Race, cognitive skills, psychological capital and wages - Springer Link

RACE, COGNITIVE SKILLS, PSYCHOLOGICAL CAPITAL AND WAGES*

Arthur H. Goldsmith, William Darity, Jr., and Jonathan R. Veum

INTRODUCTION The observation that blacks earn less than otherwise comparable whites has long been an established "stylized fact" for workers in the U.S. The Thernstroms have most visibly challenged the validity of this "stylized fact" and, in turn, the view that black workers are sabject to wage discrimination, l They argue that poor scholarship---research that neglects the influence of cognitive ability on wages--is responsible for this finding. In general, failure to control for relevant variables leads to inaccurate estimates of the relationship between variables, including the impact of a person's race on their wages. In the Thernstroms' view, research that adopts an appropriate specification for the wage equation demonstrates that black workers are paid as much as comparable white employees. For instance, in studies that ostensibly account for cognitive ability, a productivity related characteristic, black and white employees earn wages that are essentially identical. 2 Therefore, the Thernstroms assert that black workers in the U.S. do not systematically confront race based wage discrimination. 3 Findings we report below cast doubt on the validity of the Thernstroms' (1997) claim. Drawing on literature in psychology, we (Goldsmith, Veum, and Darity) have argued that psychological capital is an important determinant of personal productivity, and hence, wages. 4 However, with the exception of recent work by Goldsmith, Veum, and Darity 5 and by Dunifon and Duncan, 6 the influence of psychological capital on wages has been neglected in empirical models of wage determination. Second, using both * The authors are indebted to Stuart Low who offered valuable insights and suggestions on the ideas addressed in this paper. The views expressed in this paper are those of the authors and do not reflect the policies or views of the U.S. Bureau of Labor Statistics.

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The Review of Black Political Economy/Fall 1998

the same data and means of measuring cognitive ability as O'Neill 7 and Neal and Johnson, 8 we find that when psychological capital also is included in a model of wage determination, blacks earn significantly less than otherwise comparable white workers. Thus, we present evidence consistent with an important adverse discriminatory affect on black worker wages. WAGE DETERMINATION: THEORY AND EVIDENCE Neoclassical theory predicts that a profit-maximizing firm will pay the ith worker a real wage, wi, equal to their marginal product, M P i. Most economists believe a person's marginal product depends primarily on two factors: (i) a person's skills, typically referred to as human capital, HCi, and (ii) the physical capital, Kj, made available to them by the jth firm that employs them. In practice, human capital generally is treated as skills acquired on-the-job, both in training programs and while working, or through formal education. Psychologists believe that a person's capacity to initiate and complete tasks is influenced by their cognitive ability, CAi, a s well as human and physical capital. Demographic factors such as age, marital status, and dependent children may alter an individual's productivity, as well as institutional phenomena like union membership. Suppose all of these factors are represented by X i. Thus, the ith worker's marginal product, and hence, wage function can be written as (1)

wi = MPi (KJi, Xi, HCi, CAi)

Following the convention initiated by Mincer9 a person's wage function, equation (2), can be depicted by a linear representation of their marginal productivity function, equation (1): (2)

wi = al (Ki) + a2 (Xi) + a3 (HCi) + a4 (CAi) + e.i

Measures of cognitive ability are rarely contained in the data sets used by economists to estimate wage equations. Thus, CAi is typically treated as an omitted variable, which ends up in the error or disturbance term. Therefore, the wage equation usually estimated is of the form: (3)

wi = ot I ( g i) + Ix2 (Xi) + (x3 (HCi) + {Ei+ o~4 (CAi)}

Investigators often extend equation (3) to include an indicator for race, When a person is black, R i = RB, and when a person is white, R i = Rw.

R i.

Goldsmith, Darity, and Veum

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The race indicator usually is specified as a dummy variable, so that for black workers RB = 1 and Rw = 0. Thus, the empirical wage equation is (4)

