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. 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 administrative data, we first provide reduced-form evidence that equipment-intensive firms are relatively skill-intensive and that exogenous declines in firm-level equipment prices increase firms’ relative demand for skilled labor. We then estimate the micro-level elasticities needed for theory-guided aggregation, providing the first identification of aggregate capital-skill complementarity allowing for arbitrary firm, industry, and aggregate trends in unobserved skill-biased productivity. We find statistically and economically significant 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.