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Binary Regressions with Bounded Median Dependence

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  • Xun Tang

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    (Department of Economics, University of Pennsylvania)

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    Abstract

    In this paper we study the identification and estimation of a class of binary regressions where conditional medians of additive disturbances are bounded between known or exogenously identified functions of regressors. This class includes several important microeconometric models, such as simultaneous discrete games with incomplete information, binary regressions with censored regressors, and binary regressions with interval data or measurement errors on regressors. We characterize the identification region of linear coefficients in this class of models and show how point-identification can be achieved in various microeconometric models under fairly general restrictions on structural primitives. We define a novel, two-step smooth extreme estimator, and prove its consistency for the identification region of coefficients. We also provide encouraging Monte Carlo evidence of the estimator’s performance in finite samples.

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    File URL: http://economics.sas.upenn.edu/system/files/working-papers/09-003.pdf
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    Bibliographic Info

    Paper provided by Penn Institute for Economic Research, Department of Economics, University of Pennsylvania in its series PIER Working Paper Archive with number 09-003.

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    Length: 43 pages
    Date of creation: 20 Jan 2009
    Date of revision:
    Handle: RePEc:pen:papers:09-003

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    Related research

    Keywords: Binary response; median dependence; games with incomplete information; censored regressors; interval data; measurement error; partial identification; point identification; consistent estimation;

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    1. Powell, James L., 1984. "Least absolute deviations estimation for the censored regression model," Journal of Econometrics, Elsevier, vol. 25(3), pages 303-325, July.
    2. 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.
    3. Patrick Bajari & Han Hong & John Krainer & Denis Nekipelov, 2006. "Estimating Static Models of Strategic Interaction," NBER Working Papers 12013, National Bureau of Economic Research, Inc.
    4. Powell, James L, 1986. "Symmetrically Trimmed Least Squares Estimation for Tobit Models," Econometrica, Econometric Society, vol. 54(6), pages 1435-60, November.
    5. Ichimura, H., 1991. "Semiparametric Least Squares (sls) and Weighted SLS Estimation of Single- Index Models," Papers 264, Minnesota - Center for Economic Research.
    6. 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.
    7. 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.
    8. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-31, May.
    9. Chamberlain, Gary, 1986. "Asymptotic efficiency in semi-parametric models with censoring," Journal of Econometrics, Elsevier, vol. 32(2), pages 189-218, July.
    10. Matzkin, Rosa L, 1992. "Nonparametric and Distribution-Free Estimation of the Binary Threshold Crossing and the Binary Choice Models," Econometrica, Econometric Society, vol. 60(2), pages 239-70, March.
    11. 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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