The Rising Earnings Inequality at the Upper Tail of the Distribution

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The Rising Earnings Inequality at the Upper Tail of the Distribution

In the United States, men earn higher wages than women. Whites earn higher

wages than minorities. Northeast workers earn more than Southern workers. People are

interested in these facts because they want to know who the high income earners are and

why these earners are in this situation. In the U.S. in recent years, the conventional

wisdom holds that earners at the upper tail of the wage distribution have realized a

continuing rise in their wages. Empirical studies can investigate if this has truly been the

case. More importantly, these studies can analyze how the inequality has changed over

time and how easily the data can explain this occurrence.

Previous literature provides analysis of the earnings inequality in the United

States labor market over the past few decades. Autor, Katz, and Kearney (2005) examine

that the upper tail (90/50) inequality rose steadily from 1987 to 2003, while the lower tail

inequality (50/10) compressed or flattened. They apply methods of Machado and Mata

(2005), Dinardo, Fortin, and Lemieux (1996), and Juhn, Murphy, and Pierce (1993) to

inquire whether price or composition changes can explain the recent incidences as well as

how accurately the data can explain the inequality. Researchers can take this analysis

one step further by considering another possible wage inequality of the past few decades:

the high end of the upper tail (92.5/90), and to a greater extent, the (97/90) inequality.

The purpose of this paper is to extend the earnings inequality findings of Autor,

Katz, and Kearney (2005) to the upper tail of the wage distribution (97/90 and 92.5/90).

In addition, this paper evaluates the extent to which the data can explain this inequality,

using a modified version of the methods of Juhn, Murphy, and Pierce (1993). Autor,



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Katz, and Kearney clearly show that from 1979 to 2003, the 90/50 inequality rose

steadily; but this paper explores whether the highest earners (97 th, 95 th, and 92.5 th

percentiles) gained relative to other high earners (90 th percentile) in recent years.

The contributions of this work are to show that wage or earnings inequality not

only rose recently between the higher and median earners of the distribution, but it also

rose amongst the highest earners in the United States. Since Autor, Katz, and Kearney

(2005) do not address whether wage inequality occurs in the upper tail of the distribution,

this paper examines this issue. Finally, this paper applies the methods of previous papers

on earnings inequality to analyze the portion of the inequality in the upper tail that the

data can explain with observable variables, such as age and education (see Juhn, Murphy,

and Pierce 1993).

The results of this paper find that the 92.5/90 earnings inequality noticeably

increased from 1983-2004, and the observable data cannot explain fully this rise in

inequality. In addition, the 97/90 inequality rose by a similar margin as the 90/50

inequality from 1989-2004. Again, the data cannot explain entirely this rise in earnings

and struggles even further to explain the rise in inequality at the upper tail of the

distribution. This paper finds strong evidence to suggest that the highest earners in the

distribution realized the largest gains in earnings in recent years, both in absolute and

relative terms.

The first section of the paper discusses the data this study uses to analyze earnings

inequality. Section II presents summary statistics of these data. Then Section III

explains the methodology and econometric model this paper incorporates. Next, Section

IV presents the main results regarding the existence and magnitude of the rising wage



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topcodes the highest percentiles at a much higher rate from 1985-1988, I can only

construct the 92.5 th percentile over the entire 22-year period. In fact, the CPS MORG

even topcodes the 92.5 th percentile in 1988, but this paper avoids this potential problem

because the 92.5 th percentile in 1989 only earns $1 more than the topcoded amount for

1988.

II. Summary Statistics/Cross Tabulations

In this part of the paper, I plot informative summary statistics for the 90 th and 95 th

percentiles for the first and last years of the sample time period: 1983 and 2004. I obtain

the 90 th percentile by finding all the earners between the 90 th and 91 st percentiles, while

not including the earners who are exactly at the 91 st percentile (see Eissa 1995). I employ

the same method in obtaining the 95 th percentile. The CPS topcodes earners above the

96 th percentile for 1983; consequently, I cannot accurately tabulate the 97 th percentile for

1983. Table I illustrates how the observable variables in the 95/90 inequality changed

over a 22-year period. Finally, since the CPS MORG experienced fundamental changes

in 1994, 5-7% of the sample is missing data on usual earnings per week. Therefore, the

2004 sample in Table I has 758 observations for the 90 th percentile and 724 observations

for the 95 th percentile for usual earnings per week.



