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Testing for Causal Effects in a Generalized Regression Model With Endogenous Regressors
Author(s) -
Abrevaya Jason,
Hausman Jerry A.,
Khan Shakeeb
Publication year - 2010
Publication title -
econometrica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 16.7
H-Index - 199
eISSN - 1468-0262
pISSN - 0012-9682
DOI - 10.3982/ecta7133
Subject(s) - statistic , econometrics , mathematics , statistics , test statistic , parametric statistics , rank (graph theory) , kernel (algebra) , statistical hypothesis testing , combinatorics
A unifying framework to test for causal effects in nonlinear models is proposed. We consider a generalized linear‐index regression model with endogenous regressors and no parametric assumptions on the error disturbances. To test the significance of the effect of an endogenous regressor, we propose a statistic that is a kernel‐weighted version of the rank correlation statistic (tau) of Kendall (1938). The semiparametric model encompasses previous cases considered in the literature (continuous endogenous regressors (Blundell and Powell (2003)) and a single binary endogenous regressor (Vytlacil and Yildiz (2007))), but the testing approach is the first to allow for (i) multiple discrete endogenous regressors, (ii) endogenous regressors that are neither discrete nor continuous (e.g., a censored variable), and (iii) an arbitrary “mix” of endogenous regressors (e.g., one binary regressor and one continuous regressor).