### 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.

Publication

**Journal of Econometrics**, (156), 2, pp. 392-407