Working Paper Series 

Congressional Budget Office 

Washington, D.C. 

Panel Data Techniques and the Elasticity of Taxable Income 

Seth H. Giertz 

Tax Analysis Division 

Congressional Budget Office 

Washington, D.C. 

October 2008 

CBO Working Paper 2008-11 

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 the 

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

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

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

the authors. Papers in the series can be obtained at www.cbo.gov/publications. 
Panel Data Techniques and the Elasticity of Taxable Income 

Seth H. Giertz 

Abstract

This paper examines the elasticity of taxable income with a focus on income controls 

designed to control for divergence in the income distribution and mean reversion. 

Additional emphasis is placed on the difference between short-run and longer-run responses 

to tax rate changes. Several panel techniques are applied to tax return data for years 1991 to 

1997, followed by a cross-section analysis covering the same period. For each panel 

regression, an innovative inverted panel regression framework is employed to test the 

efficacy of the controls for mean reversion apart from controls for divergence in the income 

distribution. Finally, cross-section (and repeated cross-section) regressions are estimated for 

comparison. A major finding from comparing estimates from the standard and inverted 

panels is that even some of the more sophisticated techniques likely fail to adequately control 

for mean reversion at the top of the income distribution. Furthermore, the residual impact 

from mean reversion may still exert an enormous influence on elasticity estimates, which 

could help explain the lack of robustness reported in a number of papers in this literature. 

Analysis of cross-section data circumvents the problem of mean reversion and results in 

estimates that are robust with respect to sample income cutoffs. However, when vast 

differences likely exist between those experiencing a specific change in tax rates and other 

filers, estimates relying on either panel or cross-section data are likely to be poorly identified. 

The author thanks Emmanuel Saez, Joel Slemrod, David Weiner, Ed Harris, and Tom 

Woodward.
1

I. Introduction 

A series of CBO working papers has used panel data (primarily from tax returns) to measure 

the elasticity of taxable income (ETI).1 This line of research has been motivated by an increasing 

recognition of the importance of the ETI in tax policy design. In particular, because the ETI 

measures the responsiveness of taxable income to changes in the net-of-tax rate (NTR),2 it has 

emerged as a key parameter in assessing the efficiency and revenue implications of tax rate 

changes (Feldstein 1999). Attention in the CBO working papers has focused on the sensitivity of 

estimates to reasonable variants to the standard techniques employed in the literature. A major 

conclusion from this research is that isolating income responses to tax rate changes from the 

myriad other factors that influence income is difficult. And the range of estimates resulting 

from variations of what appear to be sound techniques is large, a conclusion supported by 

others working with panel data (Kopczuk 2005; Heim 2008). Where the true ETI falls within this 

wide range has tremendous implications for tax policy. For example, in examining the potential 

expiration of the Bush tax cuts, Giertz (2008b) reports that the deadweight loss per dollar of 

additional revenue from the federal income tax could range from $0.18 at an ETI of 0.2 to $1.25 

at an ETI of 0.8. 

It is widely recognized that mean reversion and diverging secular income trends across the 

income distribution are two of the key obstacles to identification in this literature.3 Despite 

sophisticated techniques developed to address these phenomena, identification remains elusive. 

Furthermore, it is often unclear which of the two phenomena is dominant. 

In this paper new elasticity estimates are produced with a focus on income controls 

designed to control for divergence in the distribution of income (between those with incomes in 

the highest 1 percent and the rest of filers) and mean reversion. Additional emphasis is placed 

on the difference between short-run and longer-run responses to tax rate changes. To this end, 

several different panel techniques are applied to tax return data for years 1991 to 1997, followed 

1 See Giertz (2005, 2006, 2008a, 2008c) and Eissa and Giertz (2006). 2 More precisely, the ETI measures the percent change in taxable income associated with a 1 percent change in the

NTR, where the NTR equal 1 minus the marginal tax rate – or the share of marginal income that taxpayer has after

taxes.

3 See Giertz (2004) and Slemrod (1998) for a discussion of these issues.
2

by a cross-section analysis covering the same period.4 Cross-section analysis is not plagued by 

mean reversion, but must still confront divergence in the income distribution (as well as some 

potential obstacles not present with panel data analysis). The panel techniques include 

variations of a differencing approach employed by Gruber and Saez (2002) and others, as well 

as a regression-based tabulated differences-in-differences approach similar to that used by 

Moffitt and Wilhelm (2000). Additionally, for each panel regression, an innovative inverted 

panel regression framework is employed to test the efficacy of the controls for mean reversion 

apart from controls for divergence in the income distribution.5 Finally, cross-section (and 

repeated cross-section) regressions are estimated for comparison. 

A major finding from comparing estimates from the standard and inverted panels is that 

even some of the more sophisticated techniques likely fail to adequately control for mean 

reversion at the top of the income distribution. Furthermore, the residual impact from mean 

reversion may still exert an enormous influence on elasticity estimates, which could help 

explain the lack of robustness reported in a number of papers in this literature. Analysis of 

cross-section data circumvents the problem of mean reversion and results in estimates that are 

robust with respect to sample income cutoffs. However, in instances where vast differences 

likely exist between those experiencing a specific change in tax rates and other filers, estimates 

relying on either panel or cross-section data are likely to be poorly identified. 

II. Data 

Individual tax return data are from the Statistics of Income (SOI) and span years 1991 to 1997. 

The SOI heavily oversamples high-income filers, who, earlier research suggests, play a critical 

role in determining overall responses to changes in tax rates.6 Those at the top of the income 

4 The key tax change over this period results from the Omnibus Budget Reconciliation Act of 1993 (OBRA 93),

which created two new high-income tax brackets with marginal rates of 36 and 39.6 percent. OBRA 93 also lifted

the cap on the Medicare portion of the FICA tax, which applies only to earned income.

