Post-school investment and wage differentials: some further evidence.

Robst, John

I. Introduction

The topic of wage differentials between demographic groups has received a great deal of attention in the literature. Among the most researched areas are wage differentials based on race and gender. Studies have consistently found that men earn more than women and whites earn more than blacks. Many attempts have been undertaken to explain these wage differentials with two main explanations evolving over time. The first claims one group is paid less than another due to discrimination. Thus the fact that white males earn more than black males may be due to employers' and employees' distaste for hiring and working with minorities. The second main explanation claims different groups have different levels of human capital. Thus black males earn less, not because of discrimination, but because they have fewer acquired skills than white males.

Wage differentials are obviously important for public policy. If workers are paid differing amounts simply because of their race or gender, then society is not fully utilizing its resources. This would indicate a need for stronger government intervention to remove discriminatory practices by businesses. For example, this intervention may take the form of affirmative action programs or mandating comparable worth. However, if the gap in wages is due to choices made by individuals which lead to differences in human capital, then the wage differentials may be justified. As a result government intervention is not only unnecessary, but may be an example of inefficient regulation.

Since no easy way exists to measure the extent of discrimination, the standard method has been to decompose the residual of a wage equation into explained and unexplained portions. The idea being that some of the wage gap can be explained by differences in attributes between groups of individuals. Goldin and Polachek [5] point out that attributes may also be due to discrimination. If for example, blacks are the first to be laid off, this may result in lower levels of experience. This is not by choice and may indicate discrimination. Also there is a question of which is the appropriate base group. For example, the researcher has two alternatives when examining the wage gap between black and white males. He or she can take the predicted black wage given white characteristics as a percentage of white wages or take the actual black wage as a percentage of predicted white wages given black characteristics. In many cases the choice is not really clear and as a result often an average of these two is taken by employing a dummy variable for either race. Of course this is not without criticism, as the returns to various attributes are restricted to be equal for blacks and whites.

The decomposition approach has been used extensively in the literature to examine racial and gender differentials. For example, Blau and Bellar [3; 4] explain about 50 percent of the wage differential between black and white males. Their findings indicate black males earn 83 percent as much as white males after adjusting for observed differences. Studies looking at the male-female wage gap for whites find a similar percentage can be explained by differences in attributes. A relatively small differential is generally found between white and black females.

Several potential problems with results exploring wage differentials were pointed out by Polachek [9; 10]. To begin, problems exist with the measurement of experience in many data sets. Several major sources of data, such as the U.S. Census of Population and Housing and the Current Population Survey, do not contain accurate measures of labor market experience. Rather researchers use a measure of potential experience (age - education - 6). While this may be adequate for white males, its use is clearly questionable for other demographic groups.

Other data sets, such as the Panel Study of Income Dynamics and the National Longitudinal Surveys, contain a measure of actual experience. However, one year of experience may result in different levels of post-school investment for two individuals. This is due to differing expectations of future labor market attachment. If a worker expects to be less attached to the labor force in the future, there is less incentive for this person to make post-school investments in training. Thus the individual with a lower labor force attachment will receive a lower measured return to experience. When using the decomposition method, this will appear as discrimination. However, the differential may actually be merited since the more attached individual will have invested more during the year.

Using this type of argument, Polachek [10], and Goldin and Polachek [5] have estimated levels of post-school investment for white males and white females, while Polachek and Kao [11] estimated post-school investment for workers in Taiwan. Since white males have higher labor force participation rates, they invest in more human capital than women. When taking into account differences in future labor force attachment and its influence on human capital accumulation, between 80 and 90 percent of the wage differential between white males and white females is explained.

This paper attempts to show the same analogy can explain a substantial portion of the male-female wage gap for blacks and the wage differential between black and white males. If black males are more attached to the labor force than black females, there exists an incentive for males to accumulate more human capital. As a result black males with education and experience similar to that of black females, will have more human capital since their future labor force attachment will be greater than that of black females.

In addition, white males are found to have higher labor force participation rates than black males. Therefore, white males will accumulate more on-the-job training than black males. Again it is the difference in expectations which leads to differences in human capital between black and white males with similar education and years of experience.

Results support the hypothesis that a greater portion of wage differentials can be explained by taking differences in labor force attachment into account. Thus, simply controlling for education and years of potential experience is not found to adequately capture the differences in human capital between various demographic groups.

