...mid-1970s. trend 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...

NOTE: All illustrations and photos have been removed from this article.



More articles from Economic Inquiry
Cotton in a free trade world., January 01, 2007
Employment effects of two northwest minimum wage initiatives., January 01, 2007
The success of the fed and the death of monetarism., January 01, 2007
Exit from the hospital industry., January 01, 2007
Do HMO plans reduce health care expenditure in the private sector?, January 01, 2007

Looking for additional articles?
Search our database of over 3 million articles.

Looking for more in-depth information on this industry?
Search our complete database of Industry & Market reports by text, subject, publication name or publication date.

About Goliath
Whether you're looking for sales prospects, competitive information, company analysis or best practices in managing your organization, Goliath can help you meet your business needs.

Our extensive business information databases empower business professionals with both the breadth and depth of credible, authoritative information they need to support their business goals. Whether it be strategic planning, sales prospecting, company research or defining management best practices - Goliath is your leading source for accurate information.