I. INTRODUCTION

The public-use March Current Population Survey (CPS) is the primary source of data for tracking levels and trends in U.S. labor earnings and for understanding the factors which influence these trends. Literatures that have used CPS earnings data are vast and include research on the changing returns to education or college major in the labor market (Autor 2014; Gemici and Wiswall 2014), earnings differentials across occupations (Glied, Ma, and Pearlstein 2015), earnings volatility (Hardy and Ziliak 2014), elasticity of taxable income (Burns and Ziliak Forthcoming), and more generally the causes of changes in wage structures and earnings inequality (see, e.g., Autor, Katz, and Kearney 2008; Card and DiNardo 2002; Goldin and Katz 2007; Juhn, Murphy, and Pierce 1993. Acemoglu 2002; Altonji and Blank 1999; and Katz and Autor 1999 provide reviews of this literature). However, these literatures that use the public-use CPS data have been hampered by an attenuated view of the right tail of the labor earnings distribution due to the topcoding of high earnings in the public-use CPS data. (1) Importantly, the failure to properly correct for inconsistent topcoding has been found to result in biased estimates for a range of outcomes including returns to education (Hubbard 2011), the size of the earnings gaps between gender and race groups (Burkhauser and Larrimore 2009a), the relative economic resources of individuals with and without disabilities (Burkhauser and Larrimore 2009b), and population-level income inequality (Burkhauser et al. 2012).

To correct for topcoding biases, public-use CPS-based researchers have generally pursued one of four paths: (1) ignoring the topcoding problem; (2) making an ad hoc adjustment to topcoded earnings values; (3) using a Pareto distribution to estimate earnings at the top of the distribution; or (4) using cell means or rank-proximity swapped data that is based on the still-censored internal CPS data. For example, a common ad hoc technique, based on estimates from Pareto imputations of top earnings, is to replace topcoded earnings with a multiple of the topcode threshold so all individuals with topcoded earnings in a year are assumed to have earnings at 1.3, 1.4, or 1.5 times the topcode threshold (Autor, Katz, and Kearney 2008; Juhn, Murphy, and Pierce 1993; Katz and Murphy 1992; Lemieux 2006). However, such an approach may misstate top earnings if the wrong multiple is used or if the appropriate multiple changes over time. Similarly, researchers using a Pareto imputation of top earnings may misstate those earnings if they are unable to obtain a reasonable fit for the Pareto distribution when using available public-use data.

Making use of internal March CPS files with their much higher censoring levels, we show that previous ad hoc estimates and Pareto estimations of top earnings based on public-use data understate mean earnings at the top of the earnings distribution and hence also understate earnings inequality. However, as this internal data are also censored, albeit at higher levels, any results based purely on the internal data will also fail to capture a portion of the income at the very top of the distribution and therefore will also understate inequality. Hence, while cell means based on internal data, such as those produced by Larrimore et al. (2008), and the rank-proximity swapped data series which the census began providing in 2010 each allow researchers to replicate results from the internal census data, findings using these series will be subject to the same limitations and understatement of true top incomes as the internal values.

Recognizing the limitations of the existing options to correct for topcoding, we proceed by using a continuous maximum likelihood estimator along with internal CPS data to produce a series of more accurate estimates of top earnings in the CPS data. Our estimates start with actual top earnings from the internal CPS combined with a Pareto estimate using these data for internally censored observations. With this hybrid approach, we create an enhanced cell-mean series that allows researchers who have access only to the public-use data to more accurately capture top earnings levels and trends, including estimated incomes for those above the internal censoring threshold.

To show the value of our new measure, we use it together with the public-use CPS to replicate the level and trend in labor earnings inequality from 1963 to 2004 that Kopczuk, Saez, and Song (2010) find using social security (SSA) administrative records for the subsample of U.S. workers who paid social security taxes in the commerce and industry sector of the labor market. Having done so, we then extend our analysis to 2013 and consider all workers. While earnings inequality levels are higher when considering all workers rather than just commerce and industry workers, its growth is more modest.

