtracted from total income to calculate AGI.
9

Income measures are defined according to 1990 law and adjusted by growth in gross income,

with 1992 as the point of reference.9 Over time, both tax rates and the definition of taxable

income itself change—for example, deductions and exemptions permitted in some years are not

allowed in others; the definition of income can affect responses to changes in tax rates (Slemrod

and Kopczuk 2002). Additionally, Heim (2007) shows that changes to allowable exclusions and

deductions can bias estimates, even when using a constant law definition of taxable income,

unless the cross-price elasticities between activities whose tax status has changed and those for

which it has not are zero or are known and taken into account.

The interval over which behavior is measured could have implications for the size of

responses. The year-to-year analysis is likely to capture transitory behavior, in addition to the

beginnings of a longer-term shift in behavior. Some analysts have found very large short-term

responses.10 Examining behavior over 3-year intervals is intended to capture longer-term (or

permanent) responses. In practice, however, shifting as a result of tax rate changes in years

adjacent to the years used in differencing could bias this estimate. The end-year approach is

intended to focus exclusively on permanent responses, avoiding potential biases resulting from

shifting between years adjacent to the two years used in creating each paired observation. That

is, the years used for the end-year analysis are chosen so that they are more than a year prior to

the tax change takes effect and more than a year after it is fully phased in. However, the use of

end years excludes some potentially valuable sources of variation. For example, data on income

changes for other pairs of years (in which tax rates did not change) may be helpful in

9 The adjustment for gross-income growth is analogous to adjustments that transform nominal dollars into real

dollars. Thus, for this paper, each individual's reported income is multiplied by the ratio of average gross income in

1990 over the average gross income in the year of the observation.

10 With respect to the 1990s, see Sammartino and Weiner (1997) and Goolsbee (2000).
10

constructing counterfactual income trends (i.e., absent a tax change), which is necessary for

identifying the true tax response.

The alternative controls11 for mean reversion and heterogeneous income trends across the

income distribution are a major focus of the following discussion. In addition to a specification

with no income controls, six alternatives are explored where f(incomet, incomet−1) in equation (1)

represents the different control variables shown in Table 2. Existing evidence supports both the

presence of both heterogeneous income trends and mean reversion. It also suggests that these

phenomena are large and, if not accounted for, could overwhelm tax responses.

Alternatives A and B include controls for either (A) income in the base year or (B) income in

the year before the base and the change in income from the year preceding the base. Alternative

B has the advantage over A because it includes separate controls for mean reversion and for

divergence in the income distribution. However, both alternatives are likely insufficient because

they allow only for a linear relationship between nontax factors and income growth. The

Congressional Budget Office (2001), Piketty and Saez (2003), and others show heterogeneous

rates of income growth across the income distribution during the past few decades (including the

1990s). Growth rates are much greater (and more volatile) at the very top of the income

distribution and do not increase linearly with income. This peculiarity in the evolution of the

income distribution has greatly reduced the efficacy of some otherwise sound econometric

techniques (such as differences-in-differences). Diverging income trends suggest that income

growth for a group not experiencing a tax change may be a poor counterfactual for another group

that is experiencing a tax change. And the jaggedness of these diverging trends suggests that an

11 Alternatives A and C are the same as those used by Gruber and Saez (2002); Kopczuk (2005) used alternatives B

and D through F. Both studies focused on the 1980s.
11

assumption that a group facing a tax change would have experienced income growth similar to

what they experienced in years when taxes did not change may also be specious.

In the 1990s, when the NTR was generally falling, imposing a linear control for income

growth due to nontax factors (i.e., a nonlinear phenomena) would likely attribute too little of the

income growth at the top of the distribution to nontax factors. Because those at the top of the

distribution are a driving force behind the overall response, linear controls, by overestimating the

counterfactual income trend at the top, likely underestimate the effect of rising marginal tax rates

on taxable income.

Alternatives C through F will likely do a better job because they include at least one

nonlinear component (i.e., a 10-piece spline) that allows for non-tax-related income changes that

vary by income decile. Alternative F has the greatest likelihood of adequately controlling for the

nontax effects because it includes separate and nonlinear controls for both mean reversion and

divergence in the income distribution. It is unlikely that just one variable could adequately

account for these two phenomena (see Kopczuk 2005).

The richest specification (alternative F) for the year-to-year approach can be written such

that

spline( ) ln( ) spline ln ,

1

1 ln

1

1 ln

1

1 ln ln

1

2 1 3

1

1

2

2

1

1

1

0

1

β β γ ε

β

τ

τ ξ

τ

τ ξ

τ

τ

α ξ

+ + 































+ +

+















−

− +















−

− +















−

− = + 















−

−

+

+

−

+ +

X

income

income income

year income

income

t

t

t

t

t

t

t

t

t

t

t

(2)

where ξ1 and ξ2 represent the coefficients for the lagged and lead changes in the NTR,

respectively. For analyses of behavior over the other two intervals, the lead and lag coefficients

are excluded and the full specification can be written such that
12

( )

spline ln .

spline ln( ) 1

1

ln ln

1

3

1 2 1

β γ ε

β β

τ

τ

α ξ

+ + 































+

+ + 















−

− = + 















−

−

X

income

income

year income

income

income

t

t

t

t

t

t

t

s s

(3)

For the end-year approach, lead and lagged rate changes are likely unimportant because the

two years are chosen such that rates generally are not changing in adjacent years. But for

examinations of behavior over 3-year intervals, the lead and lagged tax rates could be important

for both the base year and the subsequent year. However, including these covariates would

require a new sample that included only filers that appear in all of these adjacent years.

In addition to these controls, each specification is estimated after imposing income floors of

$10,000, $30,000, and $50,000 on the base year of each paired observation (imposing the floor

on both the base and subsequent year could introduce bias, since some near the threshold would

be included in the sample if their income rose but excluded if it fell). The restrictions are

imposed to test whether the other variables adequately control for mean reversion at the bottom

of the income distribution. Because the tax changes target upper-income filers, these floors are

unlikely to exclude those experiencing a federal tax change, but they will alter the sample of

filers used to identify counterfactual behavior (absent a tax change).12 Mean reversion is

especially pronounced at the tails of the distribution. People at the high end of the income

distribution are often not there for extended periods and will probably have a substantial drop in

income that is unrelated to tax policy. At the other extreme, students often have a large increase

in income when they enter the workforce. Estimating the ETI without fully controlling for mean

reversion will result in a spurious correlation between non-tax-related increases (by people below

12 The income cutoffs are based on gross income in 1992 dollars. The $10,000 cutoff is similar to the restriction

imposed by Gruber and Saez (2002), the $30,000 cutoff is similar to that used by Auten and Carroll (1999), and the

$50,000 cutoff is similar to that used by Carroll (1998).
13

their lifetime path) and decreases (by those above their lifetime path) in taxable income as

responses to changes in tax rates.

