Jacho-Chávez, David, Lewbel, Arthur and Linton, Oliver (2010) Identification and nonparametric estimation of a transformed additively separable model. Journal of Econometrics, 156 (2). pp. 392-407. ISSN 0304-4076
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.
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