II. DATA

The March CPS survey contains a comprehensive set of questions on sources of household earnings, including labor earnings which are the focus of this study. (2) These data are collected annually by the Census Bureau, and the CPS is one of the primary sources of data for research on income and earnings trends in the United States (see, e.g., Autor, Katz, and Kearney 2008; Burkhauser et al. 2012; Card and DiNardo 2002; Feng, Burkhauser, and Butler 2006; Gottschalk and Danziger 2005).

A known limitation of the March CPS data is that incomes are topcoded in the public-use data and censored at higher thresholds in the internal data. These topcoding and censoring thresholds change on an ad hoc basis. Figure 1 provides an overview of these changes for annual wage earnings from 1967 to 1986 and for primary labor earnings, which are primarily wages, from 1987 to 2013. (3) Internal topcoding thresholds, with the exception of 1984, have always been higher than those in the public-use data but became substantially so after 1984. As a result, while the number of individuals who are topcoded in the internal data has risen somewhat since then, the number topcoded in the public-use data has risen much more. Figure 1 shows this growth, as measured by percent of individuals with earnings above the public topcode (right axis), is erratic, rising when the Census Bureau holds topcodes nominally constant and quickly falling when they raise the topcodes.

We use both the public-use and internal CPS data to illustrate the impact of different correction techniques for topcoded earnings on earnings trends. Our preferred technique is derived from the internal CPS data, but researchers without access to the internal data can use it with the public version of the CPS data.

III. ESTIMATING TOP EARNINGS

Most researchers measuring long-term trends in earnings with public-use CPS data use ad hoc techniques to correct for topcoding, such as imputing topcoded earnings as a fixed multiple above the topcode point, with most researchers using a multiple between 1.3 and 1.5 (Autor, Katz, and Kearney 2008; Juhn, Murphy, and Pierce 1993; Lemieux 2006). Implicit in this approach, regardless of the multiplier, is an assumption that the multiple is constant across years and across changes in the threshold level.

The multiples in this approach are partially derived from attempts to fit top earnings to a Pareto distribution. In particular, following the long-standing assumption that top earnings can be described by the Pareto distribution, numerous researchers impute the top of the earnings distribution based on those fit by a Pareto distribution (Bishop, Chiou, and Formby 1994; Fichtenbaum and Shahidi 1988; Heathcote, Perri, and Violante 2010; Hubbard 2011; Mishel, Bernstein, and Shierholz 2013; Piketty and Saez 2003; Schmitt 2003). (4)

The Pareto distribution is defined by the cumulative distribution function (CDF):

(1) P(X < x) = 1 - [([x.sub.c]/x).sup.[alpha]]

where x is a given value of earnings (weakly) larger than [x.sub.c], [x.sub.c] is the scale or cutoff parameter, and a is the shape parameter of the distribution. Because the Pareto distribution is scale-free, the mean above any threshold y is given as:

(2) M(y) = ([alpha]/[alpha] - 1)y.

This provides a simple link to the fixed multiple concept. By setting y as the topcode threshold, M(y) is the Pareto-imputed mean income above the threshold.

To use the Pareto distribution to estimate top earnings, one must first estimate the appropriate shape parameter. The most common approach is to assume that the distribution is Pareto above some lower cutoff point ([x.sub.c]) and choose a second cutoff point above that point--typically the topcode threshold itself ([x.sub.t]) (Parker and Fenwick 1983; Quandt 1966; Saez 2000; Shyrock and Siegel 1975). The Pareto shape parameter is then:

(3) [alpha] = ln (C/T)/ln([x.sub.t]/[x.sub.c])

where C represents the number of individuals with earnings above the lower cutoff and T represents the number of individuals with earnings above the topcode threshold. Juhn, Murphy, and Pierce (1993) report that their choice of cutoff points in the public-use CPS did not substantially impact their results. However, Schmitt (2003) using more recent public-use CPS data found that the choice of cutoff point could matter greatly, depending on the frequency of topcoding in the empirical distribution.