5 This technique effectively inverts the data. While the standard approach might compare changes in income from

1992 to 1993 to the increase in tax rates from 1992 to 1993, the inverted approach compares the changes in income

from 1993 to 1992 to the decrease in tax rates from 1993 to 1992. For more detail, see Section III. 6 The SOI’s sampling strategy could cause regression estimates to be biased, but this possibility is averted by

weighting observations by the inverse of their probability of appearing in the sample.
3

distribution are responsible for a very large and, for more than three decades, growing share of 

both overall income and tax payments (see CBO 2001 and Piketty and Saez 2003). 

The focus of this paper is methodological (i.e., an examination of factors that may impede 

identification) rather than an attempt to produce a best estimate of the ETI, so adjusted gross 

income (AGI) may be a better measure than taxable income, since it eliminates some 

idiosyncratic variation that may be difficult to model. (And if current methods fail to 

adequately control for nontax factors influencing AGI, they will similarly fail with taxable 

income.) AGI is a simpler measure than taxable income and is likely less subject to fluctuation 

from factors such as changes to itemized deductions or exemptions. An accurate measure of the 

elasticity of AGI with respect to the net-of-tax rate (NTR) represents a lower bound for the ETI, 

since AGI responses are a subset of responses to taxable income. 

For similar reasons, marginal tax rates are imputed (using CBO’s federal tax model) only for 

the federal income tax, an approach that excludes changes in the payroll tax (which applies only 

to earned income) and in state tax rates. While this leaves an incomplete measure of the 

marginal tax rate, it has the virtue of simplicity, making it easier to focus on responses to OBRA 

93 and exclude responses to changes in state tax rates. Additionally, for itemizers the effect of 

changes in state MTRs is mitigated since their overall NTR is (1 – τfed)∙(1 – τstate). Income, 

denoted zit, is a constant-law measure of AGI for individual i at time t, excluding capital gains 

and including all Social Security benefits, such that 

z = reported_agi – realized_CG + nontaxable_SS_benefits + deducted_moving_expenses. (1) 

Dollar values are adjusted by the IRS’s inflation adjustment factors, using 1991 as the base.7

Summary Statistics 

Average income for years 1991 to 1997 is about $39,000 (in 1991 dollars) and the average federal 

MTR is 16.2 percent.8 Imputed MTRs are flat throughout the period, except at the very top of the 

income distribution (see Table 1). Data are examined in both cross-section and panel forms. For 

the cross section, individual identifiers are not used to link filers across years and thus fractiles

7 See www.irs.gov/irb/2007-34_IRB/ar10.html.

8 These averages are constructed to reflect the overall population of tax filers. This is done by weighting

observations by the inverse of the probability of each filer being sampled.
4

Table 1. Average Federal Marginal Tax Rates by Income FractileCross Section 1991 1992 1993 1994 1995 1996 1997P50-80 18.5 18.3 18.2 18.4 18.5 18.8 19.1P80-90 24.2 23.6 23.5 24.4 24.8 25.1 25.5P90-95 27.8 27.7 27.8 28.1 28.0 28.2 28.2P95-99 30.1 30.3 30.4 30.7 31.1 31.5 31.9P99-100 32.4 32.3 39.3 39.5 39.6 39.6 39.5

Base Year: 1991 1992 1993 1994 1995 1996 1997

Standard Panel

base

year

year

t+1

base

year

year

t+1

base

year

year

t+1

base

year year t+1

base

year year t+1

base

year year t+1

P50-80 18.2 18.0 18.0 17.9 18.0 18.0 18.0 18.3 18.2 18.4 18.4 18.7

P80-90 24.0 22.9 23.5 22.8 23.2 23.6 24.2 23.7 24.6 24.1 24.8 24.3P90-95 27.7 26.4 27.7 26.5 27.8 26.9 28.0 27.0 28.0 27.4 28.2 27.6P95-99 29.8 28.9 30.0 29.1 30.0 29.5 30.2 30.1 30.6 30.3 30.9 30.6P99-100 32.9 31.6 32.8 36.8 39.2 37.0 39.1 37.5 39.3 37.4 39.3 37.3Inverted Panel

base

year year t-1

base

year year t-1

base

year year t-1

base

year year t-1

base

year year t-1

base

year year t-1

P50-80 18.0 18.5 17.9 18.2 18.0 18.1 18.1 17.8 18.4 18.0 18.6 18.3

P80-90 23.4 23.3 23.2 22.8 24.1 22.6 24.6 23.4 24.9 23.5 25.3 23.9P90-95 27.7 26.8 27.8 26.9 28.0 26.9 28.0 27.5 28.2 27.4 28.2 27.4P95-99 29.8 29.2 29.9 29.3 30.1 29.6 30.5 29.9 30.8 30.2 31.2 30.6P99-100 32.9 32.1 39.2 32.4 39.1 37.8 39.3 37.8 39.3 38.1 39.3 38.3Source: Estimates are based on Statistics of Income data for years 1991 to 1997.
5

are recalculated each year based solely on reported income for the given year. Therefore, each 

year the filers composing a given fractile change based on the re-sorting of incomes. For the 

panel, individual identifiers are used and fractiles are based on the distribution of income in 

each of the base years. Thus, comparisons of income and MTRs between one year and either a 

subsequent (or preceding) year are based on the average of individual level changes. And filers 

in the subsequent (or preceding) year do not necessarily fall into the same fractile that they were 

in during the base year. 

For fractiles in the top half of the income distribution, the change in average MTRs over 

consecutive years for the cross section is often well under 1 percent. However, the change in 

MTRs from 1992 to 1993 for the top 1 percent is 21.7 percent as a result of OBRA 93 (see Table 2). 

