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Snith, Janes P. ; Welch, Finis 

Inequality: Race Differences in the Distribution of 

Earnings. Band Paper Series P5481-1. 

Rand Corp., Santa Honica, Calif. 

Oct 77 

23p. 

The Band .Corporation, 1700 Hain Street, Santa Monica, 
California 90^06 ($1.50) 

# 

HF-$0.83 HC-S1.67 Plus Eostage. 

♦Black Employment; Census figures; ♦Data analysis; 
♦Employment ; ♦Equal Opportunities (Jets); *Incoae; 
Low Income Groups; ♦Bacial Differences; Bacial 
Discrimination j 
Middle Income Groups' 



ABSTRACT 

Characteristics and determinants cf earnings 
distributions for black and vbite males are repealed in samples from 
the 1960 and 1970 censuses. Using this data, this paper describes and 
contrasts the properties^ of black and shite male earnings 
distributions. It also uses earnings functions est » iated frcm the 
census to identify and rank variables in terms cf their contribution 
in explaining relative earnings dispersion* Extensive statistical 
analysis is used to make predictions about black and vbite earnings. 
A short bibliography is included. (Autbcr/PB) ' 



************** *********************** ********************************** 

* Reproductions supplied by EDRS are the best that can be made * 

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•ML i V 1978 



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INEQUALITY: RACE DIFFERENCES IN THE DISTRIBUTION OF EARNINGS 



James P. Smith and Finis Welch 



October 1977 



nf 

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MATERIAL HAS BEEN GRANTfc 




"UCATION 

THE "EPSON OR ^OA^fflX 60 F * 0 * 
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SENT Orp1?,i°L A ^"" A ""-V REPRE. 

*OUCAT,ON C SZSXZ P^VcV 076 ° P 



P5481-1 



9 

ERIC 



I 



The Rand Paper Series 

Papers are issued by The Rand Corporation as a service to its professional Staff. Their 
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interests; Papers are not reports prepared in fulfillment of Rand's contracts or grants. 
Vidws expressed in a Paper are the author's own, and are not necessarily shared by Rand 
or its research sponsors. 

The Rand Corporation 

Santa Monica, California 90406 



INEQUALITY: RACE DIFFERENCES IN THE 

•k-k J A 

DISTRIBUTION OF EARNINGS 



James P. Smith 
and 
Finis Welch 



** 



*** 



The Rand Corporation, 1700 Main Street, Santa Monica, CA 90406 
The University of California, Los Angeles, and The Rand Corporation 
Forthcoming in the International Economic Review . 



4 



\ 



Inequality: Race Differences in the Distribution of Earnings 

» " * 1 

* James P. Smith and Finis 'Welch 

Too often incoroe inequality in the United States is characterized 
by stressing differences in average earnings between various demographic 
groups. In fact, repeated emphasis on race and sex differentials might 
lead one to suspect that mean wage differentials represents large part 
of total inequality. Yet, according to the most recent Census, the 
story of income inequality in America can be told with little mention of 
black-white differences in mean earnings: for males, the black-white 
wage differential accounts for Uess than three percent of total (log) 
earnings variances. 2 Moreover, within race, blacks' earnings are often 
less equally distributed than earnings of whites. The economic^pie may 
be smaller for blacks, but it is alsc sliced less evenly. 

In this paper, we examine characteristics and determinants of 
earnings distributions for black and white males as they are revealed in 



"^This research was supported by a contract from the Department of 
Labor and a grant from ASPER, the Department of Health, Education and Welfare 
to The Rand Corporation and a grant from the Ford Foundation to the National 
Bureau of Economic Research* We would like to thank William Gould for his as 
sistance. 

2 If blacks were to represent half of the population and if both 
average differences and variances within race were preserved, the mean dif- 
ference would still represent only six percent of total variance* 



5 



the 1/100 Public Use Samples of the 1960 and 1970 Censuses. This 
paper is divided into two sections. The first describes and contrasts 
the salient properties of black and white male earnings distributions. 
Section II relies on earnings functions estimated from the Census to 
identify and rank variables in terms of their contribution in explain- 
ing relative earnings dispersion; These earnings equations are used 
to predict the full distributions of earhings for blacks and whites 
^-/-Separately so that predicted and observed distributions can be compared 
throughout the complete range of the distributions. We think that the 
predictions capture many important features of the observed distribu- 
tions. In particular, predicted earnings variances in 1960 and 1970 are 
highdr for blacks than whites and, in 1970, this difference is also re- ' 

