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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. Manski, Charles F, 1990. "Nonparametric Bounds on Treatment Effects," American Economic Review, American Economic Association, vol. 80(2), pages 319-323, May.
    2. 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.
    3. Thierry Magnac & Eric Maurin, 2008. "Partial Identification in Monotone Binary Models: Discrete Regressors and Interval Data," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 75(3), pages 835-864.
    4. 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.
    5. Guido W. Imbens & Charles F. Manski, 2004. "Confidence Intervals for Partially Identified Parameters," Econometrica, Econometric Society, vol. 72(6), pages 1845-1857, November.
    6. 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.
    7. Manski, Charles F. & Thompson, T. Scott, 1986. "Operational characteristics of maximum score estimation," Journal of Econometrics, Elsevier, vol. 32(1), pages 85-108, June.
    8. 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.
    9. T. H. Matheiss & David S. Rubin, 1980. "A Survey and Comparison of Methods for Finding All Vertices of Convex Polyhedral Sets," Mathematics of Operations Research, INFORMS, vol. 5(2), pages 167-185, May.
    10. Bierens, Herman J. & Hartog, Joop, 1988. "Non-linear regression with discrete explanatory variables, with an application to the earnings function," Journal of Econometrics, Elsevier, vol. 38(3), pages 269-299, July.
    11. 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.
    12. 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.
    13. Cosslett, Stephen R, 1983. "Distribution-Free Maximum Likelihood Estimator of the Binary Choice Model," Econometrica, Econometric Society, vol. 51(3), pages 765-782, May.
    14. 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.
    15. Charles F. Manski, 2007. "Partial Identification Of Counterfactual Choice Probabilities," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 48(4), pages 1393-1410, November.
    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. 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.
    18. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-531, May.
    19. 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.
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    Citations

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    Cited by:

    1. Lukáš Lafférs, 2019. "Identification in Models with Discrete Variables," Computational Economics, Springer;Society for Computational Economics, vol. 53(2), pages 657-696, February.
    2. Chen, Le-Yu & Lee, Sokbae, 2019. "Breaking the curse of dimensionality in conditional moment inequalities for discrete choice models," Journal of Econometrics, Elsevier, vol. 210(2), pages 482-497.
    3. Chen, Le-Yu & Lee, Sokbae, 2018. "Best subset binary prediction," Journal of Econometrics, Elsevier, vol. 206(1), pages 39-56.
    4. Florios, Kostas, 2018. "A hyperplanes intersection simulated annealing algorithm for maximum score estimation," Econometrics and Statistics, Elsevier, vol. 8(C), pages 37-55.
    5. Alexander Torgovitsky, 2019. "Partial identification by extending subdistributions," Quantitative Economics, Econometric Society, vol. 10(1), pages 105-144, January.
    6. Khan, S. & Ponomareva, M. & Tamer, E., 2023. "Identification of dynamic binary response models," Journal of Econometrics, Elsevier, vol. 237(1).
    7. Adam M. Rosen & Takuya Ura, 2019. "Finite Sample Inference for the Maximum Score Estimand," Papers 1903.01511, arXiv.org, revised May 2020.
    8. Shakeeb Khan & Xiaoying Lan & Elie Tamer & Qingsong Yao, 2021. "Estimating High Dimensional Monotone Index Models by Iterative Convex Optimization1," Papers 2110.04388, arXiv.org, revised Feb 2023.
    9. Shosei Sakaguchi, 2020. "Partial Identification and Inference in Duration Models with Endogenous Censoring," CeMMAP working papers CWP8/20, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    10. Shosei Sakaguchi, 2021. "Partial Identification and Inference in Duration Models with Endogenous Censoring," Papers 2107.00928, arXiv.org.
    11. 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.
    12. Xi Wang & Songnian Chen, 2022. "Partial Identification and Estimation of Semiparametric Ordered Response Models with Interval Regressor Data," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 84(4), pages 830-849, August.

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    More about this item

    Keywords

    Binary response models; Discrete regressors; Partial identification; Misspecification; Linear programming; Support vector machines;
    All these keywords.

    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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