The next section briefly presents the theory behind Polachek's model. This is followed by a discussion of the data and the methodology for estimating human capital. Lastly are the empirical results.

II. The Model

The model used in this paper is based on the work of Ben-Porath [1] as modified by Polachek.(1) An objective function is assumed in which an individual seeks to maximize the present value of lifetime income:

[Mathematical Expression Omitted]

subject to the following constraint:

[Mathematical Expression Omitted]

[Q.sub.t] = gross investment in period t

[K.sub.t] = stock of human capital at time t

[w.sub.0] = rental rate of human capital, assumed to be constant

[S.sub.t] = percent of time spent investing in human capital period t

[N.sub.t] = probability of being in the labor force in period t

r = the sum of the discount rate and the depreciation rate

[Delta] = the depreciation rate 2

b = the production function parameter.

The main difference between Polachek's modified model and the model as put forth by Ben-Porath is the use of [N.sub.t]. Previous studies employing this model had assumed constant labor force participation equal to one for all groups. This may be adequate for white males, but it is clearly not reasonable for other groups. For example, white females often spend considerable time out of the labor force. Black males and black females also have lower labor force participation rates than white males of similar age and educational status.

Assuming [N.sub.t] is not equal to one leads to the Hamiltonian:

H = [w.sub.0][[N.sub.t] - [S.sub.t]][e.sup.-rt]][K.sub.t] + [Lambda][[[S.sub.t][K.sub.t]].sup.b]. (3)

Where lambda represents the marginal return on human capital investment. A great deal of research has found a positive return to human capital investment, therefore lambda is assumed to be greater than zero. Using [S.sub.t] as the control variable, the following first-order conditions can be found:

[Mathematical Expression Omitted]

[Mathematical Expression Omitted]

[Mathematical Expression Omitted]

Solving equation (4) for the amount of investment in period t yields: [S.sub.t][K.sub.t] = [[(b[Lambda][e.sup.rt])/[w.sub.0]].sup.(1/1-b)] = [[b/([w.sub.0][Psi])].sup.(1/1-b)

where

[Psi] = [Lambda][e.sup.-rt]. (7)

To determine the impact of an exogenous increase in labor force participation, equation (7) is differentiated with respect to [N.sub.t].

[([Delta][S.sub.t][K.sub.t])/[Delta][N.sub.t]] = (1/1 - b)[([S.sub.t][K.sub.t].sup.[b/(1-b)]]([Delta][Psi]/[Delta][N.sub.t]) [is greater than or equal to] 0 (8)

Thus, an increase in the labor force participation rate has a positive effect on human capital investment. In other words, if one group has a greater labor force attachment over the life cycle than another group, they will also make greater post-school investments.

Therefore, the existence of a wage differential between black males and black females, and black males and white males may be the result of different expectations. For example, if white males expect to be more attached to the labor force than black males, they will accumulate more human capital. A portion of the wage differential found in previous research would be the result of not taking into account these differing expectations and the resulting differences in post-school investment.

III. Data

The data used in this study are the 1980 Census of Housing and Population 1/1000 A sample. Blacks and whites between the ages of 16 and 64 are initially included in the sample. This provides a total of 125,903 observations for estimating labor force participation rates. Once the sample is reduced to individuals with earnings, the sample size falls to 85.503 of which 9035 are black.(3)

When comparing annual labor income of employed workers, on average white males earn 16729, black males 11464, black females 8230, and white females 8221. Thus white females earn 8508 less than white males. Black females earn 3234 less than black males. The wage differential between white males and black males is 5265, while on average black and white females earn almost exactly the same. Of course these may not represent the true wage differentials due to problems of sample selectivity.

While there is a 1.3 year differential in years of schooling between white and black males, overall the differences in education and potential experience are minor. Thus it is not surprising studies which control for differences in schooling and potential experience are unable to explain much of the wage gap.

Table I. Labor Force Participation Rates by Race, Gender, and Education(a)

Education

 0-8 9-11 12 13-16 17+

White
Males .74 .73 .88 .90 .93
Females .39 .45 .59 .63 .77

Black
Males .59 .66 .79 .84 .91
Females .41 .47 .66 .77 .86

a. The data are the Public Use Micro-data 1/1000 A sample of the 1980 Census
of Population and Housing. Individuals between the ages of 16 and 64 of white
or black ethnic background are included. The participation rate is the
predicted value from a Probit estimation with experience and experience
squared as the independent variables. The model is estimated for each race,
gender, and education group.

