Working Paper Series 

Congressional Budget Office 

Washington, D.C. 

A Sensitivity Analysis of 

the Elasticity of Taxable Income 

Seth H. Giertz 

Tax Analysis Division 

Congressional Budget Office 

Washington, D.C. 

Seth.Giertz@cbo.gov 

February 2005 

CBO Working Paper 2005-01 

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

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

series can be obtained at www.cbo.gov/tech.cfm. 
 

A Sensitivity Analysis of the Elasticity of Taxable Income 

Seth H. Giertz 

Abstract

This paper applies the methods of Gruber and Saez (2002) to a panel of tax returns spanning 

1979 through 2001 in order to examine the sensitivity of the elasticities of taxable and broad 

income to an array of factors. The paper finds that that Gruber and Saez’s approach yields an 

estimated elasticity of taxable income (ETI) for the 1990s that is about half the size of this 

paper’s corresponding estimate for the 1980s. In general, the addition of demographic 

information has little impact on elasticity estimates for the 1980s, but lowers the 1990s 

estimates, especially for broad income, which is a more encompassing income measure than is 

taxable income. Finally, the paper finds that weighting regression results by income not only 

has a substantial impact on the estimates, but also results in overall estimates that are 

influenced by a small number of predominately high-income filers. For example, excluding 

100 of the most influential observations (just 0.2 percent of the sample) lowers the estimated 

ETI for the 1980s from 0.37 to 0.11.

The author wishes to thank David Weiner, Ed Harris, Rob McClelland, Bob Williams, Roger 

Hitchner, Bob Dennis, and Emmanuel Saez for comments and for assistance with the data 

construction. 
1

I. Introduction 

The degree to which taxes alter economic activity and tax-reporting behavior is a subject of debate. 

Estimates of the effect range from extremely large to almost none. For even modest changes to tax 

rates, the range of estimates implies differences in deadweight loss and income-tax revenue of many 

tens of billions of dollars. A key variable at the center of recent research is the elasticity of taxable 

income (ETI), which measures the responsiveness of reported taxable income to changes in marginal 

tax rates.1

 The ETI, if accurately estimated, can be used to calculate both the change in deadweight 

loss2 and the change in income-tax revenues resulting from a change in tax rates.3 However, in 

practice, assessing both the efficiency and revenue implications of tax-rate changes is more complex 

than the formulas suggest. For example, if the ETI differs by income, an accurate assessment of either 

efficiency or revenue implications requires a breakdown of the responses by the level of income.4

Despite a great deal of variation in ETI estimates, both across papers and within studies that explore 

different specifications, several recent papers have reported an overall ETI of about 0.40. An oftencited study by Gruber and Saez (2002) examines responses to the tax cuts of 1981 and 1986, and finds 

an overall estimated ETI of 0.40. However, Kopczuk (2003) finds similarly estimated results to be 

quite sensitive to sample selection and model specification. It may also be the case that the results are 

not robust for the period examined or for the addition of a richer set of demographic variables. 

The estimation portion of this paper first replicates Gruber and Saez’s core results by applying their 

techniques to a dataset that is similar to the one that Gruber and Saez used. The paper’s results for the 

 

1

 Specifically, the ETI equals the percentage change in reported taxable income associated with a one-percent increase in 

the net-of-tax rate, where the net-of-tax rate equals one minus the marginal tax rate. 

2

 Feldstein (1999) shows that deadweight loss = –0.5 $ tax_rate2 $ (1 – tax_rate)

-1 $ ETI $ taxable_income. 3

 Income tax revenue equals ETI $ net-of-tax-rate $ taxable_income $ tax_rate. 4

 In addition, when external costs or benefits are present, assessing efficiency implications is also more complex. For 

example, suppose tax rates rise and, in response, taxable income falls, but a portion of that drop in taxable income comes 

from increased charitable contributions (and suppose those charities produce positive externalities). Or suppose that a tax 

increase is used to finance an underprovided public good. In such instances, the standard deadweight loss formula will 

overstate the efficiency cost of an increase in tax rates. 
2

1980s closely parallel Gruber and Saez’s results. Applying the same methodology to 1990s data and to 

data from both the 1980s and 1990s combined, however, yields estimated ETIs that are much smaller 

than corresponding estimates for the 1980s. In fact, using Gruber and Saez’s preferred specification 

yields an estimated ETI for the 1990s that is a little more than half the corresponding estimate for the 

1980s. The addition of demographic information, again using Gruber and Saez’s preferred 

specification, has a negligible effect on the 1980s estimated ETI, but lowers the 1990s estimate by 

about one-quarter, from 0.20 to 0.15. For a more encompassing income measure (broad income), 

added demographics do little to the estimated elasticity for the 1980s, but cut it for the 1990s by half, 

from 0.15 to 0.07. Finally, weighting regression results by income not only has an enormous impact 

on the estimates, but yields overall estimates that are driven by a tiny fraction of high-income filers. 

For example, excluding the 100 most influential observations (just 0.2 percent of the sample), as 

measured by a dfbeta test, lowers the estimated ETI for the 1980s from 0.37 to 0.11. 

II. Issues in the Analysis 

Tax changes take place in a changing economic environment. Changes to that environment affect 

income growth. Controlling for non-tax-induced trends in taxable income is a major obstacle to 

accurately estimating elasticities. The issue of non-tax-related trends in income is given the most 

attention in this section because the approach used to control for those trends represents the most novel 

aspect of the model employed in this study—a model developed by Gruber and Saez (2002). The 

approach also takes into account other factors such as mean reversion, tax-rate endogeneity, 

institutional changes (which often coincide with changes in the rate structure), and differences between 

transitory (or temporary) fluctuations and permanent (or longer-term) responses.5

 

5

 See Giertz (2004). 
3

Controlling for Exogenous Trends in Income

The centerpiece of Gruber and Saez’s approach is its controls for non-tax-related heterogeneous shifts 

in income distribution and mean reversion. Over the past 30 years, the distribution of reported income 

has widened. In fact, that trend accelerated in the 1980s, especially at the top of the distribution.6 

Because people with the highest income pay a disproportionate share of taxes—the top 1 percent pay 

approximately one-third of all federal income taxes—their behavior is especially important.7 Not fully 

accounting for the portion of that income growth that is unrelated to tax policy can result in large 

biases. For example, the 1980s cuts in marginal tax rates were greatest at the top of the income 

distribution and thus inversely correlated with the great income growth at the top of the distribution. If 

the exogenous (non-tax-related) portion of that income growth is not fully accounted for, that trend 

will bias ETI estimates upward. Although changes to the income distribution are widely documented 

and theories such as shifts in the returns to education and the market for superstars help explain the 

phenomenon,8

 the underlying driving factors are not well understood, nor are the year-to-year 

deviations from that trend. The fact that the exogenous-income trend 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. In addition, because the trend has been irregular, distributional 

changes in years without tax changes may not provide useful measures of exogenous shifts that occur 

during periods with tax changes. 

