A Generalized Control Function Approach to Production Function Estimation

TL;DR

This paper introduces a generalized control function method for production function estimation that handles evolving productivity and unobservable factors, improving identification and reducing bias compared to traditional methods.

Contribution

It develops a novel generalized control function approach that relaxes key assumptions and achieves nonparametric identification of output elasticity.

Findings

Traditional methods exhibit large bias in Monte Carlo simulations.

The proposed approach nearly eliminates bias in finite samples.

The method ensures oracle efficiency through Neyman orthogonal moments.

Abstract

We develop a generalized control function approach to production function estimation. Our approach accommodates settings in which productivity evolves jointly with other unobservable factors such as latent demand shocks and the invertibility assumption underpinning the traditional proxy variable approach fails. We provide conditions under which the output elasticity of the variable input -- and hence the markup -- is nonparametrically point-identified. A Neyman orthogonal moment condition ensures oracle efficiency of our GMM estimator. A Monte Carlo exercise shows a large bias for the traditional approach that decreases rapidly and nearly vanishes for our generalized control function approach.