IV. The Estimation of Human Capital

Several steps are required to estimate human capital. To begin labor force participation rates are estimated based on a person's race, gender, level of schooling, and potential experience. Probit models are estimated for each of twenty groups based on race, gender, and education:(4)

Pr([N.sub.t]) = [[Beta].sub.0] + [[Beta].sub.1] exp + [[Beta].sub.2] [exp.sup.2] + u. (9)

Once the labor force participation rates are estimated, workers who are not in the labor force are deleted from the sample. As expected, white males have greater labor force participation rates than black males, while black females are more attached than white females. The average labor force participation rate for each group is provided in Table I.

This method of estimating labor force attachment might be criticized for several reasons. First is the implicit assumption of workers following the behavior of their elders. Younger men and women are assumed to make their investment decisions based on the labor force participation rates of older cohorts. This may not be a reasonable assumption given the increasing attachment of women to the labor force, and will likely lead to an underestimation of human capital for younger women. This results from the probable underestimation of their future labor force attachment. For older women, the expected level of human capital is probably overestimated. This is due to imposing the attachment of today's younger workers on the life cycle of older women. Older women were less attached when they were younger and thus had a smaller incentive to accumulate human capital.

Secondly, participation in the labor force may not actually measure labor force attachment. For example black males and white males had virtually the same participation rates in 1955. Over the twenty-five years between 1955 and 1980, the labor force participation rates of black males have fallen below those of white males. However, this does not mean black and white males had the same labor force attachment in 1955. If blacks were more likely to work part-time or face periods of unemployment than whites, their attachment to the labor force may have been less. This would lead to differences in post-school investment which are not captured by using labor force participation rates. Thus further work may concentrate on cohort differences in labor force participation and expected hours of work in measuring labor force attachment.

Given estimates of labor force attachment, the goal is to determine annual levels of net investment, gross investment, marginal revenue, and marginal cost. These are used to find expected human capital for workers at a point in time. First, net investment is estimated for white males. White males are used as the base group in this method since their expected future labor attachment is the highest. Therefore a standard human capital regression most accurately reflects the post-school investment of white males. An earnings function is estimated for each educational group:

Ln Y = [[Beta].sub.0] + [[Beta].sub.1] exp + [[Beta].sub.2] [exp.sup.2] + u. (10)

Net investment in dollar terms is determined by the following equation:

([Delta] Ln Y / [Delta] exp) (Y / r) =([[Beta].sub.1] + [[Beta].sub.2] exp)[e.sup.([[Beta].sub.0] + [[Beta].sub.1] [center dot] exp + [[Beta].sub.2] [center dot] [exp.sup.2])] (1 / r). (11)

Expected human capital is computed by summing net investment from when the individual enters the labor force up to his current age. This figure includes the present value of innate ability and human capital from education as measured by the intercept of equation (10). Assuming an individual retires upon reaching the age of 65, the rate of depreciation ([Delta]) is determined by dividing net investment at age 65 by expected human capital at age 64.(5) Since there is zero gross investment when the individual is retired, the negative net investment while age 65 is solely depreciation. The assumption of an individual retiring at age 65 may be questioned, however an expected retirement age must be assumed and 65 appears to be the most logical choice.

[Delta] = (N[I.sub.65]/EH[C.sub.64]) (12)

Net investment and the depreciation rates are then used to find annual gross investment for white males.

G[I.sub.t] = [NI +.sub.t] +[Delta](EH[C.sub.t-1]) (13)

Marginal revenue is found by applying the following discrete formula for each demographic group.

M[R.sub.t] = [[Lambda].sub.t] = [W.sub.0] [summation of] {([N.sub.i])/[[1 ([Delta] + r)].sup.i]} where i=1 to T-t (14)

where [W.sub.o] represents the rental rate per unit of human capital and is assumed to be equal to one for each demographic group. By equating the figures for marginal revenue and gross investment, an estimate of the marginal cost curve is derived for white males. Also each demographic group is assumed to have similar innate abilities, thus the marginal cost curve is same for everyone in an educational group.

