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. 20515 

Seth.Giertz@cbo.gov 

February 2005 

Updated January 2008 

2008-01 

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/publications. 
 

A SENSITIVITY ANALYSIS OF THE ELASTICITY OF TAXABLE 

INCOME

by Seth H. Giertz*

Abstract

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

years 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 Gruber and Saez’s approach yields 

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

corresponding estimate for the 1980s. 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 0.08. Estimating the elasticities on the large SOI 

sample does not change the elasticities much, but does appear to yield results that are more 

robust to other specification changes.

* I wish to thank David Weiner, Ed Harris, Rob McClelland, Bob Williams, Roger Hitchner, 

Bob Dennis, Emmanuel Saez and Wojciech Kopczuk for helpful comments and 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. One of the key variables 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 often-cited 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 to the time-period examined or to the addition of a 

richer set of demographic variables. 

 

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

 Additionally, 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 under-provided public good. In such instances, the standard 

deadweight loss formula will overstate the efficiency cost of an increase in tax rates. 
 2 

This paper replicates Gruber and Saez’s techniques using similar data. My results for the 1980s 

closely parallel theirs. Applying the same methodology to 1990s data and to data from both the 

1980s and 1990s combined, however, yields estimated ETIs for the 1990s that are much smaller 

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

specification yields an estimated ETI that is a little over half the corresponding estimate for the 

1980s. Weighting regression results by income not only has an enormous impact on the 

estimates, but also results in 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 0.08. 

Employing the same methodology on a much larger dataset generates similar results – albeit 

somewhat more robust. The larger dataset still yields ETIs that generally differ for the 1980s 

and 1990s. The model with the richest set of controls produces an estimated ETI of 0.43 for the 

1980s and one of 0.20 for the 1990s. Turning to a more encompassing income measure, broad 

income, generally results in smaller elasticities, with again estimates for the 1990s that are 

smaller than those for the 1980s. With the richest set of controls, the estimated elasticity for 

broad income is 0.21 for the 1980s and 0.13 for the 1990s. 

II. Issues in the Analysis 

Tax changes take place in a changing economic environment in which changes to that 

environment affect income growth. Controlling for those 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). Although, the approach does also take into account other 

factors such as mean reversion, tax rate endogeneity, institutional changes (which often coincide 
 3 

with changes in the rate structure), and differences between transitory (or temporary fluctuations) 

and permanent (or longer-term) responses.5

Controlling for Exogenous Trends in Income

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

shifts in the income distribution and mean reversion. Over the past thirty years the distribution 

of reported income has widened. In fact, that trend accelerated in the 1980s, especially at the 

very 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 was 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 very 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. While changes to the income distribution are widely documented and 

theories such as shifts in the returns to education and the market for superstars8 help explain the 

phenomenon, 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. Additionally, 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. 

 

5

 See Giertz (2004), <www.cbo.gov/ftpdoc.cfm?index=6028&type=1>. 

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 www.irs.ustreas.gov/pub/irs-soi/01in01ts.xls.

8

See Rosen (1981).
 4 

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 mean reversion will erroneously count non-tax-related increases 

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

lifetime path) 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. Additionally, 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 year net-of-tax rates rise by 10 percent for all filers. Now, 

suppose half of the population is in the first group and that each filer in that group has a baseyear 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, while the high-income 

 

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 altering their taxable income.
 5 

filers have an ETI of 0.9.10 Under that hypothetical 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 one-hundred times as large as the base for the group with 

the ETI of 0.1. 

III. Data and Methods 

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

(CWHS) and from the full SOI for years 1979 through 2001. The full SOI is a stratified random 

sample of taxfilers compiled by the Internal Revenue Service and includes all information 

reported on the filers’ tax returns, plus some additional demographic information. The full SOI 

heavily oversamples high-income filers. The CWHS, by contrast, is a subset of filers from the 

SOI who are followed from year-to-year. While the CWHS contains detailed and accurate 

information, it is deficient in two important respects. First, while the overall sample is quite 

large (for some years, over 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 handful of filers. Second, the CWHS includes only people who file 

returns and are listed as the primary filer. Thus, attrition is an issue. 

As with Gruber and Saez (2002), behavior here is compared 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 CWHS sample includes close to194,000 paired observations, whereas the SOI sample 

includes nearly 700,000 paired observations. As with Gruber and Saez, income measures are 

adjusted by the growth in broad income, 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 

 

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

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

increase in taxable income by the ten percent increase in the net-of-tax rate. 

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

dollars. Thus here, each individual's reported income is divided by the ratio of average broad income in 1990 over 

average broad income in the year of the observation. 
 6 

on a 1990 constant-law definition of income and 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 CWHS sample, mean 

reported taxable income equals $28,311 (in 1992 dollars), while the corresponding means for 

broad income is $45,065. For the full SOI, the corresponding means are $26,961 for taxable 

income and $43,581 for broad income. (The SOI means are weighted so as to reflect the overall 

population of filers, subject to the income restrictions discusses earlier.) Individual marginal tax 

rates (both state and federal) are imputed using the Congressional Budget Office’s internal tax 

calculators.12

The CWHS 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 my sample extends to 2001. Third, Gruber and Saez 

impute their federal and state marginal tax rates using the National Bureau of Economic 

Research’s (NBER) TAXSIM model, whereas this 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 income growth rate 

ξ + ⋅ β + ⋅ β + ⋅ β + ⋅ β + ε ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

−

− = ⋅ ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ = + + 1 2 3 4 3 3 ( ) 1

1

log log mars year spline income demog taxrate

taxrate

income

income t

t

t

t

t .

