Identification and Estimation of Production Function with Unobserved Heterogeneity

TL;DR

This paper develops a nonparametric method to identify production functions considering unobserved heterogeneity, revealing significant disparities in input elasticities and productivity growth among latent types using Japanese plant data.

Contribution

It introduces a finite mixture model for nonparametric identification of production functions with unobserved heterogeneity, extending existing panel data methods.

Findings

Significant heterogeneity in input elasticities among latent types

Neglecting unobserved heterogeneity biases productivity growth estimates

Four-period panel data suffices for identification under certain assumptions

Abstract

This paper examines the nonparametric identifiability of production functions, considering firm heterogeneity beyond Hicks-neutral technology terms. We propose a finite mixture model to account for unobserved heterogeneity in production technology and productivity growth processes. Our analysis demonstrates that the production function for each latent type can be nonparametrically identified using four periods of panel data, relying on assumptions similar to those employed in existing literature on production function and panel data identification. By analyzing Japanese plant-level panel data, we uncover significant disparities in estimated input elasticities and productivity growth processes among latent types within narrowly defined industries. We further show that neglecting unobserved heterogeneity in input elasticities may lead to substantial and systematic bias in the estimation of productivity growth.