Can the human capital approach explain life-cycle wage differentials between races and sexes?
The trends in gender and racial wage gaps have continued to receive the attention of researchers and policy-makers due to their mounting social significance. Substantial literature concludes that after World War II, the black-white pay gap shrank rapidly until the mid-1970s. This trend was reversed in the 1980s (Card and DiNardo 2002; Couch and Daly 2002; Darity and Myers 1998; O'Neill 1990; Smith and Welch 1989). (1) In contrast, the gender pay gap persisted for four decades after World War II. Only in the 1980s did it start to narrow. Yet, it showed only a little progress in the 1990s (Blau, Ferber, and Winkler 2002; Goldin 1990; O'Neill 2003).
Although a large number of studies have been purported to investigate the sources of male-female and black-white pay gaps, most have not addressed the issue of whether or not the individuals being observed have changed their economic status over their lifetimes. The major problem is that longitudinal data are not available over a long enough period to determine the age-earnings profiles. (2)
By using the National Longitudinal Survey of Youth data-1979 cohort, (NLSY79) this paper examines gender and racial wage gaps among individuals of the same age in an effort to eliminate major life-cycle differences, while at the same time tracking the changes in the wage gaps over their life spans. In particular, we would like to provide answers to the following questions: What factors can account for the narrowing (widening) gender wage gaps among blacks (whites) as they age? Can the observed life-cycle wage gaps be attributed to different paths of postschool human capital accumulation?
Since today's individuals, regardless of race or sex, have on average completed similar years of schooling among the youth cohort, the observed disparity in wages between races and sexes may simply reflect the differences in the quality of schooling, family background, and postschool investment. (3) Given that school quality and family background are essentially fixed for an individual as he or she ages, in order to address the questions above, this paper attempts to further examine the differences in postschool human capital investment behavior among individuals.
Past estimates of the structural parameters for the model of postschool human capital accumulation have, however, not been fruitful (BenPorath 1970; Brown 1976; Haley 1976; Heckman 1976a, 1976b; Rosen 1976). The major reasons, as Heckman (1976b) points out, are that dynamic models are difficult to solve explicitly and that the proportion of time spent investing in on-the-job training cannot be measured directly. Moreover, to fulfill the dynamic concepts of human capital accumulation, longer period longitudinal data must be used to explore the life-cycle view of individual wages. (4)
The lack of empirical investigation in relation to the continuous-time dynamic model using panel data therefore leads us to develop an alternative empirical version for estimating the structural parameters of the wage function over a lifetime. In other words, the purpose of our study is to estimate a dynamic structural model based on the theory of optimal human capital accumulation. In accordance with this theory of human capital, the wage and its life path can be viewed as the outcome of an optimal path of human capital investment over an individual's life cycle. Instead of comparing the differences in the outcome of this optimization process (i.e., wages), we estimate the key parameters in determining the life-cycle wage path as well as further empirically identifying the sources of the wage gap.
Our empirical results first suggest that the male-female wage gap mainly arises from gender difference in the marginal costs of human capital production. As men in general spend more time in the labor market and gain more work experience than women, they tend to have lower marginal costs in the process of human capital production. Secondly, the existence of black-white lifetime wage differentials could be in part a result of the higher implicit interest rate experienced by blacks. Moreover, owing to their longer nonemployment duration, black males encounter a higher depreciation rate than white males. This may explain why the black-white male wage gap widens over their lifetimes.
While the study by Neal and Johnson (1996) places emphasis on the premarket factors in explaining the racial wage gap, our findings suggest that postschool human capital investment plays an increasingly important role in describing the wage gaps between the races and sexes. (5) Indeed, whether the Armed Forces Qualifications Test (AFQT) test score is really a "racially unbiased" predictor for skills or a "premarket" factor has been questioned by a number of researchers (Carneiro, Heckman, and Masterov 2003; Darity and Mason 1998; Rodgers and Spriggs 1996). (6) Given the same family background and a similar size of racial AFQT score gap faced by both black men and black women, it is difficult for the Neal-Johnson approach to account for how the male black-white wage gap could be more than two times larger than the female racial wage gap (Neal 2004, S23).
Eventually, the premarket factors become obsolete while chances for new investment in human capital emerge. These two facts have usually been neglected in the cross-sectional studies. In other words, when taking into account these two effects in the dynamic process of human capital production, the importance of premarket factors on wages is likely to decline over time. In fact, the premarket factors can hardly explain the narrowing wage gap between black and white women after the age of 28. However, it should be noted that the results of this paper are specific to the youth cohort in the NLSY79 sample, as other cohorts may face different economic and social structures.
This paper proceeds as follows. Section II presents an empirical model of the life-cycle wage path, which is developed from the theory of optimal human capital accumulation. Section III looks at the wage gaps between the races and sexes as well as the group differences in the related human capital variables. The data and the estimation method are described in Appendices A and B, respectively. Section IV presents the empirical results and discusses the causes of changes in the life-cycle wage differentials. The final section summarizes the main findings of the empirical investigation using the NLSY79 data.
II. THE MODEL
Despite the fact that other factors, such as cohort size and socioeconomic background, could affect the level and shape of wage profiles for different cohorts, differences in human capital investment behavior have been documented by many studies as the major cause of life-cycle variations in wages among individuals within a particular cohort. This observation was addressed early on in the work done by Becker (1964), Ben-Porath (1967), and Mincer (1970, 1974). Since individuals who make different decisions over their life cycles regarding investment in human capital have different age-earnings profiles, the theory of optimal human capital accumulation has been applied by many economists to explain how earnings are determined. In particular, schooling and job experience are the two major human capital factors determining an individual's earnings (Mincer 1974; Polachek and Siebert 1993) and are also the two major sources of earnings differentials between the races and sexes (O'Neill 1985, 1990, 2003; Smith 1984; Smith and Welch 1989). As the distribution of formal education has become more equal for the youth cohort, this paper focuses on the role of postschool human capital investment in explaining the life-cycle wage differentials across the race-sex subgroups.
To construct a simple, but meaningful wage function, we start from a modified Ben-Porath (1967) model of optimal human capital accumulation. The labor market is assumed to be perfectly competitive. Let [K.sub.t] be the stock of human capital at time t. The wage rate at time t, [W.sub.t], is assumed to be a linear function of human capital with [alpha] as the rental rate.
