Inference in Panel Data Models via Gibbs Sampling

  • Siddhartha Chib
Part of the Advanced Studies in Theoretical and Applied Econometrics book series (ASTA, volume 33)


In this chapter we consider the use of the recently developed Gibbs sampling method to estimate panel data models. The Gibbs sampler is a Markov chain Monte-Carlo (MCMC) method that provides an approach to simulating a given joint distribution. Although this method can be employed quite generally it has proved most useful in Bayesian inference where it has been used to simulate posterior distributions in a number of different settings (Geman and Geman [1984], Gelfand and Smith [1990], Tierney [1994], and Chib and Greenberg [1993]). Once a sample of parameter draws from the posterior distribution has been obtained it is possible to estimate a parameter of interest by taking empirical averages of the simulated values.


Posterior Distribution Gibbs Sampling American Statistical Association Markov Chain Monte Carlo Method Panel Data Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Albert, J. and S. Chib [1993]: Bayesian analysis of binary and polychotomous response data, Journal of the American Statistical Association, 88, 669–679.CrossRefGoogle Scholar
  2. Albert, J. and S. Chib [1994]: Bayesian probit modeling of binary repeated measures data with an application to a cross—over trial, in Bayesian Biostatistics(eds. D. A. Berry and D. K. Stangl), New York: Marcel Dekker, forthcoming.Google Scholar
  3. Allenby, G. & P. Rossi [1993]: A Bayesian approach to estimating household parameters. Journal of Marketing Research 30, 171–182.CrossRefGoogle Scholar
  4. Beasley, J. D. and S. G. Springer [1977]: Algorithm 111, Applied Statistics, 26, 118–121.CrossRefGoogle Scholar
  5. Best, D. J. [1978]: Letter to the Editor, Applied Statistics, 29, 181.Google Scholar
  6. Butler, J.S. and R. Moffitt [1982]: A computationally efficient quadrature procedure for the one factor multinomial probit model, Econometrica, 50, 761–764.CrossRefGoogle Scholar
  7. Chaloner, K. and Brant, R. [1988]: A Bayesian approach to outlier detection and residual analysis, Biometrika, 75, 651–659.CrossRefGoogle Scholar
  8. Chamberlain, G. [1980]: Analysis of covariance with qualitative data, Review of Economic Studies, 47, 225–238.CrossRefGoogle Scholar
  9. Chib, S. [1992]: Bayes regression for the Tobit censored regression model, Journal of Econometrics, 51, 79–99.CrossRefGoogle Scholar
  10. Chib, S. and E. Greenberg [1993]: Markov chain Monte Carlo methods in econometrics, John M. Olin School of Business, Washington University, St. Louis.Google Scholar
  11. Gelfand, A. E. and A. F. M. Smith [1990]: Sampling-based approaches to calculating marginal densities, Journal of the American Statistical Association, 85, 398–409.CrossRefGoogle Scholar
  12. Geweke, J. [1992]: Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments, Proceedings of the Fourth Valencia International Conference on Bayesian Statistics, (eds., J. M. Bernardo, J. O. Berger, A. P. Dawid, and A. F. M. Smith), New York: Oxford University Press, 169–193.Google Scholar
  13. Heckman, J.J. [1981]: Statistical models for discrete panel data, in Structural Analysis of Discrete Data with Econometric Applications, ed C. F. Manski and D. McFadden, pp 114–178, Cambridge: MIT Press.Google Scholar
  14. Liu, J. S., W. W. Wong, and A. Kon [1994]: Covariance structure of the Gibbs sampler with applications to the comparison of estimators and augmentation schemes. Biometrika, 81, 27–40.CrossRefGoogle Scholar
  15. Page, E [1977]: Approximations to the cumulative normal function and its inverse for use on a pocket calculator, Applied Statistics, 26, 75–76.CrossRefGoogle Scholar
  16. Ripley, B. [1987]: Stochastic simulation, New York: John Wiley & Sons.CrossRefGoogle Scholar
  17. Roberts, G. O. and Smith, A. F. M. [1992]: Some convergence theory for Markov chain Monte Carlo, manuscript.Google Scholar
  18. Smith, A. F. M. and G. O. Roberts [1993]: Bayesian computation via the Gibbs sampler and related Markov chain Monte Carlo methods, Journal of the Royal Statistical Society, B, 55, 3–24.Google Scholar
  19. Stout, W. F. [1974]: Almost Sure Convergence, New York, Academic Press.Google Scholar
  20. Tanner, M. A. and W. H. Wong [1987]: The calculation of posterior distributions by data augmentation, Journal of the American Statistical Association, 82, 528–549.CrossRefGoogle Scholar
  21. Tierney, L. [1991]: Markov chains for exploring posterior distributions, manuscript.Google Scholar
  22. Wakefield, J. C., A. F. M. Smith, A. Racine Poon, and A. E. Gelfand [1994]: Bayesian analysis of linear and non-linear population models by using the Gibbs sampler, Applied Statistics, 43, 201–221.CrossRefGoogle Scholar
  23. Zellner, A [1975]: Bayesian analysis of regression error terms, Journal of the American Statistical Association, 70, 138–144.CrossRefGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Siddhartha Chib

There are no affiliations available

Personalised recommendations