Nonparametric Identification and Estimation of Production Functions Invariant to Productivity Dynamics

TL;DR

This paper introduces a nonparametric method to identify and estimate production functions that are invariant to productivity dynamics, addressing biases in traditional Markov-based estimators.

Contribution

It replaces the Markov assumption with a static input market segmentation condition, enabling consistent estimation from a single cross-section.

Findings

The proposed estimator is unbiased in various environments, unlike standard methods.

Applying the method to Japanese industries yields lower, more accurate markups.

Standard methods overstate productivity losses after the Tohoku earthquake.

Abstract

Production function estimates underpin the measurement of firm-level markups, allocative efficiency, and the productivity effects of policy interventions. Since Olley and Pakes (1996), every major proxy variable estimator has identified the production function through a first-order Markov assumption on unobserved productivity; I show that misspecification of this assumption generates persistent upward bias in the materials elasticity that propagates into overestimated markups and inflated treatment effects. I replace the Markov restriction with conditional independence across three intermediate input demands, a static condition grounded in input market segmentation, and establish nonparametric identification from a single cross-section. I develop a GMM estimator and establish consistency and asymptotic normality. Monte Carlo simulations confirm that the proposed estimator is unbiased across Markov and non-Markov environments, while the standard estimator exhibits persistent bias of up to 63 percent of the true materials elasticity. In 502 Japanese manufacturing industries, the proposed method yields systematically lower markups than the standard method across the entire distribution (median 0.93 vs. 1.03), reducing the share of industries with markups above unity from 54 to 37 percent. In a difference-in-differences analysis of the 2011 Tohoku earthquake, the standard method overstates the productivity loss by 0.40 percentage points, roughly $3.6 billion (400 billion yen) per year.