Capital-Skill Complementarity in Firms and in the Aggregate Economy

We study capital-skill complementarity in a multi-sector framework featuring firm-specific, multi-factor production functions and allowing for firm-specific factor-price wedges. We characterize the elasticity of the skill premium to the price of capital equipment in terms of firm-level elasticities of substitution across factors, elasticities of substitution across firms and sectors, and factor intensities. Using French data, we provide credible identification of these firm-level elasticities. Combining these elements we offer the first identification of aggregate capital-skill complementarity that allows for arbitrary trends in the unobservable skill-bias of productivity at the firm, industry, and aggregate levels. We find an economically and statistically significant degree of aggregate capital-skill complementarity, but this force alone is insufficient to generate the full increase in the relative demand for high-skilled workers observed in the data. There is a substantial role for skill-augmenting technical change not embodied in capital equipment.