From Reduced to Structural: A New Identification Strategy for Production Functions

Standard proxy variable estimators for gross output production functions face an identification problem. These estimators often suffer from weak instrument issues, making it difficult to consistently estimate the elasticity of flexible inputs. This paper introduces a “from reduced to structural” identification strategy. We demonstrate that by first estimating a well-posed reduced-form relationship to recover a proxy for the structural unobservable, the full parameters of the original structural model can then be identified. We apply this framework to the estimation of gross output production functions. Monte Carlo simulations show our estimator is robust and substantially less biased than existing methods. An empirical application using Chilean plant-level data yields more plausible production elasticities and, consequently, more stable estimates of firm-level markups.