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Identification and estimation of semiparametric two‐step models
Author(s) -
Escanciano Juan Carlos,
JachoChávez David,
Lewbel Arthur
Publication year - 2016
Publication title -
quantitative economics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 4.062
H-Index - 27
eISSN - 1759-7331
pISSN - 1759-7323
DOI - 10.3982/qe328
Subject(s) - semiparametric model , identification (biology) , semiparametric regression , estimation , econometrics , computer science , mathematics , economics , nonparametric statistics , biology , botany , management
Let H 0 ( X ) be a function that can be nonparametrically estimated. Suppose E [ Y | X ]= 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.

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