Semiparametric Smooth Coefficient Estimation of a Production System

Abstract

AbstractThis paper addresses endogeneity of inputs in estimating a semiparametric smooth coefficient production function using a system approach. The system consists of a translog production function and the first‐order conditions (FOC) of profit maximization. Each coefficient of the production function is an unknown function of some exogenous environmental variables. This makes the production function observation‐specific so long as the environmental variables are observation‐specific. The estimation of the system involves applying the functional coefficient instrumental variable method (Cai et al., 2006) for the endogeneity of inputs in the first step, and the semiparametric smooth coefficient seemingly unrelated regression method (Henderson et al., 2015) in the second step. Using a Chinese food industry data set, we show that the semiparametric system approach gives the most economically meaningful input elasticity estimates compared with alternative models. We also calculate the returns to scale along with the technical and allocative inefficiency estimates.