A semiparametric model for binary response and continuous outcomes under index heteroscedasticity
Article first published online: 24 APR 2009
Copyright © 2009 John Wiley & Sons, Ltd.
Journal of Applied Econometrics
Volume 24, Issue 5, pages 735–762, August 2009
How to Cite
Klein, R. and Vella, F. (2009), A semiparametric model for binary response and continuous outcomes under index heteroscedasticity. J. Appl. Econ., 24: 735–762. doi: 10.1002/jae.1064
- Issue published online: 3 JUL 2009
- Article first published online: 24 APR 2009
- Research Council at Rutgers University
This paper formulates a likelihood-based estimator for a double-index, semiparametric binary response equation. A novel feature of this estimator is that it is based on density estimation under local smoothing. While the proofs differ from those based on alternative density estimators, the finite sample performance of the estimator is significantly improved. As binary responses often appear as endogenous regressors in continuous outcome equations, we also develop an optimal instrumental variables estimator in this context. For this purpose, we specialize the double-index model for binary response to one with heteroscedasticity that depends on an index different from that underlying the ‘mean response’. We show that such (multiplicative) heteroscedasticity, whose form is not parametrically specified, effectively induces exclusion restrictions on the outcomes equation. The estimator developed exploits such identifying information. We provide simulation evidence on the favorable performance of the estimators and illustrate their use through an empirical application on the determinants, and affect, of attendance at a government-financed school. Copyright © 2009 John Wiley & Sons, Ltd.