w i =t~l(Ki)+t~2(X2)+t~3(HC,)+o~5(Ri)+{E i +tx4(CAi) }

The estimated coefficient on the race indicator variable, (6c5), reveals any systematic average effect of being black relative to being white on wages. Suppose the set of explanatory variables includes all of the factors that influence a person's productivity. A negative and significant value for (6~5) indicates that a typical black worker would earn less than an equally productive white worker. Estimation of equation (3) reveals that, ceteris paribus, blacks receive approximately 10-13 percent lower annual earnings, l0 However, the status of cognitive ability as an omitted variable potentially mars the validity of this finding. If the disturbance, {ei + o~4 (CAi)}, is correlated with HCu--those with greater cognitive ability accumulate more human capital--then estimation of equation (4) yields biased or inconsistent estimates of the parameters (&l, a2, ~ 05). Since, the size of the estimated coefficients are suspect, the assertion that black workers face wage discrimination, based on (6~5) being both statistically significant and negative, may be erroneous. On the other hand, Hernstein and Murray's IZ claim that blacks possess poorer levels of cognitive ability than whites predicts that estimation of equation (4) will yield (c25 < 0). However, they would not interpret this as evidence of wage discrimination. In order to understand why this is the case consider the following situation. Suppose there are two types of people in the work force, persons with "high" cognitive ability (CASH), and individuals with "low" cognitive ability (CA,L). Suppose that all of the high ability persons are white, while every black person possesses low cognitive ability. Suppose an investigator wants to estimate equation (2), but does not have a measure of CA i. They could u s e R i as a proxy for CAl. In this case the econometrician is essentially estimating equation (4')---CAi is no longer in the error term of the estimating equation if it is measured by R i.

(4')

w i = o~1 ( g i ) + {7.2 (Xi) -I- o~3 ( H C i ) + t~ 5 (Ri) +

{Ei}

However, if equation (4') is estimated, care must be taken in interpreting (6~5). This coefficient reveals the expected impact of a one unit increase, from 0 to 1, in Ri which is equivalent to a decline in cognitive ability from CAHto CA~,. If people with poorer cognitive ability are less produc-

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tive, and hence earn lower wages, then (6~) would be negative. Thus, the finding (6~5 < 0) can be interpreted as evidence that employers reward cognitive ability, and if blacks possess less of this desired attribute, they are paid less. It need not be interpreted as evidence that employers engage in racial wage discrimination. Controversy over both the accuracy of the estimated coefficient on a dummy variable representing race in wage equations such as equation (4), and interpretation of the coefficient on the race indicator variable in equation (4'), led O'Neill and Neal and Johnson to conclude that existing evidence shed little light on the question of whether black workers face wage discrimination, lz They argued that both race and cognitive ability must be included in empirical wage equations in order to assess the wage discrimination hypothesis. Therefore, they estimated a wage equation of the form: (5)

wi = oq (Ki) + o~ (Xi) + o~3 (HCi) + o~4 (CAi) + o~5 (Ri) + s

In order to estimate equation (5) the critical step is measurement of the psychological construct "cognitive ability.'" A number of different variables have been used to serve as a proxy for CA i in literature. 13 For instance, Murnance, Willett, and Levy 14 used a person's score on a test designed to assess mastery of elementary mathematical concepts to measure their cognitive ability. 14 They estimated equation (5) using this measure as well as others drawn from the National Longitudinal Study of the High School Class of 1972 (NLS72) and from the High School and Beyond survey (HS&B). The trio of researchers report that a person's cognitive ability in 1972 was directly related to their wage six years later in 1978 for individuals in the NLS72. Similarly, 1980 math scores for persons in the HS&B sample were positively related to their wages in 1986. However, they also found that the estimated coefficient on Ri, (xs, is inversely related to wages for members of both the LHS82 and HS&B samples. Since these researchers had controlled for cognitive ability their finding can be interpreted as evidence consistent with wage discrimination. Moreover, they also discovered that the absolute value of the negative and statistically significant race coefficient in their earnings regressions was larger for the 1980 graduates than the 1972 graduates! Being black had an even stronger negative effect on wages for blacks in 1986 than in 1978, even after measured cognitive ability was taken under consideration.


