Substitution and Complementarity under Comparative Advantage and the Accumulation of Human Capital

The paper applies Ricardo's principle of comparative advantage to analyze the substitutability between types of labor. The problem of having to classify labor in a small number of types in e.g. standard CES models are avoided by applying a continuum of worker and job types, where better skilled workers have a comparative advantage in more complex jobs. The complementarity matrix,which is derived by inverting the substitution matrix, exhibits attractive features. The matrix depends only on the wage distribution and a single parameter, which is dubbed the complexity dispersion parameter.A particularly intriguing application is the accumulation of human capital. Aninvestment in human capital reduces the supply of low-skilled and increases thesupply of highly skilled workers, therefore compressing wage differentials. The training of one skill group will therefore have (positive and negative) externalities to the wage of other skill groups. The complexity dispersion parameter measures the percentage compression in log wage differentials per percent accumulation of human capital. Empirical estimates suggest that this parameter is in the range of 2.4 - 3.8. This mechanism explainsfor example the massive compression of wage differentials in some Asian tigersduring the seventies and the eighties. The inverse of the complexity dispersion parameter measures the maximum productivity gain that can be achieved by human capital accumulation.