Open AccessEstimating a nonparametric triangular model with binary endogenous regressors
Author(s) -
Jun Sung Jae,
Pinkse Joris,
Xu Haiqing
Publication year - 2016
Publication title -
the econometrics journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.861
H-Index - 36
eISSN - 1368-423X
pISSN - 1368-4221
DOI - 10.1111/ectj.12066
Subject(s) - nonparametric statistics , estimator , smoothness , monotonic function , mathematics , asymptotic distribution , econometrics , differentiable function , identification (biology) , kernel (algebra) , kernel regression , control function , nonparametric regression , binary number , function (biology) , endogeneity , statistics , computer science , control (management) , artificial intelligence , arithmetic , mathematical analysis , botany , combinatorics , evolutionary biology , biology
Summary We consider identification and estimation in a nonparametric triangular system with a binary endogenous regressor and nonseparable errors. For identification, we take a control function approach utilizing the Dynkin system idea. We articulate various trade‐offs, including continuity, monotonicity and differentiability. For estimation, we use the idea of local instruments under smoothness assumptions, but we do not assume additive separability in latent variables. Our estimator uses nonparametric kernel regression techniques and its statistical properties are derived using the functional delta method. We establish that it is n 2 / 7 ‐consistent and has a limiting normal distribution. We apply the method to estimate the returns on a college education. Unlike existing work, we find that returns on a college education are consistently positive. Moreover, the returns curves we estimate are inconsistent with the shape restrictions imposed in those papers.