A Comparison of Bayesian and Maximum Likelihood Estimations in a SUR Tobit Regression Model

SUR 토빗회귀모형에서 베이지안 추정과 최대가능도 추정의 비교

Lee, Seung-Chun;Choi, Byongsu

  • Received : 2014.08.13
  • Accepted : 2014.10.07
  • Published : 2014.12.31


Both Bayesian and maximum likelihood methods are efficient for the estimation of regression coefficients of various Tobit regression models (see. e.g. Chib, 1992; Greene, 1990; Lee and Choi, 2013); however, some researchers recognized that the maximum likelihood method tends to underestimate the disturbance variance, which has implications for the estimation of marginal effects and the asymptotic standard error of estimates. The underestimation of the maximum likelihood estimate in a seemingly unrelated Tobit regression model is examined. A Bayesian method based on an objective noninformative prior is shown to provide proper estimates of the disturbance variance as well as other regression parameters


Seemingly unrelated Tobit regression model;maximum likelihood estimate;EM algorithm;Bayes estimation;Gibbs sampling


  1. Chib, S. (1992). Bayesian inference in the Tobit censored regression model, Journal of Econometrics, 51, 77-99.
  2. Greene, W. H. (1990). Econometric Analysis, Macmillan, New York.
  3. Cowles, M. K., Carlin, B. P. and Connett, J. E. (1996). Bayesian Tobit modeling of longitudinal ordinal clinical trial compliance data with nonignorable missingness, Journal of American Statistical Association, 91, 86-98.
  4. Daniels, M, D. and Kass, R. E. (1999). Nonconjugate Bayesian estimation of covariance matrices and its use in hierarchical models, Journal of American Statistical Association, 94, 1254-1263.
  5. Efron, B. and Hinkley, D. V. (1978). The observed versus expected information, Biometirika, 65, 163-168.
  6. Greene, W. (2004a). The behavior of the maximum likelihood estimator of limited dependent variable models in the presence of fixed effects, Econometrics Journal, 7, 98-119.
  7. Amemiya, T. (1984). Tobit models: A survey, Journal of Econometrics, 24, 3-61
  8. Bruno, G. (2004). Limited dependent panel models: A comparative analysis of classical and Bayesian inference among econometrics packages, Computing in Economics and Finance. Society for Computational Economics, download.cgi?db name=SCE2004%&paper id=41.
  9. Greene, W. (2004b). Fixed effects and bias due to the incidental parameters problem in the Tobit model, Econometrics Reviews, 23, 125-147.
  10. Greene, W. (2012). Econometric Analysis. 7th edition, Pearson.
  11. Hamilton, B. H. (1999). HMO selection and medicare costs: Bayesian MCMC estimation of a robust panel data tobit model with survival, Health Economics and Econometrics, 8, 403-414.<403::AID-HEC455>3.0.CO;2-D
  12. Huang, C. J., Sloan, F. and Adamache, K, W. (1987). Estimation of seemingly unrelated Tobit regression via EM algorithm, Journal of Business & Economic Statistics, 5, 425-430.
  13. Huang, H. C. (1999). Estimation of the SUR Tobit model via the MCECM algorithm, Economics Letters, 64, 25-30.
  14. Huang, H. C. (2001). Bayesian analysis of the SUR Tobit model, Applied Economics Letters, 8, 617-622.
  15. Joreskog (2004). Multivariate censored regression, available at
  16. Johnson, S. G. and Narasimhan, B. (2014). Package Cubature,
  17. Lancaster, T. (2000). The incidental parameter problem since 1948, Journal of Econometrics, 95, 391-413.
  18. Lee, S.C. and Choi, B. (2013). Bayesian interval estimation of Tobit regression model, The Korean Journal of Applied Statistics, 26, 737-746.
  19. Lee, S.C. and Choi, B. (2014). Bayesian inference for censored panel regression model, Communications for Statistical Applications and Methods, 21, 192-200.
  20. Louis, T. A. (1982). Finding the observed information matrix when using the EM algorithm, Journal of the Royal Statistical Society: Series B, 44, 226-233.
  21. Natarajan, R. and Kass, R. R. (2000). Bayesian methods for generalized linear mixed models, Journal of the American Statistical Association, 95, 227-237.
  22. Tanner, M. A. and Wong, W. H. (1987). The calculation of posterior distributions by data augmentation (with discussion), Journal of the American Statistical Association, 82, 528-550.
  23. Tierney, L. and Kadane, J. B. (1986). Accurate approximations for posterior moments and marginal densities, Journal of American Statistical Association, 81, 82-86.
  24. Wichitaksorn, N. and Choy, S. T. B. (2011). Modeling dependence of seemingly unrelated Tobit model through copula: A Bayesian analysis, Thailand Econometrics Society, 3, 6-19.

Cited by

  1. The restricted maximum likelihood estimation of a censored regression model vol.24, pp.3, 2017,


Supported by : 한신대학교, 한성대학교