/ \ 

fleeted in our predictions. A concluding part of this section, briefly, 
presents results for a more generalized random-coefficients model that 
aims at identifying sources of residual variation. 

j. An Overview 

Because comparisons of full distributions may reveal differences not 
conveyed by summary measures, we begin with a convenient method of con- 
trasting distributions illustrated in Figure 1. In the curves labelled 

3 The sample is restricted to non-self-employed males with positive 
earnings. Including the self-employed would increase inequality and im- 
part a more positive skew to the distribution. Ignoring non-earnings 
income probably leads to an underestimation of total income at bpth the 
lower and upper tails of the income distribution - the lower tail because 
of government transfers, the upper because of non-human wealth income. 

6 - 



-3- 




"actual", earnings of black males at selected percentiles of black 
earnings distributions are presented relative to the earnings of white 
males at the same percentiles of white distributions. (The curves 
labelled "predicted" are discussed below.) Since the curve is positively 
sloped, there exists more relative dispersion for blacks up to the 70 
to 80 percentile. In the top tail oi the distribution, the relative 
dispersion of white earnings is greater, indicating greater positive 
skewness in the white distribution. The reversal at the 80th percentile 
shows that a unique ranking of inequality by race is not possible-. * Those 
summary measures which weight the bottom tail of the distribution more 
heavily (e.g., log variances) will tend to rank blacks over whites in 
inequality. Other measures (e.g., coefficients of variation) could 
produce the opposite result. Although we will initially rely on only 
one measure of inequality, logarithmic variance, we will also deal 

/ 

with some distinctions between this summary measure and the full dis- 
tribution. 

Variances of log male earnings and weekly wages are listed in 
Table 1 separately by .year (1960 and 1970), and race (blacks and whites). 
These variances exhibit their familiar U-shaped age profile. For both 
races, total variance is dominated by the within-age cell variances with 

! 4 

over 70 percent of the aggregate variance consisting of within-cell variance. 



4 

Between age cell variance is lower for blacks both absolutely and 
as a proportion of total variance reflecting a less steeply-graduated 
age earnings profile for blacks. 



8 



ERIC 







-5- 

TABLE 1 








MEASURES OF DISPERSION 






VARIANCE 


IN LOG MALE 


EARNINGS 




Ages 


1970 
Whites 


1960 
Whites 


1970 
Blacks 


1960 
Blacks 




0.8242 


0.7128 


1.0584 


0.9367 




0.4108 


0.4404 


0.6436 


0.7310 




0.3988 


0.4003 


0.5834 


0.6814 


JD *t V/ 


0.3845 


0.4592 


0.6020 


0.6710 


41-50 


0.4712 


0.4992 


0.6763 * 


0.7356 


51-60 


0.5271 


0.6087 * 0.7732 


0.8966 


21-60 


0.5858 


0.5593 


0.7595 


0.7991 


18-65 


0.8190 


0.7222 


0.9495 


0.9412 




VARIANCE 


IN LOG MALE 


WEEKLY WAGE 




21-25 


0.4638 


0.3809 


0.6557 


0.5293 


26-30 


0.2813 


0.2491 


0.4164 


0.4223 


31-35 


0.2759 


0.2606 


0.3922 


0.4307 




0.2881 


0.2951 


0.4082 


0.4282 




0.3359 


0.3341 


0.4707 


0.4917 


51-60 


■ 0.3786 


0.3873 


0.4901 


0.5565 


21-60 


0.3794 


0.3433 


0.4892 


0.4930 


18-65 


0.5006- 


0.4302 


0.6322 


0.5992 




TOTAL EARNINGS INEQUALITY USING VARIANCE IN LOG 


EARNINGS 






Within 
Race 


Between 
Race 


Total 


Actual Racial 
Proportions 








1960 
1970 




.7409 
.8310 


.0336 
.0203 


.7744 
.8511 


* 

Equal Weighting 








1960 
1970 

X 




.8317 
.8842 


.1077 
.0591 


.9394 
.9433 



') 



\ 



Assumes equal number of Che blacks and whites in population. 



ERIC 



9 



Using log variance as the criterion, we find in the Census data that 
earnings of blacks are less evenly-distributed than those of whites. 

