A Generalized Control Function Approach to Production Function Estimation

2025-11-26

AI Summary

Traditional proxy-variable approaches to production function estimation rely on the invertibility of the evolution relationship between productivity and unobserved factors (e.g., demand shocks); identification fails when this assumption is violated. This paper proposes a generalized control function method that relaxes the invertibility requirement, enabling nonparametric point identification of output elasticities and markup rates. The approach constructs Neyman-orthogonal moment conditions, ensuring that the GMM estimator achieves oracle efficiency. Monte Carlo simulations demonstrate that conventional methods suffer from substantial bias, whereas the proposed estimator’s bias converges rapidly to zero and exhibits markedly improved precision. This work provides a robust, identified, and implementable framework for productivity estimation in settings where unobserved factors co-evolve with inputs and outputs.

Technology Category

Search and Optimization: Non-convex OptimizationReasoning under Uncertainty: Relational Probabilistic ModelsIntelligent Robots: State Estimation

Application Category

Economics, Online Markets and Human Computation: Cost models of using LLMs in production systemsSecurity and Privacy: Large-scale security measurementsGraph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

We generalize the control function approach to production function estimation. Our generalization accommodates scenarios 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 proxy variable approach that decreases rapidly and nearly vanishes for our generalized control function approach.

Problem

• Generalizes control function approach for production function estimation
• Handles joint evolution of productivity with unobservable factors
• Provides identification conditions for output elasticity and markups

Innovation

• Generalized control function for production estimation
• Nonparametric identification of output elasticity
• GMM estimator with Neyman orthogonal moments