Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Journal of Econometric Methods

Ed. by Giacomini, Raffaella / Li, Tong

1 Issue per year

Online
ISSN
2156-6674
See all formats and pricing
More options …

Misspecified Discrete Choice Models and Huber-White Standard Errors

Michael Guggisberg
  • Corresponding author
  • Institute for Defense Analyses, Strategy, Resources and Forces Division, 4850 Mark Center Dr Alexandria, United States of America
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2018-02-01 | DOI: https://doi.org/10.1515/jem-2016-0002

Abstract

I analyze properties of misspecified discrete choice models and the efficacy of Huber-White (sometimes called ‘robust’) standard errors. The Huber-White correction provides asymptotically correct standard errors for a consistent estimator from a misspecified model. There is little justification for using Huber-White standard errors in discrete choice models since misspecification usually leads to inconsistent estimators. I derive necessary and sufficient conditions for consistency of the maximum likelihood estimator of any potentially misspecified random utility model (e.g. conditional logit). I also derive (easily satisfied) sufficient conditions for consistent estimation of the sign of the data generating parameter. It follows the researcher can consistently test the sign (or nullity) of the parameter from the data generating process using the (possibly) misspecified conditional logit. I investigate small sample properties of the Huber-White estimator via a simulation study and find the correction provides little to no improvement for inferences.

This article offers supplementary material which is provided at the end of the article.

Keywords: discrete choice; Huber-White standard errors; misspecified models

References

  • Bhat, C. R. 1995. “A Heteroscedastic Extreme Value Model of Intercity Travel Mode Choice.” Transportation Research Part B: Methodological 29: 471–483.CrossrefGoogle Scholar

  • Cramer, J. 2005. “Omitted Variables and Misspecified Disturbances in the Logit Model,” Tinbergen Institute Discussion Papers 05-084/4, Tinbergen Institute.Google Scholar

  • Davidson, R., and J. G. MacKinnon. 1984. “Convenient Specification Tests for Logit and Probit Models.” Journal of Econometrics 25: 241–262.CrossrefGoogle Scholar

  • Dubin, J. A., and L. Zeng. 1991. “The Heterogeneous Logit Model.” California Institute of Technology, Social Science Working Paper 759.Google Scholar

  • Dumont, J., and J. Keller. 2015. RSGHB: Functions for Hierarchical Bayesian Estimation: A Flexible Approach. r package version 1.1.2.Google Scholar

  • Eicker, F. 1967. “Limit Theorems for Regressions with Unequal and Dependent Errors.” Proceedings of Fifth Berkeley Symposium on Mathematical Statistics and Probability 1: 59–82.Google Scholar

  • Freedman, D. A. 2006. “On the So-Called “Huber Sandwich Estimator” and “Robust Standard Errors”.” The American Statistician 60: 299–302.CrossrefGoogle Scholar

  • Gartner, S. S., and G. M. Segura. 2000. “Race, Casualties, and Opinion in the Vietnam War.” The Journal of Politics 62: 115–146.CrossrefGoogle Scholar

  • Gould, E. D., V. Lavy, and M. D. Paserman. 2003. “Immigrating to Opportunity: Estimating the Effect of School Quality Using a Natural Experiment on Ethiopians in Israel.” CEPR Discussion Papers, C.E.P.R. Discussion Papers 4052, C.E.P.R. Discussion Papers.Google Scholar

  • Gourieroux, C., A. Monfort, and A. Trognon. 1984. “Pseudo Maximum Likelihood Methods: Theory.” Econometrica 52: 681–700.CrossrefGoogle Scholar

  • Haan, P. 2006. “Estimation of Multinomial Logit Models with Unobserved Heterogeneity using Maximum Simulated Likelihood.” Stata Journal 6: 229–245.Google Scholar

  • Hole, A. R. 2006. “Small-Sample Properties of Tests for Heteroscedasticity in the Conditional Logit Model.” Economics Bulletin 3: 1–14.Google Scholar

  • Hole, A. R. 2007. “Fitting Mixed Logit Models by using Maximum Simulated Likelihood.” Stata Journal 7: 388–401.Google Scholar

