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Binary choice models with discrete regressors: Identification and misspecification

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  • Komarova, Tatiana

Abstract

This paper explores the inferential question in semiparametric binary response models when the continuous support condition is not satisfied and all regressors have discrete support. I focus mainly on the models under the conditional median restriction, as in Manski (1985). I find sharp bounds on the components of the parameter of interest and outline several applications. The formulas for bounds obtained using a recursive procedure help analyze cases where one regressor’s support becomes increasingly dense. Furthermore, I investigate asymptotic properties of estimators of the identification set. I describe a relation between the maximum score estimation and support vector machines and propose several approaches to address the problem of empty identification sets when the model is misspecified.

Suggested Citation

  • Komarova, Tatiana, 2013. "Binary choice models with discrete regressors: Identification and misspecification," Journal of Econometrics, Elsevier, vol. 177(1), pages 14-33.
  • Handle: RePEc:eee:econom:v:177:y:2013:i:1:p:14-33
    DOI: 10.1016/j.jeconom.2013.05.005
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    References listed on IDEAS

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    1. Cosslett, Stephen R, 1983. "Distribution-Free Maximum Likelihood Estimator of the Binary Choice Model," Econometrica, Econometric Society, vol. 51(3), pages 765-782, May.
    2. Thierry Magnac & Eric Maurin, 2008. "Partial Identification in Monotone Binary Models: Discrete Regressors and Interval Data," Review of Economic Studies, Oxford University Press, vol. 75(3), pages 835-864.
    3. Guido W. Imbens & Charles F. Manski, 2004. "Confidence Intervals for Partially Identified Parameters," Econometrica, Econometric Society, vol. 72(6), pages 1845-1857, November.
    4. 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.
    5. 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.
    6. Rosen, Adam M., 2008. "Confidence sets for partially identified parameters that satisfy a finite number of moment inequalities," Journal of Econometrics, Elsevier, vol. 146(1), pages 107-117, September.
    7. Manski, Charles F, 1990. "Nonparametric Bounds on Treatment Effects," American Economic Review, American Economic Association, vol. 80(2), pages 319-323, May.
    8. Bo E. Honoré & Adriana Lleras-Muney, 2006. "Bounds in Competing Risks Models and the War on Cancer," Econometrica, Econometric Society, vol. 74(6), pages 1675-1698, November.
    9. Charles F. Manski & Elie Tamer, 2002. "Inference on Regressions with Interval Data on a Regressor or Outcome," Econometrica, Econometric Society, vol. 70(2), pages 519-546, March.
    10. Bo E. Honoré & Elie Tamer, 2006. "Bounds on Parameters in Panel Dynamic Discrete Choice Models," Econometrica, Econometric Society, vol. 74(3), pages 611-629, May.
    11. Manski, Charles F. & Thompson, T. Scott, 1986. "Operational characteristics of maximum score estimation," Journal of Econometrics, Elsevier, vol. 32(1), pages 85-108, June.
    12. Victor Chernozhukov & Han Hong & Elie Tamer, 2007. "Estimation and Confidence Regions for Parameter Sets in Econometric Models," Econometrica, Econometric Society, vol. 75(5), pages 1243-1284, September.
    13. Manski, Charles F. & Thompson, T. Scott, 1989. "Estimation of best predictors of binary response," Journal of Econometrics, Elsevier, vol. 40(1), pages 97-123, January.
    14. 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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    16. Han, Aaron K., 1987. "Non-parametric analysis of a generalized regression model : The maximum rank correlation estimator," Journal of Econometrics, Elsevier, vol. 35(2-3), pages 303-316, July.
    17. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-531, May.
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    Citations

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    Cited by:

    1. Le-Yu Chen & Sokbae Lee, 2015. "Breaking the curse of dimensionality in conditional moment inequalities for discrete choice models," CeMMAP working papers CWP26/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    2. Le-Yu Chen & Sokbae Lee, 2016. "Best Subset Binary Prediction," Papers 1610.02738, arXiv.org, revised May 2018.
    3. Patrick Bajari & Denis Nekipelov & Stephen P. Ryan & Miaoyu Yang, 2015. "Demand Estimation with Machine Learning and Model Combination," NBER Working Papers 20955, National Bureau of Economic Research, Inc.

    More about this item

    Keywords

    Binary response models; Discrete regressors; Partial identification; Misspecification; Linear programming; Support vector machines;

    JEL classification:

    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities

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