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Inference in Semiparametric Binary Response Models with Interval Data

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  • Yuanyuan Wan
  • Haiqing Xu

Abstract

This paper studies the semiparametric binary response model with interval data investigated by Manski and Tamer (2002, MT). In this partially identified model, we propose a new estimator based on MT's modified maximum score (MMS) method by introducing density weights to the objective function, which allows us to develop asymptotic properties of the proposed set estimator for inference. We show that the density-weighted MMS estimator converges to the identified set at a nearly cube-root-n rate. Further, we propose an asymptotically valid inference procedure for the identified region based on subsampling. Monte Carlo experiments provide supports to our inference procedure.

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Bibliographic Info

Paper provided by University of Toronto, Department of Economics in its series Working Papers with number tecipa-492.

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Length: Unknown pages
Date of creation: 25 Jun 2013
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Handle: RePEc:tor:tecipa:tecipa-492

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Keywords: Interval data; semiparametrc binary response model; density weights; U-process;

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  1. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, Cambridge University Press, number 9780521586115.
  2. Andrews, Donald W K, 1994. "Asymptotics for Semiparametric Econometric Models via Stochastic Equicontinuity," Econometrica, Econometric Society, Econometric Society, vol. 62(1), pages 43-72, January.
  3. Manski, Charles F., 1975. "Maximum score estimation of the stochastic utility model of choice," Journal of Econometrics, Elsevier, Elsevier, vol. 3(3), pages 205-228, August.
  4. Magnac, Thierry & Maurin, Eric, 2004. "Partial Identification in Monotone Binary Models: Discrete Regressors and Interval Data," IDEI Working Papers, Institut d'Économie Industrielle (IDEI), Toulouse 280, Institut d'Économie Industrielle (IDEI), Toulouse, revised Jan 2005.
  5. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, Econometric Society, vol. 60(3), pages 505-31, May.
  6. Jason R. Blevins, 2013. "Non-Standard Rates of Convergence of Criterion-Function-Based Set Estimators," Working Papers, Ohio State University, Department of Economics 13-02, Ohio State University, Department of Economics.
  7. Jason Abrevaya & Jian Huang, 2005. "On the Bootstrap of the Maximum Score Estimator," Econometrica, Econometric Society, Econometric Society, vol. 73(4), pages 1175-1204, 07.
  8. Manski, Charles F., 1985. "Semiparametric analysis of discrete response : Asymptotic properties of the maximum score estimator," Journal of Econometrics, Elsevier, Elsevier, vol. 27(3), pages 313-333, March.
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