By comparison, the average MTR for those in the 95th to 99th percentile rose just 0.5 percent from 

1992 to 1993, suggesting that OBRA 93 had little or no effect on those outside the top 1 percent. 

For the panel, again the only substantial change in imputed MTRs is for the top 1 percent of 

the income distribution and occurs between 1992 and 1993. The average MTR for this top group 

increased 12.2 percent from 1992 to 1993—much less than the 21.7 percent increase observed in 

the cross section. This smaller growth is a result of mean reversion and rank reversal.9 Many of 

those in the top 1 percent of the panel in 1992 did not experience an increase in tax rates as a 

result of OBRA 93 because their incomes fell in 1993, leaving them in a lower tax bracket. The 

average MTR for those in the 95th to 99th percentile actually fell by 2.7 percent from 1992 to 1993, 

suggesting that effects from mean reversion more than outweighed any increase in MTRs from 

OBRA 93. 

Turning to income, AGI in the top 1 percent of the cross section drops by 6.5 percent from 

1992 to 1993, as OBRA 93 takes effect (see Tables 3 and 4). In contrast, the average AGI for those 

9 Upper-income fractiles include many filers with unusually high incomes (compared to these filers’ average

incomes over a number of years). Examining the same filers over time (i.e., panel data analysis) implies that

incomes in these top fractiles will fall (or grow at a slower rate) as a result of mean reversion (than they would were

mean reversion not present). Put another way, filers are assigned to the top 1 percent fractile, for example, based on

base (or initial) year income, independent of how much their income may drop between the base and subsequent

year. Those with incomes below the top 1 percent in the base year are still assigned to their initial fractile,

independent of how much their income may increase between the base and subsequent year. Repeated cross sections

do not suffer from mean reversion because fractiles are recalculated each year. However, rank reversal is likely

present with repeated cross sections. Rank reversal refers to changes in the composition of filers with reported

incomes in a particular fractile over time. Rank reversal can make identification difficult if some sources of income

are cross-sectionally correlated.
6

Table 2. Average Percent Change in Federal Marginal Tax Rates by Income Fractile

Cross Section

1991 to

1992

1992 to

1993

1993 to

1994

1994 to

1995

1995 to

1996

1996 to

1997

P50-80 -1.17 -0.16 0.86 0.88 1.57 1.14

P80-90 -2.50 -0.66 4.08 1.59 1.12 1.56

P90-95 -0.03 0.36 0.79 -0.17 0.71 0.08

P95-99 0.45 0.51 0.75 1.50 1.21 1.42

P99-100 -0.15 21.66 -0.64 0.27 -0.13 -0.05

Standard

Panel

1991 to

1992

1992 to

1993

1993 to

1994

1994 to

1995

1995 to

1996

1996 to

1997

P50-80 -1.26 -0.17 0.44 1.30 1.28 1.49

P80-90 -4.68 -2.76 1.76 -2.20 -1.91 -2.00

P90-95 -4.85 -4.55 -3.33 -3.53 -2.05 -2.10

P95-99 -2.84 -2.74 -1.73 -0.45 -1.02 -1.15

P99-100 -3.86 12.20 -5.56 -4.16 -4.65 -5.02

Inverted

Panel

1992 to

1991

1993 to

1992

1994 to

1993

1995 to

1994

1996 to

1995

1997 to

1996

P50-80 2.74 1.56 0.40 -1.85 -2.05 -1.95

P80-90 -0.17 -1.57 -6.30 -5.07 -5.37 -5.51

P90-95 -3.17 -3.23 -3.96 -1.79 -2.98 -2.91

P95-99 -1.88 -2.09 -1.42 -2.11 -2.07 -1.90

P99-100 -2.49 -17.32 -3.29 -3.66 -3.08 -2.66

Source: Estimates are based on Statistics of Income data for years 1991 to 1997.

in the 95th to 99th percentile fell by just 0.7 percent from 1992 to 1993. And over all other twoyear comparisons, AGI rises for all income groups, although the increases are greatest for the 

top 1 percent, often more than 6 percent, and from 1991 to 1992, 11.7 percent. 

For the panel, the top 1 percent’s drop in income from 1992 to 1993 is over twice as large 

(compared to the cross section), at 13.3 percent. This larger drop in AGI is again driven by mean 

reversion (within the panel and rank reversal with the repeated cross sections) at the top of the 

income distribution. The cross-section numbers show that reported AGI for the top 1 percent 

falls and for the panel it falls even more because some of those in the top 1 percent in 1992 are 

further down in the distribution in 1993. Those in the 95th to 99th percentile saw their incomes 

fall by 4.6 percent from 1992 to 1993. For the top 1 percent, incomes fell by 5.8 percent from 1993 

to 1994 (when the cap on the Medicare portion of the FICA tax was lifted). For the other 
7

Table 3. Average Incomes by Income FractileCrossSection 1991 1992 1993 1994 1995 1996 1997P50-80 36,677 36,815 36,148 36,255 36,918 37,191 38,272P80-90 61,201 61,404 60,668 60,980 62,549 62,987 64,724P90-95 81,421 82,021 80,941 81,690 84,667 85,608 88,353P95-99

121,03

6

123,41

4

122,56

5

123,89

7

129,43

2

132,61

0

138,57

2

P99-100

411,73

3

460,01

6

429,92

1

434,02

3

466,32

1

496,21

9

538,08

4

Base Year: 1991 1992 1993 1994 1995 1996 1997

StandardPanel

base

year

year

t+1

base

year

year

t+1

base

year

year

t+1

base

year

year

t+1

base

year

year

t+1

base

year

year

t+1

P50-80 36,804 36,776 36,858 36,417 36,207 36,770 36,350 37,686 37,033 37,784 37,254 38,785

P80-90 61,241 60,107 61,419 59,755 60,679 60,629 60,984 61,915 62,522 62,215 62,952 64,094P90-95 81,482 79,909 81,987 78,743 80,963 80,072 81,740 83,302 84,659 85,157 85,651 87,930P95-99