Gross investment can be easily determined for white females and blacks by equating their marginal revenue and marginal cost. By using the depreciation rates found above, net investment and expected human capital are computed.

Thus expected human capital for white females and blacks is determined independent of their income. Since the marginal cost curves are assumed to be the same for individuals with similar levels of schooling, the levels of human capital will vary from white males only in response to differences in the marginal benefits of investment. Thus, differences in male-female or black-white human capital will be solely due to differences in labor force participation over the life cycle.

V. Results

Levels of expected human capital are provided in Table II. Several points consistent with expectations are worth mentioning. White males have the most human capital of any group. Levels of human capital tend to increase for each group as the level of education increases, and also increase over the life cycle until depreciation outweighs additional investments. Thus as workers approach retirement, they are unwilling to make substantial investments in on-the-job training.

Following the approach developed by Oaxaca [8], and Blinder 12], the initial wage gaps are typically decomposed into three parts. The first part indicates the impact of potential selectivity biases on the observed wage gap. The second part is the portion of the wage gap explained by differences in average characteristics between the two comparison groups. The last part is the portion of the wage gap due to differences in estimated returns from wage regressions. This is generally termed the unexplained portion of the wage gap and attributed to discrimination.

Since the final sample contains only individuals with wages or salary, corrections are made for potential selectivity biases. This is done using the method developed by Heckman [6]. Consistent with most previous research, the observed wage gaps are found to understate the differences in wage offers. In addition, the bias created by sample selection appears to vary depending on whether expected human capital or education and experience are used as variables. This leads to slightly different wage gaps after correcting for selectivity for each measure of human capital. For example, the mean wage corrected for sample selection biases is 17980 for white males when controlling for education and experience, and 18129 when controlling for expected human capital.

Two sets of results using the decomposition technique are often reported. The first uses the predicted female wage if females had the same characteristics as men ([Y.sub.fm]). [Y.sub.fm] is estimated by evaluating the female earnings function at the male means. The unexplained portion of the wage gap is found by subtracting [Y.sub.fm] from the average male wage. The second uses the predicted male wage if men had the same characteristics as women ([Y.sub.mf]). [Y.sub.mf] is estimated as the predicted value using the male earnings function and female means. In this case, the unexplained portion of the wage gap is found by subtracting the average female wage from [Y.sub.mf]. A similar process is used to examine the differences in wages between blacks and whites.

Table III contains the results for each stage of the decomposition. The first set of results to be examined use [Y.sub.fm] and [Y.sub.bw]. With education and experience, an unexplained wage differential of 6704 is found between white men and white women. Using expected human capital in the female earnings function provides an unexplained white male-female gap of 5410. For the black male-female wage gap, an unexplained differential of 3216 is found using traditional human capital variables, while the unexplained gap falls to 2035 with expected human capital. The decomposition technique was also applied to black-white wage differentials. When estimating the white male earnings function with traditional variables, 4109 of the differential between white males and black males is unexplained. Estimating the earnings function with expected human capital leaves 3435 of the wage gap unexplained. Results for the black-white female comparison are difficult to interpret. In this case the choice of human capital variables has an important impact on the estimated bias caused by sample selection. After correcting for sample selectivity, white females earn 890 more than black females when using education and experience, but only 102 more with expected human capital. The unexplained wage gaps are 535 and 358 respectively, but it is unclear whether the results for this comparison are due to differences in human capital or due to the sensitivity of the correction for selectivity.

Table II. Expected Human Capital by Education (in dollars)

Age / Education 0-8 9-11 12 13-16 17+

Black Males

20 39675 27095 77052 -- --
25 56727 34805 103974 122939 126608
30 70651 41408 122950 160802 196479
35 82021 49205 133917 186357 240741
40 90636 59863 138827 199775 265016
45 96408 73278 137715 203462 270849
50 98774 89198 130229 195758 258489
55 96851 91983 116530 175017 225055
60 89296 75795 97041 142138 180102
64 78671 56402 779635 111765 138447

White Males

20 30948 35286 70264 -- --
25 46971 62865 100199 101060 108607
30 66011 98033 131468 144025 162142
35 86083 134449 159010 185988 216282
40 104279 162476 177448 218038 258537
45 117404 173137 182784 232240 277299
50 122882 162724 173806 224810 266975
55 119577 134860 152539 197747 230674
60 108178 98484 123499 157962 178698
64 94728 69835 98346 123019 134476

