Identification and Estimation in a Time-Varying Endogenous Random Coefficient Panel Data Model

TL;DR

This paper introduces a novel method for identifying and estimating parameters in a complex panel data model with time-varying endogenous random coefficients, using a three-step series estimator and an application to Chinese manufacturing firms.

Contribution

It develops a new identification strategy and estimation procedure for a correlated random coefficient panel data model with time-varying effects, addressing endogeneity issues.

Findings

Substantial variation in output elasticities across firms

The method successfully estimates heterogeneous production functions

Application reveals relationships between firm characteristics and productivity

Abstract

This paper proposes a correlated random coefficient linear panel data model, where regressors can be correlated with time-varying and individual-specific random coefficients through both a fixed effect and a time-varying random shock. I develop a new panel data-based method to identify the average partial effect and the local average response function. The identification strategy employs a sufficient statistic to control for the fixed effect and a control variable for the random shock. Conditional on these two controls, the residual variation in the regressors is driven solely by the exogenous instrumental variables, and thus can be exploited to identify the parameters of interest. The constructive identification analysis leads to three-step series estimators, for which I establish rates of convergence and asymptotic normality. To illustrate the method, I estimate a heterogeneous Cobb-Douglas production function for manufacturing firms in China, finding substantial variations in output elasticities across firms that can be related to various firm characteristics.