Tax Rate Imputations and Instruments

Individual marginal tax rates are imputed using the CBO’s internal tax calculators. Only federal

rates are imputed for the year-to-year sample; for the other two samples, both federal and state

rates are imputed.13 For the year-to-year sample, an instrument for the NTR is created by

applying the tax schedule in each year to average income for years 1989 to 1995. For the other

two samples, the tax rate instrument is constructed by inflating base-year income by the growth

in mean gross income over the (either 3- or 6-year) interval between the base and subsequent

year. Next, the tax calculator computes counterfactual tax rates based on the inflated income

measure.

For the year-to-year sample, the mean federal marginal tax rate is 24.1 percent, for the

sample focused on 3-year intervals the rate is 23.6 percent, and when including state rates the

mean is 28 percent. For the end-year sample, the corresponding rates are 24.6 percent for federal

taxes and 29.1 percent overall.

Income Weighting

Income weighting places much more emphasis on responses at the top of the income distribution

and is designed to yield results that are indicative of the overall income response (and tax

revenue implications) resulting from a change in tax rates. If responses do not vary by income,

then weighting will not affect ETI estimates. However, research consistently finds that estimated

13 For information on CBO’s state tax calculator, see Bakija (2006).
14

ETIs rise with income14; thus a single overall elasticity is not applicable when considering the

impact of rate changes that target only part of the income distribution or for rate changes that

differ across the distribution. In addition, a meaningful average overall ETI must take into

account the correlation between income and elasticities.

Sample Weighting

While some of the regressions are weighted by income, all are weighted to adjust for the SOI’s

nonrandom sampling properties. Selection into the SOI is conditional on several factors,

including income. Sampling probabilities reach 100 percent for very high income filers. In

addition, filers sampled once are sampled in all subsequent years if their income increases (and

other characteristics, such as filing status, do not change). In fact, the probability that a filer is

observed in two different years is simply the minimum of the sampling probabilities for the two

years. Without weighting, the sampling strategy raises the potential for spurious correlation

between the dependent variable (ln( / )) t t income income s and the independent variables, including

the tax variable. To avoid that possibility, (paired) observations from the full SOI are weighted

by the reciprocal of their probability of appearing in the sample. That strategy is discussed in

Auten and Carroll (1999), who also employ the strategy using SOI data.15

IV. Results

14 People with higher incomes generally have more opportunities to respond to tax changes (see Saez 2004). They

generally itemize their tax returns, rely less on wage and salary income, and have more control over the timing and

sources of their income than do other groups. People with more modest incomes can change their labor supply or

alter the degree to which they use certain deductions and exemptions, but likely have relatively few alternatives to

alter their taxable income.

15 Income-weighted results are produced by simply multiplying income by the weights used to adjust for the SOI’s

nonrandom properties.
15

Table 3 presents income-weighted ETI estimates and standard errors for each of the

specifications without allowing for income shifting between years adjacent to the years used to

construct each paired observation. Using the richest set of income controls (i.e., specification F,

which includes two 10-piece splines) and imposing a $50,000 income cutoff yields incomeweighted estimated ETIs ranging from 0.33 (measuring responses over 3-year intervals) to 0.19

(measuring year-to-year responses). The corresponding estimate for the end-year approach is

0.34, although that estimate is not statistically different from 0. A comparison of estimates over

1- and 3-year intervals suggests that the longer-term responses to the 1990s tax increases were

substantially larger than transitory responses.16 Additionally and for comparison, Panel 4 of

Table 3 presents estimates using years 1985 and 1989, the same years used by Auten and Carroll

(1999).

Table 4 is constructed in the same manner as Table 3, but estimates are based on

specifications that included adjacent-year rate changes. Tables 5 and 6 are analogous to Tables 3

and 4, except that the dependent variable is based on differences in gross income rather than

taxable income. Those tables present only estimated coefficients (i.e., elasticities) and standard

errors for the key dependent variable.

Results from Year-to-Year Differencing

Income-weighted estimates are smaller when using year-to-year differences as opposed to the

other intervals examined. Panel 1 of Table 3 reports estimates for 1-year differencing. With the

richest set of controls (specification F), the estimated ETIs increase with the income cutoff from

0 to 0.19 (also see Table 4). (Although not shown, raising the income cutoff to $75,000 also

16 This finding contrasts with the findings of Sammartino and Weiner (1997) and Goolsbee (2000) who, also for the
16

leaves the estimated ETI at about 0.2.) With the $50,000 income cutoff, the estimated ETI is

−0.18 when employing the Gruber and Saez preferred set of controls. However, the four

specifications that include separate controls for mean reversion and divergence in the income

distribution all yield estimated ETIs of about 0.19.

Table 4 presents estimates for differencing based on 1- and 3-year intervals and, in addition

to the log change in the NTR, with a 1-year lag and 1-year lead in this log change. The estimated

coefficients on the lagged rate change (when including the richest set of income controls) range

from 0.30 to 0.43. By comparison, including the lagged and lead rates with the controls favored

by Gruber and Saez (i.e., specification C) results in estimated ETIs that are modestly negative

and not statistically different from 0. Note that the estimated coefficients on the lagged and lead

change in tax rates are not part of the elasticity estimate because they are not part of the

concurrent change in tax rates. These variables are included solely because these factors could

influence base- or subsequent-year income, and in turn the dependent variable. Because the years

for the lagged and leading tax changes are not endogenous, they are included without

instruments. Income shifting due to the actual lagged and lead changes in tax rates should be

taken into account, even if the change in the lagged or lead rate is due to changes in behavior and

not to a change in statute. In addition to their effect on the estimated ETIs, the estimates on the

lagged and lead NTR coefficients (sometimes in excess of 1) suggest that these variables are

important. Note that, if the lag and lead were instrumented to contain only variation resulting

from changes in statute, the estimated coefficients should be negative (or zero), since a higher

NTR in an adjacent period should induce filers to shift income from the current period to the

adjacent. However, without instruments, the predicted sign on these coefficients is ambiguous,

1990s tax changes, find evidence of large transitory shifting.
17

since in response to a legislated drop in the NTR a filer could work less, falling into a lower

actual tax bracket.

With a $50,000 income cutoff, estimates from the four specifications that include separate

controls for mean reversion (specifications B, D, E, and F from Table 4 Panel 1) are very similar,

ranging from 0.38 to 0.44. These estimates, when including both sets of income controls, are

within the 0.38–0.56 range reported by Carroll (1998) (also using year-to-year differences for the

same time period). However, Carroll does not weight estimates by income or control for

adjacent-year rate changes, and his estimates are larger than my person-weighted estimates (see

Appendix Table A1).17

Turning to gross income, estimated elasticities are smaller with the richest set of controls,

ranging from 0.14 to 0.17, depending on the income cutoff and the use (or not) of adjacent-year

controls (see Tables 5 and 6). Without the adjacent-year controls, estimates are small and not

statistically different from 0. The fact that the estimates are smaller than the corresponding

estimates for taxable income likely reflects the fact that gross income is a broader measure and

thus there are fewer opportunities to shift income outside this base. Additionally, the

denominator for the gross income elasticity is larger. Thus, for an equivalent income response,

the elasticity will be smaller for gross income than for taxable income. In examinations of

behavior over 1-year intervals, Heim (2007) and Carroll (1998) also find somewhat smaller

estimated elasticities when looking at broader income measures.

