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Semiparametric Qualitative Response Model Estimation with Unknown Heteroskedasticity or Instrumental Variables

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Author Info
Arthur Lewbel () (Boston College)

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Abstract

This paper provides estimators of discrete choice models, including binary, ordered, and multinomial response (choice) models. The estimators closely resemble ordinary and two stage least squares. The distribution of the model's latent variable error is unknown and may be related to the regressors, e.g., the model could have errors that are heteroscedastic or correlated with regressors. The estimator does not require numerical searches, even for multinomial choice. For ordered and binary choice models the estimator is root N consistent and asymptotically normal. A consistent estimator of the conditional error distribution is also provided.

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File URL: http://fmwww.bc.edu/EC-P/WP454.pdf
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Publisher Info
Paper provided by Boston College Department of Economics in its series Boston College Working Papers in Economics with number 454.

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Length: 33 pages
Date of creation: 15 Aug 1999
Date of revision:
Publication status: published, Journal of Econometrics, 97:1, 145-177, 2000.
Handle: RePEc:boc:bocoec:454

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Related research
Keywords: semiparametric discrete choice qualitative response heteroskedasticity binomial response multinomial response measurement error instrumental variables binary choice ordered choice latent variable models

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Find related papers by JEL classification:
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods
C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Horowitz, Joel & Hardle, Wolfgang, 1994. "Direct Semiparametric Estimation of Single-Index Models With Discrete Covariates," Working Papers 94-22, University of Iowa, Department of Economics.
    Other versions:
  2. Bo E. Honore & Arthur Lewbel, 2002. "Semiparametric Binary Choice Panel Data Models Without Strictly Exogeneous Regressors," Econometrica, Econometric Society, vol. 70(5), pages 2053-2063, September. [Downloadable!] (restricted)
    Other versions:
  3. Whitney K. Newey and Paul A. Ruud., 1994. "Density Weighted Linear Least Squares," Economics Working Papers 94-228, University of California at Berkeley.
  4. Haerdle,W. Hart,J.D. Marron,J.S. Tsybakov,A.B., 1989. "Bandwidth choice for average derivative estimation," Discussion Paper Serie A 200, University of Bonn, Germany.
  5. 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. [Downloadable!] (restricted)
  6. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-30, November. [Downloadable!] (restricted)
  7. Newey, Whitney K, 1994. "The Asymptotic Variance of Semiparametric Estimators," Econometrica, Econometric Society, vol. 62(6), pages 1349-82, November. [Downloadable!] (restricted)
  8. Powell, James L. & Stoker, Thomas M., 1996. "Optimal bandwidth choice for density-weighted averages," Journal of Econometrics, Elsevier, vol. 75(2), pages 291-316, December. [Downloadable!] (restricted)
  9. repec:cup:etheor:v:13:y:1997:i:1:p:32-51 is not listed on IDEAS
  10. Gallant, A Ronald & Nychka, Douglas W, 1987. "Semi-nonparametric Maximum Likelihood Estimation," Econometrica, Econometric Society, vol. 55(2), pages 363-90, March. [Downloadable!] (restricted)
  11. Horowitz, Joel L., 1993. "Semiparametric estimation of a work-trip mode choice model," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 49-70, July. [Downloadable!] (restricted)
  12. Aït-Sahalia, Yacine. & Bickel, Peter J. & Stoker, Thomas M., 1994. "Goodness-of-fit tests for regression using kernel methods," Working papers 3747-94., Massachusetts Institute of Technology (MIT), Sloan School of Management. [Downloadable!]
  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. [Downloadable!] (restricted)
  14. Horowitz, J.L., 1998. "Nonparametric Estimation of a Generalized Additive Model with an Unknown Link Function," Working Papers 98-05, University of Iowa, Department of Economics.
  15. 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. [Downloadable!] (restricted)
  16. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-54, July. [Downloadable!] (restricted)
  17. 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)
  18. Arthur Lewbel, 1998. "Semiparametric Latent Variable Model Estimation with Endogenous or Mismeasured Regressors," Econometrica, Econometric Society, vol. 66(1), pages 105-122, January.
  19. Ichimura, H., 1991. "Semiparametric Least Squares (sls) and Weighted SLS Estimation of Single- Index Models," Papers 264, Minnesota - Center for Economic Research.
  20. Arthur Lewbel & Oliver Linton & Daniel McFadden, 1997. "Estimating Features of a Distribution from Binomial Data," Boston College Working Papers in Economics 442, Boston College Department of Economics, revised 04 Sep 2006. [Downloadable!]