Controlling for Mean Reversion

Mean reversion also complicates estimation. Over a person’s lifetime, income often follows a general 

path, with many fluctuations. After income has been particularly high or low, it will often revert to a 

more normal path. That reversion is especially pronounced at the tails of the distribution. People at 

the high end of the income distribution are often not there for long, and will likely have a substantial 

drop in income that is unrelated to tax policy. At the other extreme, students will often have large 

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

 

6

 According to Piketty and Saez (2003), the share of income reported by the top 10 percent of filers rose by more than a 

third, from 32.9 percent in 1979 to 41.4 percent in 1998; two-thirds of that increase went to the top 1 percent of taxpayers. 

The share of income reported by the top one-half of one percent more than doubled, the share reported by the top one-tenth 

of one percent nearly tripled, and the share reported by the top one-hundredth of one percent more than quadrupled. 

7

 See Internal Revenue Service (2004). 8

 See Rosen (1981).
4

mean reversion will erroneously count non-tax-related increases (by people below their lifetime path) 

and decreases (by those above their lifetime path) in taxable income as responses to changes in tax 

rates. Those factors bias ETI estimates in opposite directions, depending on whether tax rates are 

raised or lowered, but there is no reason to believe the biases will cancel each other out. 

Research into the ETI is also complicated by the fact that the ETI appears to vary with income, rising 

as income increases.9

 If so, a single overall elasticity will not be applicable when considering the 

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

distribution. In addition, a meaningful average overall estimated ETI must take into account the 

correlation between income and the elasticities. The average response of all filers may poorly assess 

how taxable income or tax revenue as a whole will respond. For example, suppose there are two types 

of people, that tax rates are the sole determinant of income, and that between the base and future years 

the net-of-tax rates rise by 10 percent for all filers. Now, suppose that half the population is in the first 

group and that each filer in that group has a base-year taxable income of $10,000 and a future-year 

taxable income of $10,100, while those in the second group have a base-year taxable income of 

$1,000,000 and a future-year taxable income of $1,090,000. In that instance, the low-income filers 

have an ETI of 0.1 and the high-income filers have an ETI of 0.9.10 Under that scenario, the average 

person’s elasticity equals 0.5. But the ETI that accurately reflects the change in overall taxable income 

equals 0.82 because the 0.9 applies to a base that is 100 times as large as the base for the group with 

the ETI of 0.1. 

III. Data and Methods 

This paper uses data from the Statistics of Income’s (SOI) Continuous Work History Survey (CWHS) 

for 1979 through 2001. The basic SOI is a stratified random sample of tax filers, compiled by the 

 

9

 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 source of their 

income than do other groups. People with more modest incomes can alter their labor supply, but may have few other 

alternatives for altering their taxable income.

10 The low-income filers’ ETI is calculated by dividing their one-percent increase in taxable income by the 10-percent 

increase in the net-of-tax rate. The high-income filers’ ETI is calculated by dividing their 9-percent increase in taxable 

income by the 10-percent increase in the net-of-tax rate. 
5

Internal Revenue Service, and includes all information reported on the filers’ tax returns, plus some 

additional demographic information. The CWHS, by contrast, is a subset of filers from the SOI who 

are followed from year to year. Although the CWHS contains detailed and accurate information, it is 

deficient in two important respects. First, although the overall sample is quite large (for some years, 

more than 20,000), relatively few returns come from the top of the income distribution. If high-income 

taxpayers dominate an estimate, that estimate using the CWHS will depend heavily on just a few filers. 

Second, the CWHS includes only people who file returns and are listed as the primary filers. Thus, 

attrition is an issue. 

This paper follows Gruber and Saez (2002) in comparing behavior over three-year intervals, using only 

people who filed tax returns in both the base (or initial) year and the third subsequent year. The overall 

sample includes more than 218,000 paired observations. As with Gruber and Saez, income measures 

are adjusted by the growth in broad income, where broad income equals total income minus realized 

capital gains and Social Security benefits, using 1990 as the base.11 The other income measure, 

taxable income, equals broad income less exemptions and standard and itemized deductions. Both 

measures are based on a 1990 constant-law definition of income. The sample includes only those with 

broad income greater than $10,000 in the base year and positive income in the future year (see Table 

1). Without those restrictions, the sample is nearly twice as large. For the unrestricted sample, mean 

nominal reported taxable incomes range from $10,739 in 1979 to $25,308 in 1998; the corresponding 

means for broad income range from $17,442 to $43,289. Individual marginal tax rates (both state and 

federal) are imputed using the Congressional Budget Office’s internal tax calculators.12

The data just described are very similar to those used by Gruber and Saez, but differ in several 

respects. First, Gruber and Saez use a publicly available version of the CWHS, which is slightly 

modified in order to protect the identity of taxpayers in the sample. Second, Gruber and Saez’s sample 

ends in 1990, whereas this paper’s sample extends to 2001. Third, Gruber and Saez use the National 

 

11 The adjustment for broad-income growth is analogous to adjustments that transform nominal dollars into real dollars. 

Thus, for this paper, each individual's reported income is divided by the ratio of average broad income in 1990 over the 

average broad income in the year of the observation. 12 Jon Bakija of Williams College designed the state tax calculator used by CBO.
6

Bureau of Economic Research’s (NBER) TAXSIM model to impute their federal and state marginal 

tax rates, but this paper’s analysis uses CBO’s internal tax calculators. 