120,93

4

120,22

7

123,67

5

117,91

7

122,84

5

120,18

2

123,93

4

128,08

8

129,67

2

130,15

5

132,91

8

136,71

1

P99-100

413,88

8

426,36

6

460,50

3

399,06

6

432,30

8

407,07

4

433,71

7

448,60

0

468,29

6

463,55

6

495,59

8

498,91

7

InvertedPanel

base

year

year t1 base year year t-1 base year year t-1 base year year t-1 base year year t-1 base year year t-1

P50-80 37,056 36,975 36,213 36,393 36,337 35,528 37,016 35,570 37,206 36,285 38,307 36,628

P80-90 61,311 60,349 60,543 60,435 60,860 59,654 62,636 59,772 63,025 61,037 64,717 61,794P90-95 82,061 80,020 80,970 80,327 81,731 79,418 84,679 80,909 85,628 82,385 88,354 84,054P95-99

122,19

2

119,68

2

121,27

1

121,77

4

122,67

4

119,46

7

128,61

3

120,98

1

131,78

0

127,80

7

137,59

8

133,59

9

P99-100

439,29

2

407,55

9

422,05

0

453,98

9

424,31

8

423,41

5

456,32

7

431,61

9

485,96

9

466,86

0

523,68

6

500,34

6

Source: Estimates are based on Statistics of Income data for years 1991 to 1997.
8

Table 4. Average Percent Change in Income by Income Fractile

Cross

Section 1991 1992 1993 1994 1995 1996 1997

P50-80 0.38 -1.81 0.30 1.83 0.74 2.91

P80-90 0.33 -1.20 0.51 2.57 0.70 2.76

P90-95 0.74 -1.32 0.93 3.64 1.11 3.21

P95-99 1.96 -0.69 1.09 4.47 2.46 4.50

P99-100 11.73 -6.54 0.95 7.44 6.41 8.44

Standard

Panel

1991 to

1992

1992 to

1993

1993 to

1994

1994 to

1995

1995 to

1996

1996 to

1997

P50-80 -0.08 -1.20 1.56 3.67 2.03 4.11

P80-90 -1.85 -2.71 -0.08 1.53 -0.49 1.81

P90-95 -1.93 -3.96 -1.10 1.91 0.59 2.66

P95-99 -0.58 -4.66 -2.17 3.35 0.37 2.85

P99-100 3.01 -13.34 -5.84 3.43 -1.01 0.67

Inverted

Panel

1992 to

1991

1993 to

1992

1994 to

1993

1995 to

1994

1996 to

1995

1997 to

1996

P50-80 -0.22 0.50 -2.23 -3.90 -2.47 -4.38

P80-90 -1.57 -0.18 -1.98 -4.57 -3.16 -4.52

P90-95 -2.49 -0.79 -2.83 -4.45 -3.79 -4.87

P95-99 -2.05 0.41 -2.61 -5.93 -3.01 -2.91

P99-100 -7.22 7.57 -0.21 -5.41 -3.93 -4.46

Source: Estimates are based on Statistics of Income data for years 1991 to 1997.

two-year comparisons, AGI reported by top 1 percent of the panel either increases or marginally 

declines. 

III. Methodology 

Both panel and cross-section regressions are run on data for pairs of years in order to capture 

the short-, medium-, and long-run responses to the increase in top MTRs in 1993. The short run 

comprises responses from 1992 to 1993; the medium run, from 1991 to 1994; and the long run, 

1991 to 1997. Additionally, each of the panel specifications is followed by a pooled panel, which 

focuses on short-run responses and includes all years 1991 to 1997. Likewise, the cross-section 

analysis is followed by a repeated cross section that includes all years in the sample. 
9

Standard Panel 

As defined in the previous section, zit is the income reported by filer i in year t; τit is the 

marginal tax rate (on ordinary income); and k is the interval (one, three, or six years) over which 

behavior is examined. 

The estimating equation for the standard panel is 

log[zi,t+K/zit] = α + ψ∙log[(1 − τi,t+K)/(1 − τit)] + Xitβ + εit. (2) 

The key coefficient (ψ) is the elasticity, which measures the percent change in income associated 

with a 1 percent change in the NTR. The equation is estimated via two-stage least squares 

(2SLS) and all regressions are weighted by zit. 

All of the panel regressions are estimated using two different instruments for the tax 

variable. Instrumenting is necessary in order to focus on the effect of the NTR on income. The 

NTR is also a function of income; e.g., with a progressive rate structure, increases in income 

lead to lower NTRs. The first instrument is an imputed tax rate of the form log[(1−τi,tt+K )/(1−τit)]; 

i.e., the log change in the NTR applying to the last dollar of income from year t to t+K, where 

imputed income in year t+K equals income in year t inflated (by the IRS’s inflation adjustment 

factors) to year t+K; thus, differences across the two years arise from statute and not from 

behavioral changes. Regressions are rerun using a second instrument that targets the top 1 

percent of the income distribution (i.e., those affected by the tax change). This instrument is 

simply a dummy for those in the top 1 percent of the reported distribution of zit; the instrument 

equals 1 where pit >0.99 and zero otherwise, where p is the tax filer’s place in the income 

distribution, as measured in percentiles. The latter approach (using a dummy variable as the 

instrument) is similar in spirit to Feldstein’s (1995) tabulated differences-in-differences 

approach, but put into a regression framework (Moffitt and Wilhelm 2000). The regression 

framework allows for the inclusion of control variables. 