As we will illustrate below, this approach fails to provide reasonable estimates of top earnings in more recent public-use CPS data. This is partially because the earnings distribution may not be Pareto far enough below the public-use topcode threshold (if at all) to obtain reasonable estimates of the scale parameter and because using only two distribution points may poorly measure the parameter.

We address the first of these concerns by estimating the shape of the Pareto distribution using the internal data with its less restrictive censoring through 2007 and using the rank-proximity swap data (which offers the earnings values from the internal data but assigned to random individuals) for years since 2008.5 This allows us to reduce the portion of the distribution over which earnings must fit the Pareto distribution--l%-2% rather than the 10% or 20% with the public-use CPS data (Mishel, Bernstein, and Shierholz 2013, for example, assume that 20% of the earnings distribution fits the Pareto distribution).

To address the second concern, we adapt an alternate, but rarely used, approach to estimating the Pareto scale parameter--applying a maximum likelihood formula to the empirical distribution. We modify the widely used maximum likelihood Hill estimator (Hill 1975) such that earners under the topcode contribute an observation indicating their reported earnings to the likelihood function, while earners above the topcode contribute an observation indicating that they earn at least the topcoded amount. This differential contribution utilizes all available information to estimate the Pareto parameter, and it has been used to fit other distributions, such as the generalized beta of the second kind, to topcoded earnings data (Jenkins et al. 2011). While Polivka (2000) uses this modified Hill estimator to analyze categorical weekly earnings data, to our knowledge it has not been applied to continuous annual earnings data. Under this approach, the continuous, closed-form solution for estimating the Pareto parameter is:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where M is the number of individuals with earnings between the lower cutoff and censoring point, T is the number of individuals with earnings at or above the topcode or censoring point, and [x.sub.i] is the earnings of an individual. Using this formula allows individuals between the cutoff and censoring points to contribute to the CDF with their actual earnings, while those at the censoring point contribute to the CDF with the information that they have earnings at least as high as the censoring point.

To improve the estimate of top earnings further, rather than imputing all values the Census Bureau censors in the public-use data, we use actual internal data when available for estimating top earnings and only use the Pareto imputation for internally censored observations where the true value is unknown. In order to facilitate the use of these better estimates of top incomes, which combine actual internal data with imputations of censored observations, we create an enhanced cell-mean series consisting of the mean earnings of publicly topcoded individuals based on our combined set of internal data and Pareto estimates of censored observations. Researchers can use this series, available in Table Al, in conjunction with the public-use March CPS to obtain the best available estimate of top earnings based on these publicly available data.

In Figure 2, we compare the relative accuracy of the standard proportional and our maximum likelihood Pareto imputation approaches, along with the fixed multiple approach from Lemieux (2006) and Katz and Murphy (1992) in capturing the top part of the earnings distribution censored in the public-use CPS. Because the Pareto cutoff point matters for both approaches, when using the public-use data, we follow the approach of Mishel, Bernstein, and Shierholz (2013) and assume that the distribution is Pareto above the 80th percentile of the distribution. (6) Because we are using internal CPS data for the estimation using our maximum likelihood technique, we can use a much higher cutoff, and assume that the distribution is Pareto above the 99th percentile. (7)

To compare the accuracy of the various series, we compare the mean annual earnings of the top 5% of the distribution for each with those in the Larrimore et al. (2008) cell-mean series based on the internal CPS data. The Larrimore et al. (2008) cell-mean series uses the internal CPS data to provide the mean value for each source of income for any individual whose income from that source is topcoded. Because, as seen in Figure 1, fewer than 5% of individuals have topcoded earnings in any given year (and even fewer are censored internally), the mean earnings of the top 5% from the Larrimore et al. (2008) series will perfectly match the mean earnings of the top 5% from the actual internal data and the Census Bureau's rank-proximity swap series. But it is not designed to correct for internal censoring, and it treats each source of income at or above the internal censoring point as if it were equal to the censoring point. As a result, the Larrimore et al. (2008) series, the rank-proximity swap data, and the official Census Bureau statistics are known to represent underestimates of the true top earnings of the population.