(1) [W.sub.t] = [alpha][K.sub.t], t [member of] [0,T],
where T is the end of the individual's life.
The individual allocates a fixed amount of time for working and producing human capital. The production function of human capital is a Cobb-Douglas function (Haley 1976; Polachek and Siebert 1993, 23). That is,
(2) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
[Q.sub.t] is the amount of capital produced at time t and [S.sub.t] is the fraction of human capital used in the production of human capital at t. Investment cost [C.sub.t] consists of foregone income. Foregone income includes expected income that could be earned if the individual did not spend time in learning, namely,
(3) [C.sub.t] = [alpha][S.sub.t][K.sub.t].
The rate of change in human capital stock follows a first-order differential equation. That is,
(4) [[??].sub.t] = [Q.sub.t] - a[K.sub.t],
where a is the rate by which the stock of human capital deteriorates. The goal of the individual is to maximize the present value of the sum of his/her wealth. The objective function becomes [[integral].sup.T.sub.t] [e.sup.-[gamma][tau]][([W.sub.[tau]] - [C.sub.[tau]])]d[tau] with the budget constraint [[??].sub.t] = [Q.sub.t] - a[K.sub.t],, where [gamma] is the implicit rate of interest.
Under these assumptions, we can formulate this problem as follows:
Max G(t) = [[integral].sup.T.sub.t] [e.sup.-[gamma][tau]][([W.sub.[tau]] - [C.sub.[tau]])]d[tau]
= [[integral].sup.T.sub.t] [e.sup.-[gamma][tau]][[alpha](1 - [S.sub.[tau]])[K.sub.[tau]]]d[tau] + constant,
subject to [[??].sub.t] = [Q.sub.t] - a[K.sub.t]
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],
by which we have found that the optimal solution of [Q.sub.t] is
(5) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],
Since [K.sub.t] cannot be measured directly, [W.sub.t] is used in our empirical study.
Recall that the wage rate is assumed to be a linear function of the human capital stock, that is, [W.sub.t] = [alpha][K.sub.t] where [alpha] is the rental rate of the human capital stock. The parameters ([alpha], [[beta].sub.0], [[beta].sub.1], a, and [gamma]) may depend on individual characteristics such as sex, race, and ability. When combined with the previous equation [[??].sub.t] = [Q.sub.t] - a[K.sub.t], we obtain the following equation:
(6) [??](t) + aW(t) = [alpha]Q(t), t [member of] [0, T].
By solving this first-order differential equation, we show that, given a finite time horizon, an individual will face the following life-cycle wage path. That is,
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (7)
Ceteris paribus, a higher [[beta].sub.1] would lead to a higher level of newly produced human capital and, hence, wages; yet, the implicit interest rate ([gamma]) has the opposite effect. Also, a higher rate of depreciation rate (a) would cause a lower wage rate. In terms of elasticity, 1% change in [[beta].sub.1] would lead to the largest percent change in wages, followed by a and [gamma]. (7)
In this model, we would expect that men would have a lower depreciation rate and a higher [[beta].sub.1] than women, in that men in general spend more time in the labor market and gain more work experience than women. In addition, black males would be expected to encounter a higher depreciation rate than white males, owing to their longer nonemployment duration. Moreover, blacks would tend to face a higher implicit interest rate. As white families are relatively wealthier than black ones, white families are more likely to invest in their children's human capital at a relatively low rate of interest.
III. THE NLSY79 DATA ON HOURLY WAGES AND SCHOOLING
Data for estimating equation (7) are from the NLSY79 (1979-1994) and its Work History CD-ROM. (8) The richness of data on work history is one of this data set's strongest advantages. The detailed description of the NLSY79 data is documented in Appendix A.
Since earnings are derived from human capital in the theory of optimal human capital accumulation, the only income that should be used to estimate the human capital model is labor income. To avoid any variation in earnings or in income introduced by variations in hours worked during the period, we use data relating to the hourly wage rates rather than to earnings or income, so as to properly explain the theory of human capital accumulation. Such data, in our opinion, provide better estimates of the parameters than does total income. (9) In particular, the hourly wage rates for the current primary job are chosen for the purposes of our study.
As the data contain so few observations at both ends of the age categories (i.e., 16-19 and 34-35), our discussions will focus on the age range of 20-33. Appendix Table A1 summarizes the age profiles of hourly wage rates and their standard deviations for four groups. (10) The age profiles of the mean wages are also plotted in Figure 1. The standard deviations of wage rates among individuals increase with age. (11)
A. The Evolution of Gender and Racial Wage Gaps
Table 1 first summarizes the life paths of the wage ratios between races and sexes for the youth cohort. It shows that the ratio of the mean hourly wage rate of white females relative to white males remains fairly constant at around 0.8 until age 28, but it then begins to fall to 0.75 at age 33. However, among blacks the picture is quite different. The female-male wage ratios for blacks show a less clear U-shaped pattern, in which the wage ratio declines from 0.83 at age 20 to 0.79 at age 21, and then rises to 0.95 at age 33. In other words, the gender difference in hourly wage rates is narrowing among blacks and widening among whites until age 33. Table 1 also shows that the black-white wage gap among women has an inverted U-shaped pattern, in which the wage gap increases from 11% at age 20 to 18% at age 28, and then decreases to 9% at age 33. However, the racial wage gap among men increases from 15% at age 20 to 28% at age 33. (12)
[FIGURE 1 OMITTED]
Generally speaking, the male-female wage gap over the life cycle is much larger among whites than among blacks, while the black-white wage gap over the lifetime is considerably larger among men than among women. Although it is not yet clear whether these wage patterns will be extended after the age of 33, (13) the changes in the gender and racial wage differentials over the life span are nevertheless a cause for concern.
B. Group Differences in Schooling
This section reports the gender and racial differences in schooling for the NLSY79 data. Table 2 presents the statistical summaries and shows that blacks completed fewer years of schooling than whites and that women received more schooling than men. White females completed on average 13.00 years of schooling, slightly more than white males. Black females completed 12.84 years compared to 12.20 years for black males. The racial difference in schooling is only 0.16 years among women and 0.64 years among men. However, the black-white gap in schooling is much larger among their parents' generation: it is about 0.31 years for women and about 1.36 years for men. Among blacks, females consistently completed more years of school than males over a period of two generations. However, the differences in school completion levels between the races and sexes have been narrowing over the last two generations.
