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Semiparametric qualitative response model estimation with unknown heteroscedasticity or instrumental variables

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  • Lewbel, Arthur

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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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 97 (2000)
Issue (Month): 1 (July)
Pages: 145-177

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Handle: RePEc:eee:econom:v:97:y:2000:i:1:p:145-177

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Web page: http://www.elsevier.com/locate/jeconom

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References

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  1. Arthur Lewbel, 1998. "Semiparametric Latent Variable Model Estimation with Endogenous or Mismeasured Regressors," Econometrica, Econometric Society, vol. 66(1), pages 105-122, January.
  2. Arthur Lewbel & Oliver Linton, 2000. "Nonparametric censored and truncated regression," LSE Research Online Documents on Economics 2060, London School of Economics and Political Science, LSE Library.
  3. Lewbel, Arthur & McFadden, Daniel & Linton, Oliver, 2011. "Estimating features of a distribution from binomial data," Journal of Econometrics, Elsevier, vol. 162(2), pages 170-188, June.
  4. 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.
  5. Newey, W.K., 1991. "The Asymptotic Variance of Semiparametric Estimators," Working papers 583, Massachusetts Institute of Technology (MIT), Department of Economics.
  6. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-54, July.
  7. 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.
  8. Andrews, Donald W.K., 1995. "Nonparametric Kernel Estimation for Semiparametric Models," Econometric Theory, Cambridge University Press, vol. 11(03), pages 560-586, June.
  9. Newey, Whitney K. & Ruud, Paul A., 1994. "Density Weighted Linear Least Squares," Department of Economics, Working Paper Series qt9fc2n3jc, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
  10. Lewbel, Arthur, 1997. "Semiparametric Estimation of Location and Other Discrete Choice Moments," Econometric Theory, Cambridge University Press, vol. 13(01), pages 32-51, February.
  11. Khan, Shakeeb & Lewbel, Arthur, 2007. "Weighted And Two-Stage Least Squares Estimation Of Semiparametric Truncated Regression Models," Econometric Theory, Cambridge University Press, vol. 23(02), pages 309-347, April.
  12. repec:wop:humbsf:1998-83 is not listed on IDEAS
  13. 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.
  14. 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.
  15. 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.
  16. 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.
  17. Lewbel, Arthur, 1995. "Consistent nonparametric hypothesis tests with an application to Slutsky symmetry," Journal of Econometrics, Elsevier, vol. 67(2), pages 379-401, June.
  18. Gallant, A Ronald & Nychka, Douglas W, 1987. "Semi-nonparametric Maximum Likelihood Estimation," Econometrica, Econometric Society, vol. 55(2), pages 363-90, March.
  19. 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.
  20. Ichimura, H., 1991. "Semiparametric Least Squares (sls) and Weighted SLS Estimation of Single- Index Models," Papers 264, Minnesota - Center for Economic Research.
  21. 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.
  22. Newey, Whitney K. & McFadden, Daniel, 1986. "Large sample estimation and hypothesis testing," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 36, pages 2111-2245 Elsevier.
  23. 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.
  24. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-31, May.
  25. 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.
  26. J. Horowitz, 1998. "Nonparametric Estimation of a Generalized Additive Model with an Unknown Link Function," SFB 373 Discussion Papers 1998,83, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  27. McFadden, Daniel L., 1984. "Econometric analysis of qualitative response models," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 24, pages 1395-1457 Elsevier.
  28. 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.
  29. repec:cup:etheor:v:13:y:1997:i:1:p:32-51 is not listed on IDEAS
  30. 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.
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