For those aged 18-65, variances in log weekly or yearly earnings -rose 

) 

for white males but remained relatively constant for black men between 

1960 and 1970. The lower between-race variance in 1970 was hot suffi- 

5 N 

cient to prevent aggregate inequality from rising. 

2. Sources of Difference in Earnings Dispersion 
2.1 Regression Accounting 

Earnings distributions are determined by the functional relationship 

between earnings and personal characteristics and the underlying joint 

I 

distribution of these characteristics in/ a population. The regression 
technique has become the standard format for accounting for group dif- 
ferences in mean earnings but is less often used for examination of full 
distributions. Yet, the" interest of policymakers often resides in the 
tails of distributions rather than in comparisons of representative or 
"average 11 persons belonging to the respective population under study. 
Because the number of explanatory variables is large, the distributions 
of these variables will.be initially characterized x simply by their 
variances and covariances. Th(e regressions are based on the 1/100 
Public Use Samples of* the 1960 and 1970 Censuses. Individuals are 

"*This results from aggregate variance being heavily weighted by 
the white sample. 



10 



ERIC 



-7- 

partitioned according to estimated years of work experience^ and within 
each experience class (1-5, 6-10, 11-15, 16-20, 21-30, and 31-40), the 
regression estimated is of, the form: 

(1) 7 - x'(b Q + + d 2 6 2 + d^S^) + u 

where y = In (earnings last year/weeks worked last year), 7 x 1 is a vector 
of characteristics of the individual and 



d i = 



1 if black , 

2 = 

0 otherwise 



1 if 1960 
0 otherwise 



In accounting for explained variance, let represent the estimated 
parameter vector for the i-th group. Explained variance is: 

(2) a 2 = b'.V. (x)b. 

y i i i 

.where V^(x) is the observed variance-covariance matrix of characteris- 
tics for the i-th group. Characteristics are partitioned according to: 

^ = ^2£ 2> ' —3 * ^4 ' ""5^ ^* 



# 



^Estimates by Hanoch by ages of beginning work level by schooling: 

Schooling: 0-7 8 9-11 12 ' 13-15 16 17+, 

Age at begin- 
ning work: . 14 16 18 20 23 25 28 

7 

This is equivalent to an earnings equation with log annual earnings 

» 

as the dependent variable and weeks worked included as an independent 
variable with unit coefficient. 



-8- 



with 

x£ = (years of grade school, years of college) "= schooling; 

x' 2 = (North Central; South, West, Metropolitan, Central City 
years in current residence) = location; 

x_2 = (federal employee, employee of regulated industry, 

federal share of industry, state and local governments 
share of industry) » government employment; 

x| = (years of experience, years of experience squared) = 
/ experience; . N 

X5 = (log of weeks worked) = weeks worked • 

The earnings variation attributed to the j-th set of explanatory variables 

is: , - . 

(3) ^v^.b-vfe^ 

where V(x ) is the diagonal block in V(x) describing the variance of x. . . 
J 3 

t 

Similarly, that part of the explained -variance attributable, to covariance 

between x. and x, is: 
3 k 

(4) a2 C (x.,x k ) = 2b : ;c(x j ,x k )b k 



Where b^ and b fc refer to x^ and x fc , and C(x^, x fc ) is the covariar\ce of 

x j^ x fc* A summary of the more important accounting effects is contained 
in Table 2. 

With respect to black-white inequality, the partial effect of weeks 
worked accounts for roughly half of explained variance. Depending 'upon 
one's view of underlying causes of hours variation, it fray be preferable 



1 



12 ' , 



ERIC 



S 




Table 2 



CONTRIBUTION OF SELECTED FACTORS TO VARIANCES PREDICTED 
FROM ESTIMATED EARNINGS EQUATION 



Experience Class 



r 



1970 WHITES 

fotal* Variance iiofnnual Earnings 
Explained Varian^e^^ 

Contributions of ' 

» V %A. Log Weeks Worked 

) B. Years of Schooling 

; C. Regional Variables 

D. Government* Variables 

E. Schooling-Weejygtoked Interaction 

F. Location-Scho^jS^Cn tor action 



1970 BLACKS 



Total Variance in Annual Earnings 
Explained Variance 

Contributions of 

A. Log Weeks Worked 

B. Years of Schooling 

C. Regional Variables 

D. Government Variables 

E. Schooling-Weeks Worked Interaction 

F. Location-Schooling Interaction 



1960 WHITES 

Total Variance in Annual Earnings 
Explained Variance 

Contributions of 

A. Log Weeks Worked 

B. Years of Schooling 

C. Regional Variables 

D. Government Variables 

E. Schooling-Weeks Worked Interaction 

F. Location-Schooling Interaction 



1960 BLACKS 



Total Variance in Annual Earnings 
Explained Variance 

Contributions of .* 

}A. Log Weeks Worked 
Years of Schooling 
Regional Variables 
Government Variables 
Schooling-Weeks Worked Interaction 
Location-Schooling Interaction 



