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A Study of a Semiparametric Binary Choice Model with Integrated Covariates

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Author Info
Emmanuel Guerre
Hyungsik Roger Moon

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Abstract

This paper studies a semiparametric nonstationary binary choice model. Imposing a spherical normalization constraint on the parameter for identification purpose, we find that the MSE and SMSE are at least sqrt(n)-consistent. Comparing this rate to the parametric MLE’s convergence rate, we show that when a normalization restriction is imposed on the parameter, the Park and Phillips (2000)’s parametric MLE converges at a rate of n^(3/4) and its limiting distribution is a mixed normal. Finally, we show briefy how to apply our estimation method to a nonstationary single index model.

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File URL: http://www.usc.edu/dept/LAS/economics/IEPR/Working%20Papers/IEPR_05.37_%5BGuerre,Moon%5D.pdf
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File Function: First version, 2005
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Publisher Info
Paper provided by Institute of Economic Policy Research (IEPR) in its series IEPR Working Papers with number 05.37.

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Length: 17 pages
Date of creation: Oct 2005
Date of revision:
Handle: RePEc:scp:wpaper:05-37

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  1. Peter C.B. Phillips & Joon Y. Park, 1998. "Nonstationary Density Estimation and Kernel Autoregression," Cowles Foundation Discussion Papers 1181, Cowles Foundation, Yale University. [Downloadable!]
  2. Park, Joon Y & Phillips, Peter C B, 2001. "Nonlinear Regressions with Integrated Time Series," Econometrica, Econometric Society, vol. 69(1), pages 117-61, January.
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  3. Robinson, Peter M, 1982. "On the Asymptotic Properties of Estimators of Models Containing Limited Dependent Variables," Econometrica, Econometric Society, vol. 50(1), pages 27-41, January. [Downloadable!] (restricted)
  4. Hu, Ling & Phillips, Peter C. B., 2004. "Nonstationary discrete choice," Journal of Econometrics, Elsevier, vol. 120(1), pages 103-138, May. [Downloadable!] (restricted)
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  5. Guerre, Emmanuel & Moon, Hyungsik Roger, 2002. "A note on the nonstationary binary choice logit model," Economics Letters, Elsevier, vol. 76(2), pages 267-271, July. [Downloadable!] (restricted)
  6. Joon Y. Park & Yoosoon Chang, 2004. "Endogeneity in Nonlinear Regressions with Integrated Time Series," Econometric Society 2004 North American Winter Meetings 594, Econometric Society.
  7. 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. [Downloadable!] (restricted)
  8. repec:cup:etheor:v:9:y:1993:i:1:p:1-18 is not listed on IDEAS
  9. Chang, Yoosoon & Park, Joon Y., 2003. "Index models with integrated time series," Journal of Econometrics, Elsevier, vol. 114(1), pages 73-106, May. [Downloadable!] (restricted)
  10. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-31, May. [Downloadable!] (restricted)
  11. Moon, Hyungsik Roger, 2004. "Maximum score estimation of a nonstationary binary choice model," Journal of Econometrics, Elsevier, vol. 122(2), pages 385-403, October. [Downloadable!] (restricted)
  12. Joon Y. Park & Peter C. B. Phillips, 2000. "Nonstationary Binary Choice," Econometrica, Econometric Society, vol. 68(5), pages 1249-1280, September.
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  13. Horowitz, Joel L., 1993. "Optimal Rates of Convergence of Parameter Estimators in the Binary Response Model with Weak Distributional Assumptions," Econometric Theory, Cambridge University Press, vol. 9(01), pages 1-18, January. [Downloadable!]
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