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Maximum score estimation of preference parameters for a binary choice model under uncertainty

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  • Le-Yu Chen
  • Sokbae 'Simon' Lee

    ()
    (Institute for Fiscal Studies and Seoul National University)

  • Myung Jae Sung

Abstract

This paper develops maximum score estimation of preference parameters in the binary choice model under uncertainty in which the decision rule is affected by conditional expectations. The preference parameters are estimated in two stages: we estimate conditional expectations nonparametrically in the first stage and the preference parameters in the second stage based on Manski (1975, 1985)'s maximum score estimator using the choice data and first stage estimates. The paper establishes consistency and derives the rate of convergence of the corresponding two-stage estimator, which is of independent interest for maximum score estimation with generated regressors. The paper also provides results of some Monte Carlo experiments.

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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 CWP14/13.

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Date of creation: Apr 2013
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Handle: RePEc:ifs:cemmap:14/13

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Related research

Keywords: discrete choice; maximum score estimation; generated regressor; preference parameters; M-estimation; cube root asymptotics;

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References

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  1. Jason Abrevaya & Jian Huang, 2005. "On the Bootstrap of the Maximum Score Estimator," Econometrica, Econometric Society, vol. 73(4), pages 1175-1204, 07.
  2. Xiaohong Chen & Oliver Linton & Ingrid Van Keilegom, 2003. "Estimation of Semiparametric Models when the Criterion Function is not Smooth," STICERD - Econometrics Paper Series /2003/450, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  3. Juan Carlos Escanciano & David Jacho-Chavez & Arthur Lewbel, 2010. "Uniform Convergence of Weighted Sums of Non- and Semi-parametric Residuals for Estimation and Testing," Boston College Working Papers in Economics 756, Boston College Department of Economics, revised 31 Jan 2012.
  4. Ichimura, Hidehiko & Lee, Sokbae, 2010. "Characterization of the asymptotic distribution of semiparametric M-estimators," Journal of Econometrics, Elsevier, vol. 159(2), pages 252-266, December.
  5. Florios, Kostas & Skouras, Spyros, 2008. "Exact computation of max weighted score estimators," Journal of Econometrics, Elsevier, vol. 146(1), pages 86-91, September.
  6. Lewbel, Arthur, 2000. "Semiparametric qualitative response model estimation with unknown heteroscedasticity or instrumental variables," Journal of Econometrics, Elsevier, vol. 97(1), pages 145-177, July.
  7. Enno Mammen & Christoph Rothe & Melanie Schienle, 2011. "Semiparametric Estimation with Generated Covariates," SFB 649 Discussion Papers SFB649DP2011-064, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  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. Ahn, Hyungtaik & Manski, Charles F., 1993. "Distribution theory for the analysis of binary choice under uncertainty with nonparametric estimation of expectations," Journal of Econometrics, Elsevier, vol. 56(3), pages 291-321, April.
  10. repec:cup:cbooks:9780521496032 is not listed on IDEAS
  11. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
  12. Ahn, Hyungtaik, 1997. "Semiparametric Estimation of a Single-Index Model with Nonparametrically Generated Regressors," Econometric Theory, Cambridge University Press, vol. 13(01), pages 3-31, February.
  13. Coppejans, Mark, 2001. "Estimation of the binary response model using a mixture of distributions estimator (MOD)," Journal of Econometrics, Elsevier, vol. 102(2), pages 231-269, June.
  14. 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.
  15. Manski, Charles F., 1993. "Dynamic choice in social settings : Learning from the experiences of others," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 121-136, July.
  16. Delgado, Miguel A. & Rodriguez-Poo, Juan M. & Wolf, Michael, 2001. "Subsampling inference in cube root asymptotics with an application to Manski's maximum score estimator," Economics Letters, Elsevier, vol. 73(2), pages 241-250, November.
  17. Daniel Ackerberg & Xiaohong Chen & Jinyong Hahn, 2011. "A practical asymptotic variance estimator for two-step semiparametric estimators," CeMMAP working papers CWP22/11, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  18. Brown, Bryan W & Walker, Mary Beth, 1989. "The Random Utility Hypothesis and Inference in Demand Systems," Econometrica, Econometric Society, vol. 57(4), pages 815-29, July.
  19. 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.
  20. Andrews, Donald W.K., 1995. "Nonparametric Kernel Estimation for Semiparametric Models," Econometric Theory, Cambridge University Press, vol. 11(03), pages 560-586, June.
  21. Ahn, Hyungtaik, 1995. "Nonparametric two-stage estimation of conditional choice probabilities in a binary choice model under uncertainty," Journal of Econometrics, Elsevier, vol. 67(2), pages 337-378, June.
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