While the top earnings using the Pareto imputation based on public-use data and those using the fixed multiple series each slightly exceed the top earnings from the Larrimore et al. (2008) cell-mean series in early years, neither does so after 1993 when changes in Census Bureau collection procedures greatly improved the reporting of earnings by top earners (see Jones and Weinberg 2000 and Ryscavage 1995 for details on this change). Because the cell-mean series is a lower bound for top earnings, it is clear that these previous efforts to capture the top part of the earnings distribution based solely on public-use CPS data understate their level at the upper tail since at least 1993.

In contrast to these earlier techniques, our maximum likelihood Pareto estimation of internally censored observations, in conjunction with the internal data when available, produces mean earnings of the top 5% which exceed those of Larrimore et al. (2008). In years before 1993, the impact of this adjustment is small. However, in more recent years, the addition of an imputation of censored earnings increases the average earnings of the top 5% by as much as 10% over the values from Larrimore et al. (2008). (8)

In comparing the series, it may appear counterintuitive that imputing censored earnings using a Pareto distribution increased top earnings by more after 1993 relative to the Larrimore et al. (2008) cell-mean series, when the Census Bureau increased their censoring threshold, than it did prior to that year. However, in addition to increasing the censoring threshold, the Census Bureau implemented other survey design changes in that year--such as electronic data collection--that fundamentally changed the shape of the upper tail of the observed income distribution. This can be observed in Table 1, which shows the percent of respondents in the data with earnings in high-income ranges (not adjusted for inflation). In each year from 1990 through 1992, between 0.18% and 0.24% of respondents reported earnings of $ 199,999 or more--and 0.06% of respondents reported income at or above the $299,999 internal censoring threshold for those years. In 1993, the fraction of respondents reporting an income of at least $199,999 nearly doubled to 0.43% of respondents. Similarly, the fraction with incomes of at least $299,999 tripled to 0.19% of respondents.

If the top of the income distribution does follow the Pareto distribution, this increase in the number of individuals with earnings near the censoring threshold suggests that there is also a longer right tail of earnings above the threshold. Thus, the improvements in data collection in 1993 increased information about both the observed and unobserved portions of the distribution. The results in Figure 2, where we use the internal data with a Pareto imputation for censored values, demonstrate that the break in the data series in the raw internal data (Jones and Weinberg 2000 and Ryscavage 1995) may, in fact, underestimate the improvements in capturing top incomes occurring in that year. Recognizing that this trend break is the result of new collection procedures and not changes to topcoding, we correct for the break using the standard approach from Atkinson, Piketty, and Saez (2011) and Burkhauser et al. (2012) and upwardly adjust inequality measures from all years before 1993, thus assuming no inequality change in the 1992-1993 trend break year.

IV. COMPARISON TO SSA RECORDS

Kopczuk, Saez, and Song (2010) provide the first research using administrative records data to analyze long-run earnings inequality. Their study uses SSA earnings data from 1937 to 2004 to examine earnings inequality of commerce and industry workers between the ages of 25 and 60 with wages over $2,575 in 2004, indexed by nominal average wage growth for earlier years. (9) This minimum earnings restriction represents one-fourth of the earnings an individual working full time for a year (2,000 hours) at the federal minimum wage would receive each year. This study is the current gold standard of annual earnings inequality trends and hence an excellent benchmark for testing the validity of our CPS-based results. If results from Kopczuk, Saez, and Song (2010) can be replicated in the CPS data, then it validates the use of CPS data for analyzing earnings trends. To this end, we limit our data sample to commerce and industry workers and impose the same age and minimum earnings restriction so that we can compare Gini coefficient results across the two datasets.

