Identification and nonparametric estimation of a transformed additively separable model

Abstract

Let $r(x,z)$ be a function that, along with its derivatives, can be consistently estimated nonparametrically. This paper discusses the identification and consistent estimation of the unknown functions $H$, $M$, $G$ and $F$, where $r(x,z)=H[M(x,z)]$, $M(x,z)=G(x)+F(z)$, and $H$ is strictly monotonic. An estimation algorithm is proposed for each of the model’s unknown components when $r(x,z)$ represents a conditional mean function. The resulting estimators use marginal integration to separate the components $G$ and $F$. Our estimators are shown to have a limiting Normal distribution with a faster rate of convergence than unrestricted nonparametric alternatives. Their small sample performance is studied in a Monte Carlo experiment. We apply our results to estimate generalized homothetic production functions for four industries in the Chinese economy.