The methodology follows directly from Gruber and Saez (2002) and the model can be written such that 

the 

α ξ + ⋅ β + ⋅ β + ⋅ β + ⋅ β + ε ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

−

− = ⋅ ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ = + + + 1 2 3 4 3 3 ( ) 1

1

ln ln mars year spline income demog

taxrate

taxrate

income

income

income growth rate t

t

t

t

t .

13

The dependent variable is log of income in the future year (incomet+3) divided by income in the base 

year (incomet), where the future year is three years after the base. (The key independent variable 

equals the log of the net-of-tax rate in the future year divided by the net-of-tax rate in the base year.) 

To avoid endogeneity between the tax rate and income, an instrument is used in place of the actual log 

change in the net-of-tax rate.14 The coefficient on that variable, , represents the ETI. Control 

variables include year-fixed effects, dummies for marital status (mars), and a 10-piece spline of the log 

of base-year income. The spline is intended to control for mean reversion and for non-tax-related 

income trends that have differed across the reported income distribution in recent decades. Alternative 

specifications explored by Gruber and Saez and in this paper include a model with the log of base-year 

income in place of the spline and a specification that excludes the income control altogether. (In 

addition, Gruber and Saez 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.) 

The only addition to the model from Gruber and Saez (besides extending the years of data) is the 

addition of richer demographic information (demog), including age, gender, itemization status, and 

state-fixed effects. 

 

13 Note that, for simplicity, subscripts denoting the individual are omitted here. 

14 The instrument is constructed by inflating base-year income by the growth in mean broad income over the three-year 

interval. Next, the tax calculator computes counterfactual tax rates based on the inflated income measure. Finally, twostage least squares (2SLS) is employed, where, in the first stage, the log change in actual income is regressed against the 

counterfactual log change, along with the other independent variables. 
7

The results from Gruber and Saez are weighted by income. Weighting is intended to produce 

estimates reflective of the change in total reported taxable (or broad) income, which relates directly to 

the change in income-tax revenues. If responses were homogeneous throughout the reported income 

distribution, weighting would not affect the results. But, as a number of studies, including Gruber and 

Saez, have found, the ETI varies by income and is generally much larger for highest-income filers. 

Weighting should produce estimates that are more indicative of overall responses, but, at the same 

time, the importance of weighting suggests that the model fit may be poor. In addition, although 

overall sample sizes are quite large, weighting could result in a small number of observations having a 

substantial impact on the overall results. A dfbeta test and re-estimated elasticities after excluding 

handfuls of the most influential observations suggest that results, in fact, depend heavily on just a few 

observations. 

IV. Results 

This section begins by replicating Gruber and Saez’s approach for the 1980s and comparing the results. 

Next, the same methodology is applied to the 1990s and to the full sample, spanning 1979 to 2001. 

After a discussion of those results, demographics are added to the model, the importance of including 

state rates as opposed to using only federal tax rates is examined, and the ramifications of weighting 

regressions by income are explored in detail. 

Replicating Gruber and Saez 

Table 2 compares the results of Gruber and Saez (for broad income and taxable income, respectively) 

for the 1980s with this paper’s comparable estimates. Each pair of the first six columns reports Gruber 

and Saez’s results under these specifications: with no controls for exogenous income trends, with the 
8

log of base-year income as a control, and with a 10-piece spline of log income (Gruber and Saez’s 

most preferred specification). The next six columns report comparable results from this paper’s 

analysis of the same period. Despite using a slightly different core data set and different marginal tax 

rate calculators, the two sets of results are quite similar. Estimated with no control for base-year 

income, the elasticities are negative, which is inconsistent with theoretical predictions. Adding the log 

of base-year income to the model results in an estimated ETI of just above 0.6 and a substantially 

smaller broad-income elasticity of 0.17. Replacing the log of base-year income with the 10-piece 

spline yields an estimated ETI in the neighborhood of 0.4 and a corresponding estimated elasticity of 

broad income of 0.12. The fact that the estimated elasticities for broad income are so much lower than 

the corresponding ETI estimates suggests that a substantial portion of the taxable-income response 

may come via deductions and exemptions. Another contributing factor may be that the denominator 

for the broad-income calculation is larger, by definition; thus, for an identical dollar change, the 

estimated broad-income elasticity will be smaller than the corresponding ETI estimate. Smaller broadincome elasticities are consistent with Kopczuk’s (2003) finding that income responses are a function 

of the tax base and that. the greater the availability of exemptions and deductions, the lower the cost of 

responding to tax changes, and hence the larger the response. 

Results for the 1990s 

The same methodology generates estimated ETIs for the 1990s that are much smaller than those for the 

1980s and not statistically significant, despite a sample size of nearly 140,000 (see Panel 1 of Table 3). 

Gruber and Saez’s preferred specification, which includes a 10-piece spline, yields an estimated ETI of 

0.20, or slightly more than half the size of this paper’s estimate for the 1980s. Likewise, the 

specification using the log of reported taxable income, in place of the spline, yields an estimated ETI 

of about 0.18, less than a third the size of the corresponding estimate for the 1980s. Replacing the log 

of base-year income with the spline has little impact on the estimated ETI for the 1990s, but it reduces 

the estimated ETI by over one-third for the 1980s. 
9

Another interesting difference between the results from the 1980s and 1990s is that, without income 

controls, estimates for the 1980s are much smaller—in fact, well below zero—than with controls, but, 

for the 1990s, the estimates without income controls are much larger than those with controls. Those 

observations suggest that mean reversion at the top of the income distribution is important, even during 

a period of increasing concentration of income at the top of the distribution. People at the top of the 

income distribution have a relatively high probability of experiencing a substantial drop in income, but 

people with moderate incomes have only a small probability of experiencing tremendous income gains 

needed to push them to the top of the distribution. Thus, for the 1980s an inverse relationship exists 

between the mean reversion at the top of the distribution and changes to the net-of-tax rate. Without 

income controls, that relationship biases estimates downward. By contrast, for the 1990s, a direct 

relationship exists between mean reversion at the top of the distribution and changes to the net-of-tax 

rate, which is falling. Thus, without income controls, mean reversion at the top of the income 

distribution biases elasticity estimates upward for the 1990s. 

Although the ETI estimates are much smaller for the 1990s than for the 1980s, the corresponding 

estimated broad-income elasticities are slightly larger. Including the spline yields an estimated broadincome elasticity for the 1990s of about 0.15, compared with 0.12 for the 1980s (see Panel 1 of 

Table 3). The specification using the log of base-year income yields estimated broad-income 

elasticities that are slightly larger. 

Combined Results for the 1980s and 1990s

Not surprisingly, the same techniques applied to the full panel (from 1979 through 2001) generally 

result in estimated ETIs that are smaller than those for the 1980s and larger than those for the 1990s. 

The specification with the 10-piece spline yields an estimated ETI of 0.30, or slightly higher than the 

average of the estimates for the 1980s and 1990s. The specification with the log of base-year income 

produces an estimated ETI of 0.31, which is higher than the 1990s estimate of 0.18 but is only half the 
10

1980s estimate of 0.63. One again, estimated broad-income elasticities are stable: 0.15 with the spline 

and 0.17 with the log of income control. 

Why Do Estimates for the 1980s and 1990s Differ?

Three competing interpretations might explain the differences between the results from the 1980s and 

the 1990s: 

1. The model does a good job of explaining overall behavior for both the 1980s and the 1990s, 

but differences in policy and economic factors caused the ETI to fall between the two 

periods. That hypothesis is consistent with the view of Slemrod and Kopczuk (2002), who 

argue that the ETI is not a structural parameter and is a function of more than preferences. 

In addition, the fact that the estimates of the ETI differ substantially but the estimates of the 

broad-income elasticity remain stable is also consistent with Kopczuk (2003), which shows 

that the availability of deductions and exemptions matters in determining the ETI. Broad 

income, which includes deductions and exemptions, should be smaller, because filers have 

fewer opportunities to alter that base, and should be more stable because the opportunities to 

alter that base are less likely to change over time.15

2. The model is misspecified and does a poor job of isolating the response of taxable income to 

tax rate changes in either period. During the 1980s, for example, reported taxable incomes 

were rising, and the share of taxable income reported by the top of the income distribution 

was growing rapidly. At the same time, marginal tax rates were falling, with the largest 

reductions at the high end of the income distribution. Thus, the larger estimated ETIs for the 

1980s might occur not because the true response was greater, but because the model fails to 

fully control for the correlation between non-tax-related growth in income (especially at the 

top of the distribution) and falling tax rates. In the 1990s, the correlation between tax rates 

and income was reversed: The trend in income at the high end continued, and marginal tax 

 

15 Yet another interpretation in support of the model is that people simply respond differently to rate cuts than they do to 

rate increases. 
11

rates were increasing as a result of the Omnibus Budget Reconciliation Acts of 1990 and 

1993. For the 1990s, the failure to fully control for that correlation biases estimated ETIs 

downward, the opposite of the upward bias for the 1980s. Lending credence to that 

interpretation is the fact that the rate cuts of the 1990s applied only to upper-income groups, 

who are usually more responsive to tax rates than other groups are. Thus, it is somewhat 

surprising that the estimated ETI is lower for the 1990s, instead of higher. 

3. The model works well for the 1980s, but breaks down in the 1990s (or vice versa). It is 

possible that the spline, for example, does a good job of tracking non-tax-related trends 

during one of the periods, but, for whatever reason, fails to do so in the other period. 

The model can also be criticized in other respects. For example, measuring changes in behavior over 

three-year intervals is done in order to focus on permanent responses to tax-rate changes, as opposed to 

transitory fluctuations. But that comparison may not remove transitory influences from the elasticity 

estimates. Nearly every year of the 1980s (and of much of the 1990s) is likely to include some 

transitory behavior, in part because of multiyear phase-in periods. Thus, comparing observations three 

years apart is unlikely to avoid transitory fluctuations. If those transitory fluctuations severely 

contaminate measurement of the permanent responses, differences in ETI estimates for the two periods 

may result simply from noise. 

Adding Demographics to the Model 

The model discussed above excludes all demographic variables except marital status. Adding gender, 

age (as well as age squared and age cubed), itemization status, and geographic information (state 

dummies) to the model has only a small to moderate impact on the estimated elasticities, depending on 

the specification and time period. For the 1980s, the impact on the estimated ETIs is small (see 

Panel 2 and Panel 4 of Table 4). With the 10-piece spline, the estimated ETI rises from 0.37 to 0.39. 
12

Using the log income control, the estimated ETI rises from 0.63 to 0.67. For the 1990s, the 

demographic variables have the opposite effect, lowering estimated ETIs. For example, with the 10-

piece spline, adding demographic information reduces the estimated ETI from 0.20 to 0.15. 

The impact of additional demographic information on estimated broad-income elasticities differs 

greatly between the periods. For the 1980s, the pattern is similar to that of taxable income, with 

estimated elasticities increasing slightly. For the 1990s, the added demographics lower estimated 

broad-income elasticities by about half. With the 10-piece spline, the estimated broad-income 

elasticity falls from 0.15 to 0.07. In contrast, adding demographics affects the results only slightly 

when the two decades are combined. 

The effect of demographics on the estimates implies that those new variables are correlated with 

unobserved (and non-tax-related) factors that determine income changes and thus may help isolate the 

tax-related portion of changes in income. For example, suppose that, in the 1980s, a large number of 

filers nearing retirement age experienced drops in income that were correlated with the drops in 

marginal tax rates. Omitting the effect of age (or retirement) would lower estimated elasticities below 

their true values. For the 1990s, the same phenomenon (of incomes falling due to retirement) could 

bias elasticities upward, if the drop in income were correlated with increases in tax rates. Of course, 

that scenario is just one of many possible explanations for the results. And it fails to explain why 

demographics have a large impact on the estimated broad-income elasticities for the 1990s, but only a 

modest impact in most other instances (that is, for taxable income and for broad income during the 

1980s). 
13

Are State Tax Rates Important? Separately Estimated Responses for State and Federal Tax 

Rates 

Excluding state tax rates from the model requires identification to come from variations in federal rates 

over time or from cross-sectional variation across income groups. But individuals from different 

income groups may respond differently to tax changes. The inclusion of state tax rates in the overall 

marginal rate calculation is potentially important because it adds a source of cross-sectional variation 

across individuals who may be very similar in other respects (such as income).16 For the specification 

with limited demographic information, excluding state tax rates has only a minimal impact on 

estimated ETIs (see Panel 1 of Table 5). The estimated broad-income elasticity, in the model with the 

10-piece spline, is slightly smaller in the 1990s when state rates are excluded: 0.13 when only the 

federal rate is included versus 0.15 when the tax rate includes both the state and federal components 

(see Panel 1 of Table 3). But, for the 1980s, that same estimate is much smaller, well less than half the 

estimate that includes state rates: 0.05 when only the federal rate is included versus 0.12 when the tax 

rate includes both state and federal components (see Panel 2 of Table 2). 