Results from Differencing by 3-Year Intervals

17 Carroll (1998) does not include any nonlinear income controls, but does include industry and occupation

dummies.
18

With the richest set of income controls, estimated ETIs resulting from 3-year differencing are

about 0.33 and the income cutoff has virtually no effect on the estimate (see Table 3 Panel 2,

specification F). For most of the other specifications, ETI estimates rise with the income cutoff.

Including a spline of the log of income in (t – 1) and the difference in the logs of base-year

income and the income in (t – 1) yields similar results, with ETI estimates ranging from 0.34 to

0.38. For the other specifications, estimates are much more sensitive to income cutoffs. Gruber

and Saez’s preferred specification (C) yields estimates from 0.30 with a $10,000 income cutoff

to 0.54 with a $50,000 income cutoff.

My estimates, when including both sets of nonlinear income controls, are larger than

corresponding estimates, ranging from 0.19 to 0.26 (Giertz 2007), and smaller than the estimates

of 0.53 to 0.58 reported by Heim (2007).18 Those other estimates are also weighted by income,

based on 1990s tax data and on responses over 3-year intervals.19

As with his year-to-year analysis, Heim’s primary nonlinear income control is based on

average income. When subject to the same income controls used in this analysis (i.e., 10-piece

splines of both lagged income and the difference between base-year and lagged income), Heim’s

estimated ETIs are negative and not statistically significant. And after dropping years 1987 and

1988, his estimated ETIs of 0.53 and 0.58 jump to 1.37 and 1.58, respectively.

Table 4 Panel 2 presents estimates based on 3-year differences that, in addition to the log

change in the NTR, include a 1-year lag and 1-year lead in this log change. When including the

18Heim’s estimates, when examining behavior over 3-year intervals, are slightly larger than his corresponding

estimates when using a year-to-year analysis. By contrast, this paper reports substantially larger responses with a

year-to-year analysis (as opposed to analyzing behavior over 3-year intervals).

19 Similar analyses in Gruber and Saez (2002), Kopczuk (2005), and Giertz (2007) suggest an overall incomeweighted ETI of around 0.40 for the 1980s, but these estimates are often quite sensitive to a number of factors.

When taking into account the broadening of the tax base in the 1980s, Kopczuk reports an estimated ETI of about

0.30. And in Giertz (2007), when including both sets of nonlinear income controls, I reported an income-weighted

estimated ETI of 0.35 for the 1980s and 1990s combined.
19

adjacent-year controls, the estimated elasticities (with the richest set of income controls) are now

much larger, ranging from 1.37 to 0.98—and falling with the income cutoff. For the other three

specifications that include separate controls for mean reversion and divergence in the income

distribution (i.e., specifications B, D, and E), estimated ETIs range from 0.41 to 1.42. By

comparison, including the lagged and lead rates with the controls favored by Gruber and Saez

(specification C) results in estimated ETIs that increase with the income cutoff from 0.47 to 0.73.

Heim’s ETI estimates, when controlling for changes in tax rates in years adjacent to each base

year, are even larger than mine, ranging from 1.35 to 1.47.

Elasticities estimated with no income controls are substantially larger than those estimated

using both sets of nonlinear controls (see the first column of estimates in Table 3 Panel 2). The

much larger estimates without income controls suggest that mean reversion at the top of the

income distribution dominates the secular increase in income, also at the top.20 In a period such

as the early 1990s, falling incomes (due to mean reversion) at the top of the income distribution

are directly but spuriously correlated with an also falling NTR. Without income controls, at least

a portion of that spurious correlation will be reflected in the estimated ETI. By contrast, in a

period when the NTR is rising, such as the 1980s, that spurious correlation should bias estimates

downward because the falling incomes at the top are inversely correlated with the rise in the

NTR. In fact, this is exactly what I report when comparing estimates (over 3-year intervals) for

the 1980s with those for the 1990s (Giertz 2007).

Turning to gross income, estimated elasticities are, in contrast to the analysis based on yearto-year differences, larger than corresponding estimates for taxable income (see Table 5 Panel 2).

Gross income elasticities, when including both sets of nonlinear income controls, rise with the
20

income cutoff from 0.19 to 0.30. By comparison, Heim’s preferred estimate, using a broader

measure of income (and examining responses over 3-year intervals), is about 0.46, whereas my

preferred estimate for the 1990s is 0.13 (Giertz 2007). Again, when including adjacent year

controls, gross income elasticities are much larger.

Results from Comparing End Years

Aside from the robustness of the estimates, do the estimates capture longer-term behavioral

responses, as opposed to shorter-term income shifting? As noted earlier, comparing adjacent

years may yield estimates that reflect transitory responses more than they do fundamental shifts

in behavior, and these two can be very different. For example, Goolsbee (2000), examining the

behavior of high-paid executives, finds very large transitory responses to the Omnibus Budget

Reconciliation Act of 1993 (OBRA 1993) but only modest longer-term responses. One way to

focus exclusively on longer-term responses is to compare behavior a couple of years before a tax

change to behavior a couple of years afterward. Auten and Carroll (1999) used that approach to

examine responses to the Tax Reform Act of 1986.

When employing the richest set of controls, the end-year approach, which includes years

1989 and 1995, yields estimated ETIs ranging from 0.34 to 0.47, depending on the income cutoff

(see Table 3 Panel 3, specification F). However, estimates from this approach are rarely

statistically different from 0. (With a $50,000 income cutoff, specification C, preferred by

Gruber and Saez, yields a statistically insignificant ETI estimate of 0.47.) It appears that with just

one set of paired observations, the absence of paired observations for higher income filers over a

similar period when their tax rates did not change may greatly diminish the model’s ability to

20 Note that very few middle-income filers will move to the very top of the income distribution. But incomes for
21

identify counterfactual income trends. Furthermore, the inclusion of nonlinear functions of

income, which are necessary to account for widening inequality at the top of the income

distribution, makes identification all the more difficult since the instrumented tax rate is also a

nonlinear function of income.21

For comparison, the end-year analysis is repeated for TRA 86, using years 1985 and 1989. In

contrast to the estimates for the early 1990s, the 1980s estimates are often statistically

significant. With the most comprehensive set of income controls (specification F), incomeweighted estimates range from 0.39, with a $10,000 income cutoff, to 0.67, with a $50,000

income cutoff (see Table 3 Panel 4). (The other three specifications that include at least one

nonlinear income control yield estimates ranging from 0.41 to 0.97, depending on the income

cutoff.) It is not clear why estimated coefficients for the 1980s show strong statistical

significance whereas the 1990s estimates do not. One possibility is that TRA 86 changed tax

rates for a much larger share of the sample and by differing amounts, thus there is more crosssectional variation in rates for the TRA 86 analysis than for the 1990s.