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Table I:1983 2004

Variable 90th 95th 90th 95thAGE 41.9 43.2 44.6 44.9MARRIED 84.2 87.6 81.5 82.3WHITE 93.8 94.6 87.1 91.3EDUC (in yrs) 14.2 15.3 15.8 16.4EDUC<12 8.4 4.2 1 0.5HS EDUC 30.5 19.3 11.8 8.512<EDUC<16 21.6 16.6 23.6 13.8COLLEGE EDUC 21.1 32.4 34.6 38.4POST-COL

EDUC 18.4 27.5 29 38.7EXPERIENCE 21.7 21.9 22.8 22.4SOUTH 17.2 25.9 19.5 25.4UNION 33.4 15.9 16.9 10.6USUAL HRS/WK 44.3 46.1 46.5 48.6EARNINGS/WK 725.4 903 1663.8 2150.6# of OBS 679 784 821 773

Table I provides a helpful picture for how key observable variables changed

between 1983 and 2004. First, Table I shows that high earners are older and more likely

to be single in 2004 than in 1983. Whites are the primary race in these upper percentiles,

but this trend is less startling in the 2004 sample, indicating that minorities became higher

earners in the distribution. The next important change to notice is that high earners have

much more education in 2004. The 2004 sample not only has more years of education

but also higher-level degrees than the 1983 sample. For example, the men in the recent

sample are much more likely to have a college degree or graduate level education. In

addition, men in 2004 work more hours and are less likely to belong to a union. These

men also have higher earnings, but these figures are in nominal dollars.

Table I also allows for interpretation of the differences in observable variables

between the 95 th and 90 th percentiles. The 95 th percentile consists of men who are

slightly older, are more likely to be married and white, have more education, work more,



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and are less likely to belong to a union. Interestingly, the 95 th percentile has a much

higher percentage of Southerners than the 90 th percentile for both sample years. Another

notable figure is that the 95 th percentile in 1983 consists of more men with some college

education than in 2004, but the 90 th percentile in 2004 contains more men with this same

level of education than in the earlier sample. Most of the education statistics clearly

show that the highest earners in the distribution obtain higher levels of education, and

that this occurrence becomes more common over the sample period. Finally, the most

important finding may be that the difference-in-difference valuation for the summary

statistics in Table I is fairly small for most of the variables.

III. Methodology and Econometric Estimation

This paper first finds the following percentiles in the distribution for usual

earnings per week from 1983-2004: 97 th, 95 th, 92.5 th, 90 th, 75 th, 50 th, 25 th, 10 th, 7.5 th, 5th,

3rd, and 1 st. Next, to find the residual earnings inequality, I run the following Ordinary

Least Squares (OLS) regression:

iii X w ε β +=ln (1)

where iw is usual earnings per week, and iX includes age, age squared, experience,

experience squared, and dummy variables for educational attainment, race, ethnicity,

marriage, the South, living in a rural area, and belonging to a union. Also, iε is the

earnings component accounted for by the unobservables. I calculate the experience

variable in the following manner (Autor, Katz, and Kearney 2005):

6exp −−= educationage .

This paper illustrates the results from Regression (1) for one of the median years

in the sample, 1993, in Table II. Table II shows that all of the explanatory variables from



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Table IIObs. 77023F(19, 77003) 2494.51Prob > F 0R-squared 0.381Adj R-squared 0.381

Log Earnings Coef. Std. Error t P>tAge 0.078 0.003 23.1 0

Age Squared 0.000 0.000-

15.6 0Married 0.135 0.004 36.3 0

Black-

0.221 0.006-

36.8 0

Native Amer.-

0.064 0.017 -3.7 0

Asian-

0.127 0.009-

13.8 0

Other-

0.053 0.022 -2.4 0.02

Rural-

0.144 0.004-

37.4 0

South-

0.054 0.004-

14.7 0

Educ<12-

0.086 0.008-

11.1 0Associate Educ 0.104 0.008 13.7 0College Educ 0.279 0.009 29.7 0

Some Col Educ 0.043 0.006 7.1 0Doctorate Educ 0.436 0.019 23.2 0Masters Educ 0.311 0.014 22.4 0

Experience-

0.022 0.003 -8.7 0Experience Sq. 0.000 0.000 -7.5 0

Hispanic-

0.184 0.007-

26.5 0Union 0.130 0.004 31.4 0Intercept Term 4.367 0.056 78.2 0

this regression are highly significant, except for what the CPS defines as ‘other’ race.

