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A Semiparametric Model for Binary Response and Continuous Outcomes Under Index Heteroscedasticity

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  • Klein, Roger

    () (Rutgers University)

  • Vella, Francis

    () (Georgetown University)

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 below 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.

Suggested Citation

  • Klein, Roger & Vella, Francis, 2006. "A Semiparametric Model for Binary Response and Continuous Outcomes Under Index Heteroscedasticity," IZA Discussion Papers 2383, Institute for the Study of Labor (IZA).
  • Handle: RePEc:iza:izadps:dp2383
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    Cited by:

    1. M. Shahe Emran & Virginia Robano & Stephen C. Smith, 2014. "Assessing the Frontiers of Ultrapoverty Reduction: Evidence from Challenging the Frontiers of Poverty Reduction/Targeting the Ultra-poor, an Innovative Program in Bangladesh," Economic Development and Cultural Change, University of Chicago Press, vol. 62(2), pages 339-380.
    2. Daniel L. Millimet & Rusty Tchernis, 2013. "Estimation Of Treatment Effects Without An Exclusion Restriction: With An Application To The Analysis Of The School Breakfast Program," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(6), pages 982-1017, September.
    3. Enrique López-Bazo & Juan C. Duque & Gustavo A. García & Paula Herrera-Idágarra, 2015. "Heterogeneidad regional en las diferencias por género en las tasas de desempleo en Colombia," IDB Publications (Working Papers) 89037, Inter-American Development Bank.
    4. Lídia Farré & Francis Vella, 2008. "Macroeconomic Conditions and the Distribution of Income in Spain," LABOUR, CEIS, vol. 22(3), pages 383-410, September.
    5. 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.
    6. Witvorapong, Nopphol & Foshanji, Abo Ismael, 2016. "The impact of a conditional cash transfer program on the utilization of non-targeted services: Evidence from Afghanistan," Social Science & Medicine, Elsevier, vol. 152(C), pages 87-95.
    7. Melanie Lührmann & Jürgen Maurer, 2007. "Who wears the trousers? A semiparametric analysis of decision power in couples," CeMMAP working papers CWP25/07, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    8. M. Shahe Emran & Forhad Shilpi, 2017. "Land Market Restrictions, Women's Labour Force Participation and Wages in a Rural Economy," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 79(5), pages 747-768, October.
    9. Wang, Le, 2012. "Economic transition and college premium in urban China," China Economic Review, Elsevier, vol. 23(2), pages 238-252.
    10. Klein, Roger & Shen, Chan & Vella, Francis, 2015. "Estimation of marginal effects in semiparametric selection models with binary outcomes," Journal of Econometrics, Elsevier, vol. 185(1), pages 82-94.
    11. Chiburis, Richard C., 2010. "Semiparametric bounds on treatment effects," Journal of Econometrics, Elsevier, vol. 159(2), pages 267-275, December.
    12. Jürgen Maurer & Roger Klein & Francis Vella, 2011. "Subjective Health Assessments and Active Labor Market Participation of Older Men: Evidence from a Semiparametric Binary Choice Model with Nonadditive Correlated Individual-specific Effects," The Review of Economics and Statistics, MIT Press, vol. 93(3), pages 764-774, August.
    13. Muhammad Bashir & Steven Schilizzi, 2015. "Food security policy assessment in the Punjab, Pakistan: effectiveness, distortions and their perceptions," Food Security: The Science, Sociology and Economics of Food Production and Access to Food, Springer;The International Society for Plant Pathology, vol. 7(5), pages 1071-1089, October.
    14. 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.
    15. Alan Fernihough, 2017. "Human capital and the quantity–quality trade-off during the demographic transition," Journal of Economic Growth, Springer, vol. 22(1), pages 35-65, March.
    16. Klein, Roger & Vella, Francis, 2010. "Estimating a class of triangular simultaneous equations models without exclusion restrictions," Journal of Econometrics, Elsevier, vol. 154(2), pages 154-164, February.
    17. 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.
    18. 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.
    19. Chau, Tak Wai, 2015. "Identification through Heteroscedasticity: What If We Have the Wrong Form of Heteroscedasticity?," MPRA Paper 65888, University Library of Munich, Germany.
    20. Emran, M. Shahe & Shilpi, Forhad, 2014. "Land Market Restrictions, Women's Labor Force Participation and Wages," MPRA Paper 57989, University Library of Munich, Germany.
    21. Yuri M. Zhukov, 2014. "Theory of Indiscriminate Violence," Working Paper 365551, Harvard University OpenScholar.
    22. repec:eee:econom:v:200:y:2017:i:2:p:378-389 is not listed on IDEAS
    23. repec:bla:indres:v:56:y:2017:i:3:p:459-488 is not listed on IDEAS
    24. Xiangjin Shen & Shiliang Li & Hiroki Tsurumi, 2013. "Comparison of Parametric and Semi-Parametric Binary Response Models," Departmental Working Papers 201308, Rutgers University, Department of Economics.
    25. Aradillas-Lopez, Andres, 2010. "Semiparametric estimation of a simultaneous game with incomplete information," Journal of Econometrics, Elsevier, vol. 157(2), pages 409-431, August.

    More about this item

    Keywords

    heteroscedasticity; semiparametric; binary response; endogenous treatment;

    JEL classification:

    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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