Income Cutoffs

Because the 1990 and 1993 tax increases targeted upper-income filers, many filers experienced

no statutory change in federal tax rates over period. Lower-income filers serve to identify the

non-tax-related income trend, but only to the extent that these trends are similar across income

groups. Income growth during the period was slower for low-income groups than for higherincome groups. Thus, as the income cutoff for inclusion in the sample increases, the estimated

counterfactual income trend (i.e., the trend absent any changes in tax law) may rise. If that

most of those at the very top of the distribution will eventually fall to more moderate levels (independent of taxes).
22

phenomenon dominates, then raising the income cutoff over a period when tax rates were rising

(i.e., when the NTR was falling), as in the first half of the 1990s, would increase elasticity

estimates (as Carroll found when moving from a $50,000 to $75,000 cutoff). On the other hand,

mean reversion may also be strong for lower-income filers. For the 1990s, the impact of mean

reversion at the bottom of the distribution would have the opposite effect on estimated ETIs,

lowering the estimates.

The analysis presented in this paper shows that, when not controlling for adjacent-year tax

rate changes, estimates for the year-to-year approach are not particularly sensitive to the income

cutoff. When comparing behavior over 3-year intervals, it appears that mean reversion at the

bottom of the distribution tends to bias estimates downward. That is, when differencing over 3-

year intervals, many of the specifications produce larger ETI estimates as the income cutoff is

raised. This is also true of the end-year approach; however, estimates from that approach are

generally not statistically significant. When adding adjacent-year income controls, the pattern is

different: 1-year differencing results in ETI estimates that generally increase with the income

cutoff, while 3-year differencing yields estimated ETIs that often fall as the income cutoff is

raised.

V. Conclusion

This paper presents the results of variations of a differencing methodology applied to panels of

Internal Revenue Service tax return data for the 1990s in order to estimate the responsiveness of

taxable (and gross) income to changes in tax rates. In addition to varying the time interval over

which behavior is measured, sensitivity tests explored different combinations of control variables

as well as alternative weighting strategies and sample selection criteria. While many of the

21 Gross income elasticities too are not statistically different from 0 using the end-year approach.
23

estimates are in line with the wide range found in the recent literature, they are often quite

sensitive to factors such as specification, time period analyzed, and sample income cutoffs.

In general, income-weighted estimates are larger when behavior is measured over 3-year

intervals as opposed to 1-year intervals. This is in contrast to some reports of large transitory

responses to tax changes but smaller longer-term responses. When including the richest set of

income controls, but not allowing for adjacent-year income shifting, income-weighted ETI

estimates based on 1-year differencing range from 0 to 0.19. Similarly estimated elasticities over

3-year intervals are about 0.32 (and not sensitive to income cutoffs). The inclusion of adjacentyear tax rates to control for income shifting between years adjacent to each base and subsequent

year results in much larger estimates. Estimates based on 1-year differencing now range from

0.30 to 0.43, and those for 3-year intervals range from 0.97 to 1.37. However, among the four

specifications that include separate controls for mean reversion and income divergence, estimates

range from 0.41 to 1.37. Estimates from the end-year approach vary in magnitude, but are

generally not statistically different from 0, suggesting that, at least for this period, there is not

enough variation to identify responses with just 2 years of data.

The findings in this paper show that, for the 1990s, the use of separate controls for income

divergence and mean reversion tends to yield more robust estimates. Additionally, when

including the richest set of income controls, estimated ETIs for the 1990s are similar to recent

estimates for the 1980s, although generally much smaller than reported in some of the earlier

studies that examined that period. Other specifications (most of which exclude either separate

controls for mean reversion and divergence in the income distribution or a nonlinear income

control) often yield very different results and are usually much more sensitive to income cutoffs.

The inclusion of a 10-piece spline of logged base-year income as the sole income control, for
24

example, yields estimated ETIs that are substantially negative when measuring behavior over 1-

year intervals.

While more sophisticated control variables sometimes yield more robust estimates, estimates

are still sensitive to reasonable a priori specification decisions. This reflects the inherent

complexity of separating responses to changes in tax rates from the many other factors that also

influence income. Divergence in the income distribution remains one of the most intransigent

obstacles to correctly identifying the ETI. The fact that the divergence in incomes has persisted

through periods of both increases and decreases in the level and progressivity of tax rates

suggests that it is, in large part, not a direct response to tax changes. However, the possibility that

the phenomenon results from a longer-run and more nuanced response to the lowering of

marginal tax rates on top income since World War II cannot be ruled out.22

References

Auten, Gerald and Robert Carroll, “The Effect of Income Taxes on Household Behavior,” Review of

Economics and Statistics, November 1999, 81 (4), 681-693.

Bakija, Jon, “Documentation for a Comprehensive Historical U.S. Federal and State Income Tax

Calculator Program,” economics department working paper, Williams College, April 2006,

www.williams.edu/Economics/papers/bakijaDocumentation_IncTaxCalc.pdf.

Carroll, Robert, “Do Taxpayers Really Respond to Changes in Tax Rates? Evidence from the 1993 Act,”

Office of Tax Analysis Working Paper 78, U.S. Department of Treasury 1998.

Congressional Budget Office, An Analysis of the President’s Budgetary: Proposals for Fiscal Year 2008,

Congressional Budget Office, Washington, D.C., March 2007.

Congressional Budget Office, Effective Federal Tax Rates, 1979-1997, Congressional Budget Office,

Washington, D.C., October 2001.

Giertz, Seth, “A Sensitivity Analysis of the Elasticity of Taxable Income,” Working Paper 2008-01,

Congressional Budget Office, Washington D.C., www.cbo.gov/ftpdocs/89xx/doc8936/2008-01.pdf,

(January 2008).

——, “The Elasticity of Taxable Income over the 1980s and 1990s,” National Tax Journal, 60(4 ),

December 2007: 743-768.

22 See Piketty and Saez (2007) and Saez and Veall (2005).
25

——, “The Elasticity of Taxable Income During the 1990s: A Sensitivity Analysis,” Congressional

Budget Office, Washington D.C., Working Paper 2006-3, February 2006,

www.cbo.gov/doc.cfm?index=7037.

Goolsbee, Austan, “What Happens When You Tax the Rich? Evidence from Executive Compensation,”

Journal of Political Economy 2000, 108 (2), 352-378.

Gruber, Jonathan and Emmanuel Saez, “The Elasticity of Taxable Income: Evidence and Implications,”

Journal of Public Economics, April 2002, 84 (1), 1–32.

Heim, Bradley, “The Elasticity of Taxable Income: Evidence from a New Panel of Tax Returns,” working

paper 2007.

Internal Revenue Service, “Individual Income Tax Returns with Positive Adjusted Gross Income (AGI)”

Unpublished Statistics of Income data, September 2004, www.irs.gov/pub/irs-soi/02in01ts.xls.

Kopczuk, Wojciech, “Tax Bases, Tax Rates and the Elasticity of Reported Income,” Journal of Public

Economics, December 2005, 89 (11-12), 2093-2119.

Moffitt, Robert and Mark Wilhelm, “Taxation and the Labor Supply Decisions of the Affluent,” Does

Atlas Shrug? The Economic Consequences of Taxing the Rich, Joel Slemrod, ed., New York: Harvard

University Press and Russell Sage Foundation 2000.

Navratil, John, “The Tax Reform Act of 1986: New Evidence on Individual Taxpayer Behavior from

Panel Tax Return Data,” In Essays on the Impact of Marginal Tax Rate Reductions on the Reporting

of Taxable Income on Individual Tax Returns, Doctoral Dissertation (Chapter 3), Harvard University

1995.

Piketty, Thomas and Emmanuel Saez, “Income Inequality in the United States, 1913–1998,” Quarterly

Journal of Economics, February 2003, 118 (1), 1–39.

— , “How Progressive is the U.S. Federal Tax System? A Historical and International Perspective,”

Journal of Economic Perspectives, Winter 2007, 21(1), 3-24.

Saez, Emmanuel, “Reported Incomes and Marginal Tax Rates, 1960–2000: Evidence and Policy

Implications,” Tax Policy and the Economy 18, In Poterba, J. (Ed.) 2004, Cambridge: MIT Press,

117-173.

Saez, Emmanuel and Michael Veall, “The Evolution of High Incomes in Northern America: Lessons from

Canadian Evidence,” American Economic Review 95(3) 2005, 831-849.

Sammartino, Frank and David Weiner, “Recent Evidence on Taxpayers' Response to the Rate Increases in

the 1990s,” National Tax Journal, September 1997, 50 (3), 683-705.

Slemrod, Joel and Wojciech Kopczuk, “The Optimal Elasticity of Taxable Income,” Journal of Public

Economics, April 2002, 84 (1), 91–112.
26

Table 1. Summary Statistics

Year-toYear3-year

Intervals

End

Years

Paired Observationsa 99,421 157,083 31,142

Differencing: Years between Base

and Subsequent Observations 136

Returns with Base Year Taxable Income Greater than:

$1,000,000 7,006 26,128 6,013

$5,000,000 1,822 5,775 1,456

Mean Taxable Incomeb $36,566 $34,877 $41,360

Mean Gross Incomeb $51,827 $55,749 $60,047

Mean Federal Tax Rate 24.1 23.6 24.6

Mean State Tax Rate 4.8 4.4 4.5

Mean Net-of-Tax Rate 71.1 72.0 70.9

Source: Calculations based on Statistics of Income data from 1989 to 1995.

a. Sample sizes are based on $30,000 income cutoff, but do not include the full set

of restrictions used for the regression analysis. The year-to-year sample excludes

filers who are not observed every year.

b. Incomes are expressed in 1992 dollars, adjusted by the growth in gross income.

Table 2. Alternative Sets of Control Variables

A The log of base-year income ln( )t income

B The log of income in the year before the base year

and the difference in logs between base-year income

and that of the year prior

















−

−

1

1 ln( ) and ln

t

t

t income

income

income

C A 10-piece spline of the log of base-year income 10 - piece spline of ln( )t income

D A 10-piece spline of the log of income in the year

before the base year and the difference in logs

between base-year income and that of the year prior

















−

−

1

1 10 - piece spline of ln( ) and ln

t

t

t income

income

income

E The log of income in the year before the base year

and a 10-piece spline of the difference in logs

between base-year income and that of the year prior

10 - piece spline of ln and ln( )1

1

−

−















 t

t

t income

income

income

F A 10-piece spline of the log of income in the year

before the base year and a 10-piece spline of the

difference in logs between base-year income and that

of the year prior

















−

−

1

1 10 - piece splines of both ln( ) and ln

t

t

t income

income

income
27

Table 3. Income-Weighted ETI Estimates without Adjacent-Year MTRs: 1989-95

Income

Cutoff none A B C DEF

year-to-year

Panel 1 $10k -0.014 -0.342 -0.026 -0.141 0.007 -0.023 0.000

(0.079) (0.081) (0.073) (0.076) (0.075) (0.074) (0.075)

$30k 0.114 -0.241 0.127 -0.106 0.152 0.130 0.145

(0.067) (0.065) (0.073) (0.061) (0.075) (0.073) (0.075)

$50k 0.204 -0.255 0.186 -0.177 0.194 0.188 0.188

(0.081) (0.076) (0.089) (0.075) (0.091) (0.089) (0.091)

3-year intervals

Panel 2 $10k 1.409 -0.025 -0.015 0.3 0.36 -0.052 0.314

(0.130) (0.097) (0.103) (0.131) (0.125) (0.102) (0.123)

$30k 1.506 0.136 0.13 0.415 0.377 0.079 0.319

(0.138) (0.113) (0.119) (0.153) (0.137) (0.117) (0.136)

$50k 1.574 0.206 0.22 0.543 0.344 0.196 0.328

(0.144) (0.152) (0.159) (0.182) (0.165) (0.154) (0.163)

end years 1989 to 1995

Panel 3 $10k 1.803 -0.059 -0.063 0.424 0.451 -0.037 0.436

(0.278) (0.167) (0.177) (0.264) (0.255) (0.179) (0.253)

$30k 1.818 0.147 0.143 0.468 0.491 0.143 0.474

(0.292) (0.191) (0.202) (0.306) (0.261) (0.203) (0.258)

$50k 1.783 0.2 0.172 0.474 0.342 0.164 0.342

(0.292) (0.266) (0.261) (0.340) (0.289) (0.259) (0.288)

end years 1985 to 1989

Panel 4 $10k -0.166 0.992 0.34 0.966 0.406 0.885 0.387

(0.093) (0.153) (0.180) (0.162) (0.166) (0.164) (0.165)

$30k -0.032 0.775 0.35 0.777 0.422 0.763 0.431

(0.100) (0.170) (0.190) (0.177) (0.177) (0.178) (0.173)

$50k -0.029 0.63 0.376 0.69 0.684 0.734 0.665

(0.115) (0.223) (0.235) (0.211) (0.231) (0.210) (0.219)

Source: Estimates are based on Statistics of Income data for years 1989 to 1995.