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Mason estimated equation (5) using data drawn from the Panel Study of Income Dynamics (PSID), another longitudinal nationally representative data set. 15 The PSID contains a person's score on a 10-item sentence completion test. Mason used a person's test score to gauge their cognitive ability. He also found that the coefficient on race, t~5, is negative and significant. A person's score on the Armed Forces Qualification Tests (AFQT) now is the most commonly used measure of cognitive ability in wage equations. The Armed Forces Qualification Test (AFQT) has been utilized by the armed services for many years to test individuals for fitness for military service. In 1980 this test was administered to 94 percent of the young men and women in the National Longitudinal Survey of Youths (NLSY) sample--a nationally representative data set rich in demographic and economic information. June O'Neill was the first of several economists to demonstrate that the estimated coefficient on the dummy variable for race is insignificant when equation (5) is estimated with data drawn from the NLSY and AFQT scores are used to represent cognitive ability. 16 She also found that persons with greater cognitive ability earned significantly more than otherwise comparable individuals. Her findings have been replicated by Ferguson and by Neal and Johnson. 17 These findings reveal that employers pay the same wage to black and white workers of equivalent cognitive ability. However, the average black person in the NLSY sample scores lower on the AFQT than the typical white individual in the sample. Therefore, Neal and Johnson conclude that the racial wage differential is largely due to a racial skill differential--not discrimination. Blacks did score lower than whites on average in the NLSY sample of AFQT takers. Whether this indicates that blacks have lower average cognitive ability than whites is contingent upon the credibility one assigns to the AFQT as a measure of cognition. However~ important policy implications hinge on what factors govern a person's AFQT score (i.e., why do blacks score lower than whites?). According to Hernstein and Murray, AFQT is " . . . highly g-loaded," and " . . . AFQT is an excellent test, with psychometric reliability and validity that compare well with those of the other major tests of intelligence.''Is Thus, in their view, the AFQT gauges innate intelligence, biologically determined. In contrast, June O'Neill describes the AFQT as "an achievement test of verbal and mathematical skills that reflects the quality of schooling received as well as the effects of parental background. ''~9 Performance on

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an achievement test depends upon both nature (genetic inheritance or intelligence) and nurture (parental inculcation and educational resources). A poor AFQT test score may reflect a relatively high intelligence coupled with few educational resources. 2~ Given the potential importance of cognitive ability's influence on wages, the dispute over what AFQT measures is important from a policy perspective. If AFQT reflects genetic intelligence, AFQT is time invariant and independent of policy. However, if AFQT reflects achievement, the policy can alter community and educational resources, and possibly parental behavior. Therefore, policy action can influence a person's cognitive ability level and hence their wage. 21 Card and Krueger find a link between school resources and subsequent earnings. 22 They conclude that educational disparities play some role in explaining racial economic disparities. According to Darity this judgment is unsurprising since there is strong evidence that the black-white educational gap was engineered by deliberate social policy. 23 The dispute over what AFQT really measures (see Rodgers and Spriggs) 24 as well as the accuracy of the claim that blacks score lower on the AFQT, remains. An unfortunate byproduct of this debate is that it has diverted attention from the more fundamental issue of whether equation (5) is a model specification capable of producing reliable estimates of the relation between race and wages. The Thernstroms argument that all of the black-white gap in wages can be accounted for by racial differences in cognitive skills may be unwarranted. 25 Their conclusion depends on equation (5) being the "correct" model of wage determination. If an important determinant of personal productivity, and hence wages, is unaccounted for in equation (5)-as was the case with equation (4)--then the coefficients estimated suffer from omitted variable bias. If this is the case, reaching a conclusion about the presence of wage discrimination by evaluating the sign and significance of the estimated coefficient on race from equation (5) is inappropriate. In the next section we discuss why equation (5) is likely to be a misspecified model of wage determination. S P E C I F I C A T I O N OF THE W A G E M O D E L REVISITED: P S Y C H O L O G I C A L CAPITAL AND PRODUCTIVITY

Most economists believe that a person's human capital---education, experience, and cognitive ability--are the primary determinant of their


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personal productivity. Of course, the quantity and quality of a person's work also depends on their psychological capital, PC,---those aspects of personality that influence productivity. Erikson, founder of Life Span Development Theory, argued that individuals who were psychologically healthy would be the most productive.26 Economists acknowledge that the influence of personality on productivity is detectable and is rewarded by employers. Therefore, the appropriate model of wage determination is (6)

w, = txI (Ki) + Ur2 (Xi) + ~ (HCi) + ~4 (CAi) + tx5 (R,) + 0~6 (PC,) + Ei

Most economists have taken the position that personality is either unobservable or unmeasurable. Therefore, empirical studies of wage determination that control for cognitive ability result in the estimation of equation (7): (7)

wi = lx I (Ki) + lx2 (Xi) + lx3 (HCi) + tx~ (CA,) + ot5 (R,) + { ~. + otr (PCi) }

