Jacho-Chávez, David, Lewbel, Arthur and Linton, Oliver (2006) Identification and nonparametric estimation of a transformed additively separable model. EM/06/508. Suntory and Toyota International Centres for Economics and Related Disciplines, London School of Economics and Political Science, London, UK.
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Let r (x, z) be a function that, along with its derivatives, can be consistently estimated nonparametrically. This paper discusses identification and consistent estimation of the unknown functions H, M, G and F, where r (x, z) = H [M (x, z)] and M (x, z) = G(x) + F (z). 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, and 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 empirically apply our results to nonparametrically estimate and test generalized homothetic production functions in four industries within the Chinese economy.
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