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Identification and estimation in a correlated random coefficients binary response model

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  • Stefan Hoderlein

    ()
    (Institute for Fiscal Studies and Boston College)

  • Robert Sherman

Abstract

We study identification and estimation in a binary response model with random coefficients B allowed to be correlated with regressors X. Our objective is to identifiy the mean of the distribution of B and estimate a trimmed mean of this distribution. Like Imbens and Newey (2009), we use instruments Z and a control vector V to make X independent of B given V. A consequent conditional median restriction identifies the mean of B given V. Averaging over V identifies the mean of B. This leads to an analogous localise-then-average approach to estimation. We estimate conditional means with localised smooth maximum score estimators and average to obtain a √n-consistent and asymptotically normal estimator of a trimmed mean of the distribution of B. The method can be adapted to models with nonrandom coefficients to produce √n-consistent and asymptotically normal estimators under the conditional median restrictions. We explore small sample performance through simulations, and present an application.

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Bibliographic Info

Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP42/12.

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Date of creation: Dec 2012
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Handle: RePEc:ifs:cemmap:42/12

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Related research

Keywords: Heterogeneity; Correlated Random Coefficients; Endogeneity; Binary Response Model; Instrumental Variables; Control Variables; Conditional Median Restrictions;

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References

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  1. Sherman, Robert P., 1994. "U-Processes in the Analysis of a Generalized Semiparametric Regression Estimator," Econometric Theory, Cambridge University Press, vol. 10(02), pages 372-395, June.
  2. Gregory Kordas, 2006. "Smoothed binary regression quantiles," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(3), pages 387-407.
  3. Eric Gautier & Yuichi Kitamura, 2011. "Nonparamatric estimation in random coefficients binary choice models," Working Papers hal-00403939, HAL.
  4. Stefan Hoderlein, 2009. "Endogenous Semiparametric Binary Choice Models with Heteroscedasticity," Boston College Working Papers in Economics 747, Boston College Department of Economics.
  5. Richard W. Blundell & James L. Powell, 2004. "Endogeneity in Semiparametric Binary Response Models," Review of Economic Studies, Wiley Blackwell, vol. 71, pages 655-679, 07.
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  8. Manuel Arellano & Stéphane Bonhomme, 2009. "Identifying distributional characteristics in random coefficients panel data models," CeMMAP working papers CWP22/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
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  10. Bryan S. Graham & James Powell, 2008. "Identification and Estimation of 'Irregular' Correlated Random Coefficient Models," NBER Working Papers 14469, National Bureau of Economic Research, Inc.
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  12. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-31, May.
  13. 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.
  14. Edward Vytlacil & Nese Yildiz, 2007. "Dummy Endogenous Variables in Weakly Separable Models," Econometrica, Econometric Society, vol. 75(3), pages 757-779, 05.
  15. Diana S. Lien & William N. Evans, 2005. "Estimating the Impact of Large Cigarette Tax Hikes: The Case of Maternal Smoking and Infant Birth Weight," Journal of Human Resources, University of Wisconsin Press, vol. 40(2).
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Cited by:
  1. Fabian Dunker & Stefan Hoderlein & Hiroaki Kaido, 2013. "Random Coefficients in Static Games of Complete Information," Boston College Working Papers in Economics 835, Boston College Department of Economics.

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