Heterogeneous Factor-Augmenting Productivity

This paper studies how heterogeneous factor-augmenting productivity shapes factor allocation, aggregate labor share, and misallocation. In Chinese manufacturing, more labor-productive firms have lower labor shares, higher capital intensity, and lower employment. We first prove that, under empirically motivated restrictions on factor-market frictions, this joint pattern requires heterogeneity in relative factor-augmenting productivity. We then develop an approach that simultaneously identifies firm-level capital- and labor-augmenting productivities, labor markdowns, and marginal capital expenditures. As a validation exercise, we exploit China’s value-added tax reform that lowered equipment costs and find that the calibrated ratio of capital-augmenting to labor-augmenting productivity rises. Counterfactuals show that this ratio is central to the employment-productivity relationship and the aggregate labor share. Accounting for this heterogeneity shifts the inferred composition of misallocation toward capital and reverses the comovement of the marginal revenue products of capital and labor.