Identification and nonparametric estimation of a transformed additively separable model

David Jacho-Chávez , Arthur Lewbel , Oliver Linton

Let be a function that, along with its derivatives, can be consistently estimated nonparametrically. This paper discusses identification and consistent estimation of the unknown functions , , and , where , , and is strictly monotonic. An estimation algorithm is proposed for each of the model's unknown components when represents a conditional mean function. The resulting estimators use marginal integration to separate the components and . 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.

Mots clés: C13; C14; C21; D24; Partly separable models; Nonparametric regression; Dimension reduction; Generalized homothetic function; Production function

David Jacho-Chávez, Arthur Lewbel, Oliver Linton. Identification and nonparametric estimation of a transformed additively separable model. Econometrics, 2009, ⟨10.1016/j.jeconom.2009.11.008⟩. ⟨hal-00646004⟩