Including only state net-of-tax rates (that is, one minus the filer’s state marginal tax rate) raises 

estimated elasticities relative to specifications that include only federal rates or both federal and state 

rates (see Panel 2 of Table 5). The estimated ETI with only state rates is 0.59 for the 1980s, similar to 

Gruber and Saez’s estimate of 0.63. In contrast to most of the other results, the estimated ETI when 

including only state rates is much larger for the 1990s (0.80) than for the 1980s (0.59). Likewise, 

when only state rates are included, the estimated broad-income elasticities are much larger than when 

the sum of state and federal rates is included (or when only federal rates are included), and, for the 

 

16 It is likely that, to some degree, state tax rates are endogenous because some people base their decision to live in a 

particular state, at least partially, on its tax system. As anecdotal evidence of that possibility, a number of high-paid 

celebrities have moved their primary residence from high-tax states, such as California, to low-tax states, such as Florida, 

Texas, and Nevada, which do not have state income taxes. The phenomenon is sometimes referred to as the “Tiger Woods 

Effect.” Woods, who grew up in California and attended Stanford University, moved his primary residence from California 

to Florida shortly after turning professional. Woods recently remarked, “We're definitely residing in Florida and I don't see 

why we should leave—especially with zero income tax.” 
14

1980s, the estimated broad-income elasticities are actually larger than the corresponding ETI estimates, 

the opposite of Gruber and Saez’s finding. 

Weighting and Sensitivity to Sample Selection 

A small number of outliers can dominate coefficients estimated using least squares, resulting in 

estimated coefficients that are not indicative of the behavior of much of the sample. That possibility 

seems remote when regressions are unweighted and include well over 50,000 observations. With 

income weighting, however, that is not necessarily the case.17 With income weighting, large numbers 

of taxpayers with lower reported incomes might exert much less influence on the overall results than 

might a few very high-income filers. Also, the many paired observations that have no variation in 

marginal tax rates may do little to identify the model. 

Three approaches are used to test the importance of those factors: 

1. Excluding observations for which the base-year net-of-tax rate and the future-year 

counterfactual rate do not change; 

2. Excluding as many as 100 observations that most affect the income-weighted estimates; 

and 

3. Estimating an unweighted specification that includes quantile dummies interacted with the 

log change in the net-of-tax rate. That specification includes the 10-piece spline and other 

independent variables, but replaces the log change in the net-of-tax rate with 11 interacted 

variables, each representing a portion of the reported taxable-income distribution. If the 

ETI is uncorrelated with taxable income within each quantile, and the model is otherwise 

properly identified, then person-weighted estimated ETIs, by quantile, would represent a 

viable alternative to income-weighted 2SLS. 

 

17 Table 4 reports both dollar-weighted and unweighted elasticity estimates. The unweighted estimates are often much 

smaller for the 1980s and much larger for the 1990s than the corresponding weighted estimates. 
15

Excluding observations with no variation in tax rates18 reduces the sample by less than 10 percent in 

the 1980s sample—but by more than 45 percent in the 1990s, when rate changes affected only highincome taxpayers. Even so, that exclusion of thousands of data points has little effect on the estimated 

elasticities for both broad and taxable income. 

A dfbeta test run on the reduced 1980s sample measures the influence of each observation on the 

overall ETI estimate. For each observation, the dfbeta test calculates the difference between the 

estimated coefficient with and without that observation. Taxable-income elasticities for the 1980s are 

re-estimated based on the specification with the 10-piece spline and excluding the observations with 

the largest dfbetas (in absolute value).19 Dropping cases with the same marginal tax rate in both the 

base year and the future year leaves 49,064 paired observations and yields an estimated ETI of 0.37, 

identical to the earlier estimate that included the approximately 5,000 dropped observations (see 

Table 6). Dropping the 10 most influential observations reduces the estimated ETI by more than 

30 percent, to 0.25. Dropping the 25 most influential observations further lowers the estimated ETI to 

0.20, 45 percent below the initial estimate. Excluding the 100 most influential observations 

(0.2 percent of the sample) lowers the estimated ETI to 0.11, 71 percent lower than the initial estimate. 

Thus, despite the large sample size, income weighting makes the results highly sensitive to just a few 

observations. For the most part, the most influential observations are taxpayers with very high taxable 

incomes who also report large changes in taxable income between the base year and the future year. 

Finally, as an alternative to income-weighted 2SLS, person-weighted ETIs were estimated separately 

by quantile within a single equation framework and using the specification that includes the 10-piece 

spline. In addition, the log change in the net-of-tax rate was interacted with quantile dummies, using 

 

18 That is, observations are excluded if no variation exists between the base-year marginal tax rate and the corresponding 

rate from applying the rate schedule three years hence to base-year income inflated by the growth in broad income. 

19 Those observations are excluded not to improve the overall ETI estimate, but rather to test the model’s robustness. 
16

quantiles based on base-year taxable income.20 The resulting estimated ETIs vary greatly (see Table 7 

and Figure 1). For the first nine deciles, the coefficients are either not statistically different from zero 

or are the wrong sign (negative). Despite the lack of statistical significance, the coefficients are often 

quite different from zero (in terms of their economic importance). That lack of statistical significance 

is surprising, given that most quantiles have well over 5,000 observations. Especially surprising is the 

estimate of -1.0 for the third decile. That estimate has the wrong sign, is strongly significant, and is 

very large in absolute magnitude. The lack of statistical significance is consistent with studies that 

found minimal responses for the bulk of the distribution, but these results are inconclusive with 

estimated coefficients that are often much larger or smaller than zero. Those estimates (for the first 

nine deciles) suggest that the model is poorly identified. 