13

The left-hand side 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 

 

12Jon Bakija of Williams College designed the state tax calculator used by CBO. See Bakija (2006).

13 Note that for simplicity, subscripts denoting the individual are omitted here. 
 7 

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 ten-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 also here include a model with the log of base year income in place of the spline and a 

specification that excludes the income control altogether. Additionally, specifications that 

include separate controls for mean reversions and non-tax-related income trends are explored. 

This is done by including explanatory variables base on one year lagged income and the 

difference between base year income and the one year lag as separate controls. Gruber and Saez 

also 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. 

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 

 

14 The instrument is constructed by inflating base-year income by the growth in mean broad income over the threeyear interval. Next, the tax calculator computes counterfactual tax rates based on the inflated income measure. 

Finally, two-stage 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. 
 8 

for the 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. Additionally, although overall sample sizes are quite large, weighting could 

potentially result in a small number of observations having a substantial impact on the overall 

results. 

With the full SOI, another time of regression weighting is also requireed. Note that while 

selection into the CWHS is designed to be random, selection into the full SOI, as mentioned 

earlier, is conditional on several factors, including income. More specifically, each individual is 

assigned a number at random, which does not change from year to year. For each year, tax 

returns are separated into strata based on AGI and the forms and schedules used by the filers. 

Sampling probabilities vary by strata and reach 100 percent for very high income filers. The 

returns in each stratum are sorted by the randomly assigned values and the strata sampling 

probability is used to determine the cut point for inclusion into the SOI. Because the individual 

maintains the same random value over time and because the stratum sampling probability simply 

determines the cut point for inclusion in the sample, once included in the SOI, an individual is 

automatically included in future years if his income remains the same or if his income increases 

because this would either put him in the same stratum or in a stratum with a higher sampling 

probability – thus maintaining or lowering the cut-point for inclusion. Therefore, an individual 

observed in the base year is much more likely to be observed in the future year if his income 

rises than if it falls. In fact, the probability that one is observed in two different years is simply 

the minimum of the strata sampling probabilities for the two years. This raises the potential for 

spurious correlation between the dependent variable (ln(incomet/incomet+1)) and the 
 9 

independent variables, including the tax variable. To avoid this possibility, (paired) observations 

from the full SOI are weighted by the reciprocal of their probability of appearing in the sample. 

This same strategy is employed by Auten and Carroll (1999), who use similar data. 

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 

years 1979 to 2001. This is followed by a similar analysis applied to the full SOI sample. After 

a discussion of those results, the importance of including demographics in the model and the 

importance of state rates (as opposed to using only federal tax rates) is examined, as are the 

ramifications of weighting regressions by income are explored. 

Replicating Gruber and Saez 

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

respectively) for the 1980s with my 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 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 my analysis of that same time-period. Despite using a slightly different 

core dataset 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 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 
 10 

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 

broad income 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 

Employing the same methodology using data from the 1990s 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 my 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, whereas it reduces the 

estimated ETI by over one third for the 1980s. 

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, while 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 very top of the income distribution have a relatively high 

probability of experiencing a substantial drop in income, while 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, in 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 
 11 

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

relationship exists between mean reversion at the top of the distribution and changes to the netof-tax rate, which is falling. Thus, without income controls, mean reversion at the top of the 

income distribution biases upward elasticity estimates for the 1990s. 

While 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 

broad income elasticity for the 1990s of about 0.15 compared to 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. 

Results for the 1980s and 1990s Combined 

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 only half the 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 
 12 

than preferences. Additionally, the fact that the estimates of the ETI differ 

substantially, while 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 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 very top of 

the income distribution was growing rapidly. At that 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, while marginal tax 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 only applied to upper-income 

groups, who are usually found to be more responsive to tax rates than other groups. 

Thus, it is somewhat surprising the estimated ETI is lower for the 1990s, instead of 

higher. 

 

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

do to rate increases. 
 13 

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 much of the 1990s) is likely to 

include some transitory behavior, in part because of multi-year 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. 

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.16 With income 

weighting, large numbers of taxpayers with lower reported incomes may exert much less 

influence on the overall results than a handful of very high-income filers. Also, the many paired 

observations that have no variation in marginal tax rates may do little to identify the model. 

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

 

16 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. 
 14 

1. Excluding as many as 100 observations that most affect the income-weighted 

estimates; and, 

2. 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 eleven 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. 