In Figure 3, we compare the earnings Gini for this subsample of workers from Kopczuk, Saez, and Song (2010) to our Pareto-adjusted income series as well as to estimates using the Larrimore et al. (2008) series, which were previously the best estimates of top earnings in the CPS data. (10) For each series, these Gini coefficients are estimated directly from the data after imposing the specified topcode correction. While we do not have access to internal CPS data before 1967, to extend the comparison we go back to 1963 using public-use CPS data. (11) Over these earlier years from 1963 to 1966, topcoding was so rare that no additional topcode corrections are required. (12)

Between 1967 and 1994, the inequality trend between the CPS data with our Pareto correction and the Kopczuk, Saez, and Song (2010) series using social security records is remarkably similar. In 1995, top earnings in the CPS series falls, resulting in a level of inequality that is approximately two-Gini points below the Kopczuk, Saez, and Song series. However, after that divergence the inequality trend between 1995 and 2004 continues to grow at a similar pace across the two series. Despite this divergence, our new series using the Pareto correction more closely matches the estimates from Kopczuk, Saez, and Song (2010) than does the Larrimore et al. (2008) cell-mean series.

This provides evidence that our correction improves the ability of the public-use CPS data to measure accurately and analyze U.S. earnings levels and trends.

V. IMPACT OF AGE AND EARNINGS RESTRICTIONS

After largely matching the earnings inequality trends from Kopczuk, Saez, and Song (2010), we now focus on the extent to which limiting the sample to commerce and industry workers and imposing age and earnings restrictions influences observed inequality trends. In Figure 4, while still excluding self-employment earnings, we compare the Gini coefficient for labor earnings that we get using our enhanced cell-mean series for all workers with any earnings to the Gini coefficient for labor earnings we got using the sample restrictions imposed by Kopczuk, Saez, and Song in Figure 3. In the restricted sample, earnings inequality increases by 16.7%-0.378 to 0.441--from 1963 to 2013. When looking at workers in all industries, the level of inequality was similar, but the growth slowed from 16.7% to 11.1%. When we remove the restriction of considering only workers aged 25-60, and consider workers of all ages with earnings above the $2,575 minimum earnings restriction, the level of inequality increases (in 2013 the Gini coefficient for our all-age group is 1.0% higher than the initial commerce and industry workers sample, 0.445 compared to 0.441), but its growth since 1963 is even slower. Without the age restriction, earnings inequality in 2013 was 5.2% above than in 1963.

Finally, we remove the $2,575 minimum earnings restriction and include all workers with earnings of at least $1 in the sample. Inequality, in 2013, in this fuller sample of workers is 10.2% higher than it is in the initial commerce and industry workers sample. But rather than increasing since 1963, earnings inequality is 2% lower in 2013 than it was in 1963. In contrast to the levels and trends in earnings inequality, Kopczuk, Saez, and Song (2010) and we observe in their subsample of workers, in our full sample of workers we find the level of inequality is higher but its growth is less.

VI. CONCLUSION

Inconsistent censoring in the public-use March CPS limits its usefulness in measuring labor earnings levels and trends. We find that previous approaches for imputing topcoded earnings systematically understate top earnings. In particular, both the fixed multiple approach and Pareto estimates based solely on public-use CPS data understate the level of top earnings in the internal CPS data--which is also subject to censoring and thus represents a lower bound. Our hybrid approach of internal data and Pareto imputations provides better estimates of top earnings in the CPS data. Using our hybrid approach, we create an enhanced cell-mean series for use with the public-use data that will allow researchers to more closely approximate the actual level of top earnings in CPS data. Using public-use CPS data together with our enhanced cell-mean series and mimicking Kopczuk, Saez, and Song (2010) sample restrictions, we observe labor earnings inequality levels that are more consistent with those Kopczuk, Saez, and Song (2010) report for the subsample of U.S. workers in commerce and industry captured by administrative social security records. As a result, we believe that our series represents the best available measure of estimating top earnings in the CPS data and demonstrates that the CPS data can provide reasonable estimates of U.S. labor earnings trends.

doi: 10.1111/ecin.12299

Online Early publication November 23, 2015

ABBREVIATIONS

CDF: Cumulative Distribution Function

CPS: Current Population Survey

ORG: Outgoing Rotation Group

SSA: Social Security Administration

APPENDIX

TABLE A1
Enhanced Cell Means for Wage and Salary Earnings
(1967-1986) and for Primary Earnings (1987-2013)