There are tradeoffs between the two approaches. The downside of the dummy variable 

approach is that the top 1 percent (those for whom pit > 0.99) is an imperfect approximation of 

the group experiencing a tax change, because it will include some filers who do not experience a 

tax change and exclude others who do. Additionally, the instrument does not account for 

variation in NTR decreases for those in the top 1 percent. However, the virtue of this method is 
10

not in the precision of the instrument but in its simplicity: although the instrument is cruder 

(than the imputed rate instrument) it is also more transparent and easier to interpret.10 Its source 

of identification is the disproportionate tax change experienced by the top 1 percent. With just 

two years of data and no controls, the regression coefficient (i.e., estimated elasticity) equals the 

difference in the average income growth rate between the top 1 percent and the rest of the 

distribution divided by the difference in average NTR changes for the two groups.11

Each equation is estimated first with no controls and then with two different sets of income 

controls, where Xit equals either (1) log(zit) or (2) log(zit) plus additional splines of log(zit). Each 

equation is also estimated using three different income cutoffs: (1) pit > 0.5; (2) pit > 0.9; and (3) zit

> $20,000. Because the effects from OBRA 93 are concentrated within the top 1 percent of tax 

filers, the income cutoffs will effectively change the composition of only the “counterfactual” 

group of filers who did not experience a tax change. 

Inverted Panel 

One of the problems in identifying an ETI is that changes in tax rates can be spuriously 

correlated with mean reversion at the top of the income distribution. For tax rate increases, the 

NTR will be positively correlated with mean-reverting changes; for rate decreases, the reverse is 

true. Researchers often include control variables to account for mean reversion at the top, but 

the effectiveness of these controls is not known. A potential solution to this problem is to focus 

on samples that include both tax increases and decreases (see Giertz 2007), in the hope that 

mean reversion from the two tax changes will cancel each other out (i.e., will have a net effect of 

zero). However, mean reversion at the top of the income distribution may vary across the two 

time periods because of different macroeconomic conditions or other unobserved factors. 

Another alternative is to “construct” a tax change by inverting the panel. For example, 

instead of starting in 1991 and continuing to 1997 (with a tax increase in 1993), suppose that one 

starts in 1997 and continues to 1991 (with a tax decrease in 1993). Thus, OBRA 93 would 

10 The imputed rate instrument (log[(1−τi,t

t+K)/(1−τit)]) incorporates many factors that affect the MTR simultaneously

to estimate the elasticity. It is less transparent in the sense that is difficult to grasp what all those changes are. For

example, small changes at the lower end of the income distribution due to a quirk in the law (such as the rounding

error for adjustment for inflation) could potentially have a substantial effect on the estimated elasticities.

11 Because the equations are estimated in log form, the estimated coefficients are in percent terms.
11

represent a cut in top MTRs. If the model is correctly identified, then the estimated elasticity 

should be the same for both the standard and the inverted panel.12

For the inverted panel approach, the estimating equation is identical to equation (3) with t

and t+K inverted throughout, such that 

log[zi,t/zi,t+K] = α + ψ∙log[(1 − τit)/(1 − τi,t+K)] + Xi,t+k β + εit. (4) 

The imputed rate instrument is now log[(1 − τt

i,t+K)/(1 − τi,t+K)]—i.e., the log change in the MTR 

from year t+K to t, where year t income equals income in year t+K deflated to year t. For the 

approach that targets the top 1 percent of income distribution, the instrument equals 1 where 

pit+1 > 0.99 (i.e., for the top 1 percent of zit+k). 

Pooled Panel 

In addition to estimating equation (2) for three different pairs of years (using the different 

income cutoffs and control variables), the equation is estimated using one-year differences and 

including all years, 1991 to 1997. The estimating equation can be expressed such that 

log[zi,t+1/zit] = α + ζt + ψ∙log[(1 − τi,t+1)/(1 − τit)] + Xitβ + εit , (3) 

where ζt are year dummies. The same income cutoffs and income controls (Xit) used for the 

panel analysis that relied on a single set of paired years are also used here. The imputed rate 

instrument for the pooled regressions is constructed identically to that for the two-year panel 

regressions. The instrument for the approach that targets the top 1 percent of the income 

distribution is again a dummy variable that equals 1 for the top 1 percent of filers for paired 

observations where t equals 1992 (and t + 1 equals 1993) and equals zero for all other paired 

observations; thus, the instrument is turned on only for the reform year at the top 1 percent of 

the distribution. 

Paired Cross Sections 

A solution to the problem of mean reversion is to use pooled cross-section data instead of a 

panel. With a cross section, the data are not paired across years, so individual indentifiers are 

12 This inverted methodology was suggested to me by Joel Slemrod, who, to my knowledge, was the first to come up

with the idea (at least in the context of the tax responsiveness literature). The approach was used as a sensitivity

check by Auten and Carroll (1999).
12

not needed (except possibly to adjust for heteroskedasticity) and the sample is not restricted to 

filers present in both years. The cross-section sample is constructed such that years t and t+k are 

stacked. The estimating equation takes the form 

log zi,s = α + ψ∙log(1 − τi,s) + γ1∙post-obra_dummyis + γ2∙high-income_dummyis + εis , (5) 

where s is the year. The post-OBRA dummy equals 1 for observations for years 1993 to 1997 and 

zero otherwise. The treatment dummy equals 1 for taxpayers in the top 1 percent of the 

distribution (i.e., those affected by the reform) and zero otherwise. The instrument for the NTR 

equals the product of the NTR and a dummy that equals 1 only for the top 1 percent of the 

income distribution in the end year (s = t+k). As with the panel, regressions are run using two 

years of data (to yield short-, medium-, and long-run estimates). For each set of years, 

regressions are weighted by zis and estimated for the following segments of the income 

distribution: (1) pis > 0.5; (2) pis > 0.8; (3) pis > 0.9; (4) pis > 0.95; and (5) zis > $20,000. 

Pooled Cross Sections 

The cross-section analysis is repeated when including all years 1991 to 1997. The estimating 

equation for the repeated cross section is 

log zi,s = α + ψ∙log(1 − τi,s) + γ1∙post-obra_dummyis + γ2∙high-income_dummyis + εis . (6) 

The postreform dummy equals 1 for years 1993 to 1997 and zero otherwise. The treatment 

dummy equals 1 for observations in the top 1 percent of the distribution in years 1993 to 1997 

and zero otherwise. This model is then reestimated after adding two time trend variables, one 

of the form s and one in which s is interacted with a dummy for those in the top 1 percent of the 

income distribution (i.e., pis > 0.99). The time trends are intended to control for differing secular 

trends in income between those affected and unaffected by the tax change. 

Sample Weighting 

In addition to weighting regressions by income, regressions are also weighted to adjust for the 

SOI’s nonrandom sampling properties. Inclusion in the SOI is conditional on several factors, 

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

is also constructed such that once filers are sampled, they continue to be sampled in all 
13

subsequent years, so long as their income increases (and other characteristics, such as filing 

status, do not change). In fact, the probability that one is observed in two different years is 

simply the minimum of the sampling probabilities for the two years. Without weighting, that 

sampling strategy raises the potential for spurious correlation between the dependent variable 

and the independent variables, including the tax variable. To avoid that possibility, 

observations (or paired observations) from the full SOI are weighted by the reciprocal of their 

probability of appearing in the sample. That strategy is discussed in Auten and Carroll (1999), 

who also employ the strategy using SOI data. 

IV. Results 

Findings from the Panel and Inverted Panel Analysis 

Without income controls, mean reversion (at the top) appears to dominate. In the standard 

panel, mean reversion appears to be positively correlated with a falling NTR, leading to large 

positive elasticity estimates.13 With the inverted panel, a rising NTR is negatively correlated 

with mean reversion, resulting in negative estimated elasticities (see the panel estimates for 

specification a for each of the income cutoffs in Table 5).14 These results are consistent with those 

reported by Auten and Carroll (1999) for the Tax Reform Act of 1986. With their richest set of 

controls, Auten and Carroll report an estimated elasticity (for gross income) of 0.57. With the 

inverted approach, this estimate nearly doubles to 1.13. Note that Auten and Carroll’s result is 

also consistent with mean reversion, since their estimate is much larger when the data ordering 

simulates a tax increase (or a rising NTR). 

Sample income cutoffs, which determine the comparison group of taxpayers not 

experiencing a tax change, often have a big impact on my estimated elasticities.15 Restricting the 

sample to those in the top 10 percent of zit generally results in estimates from the standard panel 

13 Without control variables, the drop in top incomes by filers above their longer-run average incomes will likely be

spuriously correlated with a falling NTR. In addition to income controls, including multiple pairs of years (some of

which do not span a tax change) might mitigate this problem.

14 For both the standard and inverted panels, more rapid secular income growth at the top of the income distribution

will tend to bias elasticity estimates downwards—unless controls adequately account for divergence in the income

distribution.

15 Income in the subsequent year of each paired observation is not subject to the same income restriction, but is

restricted to be greater than zero.
14

Table 5. Panel Elasticity Estimates Using the Imputed Rate Instrument

Income Cutoff: pit > 0.5 pit > 0.9 zit > 20,000

specification: 1 2 3 1 2 3 1 2 3

1992v1993 1.068 0.638 0.425 1.108 -0.097 -0.019 1.268 0.917 0.739

std. err. (0.129) (0.122) (0.175) (0.092) (0.137) (0.186) (0.152) (0.156) (0.216)

obs. 52,236 52,236 52,236 32,315 32,315 32,315 55,313 55,313 55,313

1991v1994 2.248 1.819 1.941 1.323 0.403 0.133 1.284 1.028 1.090

std. err. (0.224) (0.213) (0.257) (0.154) (0.213) (0.230) (0.101) (0.102) (0.115)

obs. 45,603 45,603 45,603 28,055 28,055 28,055 47,936 47,936 47,936

1991v1997 1.956 1.285 1.370 1.030 0.305 -0.101 1.174 0.659 0.617

std. err. (0.254) (0.224) (0.261) (0.184) (0.241) (0.225) (0.120) (0.113) (0.124)

obs. 41,524 41,524 41,524 25,697 25,697 25,697 43,572 43,572 43,572

INVERTED

PANEL

dependent var:

ln(z[it]/z[it+k])

1992v1993 -0.651 -0.694 -0.703 -0.661 -0.579 -0.857 -0.738 -0.780 -0.827

std. err. (0.079) (0.098) (0.122) (0.048) (0.073) (0.090) (0.079) (0.087) (0.112)

obs. 52,211 52,211 52,211 32,248 32,248 32,248 54,935 54,935 54,935

1991v1994 -0.144 -0.079 0.099 -0.828 -0.126 -0.086 -0.289 -0.273 -0.194

std. err. (0.082) (0.095) (0.099) (0.064) (0.084) (0.092) (0.085) (0.105) (0.106)

obs. 45,593 45,593 45,593 27,813 27,813 27,813 47,859 47,859 47,859

1991v1997 -0.137 0.106 0.423 -2.207 -1.040 -1.178 -0.259 0.005 0.223

std. err. (0.099) (0.114) (0.117) (0.077) (0.104) (0.110) (0.105) (0.131) (0.132)

obs. 42,350 42,350 42,350 25,752 25,752 25,752 44,895 44,895 44,895

POOLED REGULAR PANEL with YEAR DUMMIES

dependent var:

ln(z[it+1]/z[it])

