Open AccessAn instrumental variable random‐coefficients model for binary outcomes
Author(s) -
Chesher Andrew,
Rosen Adam M.
Publication year - 2014
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.12018
Subject(s) - endogeneity , instrumental variable , mathematics , random variable , context (archaeology) , binary number , statistics , conditional expectation , econometrics , control function , conditional probability distribution , computer science , control (management) , paleontology , arithmetic , artificial intelligence , biology
Summary In this paper, we study a random‐coefficients model for a binary outcome. We allow for the possibility that some or even all of the explanatory variables are arbitrarily correlated with the random coefficients, thus permitting endogeneity. We assume the existence of observed instrumental variables Z that are jointly independent with the random coefficients, although we place no structure on the joint determination of the endogenous variable X and instruments Z , as would be required for a control function approach. The model fits within the spectrum of generalized instrumental variable models, and we thus apply identification results from our previous studies of such models to the present context, demonstrating their use. Specifically, we characterize the identified set for the distribution of random coefficients in the binary response model with endogeneity via a collection of conditional moment inequalities, and we investigate the structure of these sets by way of numerical illustration.