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). (Those observations are excluded not 

to improve the overall ETI estimate, but rather to test the model’s robustness.) Dropping the 10 

most influential observations reduces the estimated ETI by 35 percent, from 0.37 to 0.24 (see 

Table 4). Dropping the 25 most influential observations further lowers the estimated ETI to 

0.17, less than half of the initial estimate. Excluding the 100 most influential observations (0.2 

percent of the sample) lowers the estimated ETI to 0.08, 77 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. 
 15 

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

quantile within a single equation framework, 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 quantiles based on base-year taxable income.17 The resulting estimated ETIs vary greatly 

(see Table 5 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 decile three. That estimate has the 

wrong sign and is strongly significant and 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 statistically significant at the ten 

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 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 baseyear broad income exceeding $100,000. (Their estimate is weighted by income, whereas that for 

this analysis is person-weighted.18) 

 

17 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. 18 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. 
 16 

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

distribution, it still may be substantial. If within quantile ETI variation were negligible, incomeweighting 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 90 to 99.5th

percentiles from 0.21 to 0.36.) 

Results from the Full SOI 

The analysis thus far calls into question the level of precision with which the CWHS-based 

taxable income responses are estimated. Despite a sample size of well over 50,000 for the 

1980s, estimated ETIs are extremely sensitive to a tiny number of the most influential 

observations. Furthermore, despite a sample size of close to 140,000, estimated ETIs for the 

1990s are far from statistically significant. Although sample sizes are quite large, the number of 

really high-income filers is very small. This, plus income-weighting the regressions, results in 

coefficients that are driven by a small number of observations. Additionally, for the 1990s a 

large fraction of the observations experience no change in tax rates because the 1990 and 1993 

tax acts only changed tax rates for those in the upper tax brackets. Fortunately, this shortcoming 

of the CWHS can be overcome by turning to the full SOI, which, as discussed in the previous 

section, heavily over-samples high-income filers. 

Given the sensitivity of the CWHS estimates, it is surprising that, for the most part, estimated 

ETIs from the full SOI are quite similar to the CWHS estimates. For the 1980s, the estimate 

ETI is 0.43 (versus 0.37 with the CWHS) with a t-value of over 5.2. (See Table 6.) For the 

1990s, the estimated ETI is 0.20, almost exactly the same as the CWHS estimate, but with a t-
 17 

value of 3.3 (versus 1.35 with the CWHS). (See Table 7.) For both decades combined, the 

estimated ETI is 0.34 (versus 0.30 with the CWHS) with a t-value of 7.5. (See Table 8.) 

For broad income, the SOI-based elasticity estimate for the 1980s is much larger than the 

estimate from the CWHS (0.21 versus 0.12). For the 1990s, the estimates are much closer (0.13 

with the full SOI and 0.15 with the CWHS). For both decades combined, the estimated broad 

income elasticity is 0.23 (versus 0.15 with the CWHS), but still smaller than the corresponding 

ETI estimate. While the estimates (for broad income) from the CWHS are never statistically 

significant at the 5-percent level, the SOI-based estimates are all statistically significant at well 

above the 1 percent level. 

Adding Demographics to the Model 

Recall that the analysis based on the CWHS sample excluded all demographic variables except 

marital status. When turning to the full SOI, potentially important variables such as gender, age 

(as well as age squared and age cubed) and itemization status are added. As Table 9 shows, 

including demographics results in larger estimated elasticities (when using the model that 

includes a 10-piece spline) for the 1980s. The affect on the estimated elasticities for the 1990s is 

mixed; here the estimated broad income elasticity falls, while the corresponding measure for 

taxable income remains essentially unchanged. 

For the 1980s additional demographic variables raise the estimated ETI from 0.37 to 0.43 and the 

corresponding estimated elasticity for broad income from 0.18 to 0.21. For the 1990s, however, 

the added variables have almost no affect on the estimated ETI. For broad income, the 
 18 

corresponding estimated elasticity falls from 0.17 to 0.13. For the full period, the pattern of the 

1980s tends to dominate. Additional demographics raise the estimated ETI, for the full period, 

from 0.28 to 0.34 and the estimated broad income elasticity from 0.20 to 0.23. 

In most cases, the added demographics show strong statistical significance. See Table 6, Table 

6, and Table 8. Age, included as a third-order polynomial, shows strong statistical significance 

(as measured by F-tests) for both time-periods for both broad and taxable income. Itemizer 

status is negative and strongly significant. The effect of (the primary filer’s) gender, on the other 

hand, is close to zero and not statistically significant. The effect of demographics on the 

estimates implies that those new variables are somewhat correlated with unobserved (and nontax-related) factors that determine income changes and thus may help isolate the tax-related 

portion of changes in income. 

Separate Controls for Mean Reversion and Divergence in the Income Distribution 

Kopczuk (2005) makes a compelling argument that mean reversion and non-tax-related 

divergence in the income distribution are two separate phenomena and that it is unlikely that one 

variable will capture both effects. To address this, Kopczuk includes separate variables to 

control for each of the two different phenomena. To account for mean reversion, Kopczuk 

includes a function of income in the year preceding the base year. To control for divergence in 

the income distribution, he includes a function of the difference between current (or base year) 

income and income in the preceding year. 