Estimates for the top decile are both positive and statistically significant. The estimated ETI for those 

in the 90th percentile to the 99.5th percentile is 0.21 and is statistically significant at the 10-percent 

level. The estimated ETI for the top one-half of one percent is 0.57—well over twice the size of the 

estimates for any other quantile—and is strongly significant. That finding is also consistent with other 

research, which suggests that the ETI is largest at the top of the income distribution. Gruber and Saez, 

for example, estimated an ETI of 0.57 for taxpayers with base-year broad income exceeding $100,000. 

(Their estimate is weighted by income, whereas that for this analysis is person-weighted.)21 

Although ETI variation within quantile is likely lower than the variation within the entire distribution, 

it still may be substantial. If ETI variation within quantile were negligible, income weighting would 

have little impact on the estimates. Using the same specification, but weighting by taxable income, 

raises the estimated ETI for the top half of one percent from 0.57 to 0.72. Similarly, income weighting 

raises the estimated ETI for those between the 90th and 99.5th percentiles from 0.21 to 0.36. 

 

20 The first nine dummies represent the first nine deciles. The tenth dummy applies to those between the 90th and 99.5th

percentiles. The final quantile dummy applies to filers between the 99.5th and 100th percentiles. 21 For comparison purposes, reported taxable income at the 99.5th percentile in this analysis is about $203,000; the 

minimum level of reported broad income in the top one-half of one percent of the reported taxable-income distribution is 

about $218,300. 
17

V. Conclusion 

Replicating the methodology of Gruber and Saez (2002) using different data and different marginaltax-rate calculators yields estimated elasticities for the 1980s that are similar to those that Gruber and 

Saez report. Corresponding ETI estimates for the tax cuts of the 1990s are much smaller, a little over 

half the size of the 1980s estimate for the model with the 10-piece spline. Broad-income elasticities 

vary less between the two decades and are almost always smaller than the corresponding estimated 

ETIs. Broad-income elasticities are likely smaller than ETIs because tax filers have fewer 

opportunities to alter their broad-income base. Furthermore, because broad income is larger than 

taxable income, the denominator used to calculate the broad-income elasticities is larger than the 

corresponding denominator used in the ETI calculations. Thus, for a given numerator, a larger 

denominator necessarily yields a lower estimated elasticity. 

Despite the large sample used in this analysis, a dfbeta test for the 1980s shows that results depend 

heavily on a few very high-income observations, likely a product of weighting observations by income 

in the regression. In fact, eliminating just 0.2 percent of the most influential observations lowers the 

estimated ETI for the 1980s from 0.37 to 0.10, a drop of more than 70 percent. 

Finally, the interaction of the log change in the net-of-tax rate with quantile dummies results in great 

variation in estimated ETIs for the 1980s. For the first nine deciles, estimates vary greatly and have 

large standard errors. For the tenth decile, the person-weighted estimated ETI is positive and 

significant. For the top one-half of one percent, the person-weighted estimated ETI is more than twice 

as large as for any other quantile. Even within the top quantiles, however, estimated ETIs appear to 

vary with taxable income. 
18

The findings in this paper suggest a need for more research to understand why responses differ so 

much between the 1980s and the 1990s. In addition, the sensitivity of the results to just a few 

observations suggests that more can be learned by focusing on the high end of the distribution and by 

employing data sets that include many observations for that group. 

References 

Feldstein, Martin S., “Tax Avoidance and the Deadweight Loss of the Income Tax,” Review of 

Economics and Statistics, November 1999, 4 (81), 674–680. 

Feldstein, Martin S., “The Effect of Marginal Tax Rates on Taxable Income: A Panel Study of the 

1986 Tax Reform Act,” Journal of Political Economy, June 1995, 103 (3), 551–572. 

Internal Revenue Service, “Individual Income Tax Returns with Positive Adjusted Gross Income 

(AGI)” Unpublished Statistics of Income data, September 2004, www.irs.gov/pub/irssoi/02in01ts.xls. 

Giertz, Seth H., “Recent Literature on Taxable-Income Elasticities,” Congressional Budget Office, 

Technical Paper 2004-16, December 2004, www.cbo.gov/ftpdocs/60xx/doc6028/ 

2004-16.pdf. 

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

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

Harig, Bob, “The 19th Hole,” The St. Petersburg Times, October 14, 2004, C-8. 

Jones, Gregg, “The Nation on State Tax Policy: Everyone Has a Formula for Reform,” The Los 

Angeles Times, February 25, 2003, A-1. 

Kopczuk, Wojciech, “Tax Bases, Tax Rates and the Elasticity of Reported Income,” National Bureau 

of Economic Research, Working Paper 10044, October 2003, www.nber.org/ 

papers/w10044.

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

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

Rosen, Sherwin, “The Economics of Superstars,” The American Economic Review, December 1981, 71 

(5), 845–858. 

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

Implications,” National Bureau of Economic Research, Working Paper 10273, January 2004, 

www.nber.org/papers/w10273. 

Slemrod, Joel, “Methodological Issues in Measuring and Interpreting Taxable Income Elasticities,” 

National Tax Journal, December 1998, 51 (4), 773–788. 

