Identification and estimation of a nonseparable production function

Abstract

I study a nonseparable production function that does not make assumptions about the functional form of the inputs and productivity. Unlike traditional production functions with additive productivity, a nonseparable model enables me to explore the heterogenous and nonlinear effects of productivity change. I develop a novel nonparametric identification strategy for productivity and the production function. Specifically, I use the investment choice to identify productivity, which is then used to identify the production function. I address the endogeneity problem in the investment choice by using the previous period's capital and investment as control variables. Concerning estimation, I propose easy-to-implement kernel estimators and show they are consistent and asymptotically normal. Applying this model to Spanish firms' data, I find that productivity change contributes to a yearly output growth of 1.73%. Furthermore, the estimation results suggest that the effect of productivity change on output is larger for firms with higher productivity and performing R\&D, highlighting the importance of nonseparability in the analysis.

Keywords: Endogeneity, nonseparable model, production function, productivity