Estimates are from 2SLS regressions. Regressions are weighted by the inverse of sampling probabilities and by income (see

Section III). Robust standard errors, clustered by tax filer, are in parentheses.
28

Table 4. Income-Weighted ETI Estimates with Adjacent-Year MTRs: 1989-95

Income

Cutoff none A B C DEF

year-to-year

Panel 1 $10k 0.367 -0.222 0.200 -0.109 0.314 0.200 0.299

(0.079) (0.109) (0.087) (0.122) (0.095) (0.087) (0.094)

$30k 0.570 -0.059 0.342 0.030 0.433 0.342 0.418

(0.077) (0.094) (0.087) (0.099) (0.094) (0.087) (0.094)

$50k 0.668 -0.081 0.378 -0.036 0.436 0.378 0.425

(0.090) (0.108) (0.105) (0.111) (0.112) (0.105) (0.112)

3-year intervals

Panel 2 $10k 1.867 0.466 0.466 1.221 1.422 0.410 1.371

(0.141) (0.189) (0.184) (0.249) (0.255) (0.188) (0.249)

$30k 1.891 0.777 0.707 1.315 1.352 0.633 1.286

(0.146) (0.243) (0.227) (0.277) (0.278) (0.226) (0.270)

$50k 1.783 0.737 0.728 1.106 0.993 0.682 0.975

(0.151) (0.357) (0.320) (0.312) (0.317) (0.313) (0.304)

Source: Estimates are based on Statistics of Income data for years 1989 to 1995.

Estimates are from 2SLS regressions. Regressions are weighted by the inverse of sampling probabilities and by income (see

Section III). Robust standard errors, clustered by tax filer, are in parentheses.
29

Table 5. Income-Weighted Gross Income Elasticity Estimates without Adjacent-Year MTRs: 1989-95

Income

Cutoff none A BC D E F

year-to-year

Panel 1 $10k -0.011 -0.166 -0.071 -0.102 -0.019 -0.079 -0.022

(0.058) (0.058) (0.059) (0.057) (0.060) (0.059) (0.060)

$30k 0.013 -0.134 0.034 -0.107 0.062 0.026 0.056

(0.044) (0.044) (0.056) (0.043) (0.057) (0.056) (0.057)

$50k 0.067 -0.146 0.055 -0.127 0.073 0.044 0.063

(0.053) (0.056) (0.070) (0.057) (0.071) (0.070) (0.071)

3-year intervals

Panel 2 $10k 1.035 0.13 0.105 0.171 0.216 0.072 0.189

(0.086) (0.063) (0.066) (0.068) (0.068) (0.065) (0.068)

$30k 1.293 0.213 0.214 0.291 0.287 0.188 0.256

(0.111) (0.090) (0.095) (0.105) (0.101) (0.093) (0.100)

$50k 1.376 0.259 0.238 0.392 0.278 0.257 0.295

(0.119) (0.121) (0.124) (0.128) (0.123) (0.122) (0.123)

end years 1989 to 1995

Panel 3 $10k 1.254 0.285 -0.001 0.171 0.142 -0.02 0.141

(0.165) (0.115) (0.102) (0.134) (0.125) (0.101) (0.123)

$30k 1.456 0.267 0.121 0.355 0.223 0.108 0.225

(0.198) (0.130) (0.142) (0.215) (0.177) (0.142) (0.174)

$50k 1.494 0.278 0.265 0.55 0.324 0.306 0.356

(0.202) (0.178) (0.200) (0.260) (0.218) (0.197) (0.217)

end years 1985 to 1989

Panel 4 $10k -0.119 0.253 0.063 0.419 0.257 0.434 0.257

(0.069) (0.111) (0.155) (0.155) (0.148) (0.155) (0.147)

$30k 0.01 0.179 0.082 0.382 0.288 0.39 0.279

(0.082) (0.165) (0.171) (0.175) (0.171) (0.174) (0.167)

$50k 0.045 0.086 0.13 0.443 0.398 0.437 0.384

(0.104) (0.281) (0.227) (0.227) (0.237) (0.224) (0.229)

Source: Estimates are based on Statistics of Income data for years 1989 to 1995.

Estimates are from 2SLS regressions. Regressions are weighted by the inverse of sampling probabilities and by income

(see Section III). Robust standard errors, clustered by tax filer, are in parentheses.
30

Table 6. Income-Weighted Gross Income Elasticity Estimates with Adjacent-Year MTRs: 1989-95

Income

Cutoff none A BC D E F

year-to-year

Panel 1 $10k 0.222 -0.204 0.048 -0.108 0.144 0.040 0.141

(0.058) (0.074) (0.070) (0.080) (0.075) (0.070) (0.074)

$30k 0.326 -0.075 0.146 -0.035 0.201 0.135 0.193

(0.058) (0.071) (0.068) (0.074) (0.072) (0.067) (0.071)

$50k 0.387 -0.102 0.151 -0.079 0.187 0.137 0.174

(0.068) (0.082) (0.083) (0.086) (0.086) (0.082) (0.086)

3-year intervals

Panel 2 $10k 1.741 0.453 0.869 1.765 1.478 0.822 1.433

(0.138) (0.176) (0.126) (0.277) (0.162) (0.126) (0.157)

$30k 1.762 0.787 1.13 1.9 1.66 1.093 1.614

(0.143) (0.226) (0.188) (0.318) (0.241) (0.183) (0.233)

$50k 1.656 0.813 1.193 1.836 1.481 1.217 1.515

(0.148) (0.334) (0.262) (0.371) (0.291) (0.253) (0.281)

Source: Estimates are based on Statistics of Income data for years 1989 to 1995.

Estimates are from 2SLS regressions. Regressions are weighted by the inverse of sampling probabilities and by income

(see Section III). Robust standard errors, clustered by tax filer, are in parentheses.
31

Table 7. Income-Weighted ETI Estimates without Adjacent-Year MTRs

Income-Weighted ETI Estimates: 1989 to 1995

Interval Length 1-Year 3-Year 6-Year

EF E FEF

ln((1 - mtrt+s)/(1 - mtrt)) 0.682 0.975 0.196 0.328 0.164 0.342

(0.313) (0.304) (0.154) (0.163) (0.259) (0.288)

ln((1 - mtrt)/(1 - mtrt-1)) -0.495 -0.703

(0.125) (0.136)

ln((1 - mtrt+2)/(1 - mtrt+1)) 0.177 0.252

(0.107) (0.098)

ln(incomet-1)) -0.033 -0.057 -0.146

(0.019) (0.009) (0.026)

Single -0.020 -0.014 -0.035 -0.033 0.091 0.103

(0.045) (0.042) (0.040) (0.038) (0.109) (0.109)

Joint Return 0.034 0.029 0.03 0.023 0.265 0.261

(0.043) (0.040) (0.038) (0.035) (0.104) (0.103)

Head of Household

Age 0.122 0.120 0.093 0.095 0.203 0.195

(0.012) (0.013) (0.011) (0.011) (0.037) (0.037)

Age Squared/10 -0.026 -0.025 -0.02 -0.02 -0.043 -0.042

(0.002) (0.002) (0.002) (0.002) (0.008) (0.008)