To examine the implications of using one variable to control for both income divergence and 

mean reversion, two specifications employed by Kopczuk are explored. Using his richest set of 

controls has a modest and negative affect on the estimated ETI for the 1980s, but a larger and 
 19 

positive affect on the estimate for the 1990s. One specification includes both of the control 

variables (lagged income and the change in income from the previous to the current year) in log 

form; the other includes the same variables as 10-piece splines. When including the two 

variables in log form, the biggest change is observed for the 1980s, where the estimated ETI rises 

by almost 0.05 (when compared to results from the model that includes the log of base year 

income). See Table 10. When including the two logged variables as 10-piece splines, in place of 

a 10-piece spline of log income, the estimated ETI falls from 0.43 to 0.40, when compared to the 

corresponding estimate for the 1980s, and for the full period, the estimate is virtually unchanged. 

For the 1990s the impact is greater, raising the estimate from 0.20 to 0.26. 

Are State Tax Rates Important? Separately Estimated Responses For State and 

Federal Tax Rates 

The inclusion of state tax rates in the marginal rate calculation adds a source of cross-sectional 

variation across individuals who may be very similar in other respects (such as income). 

Including this cross-sectional variation may be important in identifying taxable income responses 

because exogenous income trends, which are known to fluctuate from year-to-year and to vary 

greatly across the taxable income distribution, pose problems for other identification strategies. 

Furthermore, excluding changes to state rates would likely bias the net-of-tax rate variable, thus 

contaminating the ETI estimates. 

Elasticities are estimated for models that exclude variation resulting from federal rates, and for 

models that exclude variation resulting from state tax rates. Simply excluding one component of 

the overall marginal rate will likely add little insight because doing so presumes that one 

component of the overall marginal rate is responsible for the entire tax effect. Thus, the log 

change in the overall tax rate is still used as the key dependent variable, but in one specification 

the predicted log change in the state rate is used as an instrument (instead of the corresponding 
 20 

change resulting from changes to both federal and state law) and in the other the predicted log 

change for only the federal rate is used as an instrument. Therefore, on average the key 

dependent variable will be the same as before, but the variation in this variable will now be based 

on only one of the two components of the overall marginal tax rate. 

The model that includes a 10-piece spline and uses just the federal rate as an instrument yields 

estimates that are very similar to those from the corresponding model that includes variation 

from the combination of federal and state tax rates. This is true for both broad and taxable 

income. See Panel 1 of Table 11. 

Including only variation from state net-of-tax rates yields ETI estimates that are somewhat 

smaller than when both federal and state or only federal rate changes are included. See Panel 2 

of Table 11. The estimated ETI with only variation from state rates is 0.34 for the 1980s. The 

estimated ETI is just 0.11 for the 1990s and 0.23 for the full period. For broad income, the 

estimated elasticity is much larger for the 1980s when including only variation in state rates 

(0.37 versus 0.21 when both state and federal rates are included). For 1990s, the estimated broad 

income elasticity (0.08) is slightly smaller than the earlier estimate and much smaller than the 

estimate for the 1980s. For the full period, the estimated broad income elasticity is about the 

same as when only variation in federal rates are included or when both state and federal rates are 

included. 

Estimates for High-Income Filers from the Full SOI 

A number of studies have found that estimated ETIs vary greatly by income, and that overall 

responses may be driven by high-income filers. While comparing dollar-weighted and personweighted estimates (which are generally much smaller) also suggests this, the possibility is 
 21 

explored further by using the full SOI to generate ETI estimates that apply specifically to highincome filers. 

Table 12 presents income-weighted ETI estimates for the 1980s, 1990s, and for both decades 

combined after excluding those with less than $100,000 of base-year broad income. With that 

income restriction, the 1980s and 1990s estimates are very similar to the full-sample SOI 

estimates for the respective periods. For both decades combined, though, the estimated ETI is 

0.44 (versus 0.34 for the sample without the higher income restriction), which is actually larger 

than either the 1980s or 1990s estimate. Note that restricting the sample to those with incomes 

over $100,000 alters a potentially important source for identification. I.e., the exclusion reduces 

degree of cross-sectional variation in tax rate changes and thus, the behavior of those with less 

than $100,000 of income is no longer used to help explain counterfactual income trends. 

Whether this hampers or improves the identification process depends partly on whether the nontax-related behavior of the excluded group is similar to that of the included higher-income group. 

Permanent versus Transitory Responses 

While the model is designed to capture permanent rather than transitory responses, the degree to 

which is does this is open to question. Focusing on changes in behavior over three-year intervals 

is intended to isolate permanent responses. But that comparison may not remove transitory 

influences from the elasticity estimates. Many of the years in both the 1980s and1990s are 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. To test this 

possibility, the ETI is re-estimated after excluding all paired observations that include years 

1981, 1982, 1986, 1987, 1993, 1994 and 2001. For the full time period, the overall estimated 

ETI is 0.30 (versus 0.34 when no years are dropped) and strongly significant. The corresponding 
 22 

estimated ETI is 0.36 for the 1980s and 0.15 for the 1990s. (See Table 13.) The fact that the 

estimates are all a little smaller than the corresponding estimates that do not exclude any years 

suggests that the overall estimates may contain both a permanent plus a small transitory 

component. However, this is far from conclusive – especially since the 1980s estimate is no 

longer statistically significant. 