  • Huber, P. J. 1967. “The Behavior of Maximum Likelihood Estimates Under Nonstandard Conditions.” Proceedings of Fifth Berkeley Symposium on Mathematical Statistics and Probability 1: 221–233.Google Scholar

  • Jacobs, D., and J. T. Carmichael. 2002. “The Political Sociology of the Death Penalty: A Pooled Time-Series Analysis.” American Sociological Review 67: 109–131.CrossrefGoogle Scholar

  • Jeliazkov, I., and E. H. Lee. 2010. “MCMC Perspectives on Simulated Likelihood Estimation.” In Maximum Simulated Likelihood Methods and Applications (Advances in Econometrics, Vol. 26), edited by William Greene, R. Carter Hill, 3–39. Bingley, UK: Emerald Group Publishing Limited.Google Scholar

  • Keane, M. 1992. “A Note on Identification in the Multinomial Probit Model.” Journal of Business and Economic Statistics 10: 193–200.Google Scholar

  • Koop, G., and D. J. Poirier. 1993. “Bayesian Analysis of Logit Models using Natural Conjugate Priors.” Journal of Econometrics 56: 323–340.CrossrefGoogle Scholar

  • Kullback, S., and R. A. Leibler. 1951. “On Information and Sufficiency.” Annals of Mathematical Statistics 22: 49–86.Google Scholar

  • Lange, K. 1999. Numerical Analysis for Statisticians. Statistics and computing, Springer.Google Scholar

  • Lassen, D. D. 2005. “The Effect of Information on Voter Turnout: Evidence from a Natural Experiment.” American Journal of Political Science 49: 103–118.CrossrefGoogle Scholar

  • Luce, R. D. 1959. Individual Choice Behavior: A Theoretical Analysis. New York: Wiley .Google Scholar

  • MacKinnon, J. G., and H. White. 1985. “Some Heteroskedasticity-Consistent Covariance Matrix Estimators with Improved Finite Sample Properties.” Journal of Econometrics 29: 305–325.CrossrefGoogle Scholar

  • McFadden, D., and K. Train. 2000. “Mixed MNL Models for Discrete Response.” Journal of Applied Econometrics 15: 447–470.CrossrefGoogle Scholar

  • Ramalho, E. A., and J. J. Ramalho. 2010. “Is Neglected Heterogeneity Really an Issue in Binary and Fractional Regression Models? A Simulation Exercise for Logit, Probit and Loglog Models.” Computational Statistics and Data Analysis 54: 987–1001.Web of ScienceCrossrefGoogle Scholar

  • Ruud, P. A. 1983. “Sufficient Conditions for the Consistency of Maximum Likelihood Estimation Despite Misspecification of Distribution in Multinomial Discrete Choice Models.” Econometrica 51: 225–228.CrossrefGoogle Scholar

  • Ruud, P. A. 1996. “Simulation of the Multinomial Probit Model: An Analysis of Covariance Matrix Estimation.” Working paper.Google Scholar

  • Train, K. E. 2009. Discrete Choice Methods with Simulation, no. 9780521766555 in Cambridge Books, Cambridge University Press.Google Scholar

  • White, H. 1980. “A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity.” Econometrica 48: 817–838.CrossrefGoogle Scholar

  • White, H. 1982. “Maximum Likelihood Estimation of Misspecified Models.” Econometrica 50: 1–25.CrossrefGoogle Scholar

  • White, H. 1983. “Corrigendum [Maximum Likelihood Estimation of Misspecified Models].” Econometrica 51: 513.CrossrefGoogle Scholar

  • Yatchew, A., and Z. Griliches. 1985. “Specification Error in Probit Models.” The Review of Economics and Statistics 67: 134–39.CrossrefGoogle Scholar

About the article

Published Online: 2018-02-01


Citation Information: Journal of Econometric Methods, 20160002, ISSN (Online) 2156-6674, DOI: https://doi.org/10.1515/jem-2016-0002.

Export Citation

©2018 Walter de Gruyter GmbH, Berlin/Boston.Get Permission

Supplementary Article Materials

Comments (0)

Please log in or register to comment.
Log in