1-5 


6-10 


11-15 


**O6-20 


21-30 


31-40 


.773 


7481 


.370 


' .419 


.413 


.422 


.273 


.129 


.070 


.077 


.083 


.110 


.138 


.058 


.034 


.039 


.043 


.064 


.060 


.030 


;016 


.016' 


JD17 


.016 


.008 


,-<007 K 


.007 


.007 


.010 


.012 


\.oor 


.004^ v 


.004 


■>3" 


.003 


.010 


.035 


.018 


.005 


.007 i 


.006 


.005 


.004 


,003 
t 


.002 


.003 


.003 


.004 


1.130 


.730 


.551 


.536 


.555 


.632 


.430 


.256 


' .148 


.149 


.163 


.192 


:187 


.093 


* 

.067 


.066 


.085 


.105 


.054 


'.036 


.022 


.021 


.020 


.016 


.016 


.012 


.012 


.013 


.016 


.024 


.008 * 


. .004 


.004 


.006 


.006 


.010 


.064 


.029 


.013 


.011" 


.013 


.012 


.010 


.006 


.005 


.006 


.007 


.007 


.856 


.523 


.397 


.389- 


.463 


.535 


.393 


.193 


.126 


.125 


.149 


.177 


.268 


.135 


.077 


.074 


.083 


.093 


.030 


.036 


.018 


.013 


.009 


.007 


.020 


.034 


.028 


.036 


.043 


.053 


.006 


.004 


.004 


.003 


.003 


.018 


.041 


.021 


.006 


.004 


.003 


.004 


.008 


.014 


.010 


.'Oil 


.012 


.012 


1.187 


.819 


;695 


.608 


, .648 


.734 


.591 


.398 


.314 


.273 


.286 


.32^ 


.327 


.207 


.181 


.140 


.168 


.173 


.056 


.051 


.025 


.019 


.011 


.007 


.060 


.043 


.048 


.051 


.057 


.077 


.015 


.008 


' .001 


.013 


.014 


.018 


.037 


.023 I 


• 011 


.010 


.008 


.006 


.041 


.036 


.023 


.024 


.017 


.016 



9 

ERIC 



13 



-10- 

L. 

especially for welfare statements, to partition out that part of total 
earnings dispersion due to hours worked. Clearly, if leisure time has 
value and if the hours decision is voluntary, earnings f luctuatipns re- 
sulting from fluctuations in time worked should not be viewed as equi- 
valent to variance associated with wage differentials. Even though em- 
ployment instability is an obvious cause of inequality, it is important 
to note that the interracial differences are not solely due to employment 
factors. Using variance in log weekly wage to measure inequality, the 
dispersion among blacks still exceeds that among whites. 

The distribution of schooling is a second factor underlying black- 
white differences in inequality, for all but the most recent cohorts, 
schooling is more unequally distributed among black males. There exists 
a clear secular trend for both rac£s towards less dispersion in schooling 
and a narrowing of the differentials in -variance between races. Given 
similar average returns to education within experience classes, this 
larger variance in black schooling would imply more black earnings in- 
equality. However, proportionate variation in human capital, as mea- 
sured only by years »of schooling completed, accounts for little of the 
difference in inequality. The variance attributed to schooling declines 
as work experience increases. The lower schooling variances in 1970 
also lead to a reduction in inequality for both races. Since both 
schooling and weeks^worked increase annual earnings, the positive cor-y 

i 

relation between them adds to earnings dispersion. Evidently labor sup- 

ply behavior "builds positive correlation between wages and time worked 

and spreads the distribution of earnings. Because schooling coefficients 
8 ~ * 

This is a result of lower estimated returns to schooling in the 
more experienced groups. 