Age Cubed/100 0.016 0.016 0.012 0.013 0.027 0.026

(0.002) (0.002) (0.001) (0.001) (0.005) (0.005)

Itemizer Dummy -0.125 -0.111 -0.122 -0.116 -0.168 -0.164

(0.015) (0.015) (0.013) (0.013) (0.028) (0.029)

ln(income t-1)*decile 1 -0.386 -0.410 -0.481 -0.53

(0.063) (0.068) (0.151) (0.225)

ln(income t-1)*decile 2 -0.332 -0.270 -0.731 -0.599

(0.111) (0.112) (0.211) (0.244)

ln(income t-1)*decile 3 -0.102 -0.018 -0.341 -0.652

(0.158) (0.161) (0.192) (0.188)

ln(income t-1)*decile 4 0.034 0.108 -0.274 -0.171

(0.250) (0.256) (0.095) (0.193)

ln(income t-1)*decile 5 -0.415 -0.334 -0.142 -0.271

(0.278) (0.284) (0.047) (0.122)

ln(income t-1)*decile 6 0.277 0.199 0.044 -0.015

(0.271) (0.277) (0.033) (0.092)

ln(income t-1)*decile 7 -0.817 -0.894 0.024 -0.087

(0.208) (0.210) (0.030) (0.066)

ln(income t-1)*decile 8 -0.178 -0.316 -0.1 -0.098

(0.159) (0.162) (0.035) (0.077)

ln(income t-1)*decile 9 -0.651 -0.604 -0.018 -0.034

(0.108) (0.117) (0.047) (0.094)

ln(income t-1)*decile 10 -0.432 -0.648 -0.159 -0.245

(0.083) (0.109) (0.033) (0.072)

ln((incomet)/(incomet-1))*decile 1 -0.490 -0.397 -0.407 -0.382 -0.356

(0.176) (0.050) (0.052) (0.148) (0.158)

ln((incomet)/(incomet-1))*decile 2 -0.743 -0.321 -0.269 -0.427 -0.336

(0.237) (0.099) (0.100) (0.201) (0.203)

ln((incomet)/(income t-1))*decile 3 -0.363 -0.096 -0.04 -0.323 -0.236

(0.217) (0.150) (0.153) (0.394) (0.403)

ln((incomet)/(income t-1))*decile 4 -0.460 -0.049 0.017 -0.268 -0.033

(0.116) (0.219) (0.222) (0.537) (0.544)

ln((incomet)/(income t-1))*decile 5 -0.323 -0.345 -0.294 -0.205 -0.196
32

(0.068) (0.256) (0.260) (0.575) (0.587)

ln((incomet)/(income t-1))*decile 6 0.302 0.352 0.315 -0.662 -0.625

(0.082) (0.241) (0.245) (0.460) (0.469)

ln((incomet)/(income t-1))*decile 7 -0.010 -0.86 -0.918 0.305 0.345

(0.030) (0.182) (0.185) (0.326) (0.330)

ln((incomet)/(income t-1))*decile 8 -0.007 -0.207 -0.293 -0.644 -0.609

(0.042) (0.136) (0.140) (0.242) (0.262)

ln((incomet)/(income t-1))*decile 9 -0.096 -0.609 -0.584 -0.208 -0.339

(0.045) (0.102) (0.117) (0.117) (0.161)

ln((incomet)/(income t-1))*decile 10 -0.135 -0.422 -0.607 -0.260 -0.577

(0.037) (0.064) (0.094) (0.081) (0.232)

Constant -1.480 3.385 -0.784 3.585 -1.568 2.299

(0.332) (1.635) (0.241) (1.389) (0.650) (2.122)

Observations 47,096 47,096 78,778 78,778 15,594 15,594

R-Squared 0.02 0.02 0.06 0.07 0.05 0.06

Source: Estimates based on Statistics of Income data for years 1988 to 1995.

Estimates are from 2SLS regressions. The income range is $50,000 and above. Regressions are weighted by

the inverse of sampling probabilities and by income (see Section III). Robust standard errors, clustered by tax

filer, are in parentheses.
33

Table 8. Income-Weighted ETI Estimates with Adjacent-Year MTRs

Income-Weighted ETI Estimates: 1989 to 1995

Interval Length 1-Year 3-Year

EF E F

ln((1 - mtrt+s)/(1 - mtrt)) 0.378 0.425 0.682 0.975

(0.105) (0.112) (0.313) (0.304)

ln((1 - mtrt)/(1 - mtrt-1)) 0.621 0.683 -0.495 -0.703

(0.086) (0.094) (0.125) (0.136)

ln((1 - mtrt+2)/(1 - mtrt+1)) 0.333 0.354 0.177 0.252

(0.107) (0.111) (0.107) (0.098)

ln(incomet-1) -0.029 -0.033

(0.005) (0.019)

Single -0.020 -0.014

(0.045) (0.042)

Joint Return 0.004 0.004 0.034 0.029

(0.009) (0.009) (0.043) (0.040)

Head of Household -0.010 -0.014

(0.024) (0.024)

Age 0.016 0.018 0.122 0.120

(0.009) (0.009) (0.012) (0.013)

Age Squared/10 -0.003 -0.004 -0.026 -0.025

(0.002) (0.002) (0.002) (0.002)

Age Cubed/100 0.000 0.000 0.016 0.016

(0.000) (0.000) (0.002) (0.002)

Itemizer Dummy 0.020 0.021 -0.125 -0.111

(0.009) (0.009) (0.015) (0.015)

ln(income t-1)*decile 1 -0.036 -0.386 -0.410

(0.050) (0.063) (0.068)

ln(income t-1)*decile 2 -0.022 -0.332 -0.270

(0.048) (0.111) (0.112)

ln(income t-1)*decile 3 -0.066 -0.102 -0.018

(0.068) (0.158) (0.161)

ln(income t-1)*decile 4 -0.086 0.034 0.108

(0.085) (0.250) (0.256)

ln(income t-1)*decile 5 0.038 -0.415 -0.334

(0.079) (0.278) (0.284)

ln(income t-1)*decile 6 -0.171 0.277 0.199

(0.041) (0.271) (0.277)

ln(income t-1)*decile 7 -0.042 -0.817 -0.894

(0.022) (0.208) (0.210)

ln(income t-1)*decile 8 -0.037 -0.178 -0.316

(0.012) (0.159) (0.162)

ln(income t-1)*decile 9 0.002 -0.651 -0.604

(0.014) (0.108) (0.117)

ln(income t-1)*decile 10 -0.029 -0.432 -0.648

(0.015) (0.083) (0.109)

ln((incomet)/(incomet-1))*decile 1 -0.148 -0.146 -0.490

(0.043) (0.042) (0.176)

ln((incomet)/(incomet-1))*decile 2 -0.192 -0.183 -0.743

(0.068) (0.068) (0.237)