V. Summary and Conclusion 

Replicating the methodology of Gruber and Saez (2002) using different data and different 

marginal tax rate calculators yields estimated elasticities for the 1980s that are similar to those 

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 taxfilers 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 handful of primarily 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 0.08, a drop of 

77 percent. 

However, moving to the full SOI results in estimated ETIs that are generally similar in 

magnitude to the CWHS estimates, but with much smaller standard errors. Additionally, using 

separate control variables for mean reversion and divergence within the income distribution has a 
 23 

modest and negative affect on estimated ETIs for the 1980s and a positive and larger affect on 

estimates for the 1990s (when compared to results from analogous models that include just one 

variable to account for both phenomena). While the much larger SOI sample substantially 

lowers standard errors, estimates remain sensitive to an array of factors. This belies the fact that 

underlying income changes are tremendously complex and there remains variation across 

specifications and across time-periods that is not well understood. 

This sensitivity is observed when examining responses by income quantile. The log change in 

the net-of-tax rate is interacted with quantile dummies for the 1980s (using the CWHS sample). 

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 over twice as large as for any other quantile. Even 

within the top quantiles, however, estimated ETIs appear to vary with taxable income. 

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

so much between the 1980s and the 1990s. Additionally, 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 datasets that include many observations for that group. 

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Public Economics, 89 No. 11-12 (December 2005): 2093-2119. 

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831-849. 
 25 

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Public Economics, 84 No. 1 (April 2002): 91–112.
 26 

TABLE 1. Sample of Filers Used in the Regression Analysis 

 CWHS SOI 

Paired Observationsa 193,809 699,724 

Paired Observations 1980s 54,136 250,140 Paired Observations 1990s 139,673 449,584 Returns with Base Year Taxable income Greater than: 

$1,000,000 113 113,673 $5,000,000 4 21,365 

Mean Base Year Taxable Incomeb $28,311 $26,961 

Mean Baseyear Broad Incomeb $45,065 $43,581 Mean Federal Tax Rate 21 21 Mean State Tax Rate 4 4 Mean Net-of-Tax Rate 75 75 Mean Federal Tax Liabilityb 6,246 5,720 

Mean State Tax Liabilityb 1,361 1,241 

Notes: Estimates are based on Statistics of Income data from 1979 to 2001. Filers with less than $10,000 of broad income are excluded. a. Sample sizes are for the taxable income regressions. b. Income and tax liabilities are expressed in 1992 dollars, as adjusted by the growth in broad income. Averages for the SOI are weighted to reflect the population of tax filers 
 27 

Source: Panel 1, Gruber and Saez (2002) reproduction of Table 4. Panel 2, estimates based on Statistics of Income’s Continuous Work years 1979 to 1990. Notes: Estimates from 2SLS regressions. Income range is $10,000 and above. Regressions are weighted by income. All regressions instatus and dummies for each base year. Robust standard errors are in parentheses. TABLE 2. Income Weighted Estimates for the 1980s 

Panel 1 Panel 2 

Gruber and Saez Results Replicated Results

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 

Taxab

Incom

Elasticity -0.30 -0.462 0.17 0.611 0.12 0.40 -0.25 -0.37 0.17 0.63 

 (0.120) (0.194) (0.106) (0.144) (0.106) (0.144) (0.113) (0.111) (0.113) (0.146

Married -0.008 -0.062 0.045 0.049 0.05 0.055 0.00 -0.08 0.06 0.04 

 (0.010) (0.018) (0.014) (0.023) (0.012) (0.021) (0.012) (0.016) (0.016) (0.022

single -0.037 -0.053 -0.034 -0.032 -0.036 -0.027 -0.02 -0.07 -0.01 -0.06 

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

ln(income) -0.083 -0.167 -0.10 -0.20 

 (0.015) (0.021) (0.018) (0.018

 splinedecile 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 1.98 

(0.014) (0.018) (0.187) (0.1

Observations: 69,129 59,199 69,129 59,199 69,129 59,199 60,092 54,313 60,092 54,13
 28 

Source: Estimates based on Statistics of Income’s Continuous Work History Survey data for years 1979 to 2001. Notes: Estimates from 2SLS regressions. Income range is $10,000 and above. Regressions are weighted by income. All regressions instatus and dummies for each base year. Robust standard errors are in parentheses.TABLE 3. Estimates for the 1990s and for Both Decades 

Panel 1 Panel 2 

1990s 1979-2001

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 

Taxab

Incom

Elasticity 0.475 0.738 0.184 0.177 0.148 0.195 0.121 0.192 0.174 0.305 

(0.105) (0.168) (0.094) (0.137) (0.097) (0.144) (0.077) (0.103) (0.078) (0.099

Married -0.015 -0.122 0.087 0.063 0.08 0.086 -0.01 -0.113 0.082 0.056 

(0.008) (0.014) (0.011) (0.017) (0.009) (0.015) (0.007) (0.011) (0.010) (0.015

single -0.039 -0.09 -0.014 -0.042 -0.014 -0.027 -0.028 -0.083 -0.012 -0.047 

(0.010) (0.016) (0.010) (0.017) (0.010) (0.017) (0.008) (0.012) (0.009) (0.014

ln(income) -0.099 -0.162 -0.099 -0.165 

(0.010) (0.013) (0.009) (0.013

 splinedecile 1 -0.827 

 (0.021) 