IV. THE EMPIRICAL RESULTS
Equation (7) is estimated separately for the following groups: white males, white females, black males, and black females. The estimation procedure used in this study is nonlinear least squares and is described in Appendix B. The results are shown in Table 3. The actual data and the predicted mean wage profiles are displayed in Figure 2. The simplified version of the Ben-Porath model is found to fit the data very well. The model is estimated with great precision, and the estimates are reasonable. In other words, all the parameters are estimated with small asymptotic standard errors and large asymptotic t values. (14) These results are then compared between males and females within the white and black groups. Table 4 presents the results of differences in parameter estimates across the race-sex subgroups with their t values.
First, the estimate of the depreciation rate displayed in Table 3 is about 0.181 for black males, 0.132 for white females, 0.124 for black females, and 0.116 for white males. It implies that black males' human capital depreciates at a more rapid rate than the human capital of the other three groups, which diminishes at the rate of about 12% per year. One possible explanation for this is that black males are more likely to be out of work, which could lead to both an interruption in the process of producing new human capital and a more rapid obsolescence of their existing human capital.
The explanation of "gender twist" in the demand for skill provided by Katz and Murphy (1992) could further support our argument. That is, changes in labor demand might benefit women relative to men at lower levels of skill. As a result, low-skilled men lose rent-earning jobs to a greater extent than low-skilled women. Since low-skilled men tend to be blacks, black men tend to have a higher unemployment rate when there is a shift in labor demand.
As evidenced in Figures 3 and 4, black males tend to work fewer hours and stay a longer time in a nonemployment status (i.e., unemployed and out of the labor force) at every age than their white counterparts for the 20-33 age interval. And the disparity in employment widens as they age. Table 5 shows that the black-white ratio of weeks of nonemployment for males grows from 1.38 for the group aged 20-21 to 2.44 for 31-33 years old. On the other hand, this ratio declines from 1.42 to 1.06 for females.
The fact that black males have the lowest chance among the four demographic groups of receiving training, in particular company training, could also help explain their high human capital depreciation rate. As Table 6 indicates, only about 14.6% of black males aged 25-27 receive training, as compared to 20.5% of their white counterparts. (15)
The previous estimate of the depreciation rate for white males by Heckman (1976a) is about 9% for the Ben-Porath model. The estimates of the depreciation rates for different years of schooling given in Haley (1976) are all less than 10%. Haley also finds that college graduates have lower depreciation rates than high school graduates. However, since the Ben-Porath model fits the data better at younger ages according to Heckman (1976a), we speculate that human capital depreciates more rapidly at younger ages, as is often assumed for physical capital, such as cars, machines, and buildings. Seeing that technology advances at a faster pace than before, the stock of human capital for the youth cohort is likely to deteriorate faster than for the older cohorts.
Moreover, several studies have indicated that there have long existed differences in female labor supply behavior based on race, in particular among married women (Bell 1974; Coleman and Pencavel 1993). (16) Namely, white wives work fewer hours than black wives. One possible explanation is that the negative effect of children on labor supply is substantially greater for white women than for black women, although this difference based on race is less conspicuous among highly educated women, as noted by Lehrer (1992). Figure 3 displays that while white females work more hours at every age than their black counterparts for the 20-28 age interval, the opposite is true after the age of 28.
Since working fewer hours will in general cause the human capital stock to accumulate more slowly and/or depreciate faster, this might explain why the estimate of the depreciation rate is slightly higher for white females than for black females. It in turn partly explains why the gender gaps move in the opposite direction across races after the age of 28.
Second, the parameter [[beta].sub.1] may reflect the differences both in the endowed ability of the individuals to produce human capital and in their opportunities. However, as in the previous studies, the endowed ability is assumed to be equal across race and sex, so larger values of [[beta].sub.1] imply higher rates of returns to scale and lower marginal costs of human capital production. The estimates for [[beta].sub.1] are 0.593 and 0.582 for white males and black males, respectively. The estimation procedure also yields estimates for [[beta].sub.1] of 0.489 and 0.488 for white females and black females, respectively. As shown in Table 4, the racial difference in the estimates of [[beta].sub.1] is not statistically significantly different from zero at the 5% level either for males or for females. However, gender differences in [[beta].sub.1] do exist both for whites and for blacks.
Our empirical results might reflect gender differences in motivation or socioeconomic background such as school content and the choice of occupation. Since certain courses of study may develop more valuable job-related human capital than other courses, differences in the chosen field of study could exert a significant impact on wages (Brown and Corcoran 1997). Moreover, as women tend to place a greater priority on family responsibilities, they are more likely to choose occupations that allow them to work at a flexible schedule where many of those occupations are often lower paying and female dominated. Consequently, relative to men, more women are employed in lower paying occupations (such as clerical and services), as highlighted in Appendix Table C1. (17)
Nevertheless, due to the continued improvement in women's educational attainment, younger cohorts of women have more choices in selecting their occupations than do older cohorts of women. Appendix Table C1 shows that women are represented in higher wage occupations such as professionals and managers; however, this broad occupation category includes teachers. Women are concentrated in this lower paying occupation. Thus, both the fact that a large portion of women are still employed in low-paying occupations (as shown in Appendix Table C1) and the fact that women work fewer hours than their male counterparts within all the occupations (as indicated in Appendix Table C2) are likely to result from the division of labor by gender within the family rather than from market discrimination. (18)
In other words, male-female disparity in productivity is more likely to be social rather than physiological in nature. If this story is correct, gender differences in productivity may simply reflect self-selection or discrimination exercised prior to entry into the labor market. Then, it would be less likely to narrow the gender wage gap simply by expanding occupational choices (Boraas and Rodgers 2003). (19)
The results for white males, to some extent, are comparable with previous estimates by Brown (1976), Haley (1976), and Heckman (1976a, Table 3A). But they seem small compared with the estimates by Heckman (1976b) and Heckman, Lochner, and Taber (1998). (20) Haley's estimates of [[beta].sub.1] are between 0.544 and 0.604, while Brown estimates the inverse of [[beta].sub.1] (i.e., 1/[[beta].sub.1] as falling between 1.159 and 1.792. Heckman's (1976a, Table 3A) estimate of the returns-to-scale parameters for white married males with 13-16 yrs of schooling is 0.520 for the extended Ben-Porath model. Heckman's (1976b) estimates of [[beta].sub.1] are 0.67 and 0.99 for white college graduates in two different models. Recently, the estimate of [[beta].sub.1] reported by Heckman, Lochner, and Taber (1998) has been around 0.832 for high school graduates and 0.871 for college graduates based on NLSY79 data of white male earnings.