14 



-11- 



and the covariance between education and weeks worked decline, over the 

life cycle, this interaction has its primary influence in earlier ex~ 

V 

perience intervals. Moreover, it Orally has a slightly larger effect 

for whites than blacks and thus does not help explain race differences. , 

The regional distribution of blacks combined with t|e large variance 

between regions in black earnings is important in explaining higher 

black inequality. Among our region variables, Southern residence was 

the most important. Holding constant schooling, experience and weeks 

worked, black-wiiice "ratios of earnings range from 12 to 29 percent 

lower (depending on the amount of job experience) for Southern residents 

# 

than they do for Northeastern residents. Regional disparities in 
earnings are far more important for older (more experienced) workers ^ 
and are more important in 1960 than in 1970. Also, part of schooling f s 
contribution to explained -variance is captured via covariance between 
schooling and 'geographic location \- reflecting_the fact that average 
school completion levels are higher where wages are high. 1 ~~ . - ~~ 

We attempted to measure the direct and indirect influence of 
government on aggregate wage dispersion. The direct influence is cap- 
tured simply with a dummy variable for employment in the government sec- 
tor. Since government has the potential for influencing wages in other 
sectors, as well, we also included variables indicating employment in 
those sectors that seem most susceptible to governments power - indus- 
tries regulated by the government and those that sell a significant frac- 
tion of their product to government. Compared to the other factors in- 
cluded in our regressions, government, employment, both direct and indi- 
rect, proved j to be relatively unimportant, accounting for around 10 per- 
cent of explained weekly wage variance. 



J 

-12- 

2.2 Full Distributions 



Although larger black relative 'dispersion was on average an ac- 
curate characterization, we have noted that a comparison of the top 
quarter of black and white earners reveal^ more relative dispersion 
in white earnings. We examine next complete distributions of earnings 
to see how closely our predictions compare to observations throughout 
the entire distribution.. Using our estimated wage equations, earnings . 
for all males in the Census samples with one to- forty years of market 
experience are predicted, In Figure 1, black-white earnings ratios at 
deciles of the predicted black and white distributions are compared to 
the wage ratios based on the actual black-^white distributions* Because 
a positiyely sldped curye indicates larger black relative variance, the 
rising predicted earnings ratios until the 80 decile confirm our ability 
to capture "some factors leading to larger black inequality. Although 
the decline is not as rapid as that in actual earnings, our predicted 
earnings ratios in 1970 decrease after the 80th decile. In 1960, our 
predicted distributions fail to track the decline in black-white earnings 
ratios in the upper deciles, but the rate of increase in the predicted 
ratios is clearly attenuated. The factors used earlier to explain lar- 
ger black inequality apparently also cause the reversal in relative 
variance by race in the upper section of the earnings distribution. 

We will illustrate why the reversals in relative variance occur 

4 

using the marginal distributions of the two variables identified by our 
earnings equation as the dominant causal factors in explaining wage dis- 
persion - education and geographical location. 

In Table 3, years of schooling completed at deciles of the black and 

9* 

vThite schooling distribution for 1960 are listed. The larger dispersion 



9 

A similar pattern (not shown) exists in 1970. 

/ 16 



T 



-13- 



TABLE 3 

EDUCATION DISTRIBUTIONS 1960 
A. Deciles of the Schooling Distribution 





1 


2 


3 


4 


5 


6 


" 7 


8 


9 


Black 


2.3 


4.1 


5.6 


6.8 


7.6 


8.7 


10.0 


11.2 


11.8 


White 


6.2 


7.4 


8.1 


9.5 


10.9 


11.3 


11.7 


12.4 


15.1 



B. Marginal Returns to Schooling 

Years of Schooling 

0-8 9-12 13+ 

Black .0490 .1118 .1135 

White .0601 .0972 .1048 



C. Residential Distribution by Deciles of Predicted Earnings 







1970 


Whites 








Region 


10 


30 


50 


70 


90 


100 


North Central 


.213 


.240 


.304 


.327 


.330 


.310 


South 


.402 


.453 


.238 


.189 


.174 


.165 


West 


.183 


.153 


.165 


.195 


.222 


.209 






1970 


Blacks 








Region 














North Central 


.125 


.059 


.090 


.300 


.486 


.429 


South 


.688 


.834 


.726 


.204 


.072 


.121 


West 


.055 


.028 


.048 


.115 


.117 


.157 



1? 