decile 2 -0.504 

 (0.024) 

decile 3 -0.243 -0.408 

(0.045) (0.031) 

decile 4 -0.186 -0.293 

(0.030) (0.039) 

decile 5 -0.109 -0.27 

(0.030) (0.046) 

decile 6 -0.135 -0.277 

(0.034) (0.046) 

decile 7 -0.039 -0.168 

(0.035) (0.049) 

decile 8 -0.172 -0.232 

(0.036) (0.057) 

decile 9 0.097 0.067 

(0.049) (0.071) 

decile 10 -0.122 -0.155 

(0.021) (0.028) 

constant -0.067 -0.033 0.952 1.588 0.128 7.313 -(0.090) (0.027) (0.917) (1.638

(0.011) (0.019) (0.103) (0.134) (0.019) (0.156) 0.012 0.015 0.096 0.129 

Observations: 158,679 139,673 158,679 139,673 158,679 139,673 218,771 193,809 218,771 193,8
 29 

TABLE 4. The Effect of Excluding the Most Influential Observations Income Weighted Estimates for the 1980s 

Dropped 

Observations Sample Size Estimated ETI 

 0 54,136 0.373  10 54,126 0.235  25 54,111 0.174  50 54,086 0.116  100 54,036 0.084 

 

Source: Estimates based on Statistics of Income’s Continuous Work History Survey data for years Notes: Estimates are based on Continuous Work History Survey data for years 1979 to 1990. a. Estimates are based on the specification with a 10-piece spline. Observations are dropped 

based on the size of their impact on the estimated ETI and as measured by a dfbeta test. 
 30 

TABLE 5. Person-Weighted Taxable-Income Elasticities by Decile for the 1980s 

Estimated 

ETI

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 10 0.207 

(0.126) 

99.5 to 100 percentile 0.572 

(0.289) 

Observations 54,136 

R-squared 0.28 

Source: Estimates based on Statistics of Income’s Continuous Work History Survey data for years 1979 to 1990. Notes: 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. Decile 10 excludes the top half of one percent. 
 31 

TABLE 6. Full SOI Taxable and Broad-Income Elasticities for the 1980s 

 

No Income Controls Base-Year Income 

Controls 

Spline Income Controls 

Broad 

Income 

Taxable 

Income 

Broad 

Income 

Taxable 

Income 

Broad 

Income 

Taxable 

Income 

ln(mtrt+3/mtrt) -0.033 -0.001 0.309 0.648 0.210 0.425 

 (0.036) (0.059) (0.048) (0.081) (0.048) (0.081) 

Married 0.079 0.011 0.118 0.069 0.140 0.096 

 (0.008) (0.011) (0.008) (0.012) (0.009) (0.012) 

Single 0.014 -0.012 0.023 0.007 0.031 0.028 

 (0.008) (0.012) (0.008) (0.012) (0.008) (0.012) 

Age 0.045 0.072 0.056 0.086 0.065 0.10 

 (0.003) (0.004) (0.004) (0.005) (0.004) (0.005) 

Age Squared/10 -0.011 -0.017 -0.013 -0.019 -0.015 -0.022 

 (0.001) (0.001) (0.001) (0.001) (0.001) (0.001) 

Age Cubed/100 0.008 0.011 0.009 0.012 0.010 0.014 

 (0.000) (0.001) (0.001) (0.001) (0.001) (0.001) 

sex 0.007 0.007 0.006 0.004 0.005 0.003 

 (0.001) (0.001) (0.001) (0.001) (0.001) (0.001) 

itemzer_base -0.004 -0.039 -0.055 -0.117 -0.069 -0.126 

 (0.004) (0.006) (0.005) (0.008) (0.005) (0.008) 

ln(income) -0.091 -0.145 

 (0.005) (0.008) 

decile 1 -0.918 -0.610 

 (0.186) (0.016) 

decile 2 -0.219 -0.235 

 (0.017) (0.018) 

decile 3 -0.169 -0.213 

 (0.018) (0.025) 

decile 4 -0.123 -0.168 

 (0.022) (0.030) 

decile 5 -0.142 -0.176 

 (0.022) (0.033) 

decile 6 -0.041 -0.021 

 (0.027) (0.034) 

decile 7 -0.004 -0.069 

 (0.024) (0.031) 

decile 8 -0.033 0.006 

 (0.041) (0.054) 

decile 9 -0.066 -0.136 

 (0.054) (0.100) 

decile 10 -0.137 -0.131 

 (0.035) (0.069) 

Constant -0.73 -1.12 0.049 0.111 7.738 4.119 

 (0.054) (0.073) (0.070) (0.098) (1.732) (0.157) 

Observations 248,940 250,140 248,940 250,140 248,940 250,140 

Notes: Estimates are based on Statistics of Income data for years 1979 to 1990. 

Estimates are from 2SLS regressions. The income range is $10,000 and above. Regressions are 

weighted by the inverse of sampling probabilities and by income (see Section III). Robust standard 

errors (clustered by individual) are in parentheses.

