We develop a framework that uses micro data to estimate the aggregate capital-labor elasticity of substitution. We first show that the aggregate elasticity is a convex combination of the plant-level elasticity of substitution and the elasticity of demand. This expression captures substitution within plants and reallocation across plants; the relative importance of each depends on the extent of heterogeneity across plants in capital intensity. This allows us to use micro data on the cross-section of plants to estimate the aggregate elasticity at a point in time. Because we place no assumptions on the evolution of technology over time, we separately identify the bias of technical change and the aggregate elasticity. Using the US Census of Manufactures, we find that the aggregate elasticity has been stable at about 0.7. Most of the decline in the labor share over this period stems from an acceleration of the bias of technical change.
