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Inference in Semiparametric Binary Response Models with Interval Data

Listed author(s):
  • Yuanyuan Wan
  • Haiqing Xu

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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File URL: https://www.economics.utoronto.ca/public/workingPapers/tecipa-492.pdf
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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
Handle: RePEc:tor:tecipa:tecipa-492
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  1. Andrews, Donald W K, 1994. "Asymptotics for Semiparametric Econometric Models via Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 62(1), pages 43-72, January.
  2. 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.
  3. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521355643, March.
  4. Racine, Jeff & Li, Qi, 2004. "Nonparametric estimation of regression functions with both categorical and continuous data," Journal of Econometrics, Elsevier, vol. 119(1), pages 99-130, March.
  5. Shakeeb Khan & Elie Tamer, 2010. "Irregular Identification, Support Conditions, and Inverse Weight Estimation," Econometrica, Econometric Society, vol. 78(6), pages 2021-2042, November.
  6. 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, 09.
  7. Jason R. Blevins, 2013. "Non-Standard Rates of Convergence of Criterion-Function-Based Set Estimators," Working Papers 13-02, Ohio State University, Department of Economics.
  8. 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.
  9. Jason Abrevaya & Jian Huang, 2005. "On the Bootstrap of the Maximum Score Estimator," Econometrica, Econometric Society, vol. 73(4), pages 1175-1204, 07.
  10. Songnian Chen & Shakeeb Khan & Xun Tang, 2013. "Informational Content of Special Regressors in Heteroskedastic Binary Response Models," PIER Working Paper Archive 13-021, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  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. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-1430, November.
  13. 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.
  14. 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.
  15. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-531, May.
  16. Abrevaya, Jason, 2000. "Rank estimation of a generalized fixed-effects regression model," Journal of Econometrics, Elsevier, vol. 95(1), pages 1-23, March.
  17. Hansen, Bruce E., 2005. "Exact Mean Integrated Squared Error Of Higher Order Kernel Estimators," Econometric Theory, Cambridge University Press, vol. 21(06), pages 1031-1057, December.
  18. 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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