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A semiparametric model for binary response and continuous outcomes under index heteroscedasticity

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Author Info
Roger Klein (Department of Economics, Rutgers University, New Brunswick, NJ, USA)
Francis Vella (Department of Economics, Georgetown University, Washington, DC, USA)
Abstract

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.

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File URL: http://hdl.handle.net/10.1002/jae.1064
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File URL: http://qed.econ.queensu.ca:80/jae/2009-v24.5/
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Article provided by John Wiley & Sons, Ltd. in its journal Journal of Applied Econometrics.

Volume (Year): 24 (2009)
Issue (Month): 5 ()
Pages: 735-762
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Handle: RePEc:jae:japmet:v:24:y:2009:i:5:p:735-762

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  1. Donald, Stephen G & Newey, Whitney K, 2001. "Choosing the Number of Instruments," Econometrica, Econometric Society, vol. 69(5), pages 1161-91, September.
  2. Evans, William N & Schwab, Robert M, 1995. "Finishing High School and Starting College: Do Catholic Schools Make a Difference?," The Quarterly Journal of Economics, MIT Press, vol. 110(4), pages 941-74, November. [Downloadable!] (restricted)
  3. Gregory Kordas, 2006. "Smoothed binary regression quantiles," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(3), pages 387-407. [Downloadable!]
  4. Manski, Charles F., 1975. "Maximum score estimation of the stochastic utility model of choice," Journal of Econometrics, Elsevier, vol. 3(3), pages 205-228, August. [Downloadable!] (restricted)
  5. Klein, Roger W & Spady, Richard H, 1993. "An Efficient Semiparametric Estimator for Binary Response Models," Econometrica, Econometric Society, vol. 61(2), pages 387-421, March. [Downloadable!] (restricted)
  6. Dagenais, Marcel G. & Dagenais, Denyse L., 1997. "Higher moment estimators for linear regression models with errors in the variables," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 193-221. [Downloadable!] (restricted)
  7. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-31, May. [Downloadable!] (restricted)
  8. Rummery, Sarah & Vella, Francis & Verbeek, Marno, 1999. "Estimating the returns to education for Australian youth via rank-order instrumental variables," Labour Economics, Elsevier, vol. 6(4), pages 491-507, November. [Downloadable!] (restricted)
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