Abstract

We study capital-skill complementarity in a multi-sector theory of aggregate technology featuring firms with arbitrary and heterogeneous multi-factor production functions. Importantly, the theory allows for heterogeneity in factor prices across firms. We characterize the elasticity of the aggregate skill premium to the price of equipment capital in terms of firm-level elasticitites of substitution across factors, the elasticities of substitution across firms and sectors, and the distribution of factor intensities across firms. Using micro data from France, we estimate the two sets of elasticities assuming a firm-level production function featuring heterogeneous cross-factor elasticities. The model predicts that the observed fall in equipment prices contributes to a sizable rise in the skill premium (around 6%), implying a modest degree of capital-skill complementarity. Using our framework we show how this rise is mostly counteracted by the relative decline of the skill premium among firms with higher skill intensities in France.

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