ln(z[it+1]/z[it]) 0.289 0.255 0.237 0.330 0.145 0.143 0.288 0.241 0.238

std. err. (0.077) (0.076) (0.077) (0.201) (0.201) (0.200) (0.063) (0.062) (0.063)

obs. 331,782 331,782 331,782 208,745 208,745 208,745 349,208 349,208 349,208

POOLED INVERTED PANEL with YEAR DUMMIES

dependent var: ln(z[it]/z[it-1])

ln(z[it]/z[it-1]) -0.211 -0.683 -0.606 -0.388 -1.008 -0.707 -0.180 -0.787 -0.729

std. err. (0.058) (0.046) (0.035) (0.106) (0.083) (0.054) (0.056) (0.043) (0.034)

obs. 332,720 332,720 332,720 208,711 208,711 208,711 350,781 350,781 350,781

1) No controls. 2) log z[it] control. 3) log z[it] and additional splines in log z[it].

Regressions are weigted by income.

Source: Estimates are based on Statistics of Income data for years 1991 to 1997.

that are much smaller (and not statistically different from zero) than estimates from identical 

methods applied to samples with lower income cutoffs. Even modestly raising the income 

cutoff for inclusion in the sample, from zit < $20,000 to pit < 0.5, leads to very different elasticity 
15

estimates: Estimated elasticities based on the standard panel rise sharply over the medium and 

long term, but drop over the short term. 

Including splines of log(zit) has a substantial impact on the estimates, yielding positive, but 

smaller, elasticity estimates for the standard panel that, when imposing a $20,000 income cutoff, 

range from 0.62 to 1.1 depending on the two years compared. For the inverted panel, the 

controls raise the estimated elasticity in some cases, but in many instances estimates are still 

negative (see Table 5, specification c). When imposing a $20,000 income cutoff, estimates from 

the inverted panel range from −0.83 to (a statistically insignificant) 0.22 depending on the two 

years compared. Including the richest set of controls brings the estimates for the inverted and 

standard panels closer together (when comparing results over the same time interval), but the 

differences that remain are still substantial. This suggests that while including the richest set of 

income controls may improve identification, mean reversion still appears to severely 

contaminate elasticity estimates. 

One might expect estimates for 1992 versus 1993 to be larger than those covering longer 

intervals because the literature suggests substantial intertemporal income shifting, even when 

longer-run estimated elasticities are small. A comparison of panel estimates using the richest 

controls is not consistent with this hypothesis—for both the standard and inverted panels. 

Using the cruder instrument, a dummy variable turned on for those in the top 1 percent of 

the income distribution when the reform occurs (i.e., the instrument equals 1 when both pit > 

0.99 and t = 1992, and zero otherwise) results in elasticity estimates from the model without 

income controls that are qualitatively similar to those found from the standard panel analysis. 

In other words, mean reversion appears to dominate (see Table 6). 

In contrast to the analysis with the imputed rate instrument, estimates when including the 

richest set of income controls appear to severely overcorrect for mean reversion, resulting in 

large negative estimates for the regular panel and positive estimates for the inverted panel. 

Standard errors are also very large, so even large estimates are rarely statistically different from 

zero. 

With the richest controls (and using the cruder instrument), estimates are generally much 

larger for 1992 versus 1993 than when comparing longer time intervals. This, in contrast to the 
16

Table 6. More Panel Elasticity Estimates: Tabulated Differences-in-Differences within a Regression Framework

Income Cutoff: pit > 0.5 pit > 0.9 zit > 20,000

specification: 1 2 3 1 2 3 1 2 3

1992v1993 1.878 0.814 -1.669 1.395 -0.721 -1.866 1.858 1.002 -1.701std. err. (0.184) (0.149) (1.052) (0.107) (0.213) (0.711) (0.189) (0.190) (1.139)obs. 52,236 52,236 52,236 32,315 32,315 32,315 55,313 55,313 55,3131991v1994 3.352 1.347 -2.602 2.420 2.201 -12.494 3.137 2.233 -2.795std. err. (0.446) (0.332) (2.966) (0.221) (1.115) (18.013) (0.421) (0.615) (3.414)obs. 45,603 45,603 45,603 28,055 28,055 28,055 47,936 47,936 47,9361991v1997 4.955 0.498 -3.742 3.022 -26.805 -6.482 4.720 0.362 -3.818std. err. (0.963) (0.432) (1.528) (0.382) (22.439) (1.809) (0.885) (0.751) (1.687)obs. 41,524 41,524 41,524 25,697 25,697 25,697 43,572 43,572 43,572

INVERTED PANEL dependent var: ln(z[it]/z[it+k])

1992v1993 -0.488 -0.468 0.948 -0.430 0.314 0.948 -0.484 -0.504 0.949std. err. (0.093) (0.155) (0.707) (0.058) (0.129) (0.375) (0.103) (0.133) (0.766)obs. 52,211 52,211 52,211 32,248 32,248 32,248 54,935 54,935 54,9351991v1994 1.317 13.156 0.517 2.215 0.107 0.562 1.139 10.940 0.503std. err. (0.545) (8.331) (0.910) (0.549) (0.244) (0.497) (0.556) (5.239) (0.967)obs. 48,764 48,764 48,764 30,573 30,573 30,573 51,129 51,129 51,1291991v1997 -3.272 -9.561 0.154 -3.713 0.299 0.465 -3.135 -10.440 0.165std. err. (0.192) (1.101) (1.202) (0.121) (0.511) (2.194) (0.195) (1.238) (1.302)obs. 42,350 42,350 42,350 25,752 25,752 25,752 44,895 44,895 44,895

