On the Identification of Production Functions: HowHeterogeneous is Productivity?

Abstract:

We show that existing practices for estimating production functions suffer from a fundamental non-identification problem due to flexible inputs, such as intermediate inputs. Using a transformation of the firm’s first order condition, we develop a new identification strategy and propose a simple nonparametric estimator for the production function and productivity. We show that the alternative of approximating the effects of intermediate inputs using a value-added production function does not solve the identification problem. Applying our approach to plant-level data from Colombia and Chile, we find that a gross output production function implies fundamentally different patterns of productivity heterogeneity than a value-added specification.