           Mean Wage
           and Salary
Income   Earnings above
 Year    Public Topcode

1967       68,718.88
1968       67,672.02
1969       70,602.84
1970       72,338.20
1971       69,964.24
1972       72,067.52
1973       72,276.09
1974       69,694.40
1975       68,484.37
1976       69,622.58
1977       70,377.94
1978       72,473.37
1979       77,877.91
1980       76,067.81
1981       116,517.60
1982       108,677.47
1983       110,527.71
1984       152,540.90
1985       147,726.89
1986       151,170.99

          Mean Primary
Income   Earnings above
 Year    Public Topcode

 1987      155,167.85
 1988      153,957.31
 1989      161,368.84
 1990      161.071.86
 1991      149,446.92
 1992      157,823.42
 1993      240,177.96
 1994      240,310.44
 1995      362,741.41
 1996      374,699.39
 1997      398,231.55
 1998      387,378.22
 1999      347,774.63
 2000      419,886.77
 2001      390,670.08
 2002      470,904.67
 2003      445,997.33
 2004      477,597.05
 2005      474,259.17
 2006      538,416.97
 2007      467,984.50
 2008      464,928.55
 2009      501,245.62
 2010      522,694.47
 2011      572,896.45
 2012      626,923.39
 2013      558,843.72

Notes: Figures based on authors' calculation using internal
CPS data and maximum likelihood Pareto fit at the 99th
percentile of the earnings distribution. "Income Year" records
income in the year prior to the year of the March CPS survey.
Enhanced cell means were not calculated for years before
1967 due to the lack of topcoding on earnings, when one individual
or fewer was topcoded each year. Enhanced cell means
for years since 2008 use the same hybrid procedure as used in
earlier years but base the Pareto imputation off of the rank-proximity
swap data from the Census Bureau rather than the
raw internal data. Because the rank-proximity swap data provide
the values in the internal data (albeit not matched to the
right people), we observe that this procedure allows for an
uninterrupted break in our enhanced cell-mean series up to
the most recent years of data.

Source: Authors' calculation using internal March CPS
Data.

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PHILIP ARMOUR, RICHARD V. BURKHAUSER and JEFF LARRIMORE *

* The research in this paper was conducted, in part, while the authors were Special Sworn Status researchers of the U.S. Census Bureau at the New York Census Research Data Center at Cornell University. This paper has been screened to ensure that no confidential data are disclosed. All opinions are those of the authors and should not be attributed to the Census Bureau, the Federal Reserve Board, the Federal Reserve Banks, or their staff. We thank Stephen Jenkins and participants at the Census Bureau's Center for Economic Studies Research Conference for their helpful comments on earlier drafts of this paper. Support for this research from the National Science Foundation (award nos. SES-0427889, SES-0322902, and SES-0339191) and the Employment Policy and Measurement Rehabilitation Research and Training Center at the University of New Hampshire, which is funded by the National Institute for Disability and Rehabilitation Research (NIDRR, grant no. H133B100030) are cordially acknowledged.

Armour: Associate Economist, RAND Corporation, Santa Monica, CA 90407. Phone 310-393-0411, Fax 310-3934818, E-mail parmour@rand.org

Burkhauser: Sarah Gibson Blanding Professor of Policy Analysis, Cornell University, Ithaca, NY 14853; Research Fellow, University of Melbourne, Parkville, Australia. Phone 607-255-2097, Fax 607-255-4071, E-mail rvbl@comell.edu

Larrimore: Economist, Federal Reserve Board, Washington, DC 20551. Phone 202-973-7315, Fax 202-452-3849, Email jeff.larrimore@frb.gov

(1.) Some wage inequality research focuses on the wage questions in the May outgoing rotation group (ORG) sample of the CPS, which is also subject to topcoding. Similar techniques to those used in the March CPS data have been employed in the May ORG sample to correct for topcoding, including replacing topcoded earnings with a fixed multiple of the topcode threshold (see, e.g., Acemoglu and Autor 2010).

(2.) The March CPS asks about income in the previous year, so the income year is always 1 year prior to the survey year. All references to years in this paper refer to the income year.

