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Identification and estimation of semiparametric two‐step models

Juan Carlos Escanciano (), David Jacho‐Chávez and Arthur Lewbel ()
Authors registered in the RePEc Author Service: David Tomás Jacho-Chávez ()

Quantitative Economics, 2016, vol. 7, issue 2, 561-589

Abstract: Let H 0 (X) be a function that can be nonparametrically estimated. Suppose E [Y&7CX]=F 0 [X⊤β 0 , H 0 (X)]. Many models fit this framework, including latent index models with an endogenous regressor and nonlinear models with sample selection. We show that the vector β 0 and unknown function F 0 are generally point identified without exclusion restrictions or instruments, in contrast to the usual assumption that identification without instruments requires fully specified functional forms. We propose an estimator with asymptotic properties allowing for data dependent bandwidths and random trimming. A Monte Carlo experiment and an empirical application to migration decisions are also included.

Date: 2016
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