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

Economics, April 2002, 84 (1), 91–112.
19

Table 1. Sample of Filers Used in the Regression Analysis 

Base Year Observations 

Taxable 

Incomea,b 

Broad 

Incomea,c 

1979 5,074 $ 28,301 $ 43,654 1980 5,189 28,125 43,695 1981 5,312 26,590 43,753 1982 5,369 25,991 42,956 1983 5,439 25,545 42,560 1984 5,547 25,477 42,520 1985 11,162 26,291 43,858 1986 5,706 25,807 43,435 1987 11,323 29,192 46,668 1988 11,527 29,591 46,895 1989 11,695 29,739 47,082 1990 11,772 30,000 47,329 1991 11,816 30,110 47,260 1992 11,869 30,356 47,442 1993 11,938 30,129 47,098 1994 12,112 30,370 47,169 1995 12,168 29,963 46,503 1996 13,869 29,006 45,668 1997 14,221 28,782 45,322 1998 35,734 29,075 45,518 

Source: Tabulations of paired observations are from the Statistics of Income’s Continuous Work History Survey. a. Both income measures are adjusted by the growth in broad income. See text for explanation. 

b. Taxable income is based on the 1990 definition used by the IRS and excludes realized capital gains. See Section III of the text for more detail. c. Broad income is defined as total income less realized capital gains and Social Security benefits.
20

Table 2. Income Weighted Estimates for the 1980s 

Panel 1: Gruber & Saez Results Panel 2: Replicated 

Income Controls: none log income 10-piece spline none log income 

Broad 

Income 

Taxable 

Income 

Broad 

Income 

Taxable 

Income 

Broad 

Income 

Taxable 

Income 

Broad 

Income 

Taxable 

Income 

Broad 

Income 

Tax

Inco

Elasticity -0.30 -0.462 0.17 0.611 0.12 0.4 -0.25 -0.37 0.17 0.6

 (0.120) (0.194) (0.106) (0.144) (0.106) (0.144) (0.113) (0.111) (0.113) (0.1

Married -0.008 -0.062 0.045 0.049 0.05 0.055 0.00 -0.08 0.06 0.0

 (0.010) (0.018) (0.014) (0.023) (0.012) (0.021) (0.012) (0.016) (0.016) (0.0

single -0.037 -0.053 -0.034 -0.032 -0.036 -0.027 -0.02 -0.07 -0.01 -0.0

 (0.012) (0.019) (0.013) (0.022) (0.013) (0.021) (0.013) (0.017) (0.014) (0.0

ln(income) -0.083 -0.167 -0.10 -0.2

 (0.015) (0.021) (0.018) (0.0

spline: decile 1 0.225 -0.884 

 (0.086) (0.039) 

decile 2 -2.74 -0.538 

 (1.130) (0.047) 

decile 3 -0.317 -0.279 

 (0.055) (0.057) 

decile 4 -0.071 -0.445 

 (0.051) (0.069) 

decile 5 -0.197 -0.003 

 (0.054) (0.075) 

decile 6 -0.074 -0.253 

 (0.053) (0.081) 

decile 7 -0.127 -0.124 

 (0.056) (0.083) 

decile 8 -0.061 -0.172 

 (0.057) (0.083) 

decile 9 -0.027 -0.057 

 (0.076) (0.125) 

decile 10 -0.072 -0.126 

 (0.041) (0.064) 

constant -0.09 0.01 0.94 1.9

(0.014) (0.018) (0.187) (0.1

Observations: 69,129 59,199 69,129 59,199 69,129 59,199 54,313 54,136 54,313 54,Source: Panel 1 is from Gruber and Saez (2002): reproduction of Table 4. Panel 2 is from estimates based on Statistics of Income’s Con

Survey data for 1979 to 1990. a. Estimates are from 2SLS regressions. Income range is $10,000 and above. Regressions are weighted by income. All regressions inclustatus and dummies for each base year. Robust standard errors are in parentheses. 
21

Table 3. Estimates for the 1990s and for Both Decades 

Panel 1: 1990s Panel 2: 1979-2000 

Income Controls: none log income 10-piece spline none log income 10

Broad 

Income 

Taxable 

Income 

Broad 

Income 

Taxable 

Income 

Broad 

Income 

Taxable 

Income 

Broad 

Income 

Taxable 

Income

Broad 

Income

Taxable 

Income 

B

Inc

Elasticity 0.475 0.738 0.184 0.177 0.148 0.195 0.121 0.192 0.174 0.305 0 (0.105) (0.168) (0.094) (0.137) (0.097) (0.144) (0.077) (0.103) (0.078) (0.099) (0Married -0.015 -0.122 0.087 0.063 0.08 0.086 -0.01 -0.113 0.082 0.056 0 (0.008) (0.014) (0.011) (0.017) (0.009) (0.015) (0.007) (0.011) (0.010) (0.015) (0single -0.039 -0.090 -0.014 -0.042 -0.014 -0.027 -0.028 -0.083 -0.012 -0.047 -0 (0.010) (0.016) (0.010) (0.017) (0.010) (0.017) (0.008) (0.012) (0.009) (0.014) (0ln(income) -0.099 -0.162 -0.099 -0.165  (0.010) (0.013) (0.009) (0.013) 

Spline: decile 1 0.00 -0.827 0 (0.000) (0.021) (0

decile 2 0.00 -0.504 0 (0.000) (0.024) (0decile 3 -0.243 -0.408 -0 (0.045) (0.031) (0decile 4 -0.186 -0.293 -0 (0.030) (0.039) (0decile 5 -0.109 -0.27 -0 (0.030) (0.046) (0decile 6 -0.135 -0.277 -0 (0.034) (0.046) (0decile 7 -0.039 -0.168 -0 (0.035) (0.049) (0decile 8 -0.172 -0.232 -0 (0.036) (0.057) (0decile 9 0.097 0.067 0 (0.049) (0.071) (0decile 10 -0.122 -0.155 -0

 (0.021) (0.028) (0constant -0.067 -0.033 0.952 1.588 0.128 7.313 -(0.090) (0.027) (0.917) (1.638) 0 (0.011) (0.019) (0.103) (0.134) (0.019) (0.156) 0.012 0.015 0.096 0.129 (0Observations: 158,679 139,673 158,679 139,673 158,679 139,673 218,771 193,809 218,771 193,809 21Source: Estimates are based on Statistics of Income’s Continuous Work History Survey data for 1979 to 2001. 

a. Estimates are from 2SLS regressions. Income range is $10,000 and above. Regressions are weighted by income. All regression

marital status and dummies for each base year. Robust standard errors are in parentheses.
22

Table 4. Inclusion of Demographic Variables in the Modela 

Limited Demographicsb Full Demog

Panel 1: Panel 2: Panel 3: 

Unweighted Dollar Weighted Unweighted 

 Taxable Income Elasticitiesd Taxable Income Elasticitiesd 

Base Years (1) (2) (3) (1) (2) (3) (1) (2) (3) 

