Identification and nonparametric estimation of a transformed additively separable model

摘要

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 toestimate generalized homothetic production functions for four industries in the Chinese economy.