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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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Bibliographic Info

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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References

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  1. Vella, Francis, 1994. "Gender Roles and Human Capital Investment: The Relationship between Traditional Attitudes and Female Labour Market Performance," Economica, London School of Economics and Political Science, vol. 61(242), pages 191-211, May.
  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.
  3. Powell, James L. & Stock, James H. & Stoker, Thomas M., 1986. "Semiparametric estimation of weighted average derivatives," Working papers 1793-86., Massachusetts Institute of Technology (MIT), Sloan School of Management.
  4. Ichimura, H., 1991. "Semiparametric Least Squares (sls) and Weighted SLS Estimation of Single- Index Models," Papers 264, Minnesota - Center for Economic Research.
  5. Donald, Stephen G & Newey, Whitney K, 2001. "Choosing the Number of Instruments," Econometrica, Econometric Society, vol. 69(5), pages 1161-91, September.
  6. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-31, May.
  7. Chamberlain, Gary, 1986. "Asymptotic efficiency in semi-parametric models with censoring," Journal of Econometrics, Elsevier, vol. 32(2), pages 189-218, July.
  8. Heckman, James J, 1978. "Dummy Endogenous Variables in a Simultaneous Equation System," Econometrica, Econometric Society, vol. 46(4), pages 931-59, July.
  9. 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.
  10. Chen, Songnian & Khan, Shakeeb, 2003. "Rates of convergence for estimating regression coefficients in heteroskedastic discrete response models," Journal of Econometrics, Elsevier, vol. 117(2), pages 245-278, December.
  11. Lee, Lung-fei, 1995. "Semiparametric maximum likelihood estimation of polychotomous and sequential choice models," Journal of Econometrics, Elsevier, vol. 65(2), pages 381-428, February.
  12. 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.
  13. Newey, Whitney K. & McFadden, Daniel, 1986. "Large sample estimation and hypothesis testing," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 36, pages 2111-2245 Elsevier.
  14. Gregory Kordas, 2006. "Smoothed binary regression quantiles," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(3), pages 387-407.
  15. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-57, September.
  16. 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.
  17. Arthur Lewbel, 1997. "Constructing Instruments for Regressions with Measurement Error when no Additional Data are Available, with an Application to Patents and R&D," Econometrica, Econometric Society, vol. 65(5), pages 1201-1214, September.
  18. 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.
  19. Roberto Rigobon, 2003. "Identification Through Heteroskedasticity," The Review of Economics and Statistics, MIT Press, vol. 85(4), pages 777-792, November.
  20. Amemiya, Takeshi, 1975. "The nonlinear limited-information maximum- likelihood estimator and the modified nonlinear two-stage least-squares estimator," Journal of Econometrics, Elsevier, vol. 3(4), pages 375-386, November.
  21. Pagan, Adrian & Vella, Frank, 1989. "Diagnostic Tests for Models Based on Individual Data: A Survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 4(S), pages S29-59, Supplemen.
  22. Klein, R.W., 1991. "Specification Tests for Binery Choice Models Based on Index Quantiles," Papers 71, Bell Communications - Economic Research Group.
  23. Francis Vella, 1999. "Do Catholic Schools Make a Difference? Evidence from Australia," Journal of Human Resources, University of Wisconsin Press, vol. 34(1), pages 208-224.
  24. Manski, Charles F., 1985. "Semiparametric analysis of discrete response : Asymptotic properties of the maximum score estimator," Journal of Econometrics, Elsevier, vol. 27(3), pages 313-333, March.
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Citations

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Cited by:
  1. Daniel L. Millimet & Rusty Tchernis, 2009. "Estimation of Treatment Effects Without an Exclusion Restriction: with an Application to the Analysis of the School Breakfast Program," NBER Working Papers 15539, National Bureau of Economic Research, Inc.
  2. Maurer, Jürgen, 2009. "Who has a clue to preventing the flu? Unravelling supply and demand effects on the take-up of influenza vaccinations," Journal of Health Economics, Elsevier, vol. 28(3), pages 704-717, May.
  3. Roger Klein & Francis Vella, 2005. "Estimating a class of triangular simultaneous equations models without exclusion restrictions," CeMMAP working papers CWP08/05, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  4. Melanie Lührmann & Jürgen Maurer, 2008. "Who wears the trousers? A semiparametric analysis of decision power in couples," MEA discussion paper series 08168, Munich Center for the Economics of Aging (MEA) at the Max Planck Institute for Social Law and Social Policy.
  5. Kevin E. Staub, 2014. "A Causal Interpretation of Extensive and Intensive Margin Effects in Generalized Tobit Models," The Review of Economics and Statistics, MIT Press, vol. 96(2), pages 371-375, May.
  6. Jürgen Maurer & Roger Klein & Francis Vella, 2008. "Subjective Health Assessments and Active Labor Market Participation of Older Men: Evidence from a Semiparametric Binary Choice Model with Nonadditive Correlated Individualspecific Effects," MEA discussion paper series 08169, Munich Center for the Economics of Aging (MEA) at the Max Planck Institute for Social Law and Social Policy.
  7. Lídia Farré & Francis Vella, 2008. "Macroeconomic Conditions and the Distribution of Income in Spain," LABOUR, CEIS, vol. 22(3), pages 383-410, 09.
  8. Wang, Le, 2012. "Economic transition and college premium in urban China," China Economic Review, Elsevier, vol. 23(2), pages 238-252.
  9. Khan, Shakeeb, 2013. "Distribution free estimation of heteroskedastic binary response models using Probit/Logit criterion functions," Journal of Econometrics, Elsevier, vol. 172(1), pages 168-182.
  10. Chiburis, Richard C., 2010. "Semiparametric bounds on treatment effects," Journal of Econometrics, Elsevier, vol. 159(2), pages 267-275, December.
  11. Gerry H. Makepeace & Michael J. Peel, 2013. "Combining information from Heckman and matching estimators: testing and controlling for hidden bias," Economics Bulletin, AccessEcon, vol. 33(3), pages 2422-2436.
  12. Aradillas-Lopez, Andres, 2010. "Semiparametric estimation of a simultaneous game with incomplete information," Journal of Econometrics, Elsevier, vol. 157(2), pages 409-431, August.

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