Third, the implicit interest rate is approximately equal to 15.8% for white males, 12.2% for white females, 18.8% for black males, and 19.0% for black females. (21) As shown in Table 4, the difference in the estimates of [gamma] between black males and black females is not statistically significantly different from zero even at the 10% level. Moreover, the interest rate level implied for blacks tends to be higher than for whites. Although these numbers seem large compared to the estimates of Haley (1976), who finds that the estimate of [gamma] is 6.5%, for workers with 12 yrs of schooling, they are reasonable and do not seem large when compared with the estimates made by Heckman (1976a). (22) For instance, our estimate of the implicit interest rate for blacks is 19% while the estimates of the rate of interest given by Heckman (1976a) are between 18% and 20% for white males. Nevertheless, unlike in our result, Heckman does not obtain precise estimates for this parameter in that his estimated asymptotic standard errors are large.
[FIGURE 2 OMITTED]
Since human capital cannot be offered as collateral, it is more difficult to finance investments in human capital. Hence, wealthier families tend to invest more than poorer families through internal financing. In general, white families are relatively wealthier than black ones and are more likely than blacks to have relatively low rates of interest. Since lower interest rates often imply greater acquisition of human capital, people with relatively high interest rates will spend less time investing and will tend to earn less and remain poor.
[FIGURE 3 OMITTED]
Finally, the estimates for [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] are about 0.509 for white males, 0.732 for white females, 0.879 for black males, and 0.737 for black females. However, we are unable to identify the estimates of [alpha] and [[beta].sub.0] from [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. Because of this problem of identification, we cannot say much about our estimates of the rental rate ([alpha]) or the scale effect of human capital productivity ([[beta].sub.0]). Among the earlier studies, none of them has been able to identify and estimate the rental rate. As a result, the rental rate of human capital ([alpha]) is usually normalized to unity in the estimation of the human capital model. For instance, in Heckman (1976a) and Heckman, Lochner, and Taber (1998), [alpha] is normalized to unity and only the estimate of [[beta].sub.0] is obtained.
[FIGURE 4 OMITTED]
To sum up, Table 4 shows that the main determinant of the male-female wage gap, regardless of race, is the gender difference in the rate of returns to scale of the human capital production function ([[beta].sub.1]). At the same time, the racial difference in the implicit rate of interest ([gamma]) plays an important role in explaining the existence of the black-white wage gap, regardless of gender. Table 4 also indicates that the difference in the depreciation rate has been the major determinant of the widening black-white male wage gap. Since the level of depreciation rate is often caused by labor market factors as opposed to [[beta].sub.1] and [gamma], (23) our results might imply that the male racial wage gap is mainly determined by the market factors.
Overall, the modified Ben-Porath model of postschool human capital investment provides a good explanation for both the white male-female wage gap and the black-white male wage gap, with the values of [R.sup.2] being .89 and .96, respectively. Nevertheless, the proportions of the wage gaps as explained by the model for the black male-female gap and the black-white female gap are only .62 and .60, respectively.
Eventually, the premarket factors, defined by Neal and Johnson (1996, 871) as "human capital formation before the age of 16-18," become obsolete, while chances for new investment in human capital emerge. In other words, the effects of premarket factors on wages are likely to decline over time. (24) In fact, the premarket factors can hardly explain the narrowing wage gap between black and white women after the age of 28.
This paper estimates a continuous-time model of wage determination over the life cycle using the theory of optimal human capital accumulation. The data for the empirical study are taken from the NLSY79 for the period from 1979 to 1994. We find that the human capital approach provides a good explanation for both the white male-female wage gap and the black-white male wage gap, with the values of [R.sup.2] being .89 and .96, respectively. One limitation of our empirical study is that only the rising portion of the life-cycle wage profiles is observed. However, since most of the investment in human capital takes place at younger ages, the NLSY79 allows us to observe the most important part of the life cycle in relation to postschooling human capital investment.
This study finds that the main factor behind the male-female wage gap is the gender difference in the marginal costs of human capital production. The greater amount of work experience gained by men translates into lower marginal costs in the process of human capital production. Furthermore, lifetime wage differentials between blacks and whites may be partly due to the higher implicit interest rate for blacks.
Moreover, owing to their longer nonemployment duration, black males encounter a higher depreciation rate than white males. Finally, the likelihood of receiving training, in particular company training, is the lowest for black males among the four demographic groups. This may explain why the black-white male wage gap widens over their lifetimes. Consequently, the greater attention that black males receive among researchers and policymakers seems warranted.
AFQT: Armed Forces Qualifications Test
CPI: Consumer Price Index
NLSY79: National Longitudinal Survey of Youth 1979 cohort
APPENDIX A: DESCRIPTION OF THE NLSY79 DATA
The National Longitudinal Survey of Youth-1979 cohort (NLSY79) is a survey of 12,686 people whose ages ranged from 14 to 21 years at the end of 1978. The NLSY79 contains detailed information on schooling, employment history, training programs, occupation, marital status, and fertility history. The data set consists of a randomly chosen sample of 6,111 youths, an oversample of 3,652 blacks and Hispanics, a supplemental sample of 1,643 economically disadvantaged whites, and a sample of 1,280 youths on active duty in the military. It includes about equal numbers of males and females. The supplemental sample of economically disadvantaged whites is excluded from our analysis. Since our sample was divided into four subsamples by race and sex, the resulting subsamples would be nationally representative of their populations. Thus, as we estimate the model separately for . each demographic group, no sampling weights are used in this study.
Our sample is restricted to those who had completed their schooling by the 1994 interview date and had started to work full time. Those who were still enrolled in school in 1994 were dropped from the sample. The remaining individuals were then tracked from the time they started their first job after leaving school. The hourly wage observations are obtained from the NLSY79 Work History CD-ROM. The NLSY79 Work History Data provide us with week-by-week longitudinal work records of each respondent. Individuals who were in the agricultural sector or sell: employed were excluded from the sample. These selection criteria yielded a final sample of 6,901 individuals.