 
 32 

TABLE 7. Full SOI Taxable and Broad-Income Elasticities for the 1990s 

 

No Income Controls Base-Year Income Controls Spline Income Controls 

Broad 

Income 

Taxable 

Income 

Broad 

Income 

Taxable 

Income 

Broad 

Income 

Taxable 

Income 

ln(mtrt+3/mtrt) 0.478 0.745 0.133 0.144 0.125 0.198 

 (0.044) (0.071) (0.038) (0.058) (0.037) (0.060) 

Married 0.091 0.013 0.139 0.082 0.137 0.092 

 (0.010) (0.011) (0.009) (0.010) (0.010) (0.011) 

Single 0.017 -0.024 0.029 0.002 0.029 0.014 

 (0.009) (0.011) (0.009) (0.010) (0.009) (0.010) 

Age 0.016 0.028 0.028 0.043 0.028 0.050 

 (0.006) (0.007) (0.006) (0.006) (0.006) (0.006) 

Age Squared/10 -0.006 -0.008 -0.007 -0.010 -0.007 -0.011 

 (0.001) (0.001) (0.001) (0.001) (0.001) (0.001) 

Age Cubed/100 0.004 0.006 0.005 0.006 0.005 0.007 

 (0.001) (0.001) (0.001) (0.001) (0.001) (0.001) 

sex 0.004 0.002 0.001 -0.002 0.001 -0.001 

 (0.001) (0.001) (0.001) (0.001) (0.001) (0.001) 

itemzer_base 0.012 -0.023 -0.096 -0.127 -0.083 -0.119 

 (0.005) (0.005) (0.006) (0.006) (0.006) (0.006) 

ln(income) -0.107 -0.120 

 (0.004) (0.004) 

decile 1 -0.025 -0.554 

 (0.022) (0.014) 

decile 2 -0.19 -0.201 

 (0.021) (0.014) 

decile 3 -0.102 -0.170 

 (0.018) (0.017) 

decile 4 -0.153 -0.147 

 (0.020) (0.020) 

decile 5 -0.075 -0.021 

 (0.020) (0.016) 

decile 6 -0.033 -0.053 

 (0.013) (0.016) 

decile 7 -0.094 -0.097 

 (0.015) (0.022) 

decile 8 -0.139 -0.204 

 (0.026) (0.039) 

decile 9 -0.311 -0.314 

 (0.064) (0.079) 

decile 10 -0.095 -0.08 

 (0.046) (0.049) 

Constant -0.218 -0.304 0.776 0.720 0.080 4.472 

 (0.096) (0.104) (0.100) (0.103) (0.100) (0.150) 

Observations 323,776 449,584 323,776 449,584 323,776 449,584 

Notes: Estimates are based on Statistics of Income data for years 1988 to 2001. 

Estimates are from 2SLS regressions. The income range is $10,000 and above. Regressions are weighted by the 

inverse of sampling probabilities and by income (see Section III). Robust standard errors (clustered by individual) are 

in parentheses. 

 
 33 

TABLE 8. Full SOI Taxable and Broad-Income Elasticities for the 1980s and 1990s 

 

No Income Controls Base-Year Income Controls Spline Income Controls 

Broad 

Income 

Taxable 

Income 

Broad 

Income 

Taxable 

Income 

Broad 

Income 

Taxable 

Income 

ln(mtrt+3/mtrt) 0.168 0.277 0.247 0.359 0.227 0.339 

 (0.028) (0.045) (0.027) (0.044) (0.028) (0.045) 

Married 0.081 0.01 0.131 0.074 0.141 0.093 

 (0.006) (0.008) (0.007) (0.008) (0.007) (0.008) 

Single 0.012 -0.019 0.029 0.002 0.034 0.017 

 (0.006) (0.008) (0.006) (0.008) (0.006) (0.008) 

Age 0.031 0.046 0.041 0.057 0.045 0.068 

 (0.004) (0.005) (0.003) (0.004) (0.004) (0.004) 

Age Squared/10 -0.009 -0.012 -0.01 -0.013 -0.011 -0.015 

 (0.001) (0.001) (0.001) (0.001) (0.001) (0.001) 

Age Cubed/100 0.006 0.008 0.007 0.008 0.007 0.009 

 (0.001) (0.001) (0.001) (0.001) (0.001) (0.001) 

sex 0.006 0.004 0.003 0.001 0.003 0.000 

 (0.001) (0.001) (0.001) (0.001) (0.001) (0.001) 

itemzer_base 0.009 -0.024 -0.076 -0.123 -0.079 -0.125 

 (0.003) (0.004) (0.004) (0.005) (0.004) (0.005) 

ln(income) -0.098 -0.121 

 (0.003) (0.003) 

decile 1 -0.033 -0.573 

 (0.122) (0.011) 

decile 2 -0.203 -0.218 

 (0.013) (0.011) 

decile 3 -0.154 -0.182 

 (0.012) (0.014) 

decile 4 -0.125 -0.175 

 (0.014) (0.017) 

decile 5 -0.133 -0.062 

 (0.014) (0.015) 

decile 6 -0.016 -0.031 

 (0.013) (0.015) 

decile 7 -0.062 -0.065 

 (0.013) (0.018) 

decile 8 -0.101 -0.143 

 (0.021) (0.030) 

decile 9 -0.267 -0.296 

 (0.047) (0.058) 

decile 10 -0.130 -0.120 

 (0.038) (0.037) 

Constant -0.529 -0.749 0.363 0.343 -0.217 4.249 

 (0.056) (0.070) (0.062) (0.075) (0.112) (0.114) 

Observations 572,716 699,724 572,716 699,724 572,716 699,724 

Notes: Estimates are based on Statistics of Income data for years 1979 to 2001. 