Also, all of the coefficients for these variables have the expected sign, except that the

experience term is negative. One reason for this result is that I also include age in the

regression, and experience is partially co-linear with age. Finally, for the most part, the

coefficients have the expected size.



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After running Regression (1) for each of the 22 years in the sample, I find the

residuals from this regression. Next, I find the same percentiles for the residuals that I

find for the raw earnings data. These OLS residuals describe the portion of the earnings

inequality that the data cannot explain from 1983 to 2004.

IV. Empirical Results

The first part of this section examines the 92.5/90 inequality over the 1983-2004

period. Figure 1 presents the 92.5 th, 90 th, 50 th and 10 th percentiles for usual earnings per

week for the 22-year period. As Autor, Katz, and Kearney (2005) show, the 50/10

inequality increased slightly over this period, but the 90/50 inequality increased

dramatically (see Figure 1). The results from this paper show that the 92.5/90 inequality

widened slightly over the recent time period. Figure 1 displays that the 92.5/90

inequality increased by roughly $150, whereas the 90/50 widened by about $500.

Interestingly, these facts mean that the 92.5/90 inequality increased by $60 per percentile,

while the 90/50 inequality only increased by $12.5 per percentile, or five times less.

Figure 1: 1983-2004 Earnings

0

200

400

600

800

1000

1200

1400

1600

1800

2000

19831985

19871989

19911993

19951997

19992001

2003

Year

Earnin

92.5th Percentile

90th Percentile50th Percentile

10th Percentile



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This paper next plots the residuals from Regression (1) for the 92.5 th, 90 th, and

50 th percentiles for the 22-year period. If the residuals do not change at all over time,

then the data can completely explain the rise in wage inequality. Figure 3 shows that the

residuals for the 92.5 th and 90 th percentiles move in unison over the time period. In more

recent years, the residuals are upward sloping (see Figure 3). Also, the 92.5/90 residuals

inequality increased slightly over the 22-year period, meaning that the data cannot fully

explain the inequality increase.

Figure 3: 1983-2004 Residuals

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

19831985

19871989

19911993

19951997

19992001

2003

Year

Resi

92.5th Percentile

90th Percentile

50th Percentile



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The second part of this section examines the 97/95/90 inequality from 1989 to

2004. Figure 4 illustrates a striking result for the raw earnings data: The 97/90

inequality widened almost as much over the 16-year period as the 90/50 inequality. This

result means that the very high earners in the distribution realized a large increase in their

earnings relative to high earners in recent years. Also, Figure 4 shows that not only did

the 95/90 and 97/95 inequality both increase, but also they increased at similar rates.

These results imply that the earners in the upper tail of the distribution experienced the

largest increase in earnings in recent years, even in relative terms.

Figure 4: 1989-2004 Earnings

0

500

1000

1500

2000

2500

3000

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

Year

Earnin

97th Percentile

95th Percentile

90th Percentile

50th Percentile



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This paper next displays the 1989-2004 earnings data in log points. Figure 5

illustrates the interesting result that the 97/90 inequality and 90/50 inequality did not

noticeably widen in log points. Also, Figure 5 suggests that the 97/90 inequality

increased more than the 90/50 inequality, reinforcing the idea that the highest earners

gained the most relative to other earners in the distribution over the 16-year period.

Figure 5: 1989-2004 Log Earnings

5.75

6.25

6.75

7.25

7.75

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

Years

Log Earni 97th Percentile

95th Percentile

90th Percentile

50th Percentile



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In conclusion of this section, this paper plots the 97/95/90 residual inequality

from 1989 to 2004. As shown in Figure 6, the 50 th and 75 th percentiles remained fairly

flat when compared to the higher percentiles, illustrating that the data explains a larger

percentage of these lower percentiles. The higher residual percentiles slightly increased

over the time period, which conforms fairly closely to the movements of the higher

percentiles in log points. This detail means that the 97/90 inequality, like the 90/50

inequality, is not completely observable in the data. This finding is also consistent with

the 92.5/90 inequality over the 1983-2004 period.