ln((incomet)/(income t-1))*decile 3 -0.123 -0.120 -0.363

(0.082) (0.083) (0.217)

ln((incomet)/(income t-1))*decile 4 -0.182 -0.165 -0.460

(0.092) (0.093) (0.116)

ln((incomet)/(income t-1))*decile 5 0.060 0.057 -0.323
34

(0.087) (0.088) (0.068)

ln((incomet)/(income t-1))*decile 6 -0.147 -0.157 0.302

(0.065) (0.065) (0.082)

ln((incomet)/(income t-1))*decile 7 -0.080 -0.084 -0.010

(0.052) (0.053) (0.030)

ln((incomet)/(income t-1))*decile 8 -0.106 -0.110 -0.007

(0.043) (0.044) (0.042)

ln((incomet)/(income t-1))*decile 9 -0.096 -0.105 -0.096

(0.032) (0.033) (0.045)

ln((incomet)/(income t-1))*decile 10 0.005 0.003 -0.135

(0.017) (0.019) (0.037)

Constant 0.126 0.196 -1.480 3.385

(0.163) (0.444) (0.332) (1.635)

Observations 44,438 44,438 64,554 64,554

R-Squared 0.02 0.02 0.06 0.07

Source: Estimates based on Statistics of Income data for years 1988 to 1995.

Estimates are from 2SLS regressions. The income range is $50,000 and above. Regressions are weighted by

the inverse of sampling probabilities and by income (see Section III). Robust standard errors, clustered by tax

filer, are in parentheses.
35

Appendix Table A1. Person-Weighted ETI Estimates without Adjacent-Year MTRs: 1989-95

Income

Cutoff none AB C D EF

year-to-year

Panel 1 $10k 0.069 -2.904 -0.982 -0.696 0.113 -0.602 0.065

(0.380) (0.320) (0.314) (0.433) (0.516) (0.319) (0.497)

$30k 0.034 -2.751 -0.843 -1.148 -0.223 -0.543 -0.217

(0.331) (0.277) (0.271) (0.349) (0.410) (0.282) (0.407)

$50k 0.403 -2.085 -0.285 -1.02 0.234 -0.141 0.162

(0.223) (0.264) (0.206) (0.231) (0.279) (0.210) (0.273)

3-year intervals

Panel 2 $10k 0.251 -0.555 -0.46 -0.292 -0.247 -0.309 -0.198

(0.109) (0.098) (0.100) (0.102) (0.105) (0.098) (0.104)

$30k 0.377 -0.262 -0.229 0.012 0.031 -0.172 -0.01

(0.120) (0.106) (0.110) (0.135) (0.129) (0.111) (0.128)

$50k 0.756 -0.15 -0.045 0.181 0.092 -0.003 0.067

(0.127) (0.116) (0.124) (0.143) (0.135) (0.125) (0.134)

end years 1989 to 1995

Panel 3 $10k 1.408 -0.565 -0.857 -0.084 -0.488 -0.634 -0.408

(0.390) (0.154) (0.171) (0.178) (0.197) (0.185) (0.213)

$30k 0.889 -0.241 -0.291 0.084 0.062 -0.146 0.029

(0.260) (0.212) (0.245) (0.293) (0.302) (0.248) (0.301)

$50k 0.953 -0.382 -0.344 -0.024 -0.154 -0.138 -0.112

(0.245) (0.240) (0.284) (0.275) (0.306) (0.282) (0.300)

end years 1985 to 1989

Panel 4 $10k -2.099 1.328 0.318 1.131 0.572 0.753 0.297

(0.109) (0.155) (0.165) (0.180) (0.189) (0.166) (0.175)

$30k -0.34 0.747 0.178 0.728 0.262 0.667 0.314

(0.086) (0.141) (0.148) (0.164) (0.164) (0.160) (0.165)

$50k -0.156 0.822 0.169 0.879 0.717 0.792 0.633

(0.091) (0.181) (0.162) (0.211) (0.204) (0.198) (0.194)

Source: Estimates based on Statistics of Income data for years 1989 to 1995.

Estimates are from 2SLS regressions. Regressions are weighted by the inverse of sampling probabilities and by income

(see Section III). Robust standard errors, clustered by tax filer, are in parentheses.
36

Appendix Table A2. Person-Weighted ETI Estimates with Adjacent-Year MTRs: 1989-95

Income

Cutoff none AB C D EF

year-to-year

Panel 1 $10k 0.375 -0.118 0.182 0.201 0.309 0.214 0.297

(0.105) (0.107) (0.102) (0.102) (0.105) (0.098) (0.102)

$30k 0.458 -0.024 0.255 0.173 0.350 0.278 0.339

(0.087) (0.090) (0.087) (0.085) (0.091) (0.085) (0.089)

$50k 0.477 -0.066 0.254 0.026 0.332 0.290 0.329

(0.096) (0.104) (0.094) (0.102) (0.098) (0.093) (0.097)

3-year intervals

Panel 2 $10k 0.763 -0.646 -0.319 0.234 0.279 0.023 0.468

(0.183) (0.166) (0.171) (0.180) (0.204) (0.172) (0.205)

$30k 1.463 0.264 0.292 1.004 0.955 0.405 0.937

(0.190) (0.194) (0.195) (0.246) (0.267) (0.199) (0.265)

$50k 1.406 0.337 0.453 0.825 0.738 0.522 0.705

(0.169) (0.269) (0.266) (0.251) (0.281) (0.274) (0.279)

end years 1989 to 1995

Panel 3 $10k 1.408 -0.565 -0.857 -0.084 -0.488 -0.634 -0.408

(0.390) (0.154) (0.171) (0.178) (0.197) (0.185) (0.213)

$30k 0.889 -0.241 -0.291 0.084 0.062 -0.146 0.029

(0.260) (0.212) (0.245) (0.293) (0.302) (0.248) (0.301)

$50k 0.953 -0.382 -0.344 -0.024 -0.154 -0.138 -0.112

(0.245) (0.240) (0.284) (0.275) (0.306) (0.282) (0.300)

end years 1985 to 1989

Panel 4 $10k -2.099 1.328 0.318 1.131 0.572 0.753 0.297

(0.109) (0.155) (0.165) (0.180) (0.189) (0.166) (0.175)

$30k -0.34 0.747 0.178 0.728 0.262 0.667 0.314

(0.086) (0.141) (0.148) (0.164) (0.164) (0.160) (0.165)

$50k -0.156 0.822 0.169 0.879 0.717 0.792 0.633

(0.091) (0.181) (0.162) (0.211) (0.204) (0.198) (0.194)

Source: Estimates are based on Statistics of Income data for years 1989 to 1995.

Estimates are from 2SLS regressions. Regressions are weighted by the inverse of sampling probabilities and by income

(see Section III). Robust standard errors, clustered by tax filer, are in parentheses.