(3.) Because of Census Bureau changes in their aggregation techniques, we use wage and salary earnings for years prior to income year 1987 and all primary labor earnings thereafter. Because the vast majority of primary earnings are from wages and salaries, this break does not appear to have a noticeable impact on our results.

(4.) A smaller literature has used more flexible functional forms, such as the four-parameter generalized beta of the second kind (GB2) distribution or its special cases such as the Singh-Maddala (Burr type 12) distribution and Dagum (Burr type 3) distribution as alternatives to the Pareto (see, e.g., Bandourian, McDonald, and Turley 2003; Bordley, McDonald, and Mantrala 1996; Burkhauser et al. 2011; Feng, Burkhauser, and Butler 2006; and McDonald 1984). However, while such approaches offer additional flexibility in fitting the distribution, they have been criticized as being less easily interpretable than the single-parameter Pareto distribution which has gained wide usage including in the top income share literature using tax return data (see Atkinson, Piketty, and Saez 2011 for a detailed discussion of the use of the Pareto distribution in this literature).

(5.) Our access to internal CPS data extends through 2007. However, when the Census Bureau began providing rank-proximity swapped incomes in the public-use data for topcoded incomes in 2010, they did so for earlier years retroactively. This approach is intended to yield the same distribution for each earnings source as in the internal data, but randomly swaps earnings values among topcoded individuals to protect confidentiality. Because this data contain the same values as the internal data, but randomly assigned to individuals, it provides the same base of information as the internal data for our Pareto procedure. Hence, using these data with the same Pareto imputation technique for observations above the internal censoring point allows us to extend our series to include years after 2007. To ensure consistency, we used both the internal data and the rank-proximity swap data as a base for the Pareto estimation for overlapping years when we have access to both files. When doing so, we found consistent results. Results of this consistency check are available upon request from the authors.

(6.) We also used cutoffs at the 85th, 90th, and 95th percentiles. In general, increasing the income cutoff for the lower bound of the estimation lowered the estimated mean earnings of the top 5%.

(7.) We also used cutoffs at the 95th, 97th, and 98th percentiles and produced largely consistent results for the mean earnings of the top 5%.

(8.) As a further test of the validity of the Pareto at this income level, we compare the Pareto scale parameter for the 95th, 97th, 98th, and 99th percentiles. The Pareto parameters are generally stable, with the average difference between the maximum and minimum scale parameter in this range being just 16% apart. Pareto scale parameters are available upon request from the authors.

(9.) Commerce and industry workers are all nonfarm, nonself-employment wage and salary workers not working in agriculture, forestry, fishing, hospitals, educational services, social services, religious organizations, private households, and public administration.

(10.) While the cell-mean procedures used both by Larrimore et al. (2008) and in our enhanced cell-mean series removes the variance of topcoded earnings, Larrimore et al. (2008) demonstrated that the fraction of respondents who are topcoded is small enough that obtaining the level of their income is sufficient to correct for the trend in the Gini coefficient even without their variance. Larrimore et al. (2008) observed that the trend using the Gini coefficient for household income using the cell-mean series nearly perfectly matches the internal CPS data in both levels and trends. Because the Census Bureau's rank-proximity swap data also are based purely on the internal data, the Gini coefficient using that series would similarly match the results using the Larrimore et al. (2008) series presented here.

(11.) CPS data from 1961 are also available; however, the survey format changed between 1961 and 1963 which make the data incomparable between these years. Hence, we start our series in 1963, which is the earliest year for which we can create a consistent CPS series.

(12.) No more than one worker was topcoded on wage and salary earnings each year over this period.

TABLE 1
Percent of Earners in High Earnings Brackets
(in Nominal Dollars) in Years Before and After
Census's 1993 Changes to Data Collection
Procedures

                    Before Changes       After Changes
                    to Data              to Data
                    Collection           Collection
                    Procedures           Procedures

High earnings       1990   1991   1992   1993   1994   1995
  bracket

$199,999-$299,998   0.16   0.12   0.18   0.24   0.26   0.24
$299,999 or above   0.06   0.06   0.06   0.19   0.20   0.21

Note: Public-use CPS data with rank-proximity swap data.