Because of the dramatic changes in female labor market activities over the past 50 years and the differences in these patterns between blacks and whites, any meaningful analysis of wage differences requires separate treatment by race and gender. Our sample was therefore divided into four subsamples: 2,440 white men, 2,300 white women, 1,139 black men, and 1,022 black women. Due to its large sample size, the NLSY79 allows us to conduct a meaningful disaggregated analysis by gender and race.
Moreover, as the wage distributions usually shift rightward over time, Chandra (2003, 13-14) points out that imposing fixed real-dollar cutoffs would delete a disproportionate number of the low-skilled blacks in earlier years and a disproportionate number of the high-wage whites in later years from the sample. Since trimming wages on the basis of real-dollar cutoffs could be a source of selection bias, the top and bottom 0.5% of the wage observations are trimmed off within each group's wage distribution in this analysis. Furthermore, all wage rates are deflated by the CPI (1990 = 100).
Existing studies show that selecting only the full-time workers in the sample would understate the black-white male wage gap or male-female wage gap (Brown 1984; Butler and Heckman 1977: Chandra 2003). Unlike most other studies that impose sample-selection criteria based on labor supply, all 6,901 individuals are kept in our sample throughout the analysis regardless of their status in the labor market. By doing this, we can avoid the sample-selection problem. For those nonworkers, their wages are assumed to be the same level as when they last worked. Although this approach tends to overstate the wages of the nonworkers when in nonemployment status, it can reveal the reemployment wage gap once they are again employed.
Regarding the formal job training data, the 1979-1986 NLSY79 surveys collected detailed information on both government-sponsored training programs and privately supported training programs that lasted at least 4 weeks. In the 1987 survey, no detailed information on training is collected. Following the 1988 interview, the training questions were changed and respondents were asked about all types of training regardless of duration. Because of the changes in questionnaires in 1988, only the 1988-1994 data are employed for Table 6.
APPENDIX B: THE ESTIMATION METHOD
Following the approach of previous studies (Brown 1976; Haley 1976; Heckman 1976a, 1976b; Heckman, Lochner, and Taber 1998), the estimation procedure employed is nonlinear least squares. Namely, the set of parameter estimates in equation (7) for each demographic group was obtained from minimizing the sum of squared deviations of actual wages from predicted wages (MSE) by using the Gauss-Newton optimization technique at the group mean level.
This technique performs well, but difficulties occur when it comes to finding a global minimum, as the sum of the squares' surface is irregular with respect to some parameters. The technique we used to find initial values for the parameters was to simulate the wage profile for various values of the parameters. We then used the random number generator to obtain different initial values from the reasonable range of values found in the previous step. The optimization process was repeated over a substantial range of initial values. The parameter estimate of the depreciation rate was found to be insensitive to the initial values chosen.
All estimates are conditional on an assumed value of the unknown parameter T, which represents the end of the earning life cycle. For the empirical work, T is taken to be 65 as a representative age for retirement (Brown 1976; Haley 1976). In a way similar to the work done by Haley (1976), our qualitative analysis using computer simulations indicates that the initial stock is not very influential. (25) Overall, the appearance of longer period panel data sets and the advances in computer technology have made it possible to estimate the age-earnings function in a more satisfactory manner.
APPENDIX TABLE A1 Means and Standard Deviations of Hourly Wage Rates by Race, Gender, and Age (in 1990 dollars) White Males (1) (2) (3) Age No. Mean Standard (yrs) Observed Deviation 20 833 7.90 3.59 21 1,094 8.22 3.76 22 1,251 8.62 4.08 23 1,421 9.01 4.16 24 1,591 9.57 4.53 25 1,740 9.99 4.70 26 1,845 10.43 4.93 27 1,934 10.85 5.09 28 2,008 11.17 5.28 29 1,978 11.59 5.60 30 1,745 11.90 5.82 31 1,490 12.15 6.00 32 1,180 12.42 6.24 33 882 12.52 6.36 34 594 12.88 6.43 White Females (4) (5) (6) Age No. Mean Standard (yrs) Observed Deviation 20 688 6.24 2.29 21 925 6.53 2.63 22 1,085 6.73 2.99 23 1,242 7.22 3.32 24 1,400 7.66 3.73 25 1,505 7.98 3.98 26 1,586 8.37 4.37 27 1,653 8.62 4.64 28 1,712 8.96 4.83 29 1,699 9.12 4.88 30 1,509 9.29 5.11 31 1,291 9.38 5.17 32 1,033 9.34 5.49 33 765 9.38 5.65 34 539 9.19 5.42 Black Males (7) (8) (9) Age No. Mean Standard (yrs) Observed Deviation 20 345 6.72 2.98 21 532 7.07 3.43 22 637 7.24 3.50 23 721 7.46 3.61 24 809 7.70 4.01 25 866 7.95 4.05 26 902 8.37 4.25 27 929 8.67 4.34 28 934 8.78 4.32 29 920 8.87 4.46 30 814 8.86 4.60 31 692 8.87 4.54 32 538 8.78 4.41 33 393 8.95 4.76 34 257 9.28 5.04 Black Females (10) (11) (12) Age No. Mean Standard (yrs) Observed Deviation 20 200 5.56 2.51 21 327 5.61 2.32 22 433 5.81 2.36 23 527 6.14 2.73 24 603 6.52 3.01 25 674 6.74 3.27 26 718 7.03 3.39 27 753 7.35 3.54 28 784 7.37 3.92 29 763 7.68 3.97 30 688 7.78 3.97 31 581 7.92 3.89 32 459 8.29 4.31 33 354 8.53 4.42 34 243 8.53 4.40 APPENDIX TABLE C1 Occupational Distribution by Race and Gender, at Age 29 (in %) White White Black Black Occupation Males Females Males Females Professional/technical 13.9 20.8 8.2 13.2 Managers 14.7 12.8 7.2 6.7 Sales 6.1 5.0 3.2 3.2 Clerical 7.3 31.1 9.9 35.3 Craft and kindred 22.2 2.1 16.4 2.3 Operatives 17.1 7.6 19.0 11.7 Laborers/farmers 10.9 2.1 19.6 2.2 Service workers 7.8 18.6 16.6 25.4 Notes: Military is the omitted category; private household service workers are included in the category of service workers. APPENDIX TABLE: C2 Selected Characteristics by Occupation, Race, and Gender, at Age 29 White White Black Black Variable Males Females Males Females Professional speciality, technicians, and managers Years of schooling 14.8 14.8 14.4 14.6 Hourly wage (in 1990 dollars) 14.7 12.2 12.1 10.2 Number of weeks worked 49.9 47.3 48.4 47.6 Number of hours