ERIC 



-14- 



in black schooling is not present throughout the education range. 
Between the 10 and 70 percentile, black schooling increased by 5.9 
years while white schooling increases by 4.3 years. Given similar 
returns to schooling by race, this is consistent with the rising 
income by decile curve observed in Figure 1. But after the 70 per- 
centile, we increment black schooling by only 1.8 years and white 
schooling by 3.4 years. Therefore, in the top three deciles, the 
schooling distributions predict more relative earnings dispersion 
among whites. This pattern of differential -variances in schooling is 
reinforced by rising income returns with schooling level. Although 

\ 

schooling coefficients are similar within schooling class by race, 
whites achieve higher schooling categories at earlier percentiles. Com- 
paring individuals in the top third of the earnings distribution, an 
additional year of schooling adds more to white earnings, spreading out 
the distribution of white earnings compared to that among blacks. 

The geographical distribution of blacks and whites is also listed 
in Table 3 at selected percentiles of the 1970 predicted earnings distri- 
bution. White males are fairly uniformly distributed over their deciles. 
For blacks, however, the disparities between the deciles are large. For 
example, over 70 percent of blacks with less than the median black in- 
come live in the South, but less than 20 percent of the blacks in the 
top three deciles are Southerners. Moving across the lower 75 percent 
q£ the .earnings distributions, the region variables contribute to a 
rising black-white earnings ratio. This is due to the larger black wage 
differentials between regions and the extensive outmigration of blacks from 



the South over this range of the distribution. With substantial black 

North-ScHith wage differentials, black earnings will rise relative to 

\ 

whites as bJLack representation in the South is decreased. 
Within region\ dispersion is also significantly larger in the South 



\ 



ERIC 



so that those sections of the distribution more heavily weighted by 




Southerners will exhibit more ^dispersion. Among high earners, the 
movement across regions is considerably smaller so that the power of 
region variables in affecting these earnings ratios is largely eliminated. 

2.3 Residual Variation 

\ 

After adjusting for personal attributes, the residual variances ob- 
tained from our regressions were substantial and were also larger among 
blacks. Although these residuals are "unexplained" by our regressions, 
they contain useful. information about the process determining individual 
earnings. In this section, we employ a random coefficients framework to 
determine whether the residual variation about our estimated earnings 
equations is systematically related to individual differences in the 

returns to certain characteristics, 

10 • . 

As ,an approximation, the expected value of an individual's 

squared residual can be written as 

k ■ kk * 

T?he diagonal terms in the double summation are the variance in the coef- 
ficient among Individuals; the off diagonal terms represent the covariances 
in these coefficients. For example, if the earnings equation included 

- i 

_.only schooling and a constant term, we would write \ 

, v 

' E < E i> - °u + 2W 5 ! ■' a Bi S i 

f 

The coefficient of schooling squared measures the variance in the return 
to schooling among individuals; the schooling coefficient measures the 
covariance between the individual intercept and the return to schooling. 
^Instead of the standard linear model with randomness only in the 

intercept, assume that individuals differ in all parameters. 

,-1 ,~ . ...... ...s ,„.„v-l 



V(&) - (X'X) (Z.x.x'Vx.x') (X f X)" 

19 



-16- 



The intercept measure the underlying residual variation unrelated to 
characteristics. We estimated equation (5) for blacks and whites in 
six experience groups in 1970, An individual's residual was "computed 
by subtracting from his actual earnings his earnings predicted by our 
OLS earnings equation, ^ After squaring these residuals, we estimated 
equation (5) • 

The only variables that ployed significant were schooling and 



(footnote 10 continued) 
For the -th individual, we have the prediction, 

Y = xj3 with the observation Y = X *3 + n 0 

The expectation of the squared calculated resfdual (e = Y - Y ) is 

X* Z % 

E(ej|) = xJV(|) Xjl - 2x^(3-3)11^ + E<h*) 
since E(3-3)n. £ = (X'X)" 1 x^Vx^ and 

=X £ Vx )f " e haVe 

B(«J) = x'VC3)x £ + (l-^CX'X)- 1 ^) a^. 

In general, estimation of V, the individual covariance structure of 
parameter differences from the population mean presents a formidable 
problem. But, in this case, since the number of observations ranges 
between 4,000 and 7,000, we can appeal to large numbers. Notice, in 
particular, \ that both x^V(3)x^ and x^ CX f X) -1 x^ are of order, T~\ 



where T refers to the number of observations. It follows that 

2 \ * 

plim i = xlVx rt , = o 2 „ and as an approximation e£ - xJVx 0 + W 0 is used 

T ^oo ^ a n * * * * * 

along with the assumption that W has zero expectation and is independent of X. 