Black Females
20 29494 18194 62320 -- --
25 38231 21531 72415 106594 123329
30 43602 23565 79701 133910 186525
35 47989 24805 83079 149317 228181
40 51571 25561 84454 155599 238595
45 52752 27388 83074 154430 235195
50 52649 30106 79274 145467 216054
55 50884 29808 72241 128868 185452
60 46556 26850 61379 106408 145906
64 41740 20783 50126 84432 110897

White Females

20 29112 23839 61027 -- --
25 36156 24972 68538 86396 106075
30 41908 25663 72695 98286 137254
35 45517 26084 73452 102964 152834
40 47809 26341 71843 101899 158171
45 47970 26497 67420 96217 155651
50 47063 24832 61188 86760 144617
55 44693 22902 53882 75072 126021
60 40582 18848 44816 61144 101095
64 36094 14631 36679 48456 77982
Table III. Decomposition of Income Differentials

 White Male-Female Black Male-Female

 Reg 1 Reg 2 Reg 1 Reg 2

[1] Observed Y(m) 16728 16728 11464 11464
[2] Observed Y(f) 8221 8221 8230 8230
[3] Observed gap 8507 8507 3234 3234
[4] Y(m) 17980 18129 11820 12287
[5] Y(f) 8966 8712 8076 8610
[6] Y(m) - Y(f) 9014 9417 3744 3677
[7] Y(fm) 11276 12719 8604 10252
[8] Y(fm) - Y(f) 2310 4007 528 1642
[9] Y(m) - Y(fm) 6704 5410 3216 2035
[10] Y(mf) 14530 10225 10944 10163
[11] Y(m) - Y(mf) 3450 7904 876 2124
[12] Y(mf) - Y(f) 5564 1513 2868 1553

White-Black Male White-Black Female

Reg 1 Reg 2 Reg 1 Reg 2

[1] Observed Y(w) 16728 16728 8221 8221
[2] Observed Y(b) 11464 11464 8230 8230
[3] Observed gap 5264 5264 -9 -9
[4] Y(w) 17980 18129 8966 8712
[51 Y(b) 11820 12287 8076 8610
[6] Y(w) - Y(b) 6160 5842 890 102
[7] Y(bw) 13871 14694 8431 8354
[8] Y(bw) - Y(b) 2051 2407 355 -256
[9] Y(w) - Y(bw) 4109 3435 535 358
[10] Y(wb) 14917 14097 8849 9078
[1] Y(w) - Y(wb) 3063 4032 117 -366
[12] Y(wb) - Y(b) 3097 1810 773 468

Notes:

Reg 1 - with traditional human capital variables

Reg 2 - with expected human capital

[1] - mean male (white) earnings; found by substituting the group means for
each independent variable (including the inverse mills ratio) into the
regression equation for that group
[2] - mean female (black) earnings
[3] - observed wage gap
[4] - mean male (white) earnings after adjusting for selectivity; found using
regression results from [1] but with a [Lambda] set to zero
[5] - mean female (black) earnings after adjusting for selectivity
[6] - wage gap after adjusting for selectivity
[7] - female (black) earnings if they had average male (white)
characteristics; found as in [4] but by substituting the male (white) means
into the female (black) regression
[8] - wage gap explained by differences in characteristics
[9] - unexplained wage gap using female (black) earnings function
[10] - male (white) earnings if they had average female (black)
characteristics; found as in [4] but by substituting the male (white) means
into the female (black) regression
[11] - wage gap explained by differences in characteristics
[12] - unexplained wage gap using male (white) earnings function

In addition to a measure of human capital, variables in the regressions
included weeks worked, hours per week, the inverse mills ratio, dummy
variables for occupation (1 digit), industry (1 digit), sector (federal,
state, local, self-employed), region (west, north central, northeast), and
whether living in a SMSA. The variables in the probit models used to estimate
the inverse mills ratios included age, education, non-wage income, other
household income, kids (for women), and dummy variables for marital status,
disability, regions, and whether living in a SMSA. Complete earnings
regression and probit results are available upon request.

Results using [Y.sub.mf] and [Y.sub.wb] are also reported in Table III. From this perspective, a 5564 white male-female wage gap is unexplained when including traditional human capital variables, however an unexplained differential of 1513 is found when using expected human capital. For the black male-female differential, the figures are 2868 and 1553 percent respectively. When comparing black males and white males, traditional variables leave an unexplained gap of 3097, while using expected human capital reduces the differential to 1810.

