On the identification of production functions: How heterogeneous is productivity?

The estimation of production functions suffers from an unresolved identification problem caused by flexible inputs, such as intermediate inputs. We develop an identification strategy for production functions based on a transformation of the firm's short-run first order condition that solves the problem for both gross output and valueadded production functions. We apply our approach to plant-level data from Colombia and Chile, and find that a gross output production function implies fundamentally different patterns of productivity heterogeneity than a value-added specification. This finding is consistent with our analysis of the bias induced by the use of value-added.