The random coefficient model suggests that a GLS approach may 
have been more appropriate. The absence of any meaningful heteroscedascity 
(noted below) indicates that this would not alter our results. 

20 



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schooling squared. The coefficients of these two variables along 
with the mean squared residual for each experience group is reported 
in Table 4. 

Table 4 

A. Coefficients from Regressions on Squared Residuals 
Experience Grojap 

1970 Whites 1-5 6-10 11-15 16-20 21-30 31-40 

Schooling ,0069 .0062 ' .0050 .0030 .0047 .0027 

Squared 

Schooling -.2073 -.1861 -.1355 -.0964 -.0807 -.0572 

Mean White .453 .284 .245 .283 .298 .294 

Squared Re- 
sidual 

1970 Blacks 

Schooling .0066 .0045 .0025 .0080 .0001 .0063 

Squared , ^ 

Schooling -.3176" -.1913 -.0461 -.0107 -.0186, -.0717 

Mean Black .772 .457 , .388 .374. .-402 .453 

Squared Re- 
sidual 



9 

ERIC 



In all twelve regressions, the schooling squared variable had the required 
positive coefficient. The negative coefficient on schooling may indicate 
that earnings from other pursuits and schooling are substitutes. Indivi- 
duals who are able to obtain -high earnings in endeavors unrelated to 
schooling may well behave so that they achieve low ex post returns to 
schooling. Based on these regressions, variation in rates of return to 
schooling are large and are an important source of the residual variances. 
For racial comparisons > variation in schooling returns may be slightly 
Uarger for whites so that they explain little of the black-white difference. 

21 ■ 



-18- 

} 

* i 

Our results suggest that at least additional research on this topiq 
usinft (more) appropriate panel data may be fruitful. 

3* Conclusion 

We have examined the p6tential for using earnings equations esti- 
mated from two large cross-sectional data bases Uri explaining 
the complete distributions of black and white male earnings. 
Although we have achieved some success iri documenting the contribution 
of several variables, there are numerous factors omitted in our study. 
Perhaps, the most serious omission involves the role of differences in 
the underlying distribution of ability within population, Assortative 
mating patterns alone could produce differential distributions: of 
ability. The more positive the degree of assortative mating, the lar- 
ger the dispersion iQ genetic traits in succeeding generations. Dis- 
crimination against blacks'* may also operate in a manner that increases 
dispersion in black incomes If discrimination takes^the form of quotas 
or non-price rationing, it is the least able and qualified blacks who 
will bear the major burden ♦ Unionism and minimum wage laws will tend to 
produce similar results as the least skilled blacks are crowded into the 
unprotected sectors ♦ Although the evidence we have suggests that on net 
government is relatively unimportant and that its contribution probably 
receives too much emphasis, the influence of a broad package of govern- 
mental, welfare legislation should surely * be investigated. 



22 



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* 

BIBLIOGRAPHY 

i 

Brimmer, Andrew, fl The Negro in the National Economy," T}ie American Negro 
Reference Book, John P. Davis, editor (New Jersey, Prentice Hall, 1966). 

Chiswick, Barry, "income Inequality," National Bureau of Economic Research, 
(1974). 

, "Racial Differences in the Variation in Rates of Return from 

Schooling," printed in Patterns of Racial Discrimination^ Volume II, 
Employment and Income, Voxt Turstenberg et al. , (1974). 

Jensen, Arthur,, "How Much Can We Boost I.Q. and Scholastic Achievement," 
Harpard~%ducational Review, 39, No. 1, (Winter 1960). 

J 

Lillgra, Lee and Robert Willis, "Dynamic Aspects of Earnings Mobility," 

unpublished manuscript, (June 1976). 
Mincer, Jacob, Schooling > Experience and Earnings (New York: National* 

Bureau of Economic Research, 1974) v f 
Oster, Sharon M. , Are Black Incomes More Unequally Distributed," American 

Economists? all 1974). 
Smith, James P., The Distribution of Family Earnings, unpublished paper, 

(1976). 

, and Finis Welch, Black-White Male Earnings and Employment: 1960-1970, 

R-1666-DOL, (Santa Monica: The Rand Corporation, July 1975). 

Wohlstetter, Albert and Sinclair Coleman, Race Differences in Income^ R-578-OEO 
(Santa Monica: The ^and Corporation, 1970). 



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