Treating psychological capital as an omitted variable, and thereby transferring it to the error term of equation (7), leads to biased coefficient estimates and inaccurate hypothesis tests if PC, is correlated with any of the other explanatory variables. Because psychological capital is likely to influence the accumulation of human capital, it is necessary to include measures of psychological capital in wage equation (6) to attain an accurate estimate of the relation between race and wages. Psychological capital encompasses a host of personal attributes expected to influence productivity. Many features of a person's psychological capital are reflected in a person's self-view or sense of self-esteem. Following Rosenberg, psychologists treat self-esteem as a multidimensional construct, comprising notions of worth, goodness, health, appearance, and social competence.27 The broad scope of factors contributing to self-esteem allows it to capture many aspects of a person's psychological capital. Therefore, self-esteem is an ideal way to measure psychological capital. Rosenberg 28 and other psychologists have developed and validated measures of self-esteem based upon self-reported responses to an inventory of survey questions. 29 Rosenberg's scale contains 10 questions used to construct six subscales, each yielding a single measure represented on a two point (0, I) scale. Therefore, the Rosenberg measure of self-esteem ranges in value from 0--6, with a higher value representing a greater level of self-esteem. Brockner 3~ found a positive correlation between self-esteem and job

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performance-----evidence consistent with Erikson's 31 assertion that persons with better psychological health are more productive. 32 In spite of Brockner's findings, the notion that self-esteem contributes to personal productivity, and hence wages, was unrecognized by economists--leading them to continue to estimate equation (7)--until the recent work by Goldsmith, Veum, and Darity. 33 Goldsmith, Veum, and Darity estimate equation (6) using data drawn from the NLSY. The NLSY is a sample of 12,686 males and females who were between the ages of 14 and 21 in 1978 and who have been interviewed each year since 1979. It includes data on wages and numerous aspects of human capital. In also contains a person's responses to Rosenberg's inventory of questions for his Self-Esteem Scale (SES). In our empirical work, psychological capital (PCi) is measured by a person's score on the Rosenberg Self-Esteem Scale, and cognitive ability by an individual's score on the AFQT. Thus, apart from our inclusion of a measure of psychological capital, we used the same data as O'Neill and Neal and Johnson. 34 Unlike them, we are able to estimate equation (6) rather than equation (5), which on theoretical grounds appears to be misspecified and which in practice becomes equation (7)--an equation estimated subject to omitted variable bias. We are able to examine the influence of cognitive ability, psychological capital, and race on a person's real wage at two different points in time for NLSY participants, 1980 and 1987. In both of these years respondents were asked the entire set of questions which comprise Rosenberg's Self-Esteem Scale. 35 We limit the 1980 data to persons who were old enough to have a work permit in 1979 and had finished their formal schooling; this gives us 2,225 young people of whom 1,411 were employed in 1980. Our 1987 data set consists of 8,132 observations of persons not enrolled in school in 1987---6,911 of these persons were working in 1987. 36 Table 1 presents our findings on the influence on a person's wage of human capital (nci) , cognitive ability (CAi), psychological capital (PCi), and race (Ri). The summary table does not include our findings on the contribution to a person's wage of: age, marital status, dependents, wealth, adolescent environment, residence, local labor market conditions, occupation, and industry of employment.37


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TABLE 1 OLS Log Wage Estimates Equation (6)v (t-statistics in parentheses) VARIABLE NAME

VARIABLE MEASURE

1980 I)ATA

1987 DATA

HCt

EDUCATION

.12e-01 (1.67)**

.27e-01 (6.75)***

HCl

EXPERIENCE

.76e-02 (5.29)***

.51e-03 (3.92)***

HCt

TENURE

(3.11),***

,69e-03

.54e-03 (12.07)***

CA,

AFQT

.19e-02 (2.34)***

. t 2e-02 (1.58)*

PC,

SELFESTEEM

.13 (2.97)***

.25 (3.73)***

R,

BLACK

-.53e-0 t (1.98)**

-.30e-01 (1.73)**

NUMBER OF OBSERVATIONS

1411

6911

F

18.90"** (34,1376)

115.84"** (34,6876)

R2

.32

.36

u

Statistically significant different from zero at the. 1 confidence level. Statistically significant different from zero at the .05 confidence level. Statistically significant different from zero at the .0P1 confidence level. EDUCATION is measured in years of schooling completed, tenure is represented by weeks of employment with current employer, EXPERIENCE is measured by all weeks of employment prior to current job, SELF-ESTEEM is measured using Rosenberg's scale (0-6), and cognitive skills are captured by AFQT scores which range from 0-60.