1979 to 1987 -1.728 0.63 0.065 -0.369 0.625 0.373 -1.716 0.628 -0.05 

(0.085) (0.103) (0.096) (0.111) (0.146) (0.160) (0.088) (0.104) (0.095) 

1988 to 1998 1.211 0.357 0.293 0.738 0.177 0.195 0.882 0.144 0.027 

(0.107) (0.080) (0.077) (0.168) (0.137) (0.144) (0.097) (0.072) (0.069) 

1979 to 1998 0.013 0.346 0.123 0.192 0.305 0.298 -0.133 0.234 -0.057 

(0.065) (0.059) (0.056) (0.103) (0.099) (0.100) (0.063) (0.056) (0.053) 

 Broad Income Elasticitiesd Broad Income Elasticitiesd 

(1) (2) (3) (1) (2) (3) (1) (2) (3) 

1979 to 1987 -0.312 0.092 -0.001 -0.249 0.173 0.134 -0.364 0.060 -0.067 

(0.052) (0.064) (0.065) (0.111) (0.113) (0.111) (0.052) (0.065) (0.064) 

1988 to 1998 0.321 0.217 0.208 0.475 0.184 0.148 0.122 0.047 0.035 

(0.050) (0.047) (0.047) (0.105) (0.094) (0.097) (0.044) (0.041) (0.042) 

1979 to 1998 0.073 0.135 0.112 0.121 0.174 0.149 -0.053 0.029 0.000 

(0.036) (0.036) (0.036) (0.077) (0.078) (0.080) (0.034) (0.035) (0.035) 

Source: Estimates are based on Statistics of Income’s Continuous Work History Survey data for years 1979 to 2001. 

a. Coefficients other than the elasticities are suppressed. Robust standard errors are in parentheses. 

 b. Marital status 

 c. Gender, age, age squared, age cubed, itemizer dummy, and state dummies 

d. Elasticity Specifications: (1) No Controls; (2) ln(Income); (3) 10-Piece Spline of ln(Income) 
23

Table 5. Comparison of Dollar-Weighted Estimates 

Using Federal and State Marginal Tax Ratesa

Panel 1: Federal Rates Only

Panel 2: State Rates Only

Taxable-Income Elasticitiesb Taxable-Income Elasticitiesb

(1) (2) (3) (1) (2) (3) 

1979 to 1987 -0.478 0.677 0.375 0.286 0.546 0.59 

(0.136) (0.178) (0.194) (0.457) (0.507) (0.470) 

1988 to 1998 1.035 0.151 0.174 0.694 0.809 0.798 

(0.217) (0.184) (0.196) (0.367) (0.371) (0.373) 

1979 to 1998 0.224 0.319 0.309 0.598 0.757 0.76 

(0.134) (0.128) (0.129) (0.304) (0.311) (0.310) 

Broad-Income Elasticitiesb Broad-Income Elasticitiesb

(1) (2) (3) (1) (2) (3) 

1979 to 1987 -0.363 0.103 0.046 0.504 0.667 0.663 

(0.138) (0.136) (0.130) (0.364) (0.376) (0.369) 

1988 to 1998 0.625 0.171 0.127 0.43 0.523 0.503 

(0.131) (0.119) (0.122) (0.238) (0.244) (0.243) 

1979 to 1998 0.112 0.145 0.109 0.444 0.566 0.56 

(0.10) (0.099) (0.102) (0.204) (0.213) (0.214) 

Source: Estimates are based on Statistics of Income’s Continuous Work History Survey data for 1979 to 2001. a. Estimates are based on the specification with limited demographic information. Coefficients other than the elasticities are suppressed. Robust standard errors are in parentheses. b. Income Specifications: (1) No Controls; (2) ln(Income); (3) 10-Piece Spline of ln(Income) 
24

Table 6. The Effect of Excluding the Most Influential Observations 

of Income-Weighted Estimates for the 1980sa

Dropped 

Observations Sample Size Estimated ETI 

 0 49,064 0.368  10 49,054 0.249  25 49,039 0.203  50 49,014 0.139  100 48,964 0.105 

Source: Estimates are based on Statistics of Income’s Continuous Work History Survey data for 1

 to 1990. a. Estimates are based on the specification with the 10-piece spline and with limited demographic information. Those with no variation in marginal tax rates between the base year and three years hare excluded from this sample. Observations are dropped based on the size of their impact on the estimated ETI and as measured by a dfbeta test. 
25

Table 7. Person-Weighted Taxable-Income Elasticities 

by Decile for the 1980s 

Quantile 

Estimated 

ETIa

Decile 1 -0.101 

(0.295) 

Decile 2 -0.259 

(0.342) 

Decile 3 -1.009 

(0.337) 

Decile 4 -0.149 

(0.297) 

Decile 5 0.214 

(0.219) 

Decile 6 0.252 

(0.200) 

Decile 7 0.083 

(0.169) 

Decile 8 -0.12 

(0.164) 

Decile 9 0.192 

(0.132) 

Decile 10b 0.207 

(0.126) 

Percentiles 99.5 to 100 0.572 

(0.289) 

Observations 54,136 R-squared 0.28 

Source: Estimates are based on Statistics of Income’s Continuous Work History Survey data for 1979 to 1990. a. Estimated quantile ETIs are generated by interacting quantile dummies with the net-of-tax rate. Estimates are based on the specification with the 10-piece spline and with limited demographic information. Standard errors are in parenthesis. b. Decile 10 excludes the top one-half of one percent. 
26

* Statistically significant at the 10% level. ** Statistically significant at the 5% level. Source: Estimates are based on Statistics of Income’s Continuous Work History Survey data for 1979 to 1990. Note: Estimates are based on the specification with the 10-piece spline and with limited demographic information

are estimated by interacting dummies for each quantile with the log change in the net-of-tax rate. 

Figure 1: Taxable-Income Elasticities by Decile for the 1980s

-1

-0.8-0.6-0.4-0.2

0

0.20.40.6

Decile 1Decile 2Decile 3Decile 4Decile 5Decile 6Decile 7Decile 8Decile 9 Percentiles 90 to 99

Elasticity of Taxable Income

**