worked per week 47.5 40.5 46.7 43.6 Number of children 0.8 0.8 0.7 1.0 Age at first marriage (a) 25.2 24.0 26.5 24.4 Number of observations 615 607 148 161 Clerical and sales Years of schooling 13.6 12.8 13.1 13.3 Hourly wage (in 1990 dollars) 11.8 9.1 9.8 8.6 Number of weeks worked 47.7 44.3 43.4 42.9 Number of hours worked per week 45.5 37.7 43.0 39.7 Number of children 0.7 1.1 0.6 1.3 Age at first marriage (a) 25.2 22.4 26.1 24.1 Number of observations 288 652 126 313 Service workers Years of schooling 12.5 12.1 11.9 12.2 Hourly wage (in 1990 dollars) 10.0 7.2 7.5 5.9 Number of weeks worked 48.0 37.7 43.2 37.9 Number of hours worked per week 44.1 36.0 43.4 38.2 Number of children 0.8 1.4 0.7 1.7 Age at first marriage (a) 23.8 21.3 25.2 23.8 Number of observations 167 335 160 206 Craft Years of schooling 11.7 12.4 11.8 12.1 Hourly wage (in 1990 dollars) 12.1 10.8 9.6 9.2 Number of weeks worked 47.1 47.6 43.9 42.2 Number of hours worked per week 45.0 38.0 43.1 41.7 Number of children 1.1 1.3 0.8 1.7 Age at first marriage (a) 23.5 20.9 25.7 21.2 Number of observations (b) 478 37 158 19 Operators and laborers Years of schooling 11.6 11.2 11.5 12.0 Hourly wage (in 1990 dollars) 9.6 7.1 8.2 6.7 Number of weeks worked 45.2 41.3 41.2 40.9 Number of hours worked per week 45.8 39.4 42.7 39.9 Number of children 1.0 1.6 0.7 1.7 Age at first marriage (a) 23.5 20.3 25.3 23.7 Number of observations 602 174 372 113 (a) Calculated only for those who were married before. (b) The numbers of observations are quite small for both white females and black females who are craft workers at age 29.
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(1.) Regarding the period of the 1990s, existing research has less consensus on the direction of the racial wage gap. For instance, while Card and DiNardo (2002) note that the racial wage gap was stable during the 1990s, Couch and Daly (2002) find that the black-white wage gap for men declined slightly over this same period.
(2.) Wellington (1993) utilizes the 1976-1985 Panel Study of Income Dynamics data to examine the trend of the gender wage gap among whites. Recently, Mason (2000) addresses the timing issue regarding when the racial wage disparity began to expand or to be stagnant by utilizing the same data set for the 1967-1988 period. However, our paper differs from theirs by adding an important dimension to the previous studies on wage inequality: a life-cycle analysis.
(3.) Standard measures of school quality are found to have no effect on the wages of young men in the NLSY79 sample (O'Neill 1990, 39). As June O'Neill (1990, 31-32) states, "the black-white gap in basic school resources was extremely large around World War I and then fell to relatively small magnitudes by the mid-1950s.... However, the effect is likely to be negligible for cohorts reaching their twenties in 1980 and beyond because racial differences in school resources have been substantially eliminated by the time they were in school." While Card and Krueger (1992) find that school quality did affect the black-white earnings gap for the 1920s, 1930s, and 1940s birth cohorts, Grogger (1996) shows that school quality has little effect on the racial wage differences for younger men born in the mid-1950s and the early 1960s. Thus, if the observations of O'Neill (1990) and Grogger (1996) are correct, racial differences in school quality and its impact on the earnings gap are likely to be small for the NLSY79 sample since the NLSY79 sample is the birth cohort born between 1957 and 1964.
(4.) Welch (1975) points out that the absence of longer period panel data for life-cycle wage profiles of individuals would prevent economists from evaluating the impact of investments in human capital in shaping wages. As a result, most of the previous work employs cross-sectional data on earnings or yearly income to approximate a typical individual's lifetime earnings profile. However, Murphy and Welch (1990) note that the widely used Mincerian "human capital earnings function" provides a simple but poor approximation of the true empirical age-earnings profile.
(5.) In the Neal-Johnson study, they find that the age-adjusted AFQT test score can explain about 75% of the black-white wage gap for men and all of the racial wage gap for women.
(6.) Since the results obtained by Neal and Johnson are not robust to different model specifications, Darity and Mason (1998) point out that evidence based on the AFQT needs to be interpreted cautiously. For instance, Rodgers and Spriggs (1996) note that blacks and whites had different grade completion distributions at the time of the examination. As the performance of the AFQT is influenced not only by age but also by the schooling level, Rodgers and Spriggs (1996) adjust the AFQT for both age and school disparity at the date of the test and find that a racial wage gap reemerges. In other words, AFQT test score may exaggerate racial differences in skills. Moreover, as the performance of the AFQT is positively correlated with the schooling level, Carneiro, Heckman, and Masterov (2003, 7) posit that AFQT scores are likely to reflect the expectations of market discrimination embodied in schooling and are not truly premarket factors.
(7.) Due to the nonlinear nature of the model, the effects of changes in the parameters are based on the simulation results.
(8.) NLSY79 changed its survey schedule from once-a-year to every-other-year after its 1994 round. Pierret (2001) points out that a longer interval between interviews is likely to result in a larger number of response errors and poorer data quality.
(9.) Earnings over a period of time are a product of hourly wage rates and hours worked during the period. Hence, how much an individual earns will be affected by his/her labor supply decision. On the other hand, income data include labor as well as nonlabor income, which biases the estimation of the parameters. For instance, the income data used by Haley (1976) include property income, which biases the estimated coefficients. Thus, the most appropriate data for the purposes of our study are the hourly wage rates.
(10.) The method used to calculate the mean hourly wage rate for each age group is described below. For instance, the mean hourly wage rate of white men aged 20 is obtained by calculating the mean real wage rate for all the white men in the sample when they were 20 years old.