    Other versions:
  21. J. Horowitz, . "Nonparametric Estimation of a Generalized Additive Model with an Unknown Link Function," Sonderforschungsbereich 373 1998-83, Humboldt Universitaet Berlin.
    Other versions:
  22. Ruud, Paul A, 1983. "Sufficient Conditions for the Consistency of Maximum Likelihood Estimation Despite Misspecifications of Distribution in Multinomial Discrete Choice Models," Econometrica, Econometric Society, vol. 51(1), pages 225-28, January. [Downloadable!] (restricted)
Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Shakeeb Khan & Arthur Lewbel, 2002. "Weighted and Two Stage Least Squares Estimation of Semiparametric Truncated Regression Models," Boston College Working Papers in Economics 525, Boston College Department of Economics, revised 04 Sep 2006. [Downloadable!]
    Other versions:
  2. Jaap Abbring & James Heckman, 2008. "Dynamic policy analysis," CeMMAP working papers CWP05/08, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
  3. D'Haultfoeuille, Xavier & Davezies, Laurent & Fougère, Denis, 2006. "Identification of Peer Effects Using Group Size Variation," CEPR Discussion Papers 5865, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
    Other versions:
  4. Arthur Lewbel, 2002. "Ordered Response Threshold Estimation," Boston College Working Papers in Economics 535, Boston College Department of Economics, revised 29 Oct 2003. [Downloadable!]
  5. Goux, Dominique & Maurin, Eric, 2003. "The Effects of Overcrowded Housing on Children's Performance at School," CEPR Discussion Papers 3818, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
    Other versions:
  6. Arthur Lewbel & Susanne M. Schennach, 2003. "A Simple Ordered Data Estimator For Inverse Density Weighted Functions," Boston College Working Papers in Economics 557, Boston College Department of Economics, revised 01 May 2005. [Downloadable!]
  7. James J. Heckman & Salvador Navarro, 2005. "Dynamic Discrete Choice and Dynamic Treatment Effects," IZA Discussion Papers 1790, Institute for the Study of Labor (IZA). [Downloadable!]
    Other versions:
  8. Arthur Lewbel, 2005. "Simple Endogenous Binary Choice and Selection Panel Model Estimators," Boston College Working Papers in Economics 613, Boston College Department of Economics, revised 04 Sep 2006. [Downloadable!]
  9. Arthur Lewbel & Oliver Linton & Daniel McFadden, 2001. "Estimating features of a distribution from binomial data," CeMMAP working papers CWP07/01, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
    Other versions:
  10. Arthur Lewbel, 2000. "Endogenous Selection Or Treatment Model Estimation," Boston College Working Papers in Economics 462, Boston College Department of Economics, revised 13 Jun 2007. [Downloadable!]
    Other versions:
  11. Francisco Alvarez-Cuadrado, 2006. "Improving The Efficiency And Robustness Of The Smoothed Maximum Score Estimator," Departmental Working Papers 2004-01, McGill University, Department of Economics. [Downloadable!]
  12. Bo E. Honore & Arthur Lewbel, 1998. "Semiparametric Binary Choice Panel Data Models without Strictly Exogeneous Regressors," Boston College Working Papers in Economics 455, Boston College Department of Economics, revised 22 Sep 2001. [Downloadable!]
    Other versions:
  13. Alban Thomas, 2002. "Consistent estimation of discrete-choice models for panel data with multiplicative effects," 10th International Conference on Panel Data, Berlin, July 5-6, 2002 D6-2, International Conferences on Panel Data. [Downloadable!]
  14. Arthur Lewbel & Linton, Oliver Linton, 1998. "Nonparametric Censored Regression," Cowles Foundation Discussion Papers 1186, Cowles Foundation, Yale University. [Downloadable!]
  15. Arthur Lewbel, 2000. "Asymptotic Trimming for Bounded Density Plug-in Estimators," Boston College Working Papers in Economics 479, Boston College Department of Economics, revised 30 Oct 2000. [Downloadable!]
  16. Andrew Chesher, 2005. "Identification with excess heterogeneity," CeMMAP working papers CWP19/05, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
  17. Arthur Lewbel, 2006. "Modeling Heterogeneity," Boston College Working Papers in Economics 650, Boston College Department of Economics. [Downloadable!]
  18. MAGNAC, Thierry & MAURIN, Eric, 2004. "Partial Identification in Monotone Binary Models: Discrete Regressors and Interval Data," IDEI Working Papers 280, Institut d'Économie Industrielle (IDEI), Toulouse, revised Jan 2005. [Downloadable!]
  19. Arthur Lewbel & Oliver Linton, 2000. "Nonparametric Censored and Truncated Regression," STICERD - Econometrics Paper Series /2000/389, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
    Other versions:
  20. MAGNAC, Thierry & MAURIN, Eric, 2003. "Identification and Information in Monotone Binary Models," IDEI Working Papers 180, Institut d'Économie Industrielle (IDEI), Toulouse, revised Oct 2004. [Downloadable!]
    Other versions:
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