Identification and nonparametric estimation of a transformed additively separable model

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.