(11.) Mincer (1970) shows that if the correlations between schooling and postschool investments are positive, dollar variances tend to increase with age monotonically. If the correlations are negligible, logarithmic variances tend to decline first and increase later. His empirical observation also supports dollar variances increasing strongly with age, but is somewhat less clear regarding U-shaped age profiles of relative variances.
(12.) For the older cohorts, the black-white earnings ratios may increase or decrease with age. For instance, O'Neill (1990) shows that the black-white earnings ratio rose from 69.8% for 25- to 34-yr-old high school male graduates in 1960 to 78.5% in 1980. This decline in black-white earnings differentials can be viewed as either an improvement in school quality available to blacks or a decline in labor market discrimination against blacks during the same period. Smith (1993) shows that among college graduates who entered the job market in 1971, wages of black males exceeded those of comparable whites by 2%. However, within this cohort, black-white wage ratios declined to 75% in 1989 as their work experiences increased.
(13.) For black male-female wage patterns, age 33 seems to be a pivotal point. While the gender wage gap for blacks narrows up until the age of 33, it begins to widen alter that age. Since this phenomenon may be attributed to the problem of a relatively small sample size at ages 34-35, more data and evidence are needed before answering the question as to whether or not this observation will continue to exist alter the age of 33.
(14.) Larger t values partly arise from the availability of a larger number of week-by-week wage observations provided by the NLSY79 Work History Data File.
(15.) By using the 1979-1994 Current Population Survey Outgoing Rotation Group files, Rodgers (2006) finds that the black-white male wage gap expanded as new entrants turned into prime-age workers. He points out that the growing male racial wage gap as these men aged could be a result of racial differences in regenerative human capital investment.
(16.) Please refer to Tables 1-6 and 17 in Coleman and Pencavel (1993) for specific figures. Using the 1967 Survey of Economic Opportunity, Bell (1974, 465) finds that "fulltime work was more common among black wives in better educated, more stable families, and among white wives in less educated, poorer, unstable families. The reverse applied to part-time employment."
(17.) Appendix Table C2 further indicates that women in low-paying occupations tend to be less educated, marry earlier, have more children, and work fewer hours than those in prestigious occupations.
(18.) The crowding hypothesis suggests that the existence of a gender gap can be attributed to occupational segregation. Two possible explanations for the existence of occupational segregation and lower relative earnings for women include the discrimination approach and the human capital approach. The first explanation is proposed by Bergmann (1974). According to her model, employers discriminate against women by excluding them from male occupations. Consequently, women are crowded into other occupations, which become female dominated, and receive less pay. The second approach provides an explanation in terms of women's optimization behavior. According to Polachek (1979), husbands would choose occupations that require continuous and full-time participation. On the other hand, women with greater likelihood of work interruptions would choose occupations characterized by a low depreciation rate of skills. It would be an empirical problem as to which model would provide a better explanation. For a review of these two approaches, please see chapters 5-7 in Blau, Ferber, and Winkler (2002).
(19.) Boraas and Rodgers (2003) find that education and age (as a proxy of work experience) are the key factors in explaining the negative relationship between wages and the concentration of women in an occupation. They point out that so long as education and work experience reflect personal preferences, it is less likely to narrow the gender wage gap by expanding occupational choices.
(20.) While the samples used in Heckman (1976b) and Heckman, Lochner, and Taber (1998) consist only of individuals who are high school educated and above, about 22.8% of our white-male sample received less than 12 yrs of schooling. These sample-selection differences between our study and their studies might provide an explanation for the larger estimate of 131 obtained by Heckman (1976b) and Heckman, Lochner, and Taber (1998).
(21.) While Ben-Porath (1970), Brown (1976), Heckman (1976b), Heckman, Lochner, and Taber (1998), and Mincer (1970) define [gamma] as the rate of interest, Haley (1976) and Rosen (1976) treat [gamma] as the rate of discount. In fact, [gamma] may reflect both the interest rate and the discount rate. By holding interest rates constant, some individuals may have a greater preference for the present than others, and therefore [gamma] will be greater due to a higher personal discount rate. On the other hand, all individuals may discount the future equally, but some will face higher interest rates. Individual differences in time preferences may also lead to differences in discount rates. Nevertheless, imperfections in the capital markets may cause differences in interest rates. Blacks usually come from poorer families than whites and are more likely to face higher interest rates on their investments in human capital. Among whites, a higher estimate of [gamma] for males than for females may reflect the fact that white males earn more and have higher opportunity costs in relation to their investments. Thus, white males may have a higher rate of discount than white females.
(22.) As Heckman (1976a, S35) points out, the rate of interest is not the average internal rate of return: however, the rate of interest would be very close to the average rate of return if a life span is finite and the stock of human capital depreciates over time.
(23.) In accordance with the arguments of Becker and Chiswick (1966), [[beta].sub.1] and [gamma] could affect the demand and supply of funds for investment in human capital, respectively. These two factors themselves are partly influenced by individual's family background.
(24.) A similar concept has been presented in a study of lags structure about firm's knowledge-producing activities by Hall, Griliches, and Hausman (1986, 265). They note that while research and development (R and D) activities can add to a firm's stock of knowledge, "This stock of knowledge is depreciating over time so that the contribution of older R and D investment becomes less valuable as time passes."
(25.) The initial human capital stock at the age of 13 yrs is taken to be zero in this paper. When we treat the initial stock of human capital as an estimable parameter, the parameter estimates do not change much from those listed in Table 3.
HUOYING WU *
* Portions of this work were completed while the author was a visiting fellow at Yale University. The author wishes to thank T. Paul Schultz, Randy J. Olsen, and two anonymous referees for helpful comments and suggestions.