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RESULTS AND CONCLUSIONS The coefficient estimates on each of three different types of human capital (EDUCATION, EXPERIENCE, TENURE) are positive and significant in both the data set primarily composed of people at a very early stage of their working life-cycle and the data set containing more mature individuals. In addition, self-esteem, a broad measure of psychological capital, is positively and significantly related to the real wage in both the 1980 and 1987 data. For the average person in the entire data set, a 10 percent increase in self-esteem improves the real wage by 4.8 percent using 1980 data and 13.3 percent using 1987 data. 39 Persons with greater cognitive ability, measured by their score on the AFQT, earned significantly more than otherwise comparable individuals for both the 1980 and 1987 data sets. 4~ The striking result, in the context of the debate over the existence of wage discrimination, is that the race coefficient (~ts) is negative and statistically significant at the .05 confidence level in both 1980 and 1987 despite the presence of a measure of cognitive ability (AFQT score) in the wage equation regression. When the contribution to wages of both cognitive ability and psychological capital are explicitly taken into account we find that black workers, with comparable skill characteristics, still earn significantly less than white employees. For very young workers, persons 16-22 years old, blacks earn 5 percent less per hour. When these individuals are still young, 22-29 years of age, black employees earn 3 percent less per hour. Our findings suggest that among working persons there is a positive correlation between being black and self-esteem.41 Thus, when psychological capital is excluded from the wage equation, the dummy variable identifying black employees captures both the negative effect of being black on wages as well as the positive correlation between greater selfesteem--which black employees possess--and wages. If the positive effect on wages of being black, operating through self-esteem, is offset by the negative impact of being black on wages then being black would be unrelated to wages--the finding reported by O'Neill and Neal and Johnson. 41 When psychological capital is included in the wage equation, the contribution of race to wages is isolated and being black has a negative effect on a person's wage. What can we conclude? Empirical wage equation specification matters. The Themstrom's claim that differences in "pre-market factors"-particularly cognitive ability---explain the black-white earnings gap. How-

Goldsmith, Darity, and Veu_m

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ever, their conjecture is based upon an empirical model of wage determination that neglects the role of psychological capital. Race is an important determinant of wages when the influence of both cognitive skills and psychological capital is taken into account in a wage equation. The average black person in the sample possesses a lower level of psychological capital and a lower AFQT score. However, black workers with identical cognitive talent and equivalent levels of both human and psychological capital still receive lower wages than white workers. The latter finding is inconsistent with the Thernstrom's assertion that labor market discrimination against blacks is negligible or nonexistent. It is consistent with the presence of wage discrimination in the labor market. NOTES 1. Themstrom, A., and S. Thernstrom, "The Real Story on Black Progress," The Wall Street Journal, September 3, 1997. 2. O'Neill, June, "The Role of Human Capital in Earning Differences Between Black and White Men," The Journal of Economic Perspectives, Winter 1990, 25-45; Neal, Derek A. and William R. Johnson, "The Role of Premarket Factors in BlackWhite Wage Differences," The Journal of Political Economy, October 1996, 86995. 3. Thernstrom and Thernstrom, 1997. 4. Goldsmith, Arthur H., Jonathan R. Veum, and William Darity, Jr., '`The Impact of Psychological and Human Capital on Wages," Economic Inquiry, October 1997, 815-29. 5. Goldsmith, Veum, and Darity, 1997. 6. Dunifon, Rachel, and Greg J. Duncan, "Long-Run Effects of Motivation on Labor-Market Success," Social Psychology Quarterly, 1998, 61:1, 33--48. 7. O'Neill, 1990. 8. Neal and Johnson, 1996. 9. Mincer, Jacob, "On-the-Job-Training:Costs, Returns, and Some Implications," Journal of Political Economy, October 1962, $50-$79; Mincer, Jacob, Schooling, Experience, and Earnings. New York: Columbia University Press for the National Bureau of Economic Research, 1974. 10. Gottschalk,Peter, "Inequality,Income Growth, and Mobility:The Basic Facts," Journal of Economic Perspectives, Spring 1997, 11:2, 21-40. 11. Herrnstein, Richard, and Charles Murray, The Bell Curve: Intelligence and Class Structure in American Life. New York: Basic Books, 1994. 12. O'Neill, 1990; Neal and Johnson, 1996. 13. Altonji and Spletzer (1991) use either high school class rank or a person's score on the Scholastic Aptitude Test to measure cognitive ability. Card and Krueger (1990) use secondary school quality to gauge ability. Hanushek, (1986) provides an excellent review of the literature on measurement of personal ability and its subsequent impact on wages. 14. Murname, Richard J., John B. Willett, and Frank Levy, '"I'he Growing Importance of Cognitive Skills in Wage Determination," The Review of Economics and Statistics, May 1995, 77:2. 251-66.