POOLED REGULAR PANEL with YEAR DUMMIES

dependent var: ln(z[it+1]/z[it])

ln(z[it+1]/z[it]) 1.878 0.955 0.723 1.395 0.537 0.564 1.858 1.115 0.736

std. err. (0.338) (0.247) (0.260) (0.296) (0.264) (0.259) (0.325) (0.276) (0.257)obs. 331,784 331,784 331,784 208,747 208,747 208,747 349,210 349,210 349,210

POOLED INVERTED PANEL with YEAR DUMMIES

dependent var: ln(z[it]/z[it-1])

ln(z[it]/z[it-1]) -0.488 -3.996 -1.874 -0.430 -3.003 -1.897 -0.484 -4.150 -1.913

std. err. (0.099) (0.064) (0.083) (0.115) (0.097) (0.079) (0.101) (0.063) (0.085)obs. 332,720 332,720 332,720 208,711 208,711 208,711 350,781 350,781 350,7811) No controls. 2) log z[it] control. 3) log z[it] and additional splines in log z[it].Regressions are weigted by income.

Source: Estimates are based on Statistics of Income data for years 1991 to 1997.
17

standard panel analysis, is consistent with the larger short-term responses and smaller longterm responses often reported in the literature. 

Findings from the Pooled Panel Analysis 

The pooled analysis confirms the results from the separate panels. Using either of the two 

instruments, mean reversion still seems to dominate regression estimates when excluding 

income controls (see Tables 5 and 6). With the richest set of income controls, comparing 

estimates from the standard and inverted panels suggests that mean reversion is still present 

and likely severe. Standard errors are much smaller than for the separate panels, so that 

estimates from applying the cruder instrument are now statistically significant. In contrast to 

the two-year panels, the pooled panel analysis suggests that the approach using the cruder 

instrument still undercorrects for mean reversion. Estimated elasticities when using the 

standard panel are positive and estimates from the inverted panel are negative. The disparity 

between the standard and inverted panel estimates is smaller (but still very large in terms of its 

economic importance) when using the imputed rate instrument. 

Findings from the Cross-Section Analysis 

In contrast to the panel analysis, estimates from the cross-section analysis are robust to changes 

to the sample income cutoff. Estimates are large (and positive) when including just years 1992 

and 1993. For the other pairs of years, estimated elasticities are negative. This suggests that 

short-term shifting is much larger than longer-term behavioral responses. However, the large 

negative estimates for the other pairs of years suggest that the model is not identified. 

Findings from the Repeated Cross-Section Analysis 

The simple repeated cross-section analysis, which excludes time trends, yields negative 

elasticity estimates (see Table 7). This result may suggest that differential secular income trends 

are driving the estimates. Those at the top of the income distribution, whose NTR falls in 1993, 
18

Table 7. Cross-Section-Based Elasticity Estimates

Income Cutoff: pit > 0.5 pit > 0.8 pit > 0.9 pit > 0.95 zit > $20k

dependent var: ln(zit)

1 1992v1993 0.958 0.977 0.998 1.024 1.026

(0.107) (0.108) (0.109) (0.111) (0.108)

133,825 100,446 86,869 78,193 140,634

2 1991v1994 -0.576 -0.536 -0.481 -0.409 -0.520

(0.111) (0.113) (0.115) (0.117) (0.109)

145,751 111,310 96,930 86,550 152,349

3 1991v1997 -2.830 -2.768 -2.565 -2.587 -2.801

(0.139) (0.144) (0.143) (0.159) (0.134)

159,046 123,170 108,482 98,169 166,708

4 Repeated CS -0.570 -0.499 -0.404 -0.315 -0.542

(0.087) (0.089) (0.089) (0.093) (0.086)

519,265 395,489 345,990 313,126 544,360

5 Repeated CS 1.342 1.326 1.329 1.280 1.460

w/ 2 time-trend vars (0.104) (0.104) (0.107) (0.106) (0.105)

519,265 395,489 345,990 313,126 544,360

Regressions are weigted by income.

Repeated cross-section regressions include year fixed effects.

Source: Estimates are based on Statistics of Income data for years 1991 to 1997.

experience a sharp increase in their share of total income (due to nontax factors). This could 

lead to a spurious negative correlation between the falling NTR and their rising incomes. 

Adding two time trends to the model (i.e., a standard time trend and a second time trend that 

applies only to those in the top 1 percent of the income distribution) fundamentally changes the 

elasticity estimates. They are now very large, ranging from 1.28 to 1.46, depending on the 

income cutoff for inclusion in the sample. The time trends, by allowing for separate secular 

income trends for those experiencing the tax change, counteracts the negative bias present in the 

first set of repeated cross-section estimates. While the time trends have an enormous impact, the 

model may still not be identified. Income trends differ within the top 1 percent of the income 

distribution, which are not accounted for here. Furthermore, there are a host of unobservables 

between those experiencing the tax increase and the rest of the income distribution that likely 

influence income growth in complex ways that cannot be accurately modeled with simple time 

trends. 
19

V. Conclusion 

This paper examines behavioral responses to the 1993 tax increase that primarily affected the 

top 1 percent of the income distribution. Several different panel techniques are applied to tax 

return data for years 1991 to 1997, followed by a cross-section analysis covering the same 

period. For each panel regression, an inverted regression is also run to test the efficacy of the 

controls for mean reversion. Estimates from the panel analysis are sensitive to sample income 

cutoffs, income controls and choice of instrument. Additionally, comparing similarly estimated 

elasticities from the standard and inverted panels suggests that even the richest income controls 

imperfectly control for mean reversion—and the residual impact from mean reversion may still 

be of enormous economic importance. Analysis of cross-section data circumvents the problem 

of mean reversion and results in estimates that are robust with respect to sample income cutoffs. 

However, when vast differences likely exist between those who experience a specific change in 

tax rates and other filers, estimates relying on panel or cross-section data are likely to be poorly 

identified. 
20

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