Wu: Associate Professor, Department of Economics, Chinese Culture University, Taipei, Taiwan 111. Phone 886-2-26511450, Fax 886-2-26513338, E-mail hwu@faculty. pccu.edu.tw
TABLE 1 Mean Hourly Wage Ratios by Race, Gender, and Age Age Female/Male Ratios Black/White Ratios Whites, Blacks, Males, Females, (5)/(2) (a) (11)/(8) (a) (8)/(2) (a) (11)/(5) (a) 20 0.790 0.827 0.851 0.891 21 0.794 0.793 0.860 0.859 22 0.781 0.802 0.840 0.863 23 0.801 0.823 0.828 0.850 24 0.800 0.847 0.805 0.851 25 0.799 0.845 0.796 0.845 26 0.802 0.840 0.802 0.840 27 0.794 0.848 0.799 0.853 28 0.802 0.839 0.786 0.823 29 0.787 0.866 0.765 0.842 30 0.781 0.878 0.744 0.837 31 0.772 0.893 0.730 0.844 32 0.752 0.944 0.707 0.888 33 0.749 0.953 0.715 0.909 34 0.714 0.919 0.720 0.928 (a) Column number in Appendix Table A1. TABLE 2 Descriptive Statistics by Race and Gender White Black Variable White Males Females Black Males Females Age in 1979 17.78 (2.21) 17.90 (2.19) 17.77 (2.18) 17.87 (2.19) Years of schooling 12.84 (2.65) 13.00 (2.53) 12.20 (2.15) 12.84 (2.08) Mother's schooling 11.11 (3.28) 11.02 (3.23) 10.80 (2.60) 10.70 (2.60) Father's schooling 11.44 (3.98) 11.38 (3.76) 10.08 (3.38) 10.10 (3.59) Sample size 2,440 2,330 1,139 1,022 t-Test Statistics on Group Differences Racial Gap Gender Gap Males Females Whites Blacks Years of schooling 7.11 1.72 -2.13 -7.05 Mother's schooling 2.66 2.63 1.00 0.85 Father's schooling 8.74 8.15 0.49 -0.10 Note: Standard deviations are in parentheses. TABLE 3 Parameter Estimates of the Wage Process Parameter White Males White Females a 0.116 (246.5) 0.132 (210.5) [[beta].sub.1] 0.593 (106.3) 0.489 (218.6) [gamma] 0.158 (20.4) 0.122 (57.0) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] 0.509 (1036.1) 0.732 (268.0) Number of individuals 2,440 2,300 [R.sup.2] .89 .62 Parameter Black Males Black Females a 0.181 (186.9) 0.124 (100.3) [[beta].sub.1] 0.582 (321.5) 0.488 (53.8) [gamma] 0.188 (107.8) 0.190 (19.4) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] 0.879 (750.6) 0.737 (55.9) Number of individuals 1,139 1,022 [R.sup.2] .96 .60 Notes: Asymptotic t values are reported in parentheses. In this table, "a" denotes the depreciation rate of human capital stock; [gamma] denotes the implicit rate of interest; [[beta].sub.0] and [[beta].sub.1] denote the parameters in the human capital production [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]; larger values of [[beta].sub.1] imply higher rates of returns to scale and lower marginal costs of human capital production; and a denotes the rental rate of human capital. The [R.sup.2] is calculated as the correlation coefficient between the actual wage gaps and the predicted wage gaps. TABLE 4 Differences in the Parameter Estimates Gender Gap Whites Blacks White Males Black Males versus versus White Females Black Females [alpha] -0.016 (-19.96) 0.057 (36.16) [[beta].sub.1] 0.104 (17.29) 0.094 (10.18) [gamma] 0.036 (4.49) -0.002 (-0.23) Racial Cap Males Females White Males White Females versus versus Black Males Black Females [alpha] -0.065 (-60.34) 0.007 (5.39) [[beta].sub.1] 0.011 (1.83) 0.001 (0.11) [gamma] -0.029 (-3.72) -0.068 (-6.77) Notes: Asymptotic t values are in parentheses. TABLE 5 Labor Market Statistics by Race, Gender, and Age Age (yrs) White Males White Females Black Males Black Females A. Average number of weeks worked 20-21 34.6 32.3 27.9 24.2 22-24 39.7 35.6 33.7 29.8 25-27 44.8 37.4 39.2 34.6 28-30 46.5 37.9 40.4 36.6 31-33 47.0 38.7 39.9 37.9 B. Average number of weeks in unemployment 20-21 4.8 3.1 8.6 7.2 22-24 4.3 2.7 7.2 6.3 25-27 2.7 1.8 5.6 4.7 28-30 2.2 1.4 4.8 3.7 31-33 1.9 1.6 4.7 3.1 C. Average number of week force 20-21 12.6 16.5 15.4 20.4 22-24 7.9 13.6 10.9 15.9 25-27 4.5 12.6 7.1 12.6 28-30 3.2 12.4 6.7 11.5 31-33 3.0 11.6 7.2 10.9 D. Average hours worked per week 20-21 39.4 34.3 37.4 33.6 22-24 42.6 37.6 41.2 37.5 25-27 44.8 38.9 43.3 39.9 28-30 46.1 39.0 44.0 40.6 31-33 46.4 38.5 44.4 40.4 TABLE 6 The Incidence and Completion Rate of Job Training by Race and Sex (in %) Incidence by Type of Training Race-Sex Off-job and Group Age (yrs) Any Company Apprenticeships White males 25-27 20.5 13.8 4.9 28-30 18.5 13.3 3.7 31-33 16.9 12.7 3.1 White females 25-27 16.6 11.6 3.7 28-30 16.6 12.2 3.4 31-33 17.1 13.3 2.7 Black males 25-27 14.6 8.0 4.6 28-30 13.6 7.9 3.6 31-33 13.6 8.6 3.2 Black females 25-27 17.4 9.3 6.8 28-30 15.8 9.8 4.3 31-33 17.0 11.1 4.5 Incidence by Type of Training Race-Sex Other Completion Group Age (yrs) Rate White males 25-27 1.5 96.1 28-30 1.6 97.4 31-33 1.4 97.5 White females 25-27 1.5 94.8 28-30 1.6 96.8 31-33 1.5 97.8 Black males 25-27 1.8 94.1 28-30 1.7 94.6 31-33 1.8 95.4 Black females 25-27 1.4 89.2 28-30 1.3 95.0 31-33 1.9 95.4 Notes: The training data are divided into four categories: company training, apprenticeships, off-job training, and other. "Company training" includes formal company training (8), seminars or training programs at work (9), and seminar or training programs outside of work (10). "Off-job training" includes training obtained from business schools (1), vocational and technical institutes (4), and correspondence courses (7). "Other training" includes vocational rehabilitation centers (11) and other (12). Since the sample size of apprenticeship is quite small, apprenticeship is grouped together with off-job training.
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|Date:||Jan 1, 2007|
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