Estimates are from 2SLS regressions. The income range is $10,000 and above. Regressions are 

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

(clustered by individual) are in parentheses. 

 
 34 

TABLE 9. Inclusion of Additional Demographic Variables  Broad Income Taxable Income 

(1) (2) (3) (4) 

Added Demographics No Yes No Yes 

1979 to 1987 0.183 0.210 0.365 0.425 

 (0.052) (0.048) (0.083) (0.081) 

1988 to 1998 0.174 0.125 0.192 0.198 

 (0.038) (0.037) (0.060) (0.060) 

1979 to 1998 0.198 0.227 0.276 0.339 

 (0.029) (0.028) (0.046) (0.045) 

Notes: Estimates are based on Statistics of Income data. Estimates are from 2SLS regressions. The income range is $10,000 and above. Regressions are weighted by the inverse of sampling probabilities and by income. Robust standard errors (clustered by individual) are in parentheses. 
 35 

TABLE 10. Separate Controls for Mean Reversion and Divergence in the Income Distribution 

Income Controls 

1980 to 

1987 

1988 to 

1998 

1980 to 

1998 

ln(taxable incomet-1) and ln(taxable incomet/taxable incomet-1) 0.666 0.191 0.334 

(0.116) (0.059) (0.053) 

Spline of ln(taxable income 0.400 0.264 0.345 t-1) and spline of ln(taxable 

incomet/taxable incomet-1) (0.108) (0.060) (0.056) 

Observations 

148,837 350,03

0 

498,86

7 

Notes: Estimates are based on Statistics of Income data. Estimates are from 2SLS regressions. The income range is $10,000 and above. Regressions are weighted by the inverse of sampling probabilities and by income. Robust standard errors (clustered by individual) are in parentheses. 
 36 

TABLE 11. Comparing Dollar Weighted Estimates Using Federal and State Marginal Tax Rates Comparison of Estimates Using Federal and State Marginal Tax Ratesa

Panel 1: Federal Rates Only

Panel 2: State Rates Only

1979 

to 

1987 

1988 

to 

1998 

1979 

to 

1998 

1979 

to 

1987 

1988 

to 

1998 

1979 

to 

1998 

Taxable 0.423 0.212 0.347 0.343 0.105 0.226 Income (0.061) (0.060) (0.038) (0.098) (0.103) (0.066) 

0.205 0.11 0.192 0.365 0.081 0.215 Broad Income 

(0.046) (0.037) (0.026) (0.070) (0.059) (0.041) 

Notes: Estimates are based on Statistics of Income data. Estimates are from 2SLS regressions and include a 10-Piece Spline of ln(Income). The income range is $10,000 and above. Regressions are weighted by the inverse of sampling probabilities and by income. Robust standard errors (clustered by individual) are in parentheses. Coefficients other than the elasticities are suppressed. 
 37 

TABLE 12. Full SOI Dollar-Weighted Taxable-Income Elasticities for Upper-Income Filers  

ETI 

Time-Period $100k and Up 

1979 to 1998 0.441 

 (0.089) 

1979 to 1987 0.426 

 (0.148) 

1988 to 1998 0.232 

 (0.098) 

Notes: Estimates are based on Statistics of Income data for years 1979 to 2001. Estimates are based on the specification with a 10-piece spline. Regressions are weighted by the inverse of sampling probabilities and by income. Robust standard errors (clustered by individual) are in parenthesis. 
 38 

TABLE 13. Full SOI Estimates after Excluding 

Years Most Likely Contain Transitory Behavior 

Broad Income 

Taxable Income 

1979 to 1987 0.102 0.356 

 (0.113) (0.255) 

obs 64,769 57,709 

1988 to 1998 0.076 0.149 

 (0.048) (0.074) 

Obs 291,611 255,492 

1979 to 1998 0.183 0.299 

 (0.040) (0.064) 

obs 356,380 313,209 

Notes: Estimates are based on Statistics of Income data. Estimates are from 2SLS regressions and include a 10-Piece Spline of ln(Income). The income range is $10,000 and above. Regressions are weighted by the inverse of sampling probabilities and by income. Robust standard errors (clustered by individual) are in parentheses. Coefficients other than the elasticities are suppressed. 
 39 

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

Deciles ETIs 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 1

Decile 2

Decile 3

Decile 4

Decile 5

Decile 6

Decile 7

Decile 8

Decile 9

90 - 99.5 percentiles

Top 0.5 

Elasticity of Taxable Income

**

*