Overall, by using expected human capital, this paper finds the white male-female, black male-female, and white-black male wage differentials are smaller than indicated by traditional methods.

However, one of the many assumptions in the model is that the rental rate of human capital is equal for each demographic group. This assumption does not appear to hold as the returns to expected human capital are found to vary between demographic groups. White males are found to earn 7.0 cents for each dollar of human capital, black males receive 2.8 cents, black females 2.4 cents, and white females 2.6 cents. Several reasons may account for this differential. First, as discussed above, the measure of labor force attachment is far from perfect. By using labor force participation rates, some of the differences in labor force attachment between white males and other individuals are not taken into account. Also, since the returns to expected human capital are found to differ, the rental rate of human capital for white males appears to be greater than the rental rate for other groups. Each of these leads to an understatement in the differences in human capital between white males and other individuals.(6)

Another potential explanation for the different returns to expected human capital is this paper does not distinguish between married and single individuals. For example, single white males are more likely to marry in the future than single black males. The post-school investment of males who expect to marry in the future will be greater than those who do not expect to marry. This results from their expectation of increased future labor force attachment once they marry. This indicates the differences in human capital between black males and white males may be underestimated since single white males are more likely to marry.

Lastly, this paper does not claim a complete lack of discrimination. Thus even if labor force attachment and expected human capital were measured perfectly, a wage differential may still be found. Rather the goal is to provide some further evidence that traditional methods overestimate the extent of wage discrimination in the labor market.

VI. Conclusion

Many previous studies have examined the differences in wages between men and women, and blacks and whites. A traditional method often used, controls for differences in education, experience, and experience squared between the groups of interest. However, this type of specification is subject to several problems. For example, a measure of experience is not available in many data sets and often a proxy of age -- education -- 6 is used. Even if a true measure of experience is available, it does not account for the intensity of experience. Polachek has shown differences in labor force attachment can influence the amount of post-school investment during a year of experience. This differential in post-school investment has been shown to explain much of the differential in wages between white males and white females.

This paper has sought to apply this method to the issue of wage differentials between black males and black females, and white males and black males. We find a larger portion of the black male-female and black-white male wage differentials are explained by differences in labor force attachment than by differences in potential experience.

Of course the estimates provided in this paper are only for a point in time and do not reflect trends. Much attention has been given to the increasing labor force participation rates of women. This coupled with the decline in participation rates for males should lead to a continued decline in the male-female wage gap for both whites and blacks. However since participation rates have fallen more for black males than white males, the racial wage gap will likely persist for males in the foreseeable future.

Future work may concentrate on several areas. To begin the method of computing labor force attachment could be improved. A possible solution would be to use labor force participation rates from previous census data, and attempt to forecast the future rates of younger people instead of assuming they will follow their elders. Also men and women are assumed to gain the same human capital from an equal level of schooling. This assumption may not be true as future labor force attachment has been shown to influence the types of courses taken in school. Thus this method may be extended to determine how these differences in attachment impact the measured estimate of human capital.

1. The following is a brief review of the model. A complete examination is provided by Polachek [10].

2. The depreciation rate is assumed to be zero for this portion of the paper. Depreciation rates are estimated in the empirical section.

3. Variable means and programs used to create the sample are available upon request.

4. Alternatively, one regression could be run for the population with controls for race and gender, as well as interactions between race, gender, and experience. The interactions would be necessary since the slopes of the profiles are generally found to differ between men and women.

5. Depreciation rates range from 3.9 percent to 9.6 percent. While this method of computing depreciation is rather simplistic, Johnson [7] has found similar results for cross sectional data using more complex methods. Also, depreciation rates are assumed to be the same for all individuals in an educational group.

6. [W.sub.0] for blacks and white females has been set at various percentages of the white male rate to determine the effect on estimated wage gaps. By comparing the impact on marginal revenue for each group, it can be seen the differences in expected human capital become even larger for the white male-female and black-white male comparisons. This results in smaller unexplained wage differentials. For the black male-female and black-white female comparisons, marginal revenue falls by roughly the same percentage for each group. Thus the unexplained wage differentials do not vary substantially.

References

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