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15. Mason, Patrick L., "Race, Culture, and Skill: Interracial Wage Differences among African Americans, Latinos, and Whites," The Review of Black Political Economy, forthcoming. 16. O'Neill, 1990. 17. Ferguson, Ronald F., "Shifting Challenges: Fifty Years of Economic Change toward Black-White Earnings Equality," Deadalus, Winter 1995, 124, 37-76; Neal and Johnson, 1996. 18. Hermstein and Murray, 1994. 19. O'Neill, 1990, p. 32. 20. Given O'Neill's perspective on what the AFQT reflects, discrimination in the provision of school resources and perceived disparate social and economic treatment could influence AFQT scores. 21. Goldberger and Manski (1995), in their review of the Bell Curve, argue convincingly that AFQT scores are influenced by factors including educational attainment and social resources--AFQT is not fixed at birth--and therefore AFQT is a poor measure of cognitive ability. Their view, which is now shared by most economists including O'Neill and Neal and Johnson, is that AFQT reveals mastery level of basic academic skills. In a wage regression that controls for both a person's educational attainment and the resources they received during childhood and adolescence an individual's AFQT score performs better as a measure of cognitive ability, but remains less than ideal. 22. Card, David, and Alan Krueger, "School Quality and Black-White Relative Earnings: A Direct Assessment," Quarterly Journal of Economics, February 1992, 107:1, 151-200. 23. Darity, William, Jr., "Programmed Retardation and the Theory of Noncompeting Groups," unpublished manuscript, University of North Carolina at Chapel Hill, May 1997. 24. Rodgers, William M., and William E. Spriggs, "What Does AFQT Really Measure: Race, Wages, Schooling, and the AFQT Score," The Review of Black Political Economy, Winter 1996. 24:4, 13--46. 25. Thernstrom and Thernstrom, 1997. 26. Erikson, Erik H., "Identity and the Life Cycle," Psychological Issues, January 1959, 50--100. 27. Rosenberg, Morris, Society and the Adolescent Self-lmage. Princeton, NJ: Princeton University Press, 1965. 28. Ibid. 29. Robinson and Wrightsman (1991) offer an excellent description and psychometric evaluation of all the commonly used measures of self-esteem. See also Wylie (1989) for an extensive discussion of Rosenberg's SES. 30. Brockner, Joe, Self-Esteem at Work. Lexington, MA: Lexington Books, 1988. 31. Erikson, 1959. 32. He found self-esteem was directly linked to productivity in two ways. First, managers perceived that high self-esteem workers tend to use their time more effectively. The latter needed less direction from supervisors, leading to shorter periods of "down time." Second, workers high in self-esteem exercised a more efficient use of group time by exhibiting a willingness to consider a wider range of solutions to problems; and they were more confident decision makers. These characteristics led to groups with high levels of cooperation and, groups less inclined to seek guidance from managers. 33. Goldsmith, Veum, and Darity, 1997. 34. O'Neill, 1990; Neal and Johnson, 1996.


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35. Rosenberg, 1995. 36. Wage data are only available on working individuals. Unobserved personal characteristics may exists that influence both the decision to work and compensation if employed. We adopt a technique developed by Heckman (1979) to account for these differences. 37. A detailed discussion of our results for equation (6) and the empirical procedures used appears in Goldsmith, Veum, and Darity, 1997. 38. Some caution is called for when comparing the 1980 and 1987 results, since the latter year has a much larger sample size. 39. For complete results as well as a detailed description of how all the variables in equation (7) are measured and the procedure used to estimate equation (7) see Goldsmith, Veum, and Darity, 1997. 40. This finding is consistent with Mason's (1998) speculation that there may be unobservable variables in wage equations that favor black productivity. See Darity and Mason (1998, footnote 13) for a thorough discussion of this argument. 41. O'Niell, 1990; Neal and Johnson, 1996.