0

0.1

0.2

0.3

0.40.5

0.6

0.7

0.8

0.9

1

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

Years

Resi

97th Percentile

95th Percentile

90th Percentile

50th Percentile

75th Percentile

V. Robustness of the Results

This paper examines wage inequality from 1983 to 2004 because the CPS MORG

began tabulating union status in 1983. Since CPS MORG data is also available from

1979 to 1982, this paper examines the robustness of the results in Section IV by using

these additional four years of data. The only change in methodology for these four years



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indicating that the data cannot fully explain the rising earnings inequality at the upper tail

of the distribution.


0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

1979

1982

1985

1988

1991

1994

1997

2000

2003

Year

Residua 92.5th Percentile

90th Percentile50th Percentile

Researchers have a number of other ways to check for the robustness of the

results in Section IV. The first method is to redo the methodology of Section III by

eliminating men who earn less than one-half of the 1982 minimum wage, or $67 a week

(see Katz and Murphy 1992, Juhn, Murphy, and Pierce 1993, and Autor, Katz, and

Kearney 2005). Since Juhn, Murphy, and Pierce (1993) state their results are sensitive to

this restriction, I do not make this restriction in my analysis; but clearly researchers need

to make this restriction for a complete robustness check. Another robustness check is to

include citizen status as one of the explanatory variables in Regression (1) for the

available CPS MORG years of 1994-2004. Finally, another way for researchers to check

for robustness is to drop either the age or experience terms in Regression (1) to eliminate



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any partial co-linearity problems. I did not accomplish these robustness checks due to

time constraints, but they are important for additional analysis of earnings inequality.

VI. Conclusion

Researchers have a number of ways to extend the work of this paper in the future.

While this paper provides evidence of a rising earnings inequality at the upper tail of the

distribution, the analysis does not truly address the underlying causes of this

phenomenon. Future research can attempt to determine the causes of these labor market

changes by examining behavioral factors, such as governmental policy, labor demand, or

skill biased technological change. Another way to extend the work of this paper is to

employ some of the methods of Autor, Katz, and Kearney (2005) and decompose the

observable portion of the inequality in the upper tail into price and composition changes.

This paper only attempts to decompose the inequality into the observable and

unobservable portions.

By using a sample from the CPS MORG that is representative of a strong labor

force attachment, I find that the 92.5/90 and 97/90 inequality noticeably increased in

recent years. Interestingly, the 97/90 inequality widened by roughly the same amount as

the 90/50 inequality from 1989 to 2004. Furthermore, the observable variables in the

data cannot explain a considerable portion of the rising inequality at the upper tail of the

distribution. If equity is an important policy goal, policymakers have an incentive to use

this evidence of a rising wage inequality to explore why the highest earners have gained

in recent years in both absolute and relative terms.



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References

Autor, David H., Lawrence F. Katz, and Melissa S. Kearney. 2005. “Rising WageInequality: The Role of Composition and Prices.” NBER Working Paper No.11628, September.

Card, David and Thomas Lemieux. 1996. “Wage Dispersion, Returns to Skill, and Black-White Differentials.” Journal of Econometrics , 74, 319-361.

DiNardo, John, Nicole M. Fortin, and Thomas Lemieux. 1996. “Labor MarketInstitutions, and the Distribution of Wages, 1973-1992: A SemiparametricApproach.” Econometrica, 64 (September), 1001-1044.

Eissa, Nada. “Taxation and Labor Supply of Married Women: The Tax Reform Act of 1986 as a Natural Experiment.” NBER Working Paper No. 5023, February.

Juhn, Chinhui, Kevin M. Murphy and Brooks Pierce. 1993. “Wage Inequality and theRise in the Returns to Skill.” Journal of Political Economy , 101(3), 410-442.

Katz, Lawrence F. and Kevin M. Murphy. 1992. “Changes in Relative Wages, 1963-87:Supply and Demand Factors.” Quarterly Journal of Economics , 107 (February):35-78.

Machado, Jose and Jose Mata. 2005. “Counterfactual Decompositions of Changes inWage Distributions Using Quantile Regression.” Journal of Applied Econometrics , 20(4), 445-465.

Piketty, Thomas and Emmanuel Saez. 2003. “Income Inequality in the United States,1913-1998.” Quarterly Journal of Economics , 118 (February): 1-39.

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