Production Function Estimation without Invertibility: Imperfectly Competitive Environments and Demand Shocks

TL;DR

This paper extends the proxy variable approach to production function estimation by addressing invertibility issues, proposing bias correction methods, and improving estimator robustness in imperfectly competitive environments with demand shocks.

Contribution

It introduces a test for invertibility failure and proposes a simple bias correction and a modified moment condition to enhance estimator accuracy and robustness.

Findings

Invertibility assumption is testable.

Bias correction improves GMM estimator accuracy.

Modified moment condition enhances robustness and efficiency.

Abstract

We advance the proxy variable approach to production function estimation. We show that the invertibility assumption at its heart is testable. We characterize what goes wrong if invertibility fails and what can still be done. We show that rethinking how the estimation procedure is implemented either eliminates or mitigates the bias that arises if invertibility fails. In particular, a simple change to the first step of the estimation procedure provides a first-order bias correction for the GMM estimator in the second step. Furthermore, a modification of the moment condition in the second step ensures Neyman orthogonality and enhances efficiency and robustness by rendering the asymptotic distribution of the GMM estimator invariant to estimation noise from the first step.