Physical Capital, Human Capital Distribution of Earnings

The relationship between physical capital. human capital and the distribution of turnings is examined empirically using cross-sectional microdata within SklSAs. Comprtrarive advantage in workers and a scale-of-resources effect among firms is predicted to lead to a rel~ti~)n~hip between capital and earnings. The level of earnings is found to be positively related to capital intensity and nrgntiveiy related to capital dispersion. Earnings inequality appears to be greater the ktrger the dispersion in capital. The results support the view that industry structure and tho distribution of physical capital have direct effects on the structure and distribution of earnings. after controlling for differences in human capital. WHILE the rel~tionshjp between human capital and earnings has been studied extensively, the retationship between physical capital and the distribution of earnings has received relatively little theoretical or empirical attention. A well-known article by GriIiches (1969) proposed the capital-skill complementarity (CSC) hypothesis, which implies that the elasticity of substitution between capital and highskill labor is less than between capital and low-skill labor. A number of recent empirical studies estimating cost (or production) functions have lent support to the hypothesis of capital-skill complementarity.’ Brogan and Erickson (1975). examining the monopoly-wage hypothesis. provided some direct evidence that greater capital intensity rather than concentration per se leads to higher earnings, and suggested that capital-skill complementarity provided the explanation for their results.’ Despite this work, the large empirical literature urilizing microor aggregate human capital earnings functions generaliy has ignored the effects of capital on the earnings distribution.’ Recent work by Sattinger has provided some theoretical analysis and empirical evidence regarding the relationship between the distribution of earriings, capital intensity and comparative advantage.’ Sattinger has demonstrated that more productive workers will tend to work at more capjtal-intensive jobs and that the distributi(~n of earnings will be more unequal the more unequally capita! is distributed among workers, with everything else the same. This results, Sattinger proposes, because of comparative advantage and a scale-ofresources effect in the job-assignment process. In addition, he has examined the conditions under which earnings inequality increases with the Ievel of capital jntens~ty in a labor market. The purpose of this article is to test further some hypotheses associated with Sattinger‘s work. In particular, it examines the rel~ltio~ship of a labor market’s earnings level and earnings dispersion with its dispersion in capital among workers and its mean capital-to-labor ratio. Detailed microdata within 48 U.S. metropolitan areas are utilized, thus allowing differences to be accounted for across labor markets in human capital and in earnings-function parameters. As recently argued by Hanushek f1981), significant differences across labor markets in earn[klanuscript received 2i July 1981; revision accrptcd for publication 71 November 19Sl.] ings structure (parameters) makes the use of microdata within labor markets particularly advantageous.” The empirical results generally support Sattinger‘s hypothesis of a positive relationship between the dispersion in capital and the ifispersion in earnings. In addition. earnings levels are found to be positively related to capital intensity and negatively related to capital dispersion. Because of the quality of the capital stock data and some inherent methodologicnl problems, the results in this article are regarded as suopestive rather than conclusive. D. THE XSSIGNMENT PROCESS Sattinger is most interested in the relationship between capital and the distribution of earnings. Utilizing a d~rn~~nd-supply framework. he focuses on the assignment problem whereby an equilibrium matching of workers and machines is determined. The predicted positive relationship between the dispersion in capital among workers and the dispersion in earnings results from compaixtive advantage in individuals and from n scale-of-resources effect among employers. Sattinger (19SO. Ch. 5) shows that if a comparative advantage exists such that more productive (more highly schooled) workers have a comparative advantage in more difficult jobs. they wilt be found working at these jobs. In addition, a scale-of-resources effect exists such that empioyers maximize profits by matching more productive workers with greater resources or cooperating factors. It then follows that the greater the resources with which more productive labor is combined the greater will be the value of productivity differences among individuals. The scale-ofresourct’s effect exists even in the absence of comparative advantage: that is. where workers differ in absolute but not relritivc prod~lctivities among jobs. It should be noted that the scale-of-resources effect is similar to, but distinct from. capital-skill complimentarity. CSC concerns the reaction of firms with fixed production fLinction~ to differences in factor prices, while the scale-of-resources effect concerns how firms with different production functions behave in response to similar factor prices.h If comparative advantage exists along with the scale-of-resources effect. a sufficient but not nccessnry condition for the matching of more productist’ workers with relatively larger amounts of capital is that these workers possess a relative advantage in more capital-intensive jobs. If skilied individuals have a comparlttive advantage at less capital-intrnsive jobs. the matching of high-skill workers may be with either more or less capital. Lvhicheksr asignment maximizes the net value of output. If. as seems likely, more able workers are found generally nt jobs with greater capital, it is clear that the inequality in earnings in ;L labor market will be greater the more dispersed is the distribution of capital smonp jobs, even after accounting for differences in workers‘ human capital. !Vhile personal characteristics (human capital) may account for all (most) earnings differences within a single labor market, its earnings structure is detamined by both demand and supply. The assignment process implkd by comparative advantape and the scale-of-resources effect can be illustrated by some simple numerical euample~. Assume that \ve have two workers and two jobs, where worker 1 is more productive than worker 2. and where the jobs are characterized by the machine size that complements these workers. \rjie know that workers (machines) will be assigned bo as to maximize the value of output or earning. Suppose that the matrix af output values over ;I time period is as foilows: