Abstract
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.
Keywords
- 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.
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References
Albert, J. and S. Chib [1993]: Bayesian analysis of binary and polychotomous response data, Journal of the American Statistical Association, 88, 669–679.
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.
Allenby, G. & P. Rossi [1993]: A Bayesian approach to estimating household parameters. Journal of Marketing Research 30, 171–182.
Beasley, J. D. and S. G. Springer [1977]: Algorithm 111, Applied Statistics, 26, 118–121.
Best, D. J. [1978]: Letter to the Editor, Applied Statistics, 29, 181.
Butler, J.S. and R. Moffitt [1982]: A computationally efficient quadrature procedure for the one factor multinomial probit model, Econometrica, 50, 761–764.
Chaloner, K. and Brant, R. [1988]: A Bayesian approach to outlier detection and residual analysis, Biometrika, 75, 651–659.
Chamberlain, G. [1980]: Analysis of covariance with qualitative data, Review of Economic Studies, 47, 225–238.
Chib, S. [1992]: Bayes regression for the Tobit censored regression model, Journal of Econometrics, 51, 79–99.
Chib, S. and E. Greenberg [1993]: Markov chain Monte Carlo methods in econometrics, John M. Olin School of Business, Washington University, St. Louis.
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.
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.
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.
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.
Page, E [1977]: Approximations to the cumulative normal function and its inverse for use on a pocket calculator, Applied Statistics, 26, 75–76.
Ripley, B. [1987]: Stochastic simulation, New York: John Wiley & Sons.
Roberts, G. O. and Smith, A. F. M. [1992]: Some convergence theory for Markov chain Monte Carlo, manuscript.
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.
Stout, W. F. [1974]: Almost Sure Convergence, New York, Academic Press.
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.
Tierney, L. [1991]: Markov chains for exploring posterior distributions, manuscript.
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.
Zellner, A [1975]: Bayesian analysis of regression error terms, Journal of the American Statistical Association, 70, 138–144.
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© 1996 Kluwer Academic Publishers
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Chib, S. (1996). Inference in Panel Data Models via Gibbs Sampling. In: Mátyás, L., Sevestre, P. (eds) The Econometrics of Panel Data. Advanced Studies in Theoretical and Applied Econometrics, vol 33. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0137-7_24
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DOI: https://doi.org/10.1007/978-94-009-0137-7_24
Publisher Name: Springer, Dordrecht
Print ISBN: 978-0-7923-3787-4
Online ISBN: 978-94-009-0137-7
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