Spatial econometrics has relied extensively on spatial autoregressive models. Anselin (1988) developed a taxonomy of these models using a regression model framework and maximum likelihood estimation methods. A Bayesian approach to estimating these models based on Gibbs sampling is introduced here. It allows for non-constant variance over space taking an unspecified form and outliers in the sample data. In addition, estimates of the non-constant variance at each point in space allow inferences regarding the spatial nature of heteroskedasticity and the position of outliers.
Get full access to this article
View all access options for this article.
References
1.
Anselin, L.1980. Estimation methods for spatial autoregressive structures. Ithaca, NY: Regional Science Dissertation and Monograph Series #8.
2.
Anselin, L.1988. Spatial econometrics: Methods and models. Dordrecht: Kluwer.
3.
Anselin, L.
, and D. A. Griffith. 1988. Do spatial effects really matter in regression analysis?Papers of the Regional Science Association65: 11-34.
4.
Casella, G.
, and E. I. George. 1992. Explaining the Gibbs sampler. American Statistician46: 167-174.
5.
Chib, S.1993. Bayes regression with autoregressive error: A Gibbs sampling approach. Journal of Econometrics58: 275-294.
6.
Chib, S.
, and E. Greenberg. 1994. Bayes inference in regression models with ARMA(p,q) errors. Journal of Econometrics64: 183-206.
7.
Devroye, L.1986. Non-uniform random variate generation. New York: Springer-Verlag.
8.
Gelfand, A. E.
, and A. F. M. Smith. 1990. Sampling-based approaches to calculating marginal densities. Journal of the American Statistical Association85: 398-409.
9.
Gelfand, A. E.
, S. E. Hills, A. Racine-Poon, and A. F. M. Smith. 1990. Illustration of Bayesian inference in normal data models using Gibbs sampling. Journal of the American Statistical Association85: 972-985.
10.
Gelfand, A. E.
, A. F. M. Smith, and T.-M. Lee. 1992. Bayesian analysis of constrained parameter and truncated data problems using Gibbs sampling. Journal of the American Statistical Association87: 523-532.
11.
Geweke, J.1992a. Bayesian treatment of the heteroscedastic normal and independent Student-t linear models. Federal Reserve Bank of Minneapolis, Institute for Empirical Macroeconomics, Working paper 495.
12.
Geweke J.1992b. Priors for macroeconomic time series and their application. Federal Reserve Bank of Minneapolis, Research Department, Discussion Paper 64.
13.
Hardle, W.1990. Smoothing techniques with implementation in S. New York: Springer-Verlag.
14.
LeSage, J. P.1994. Bayesian estimation of spatial autoregressive models. Toledo, OH: University of Toledo, Department of Economics Working Paper. Available at http://www.econ.utoledo.edu.
15.
McMillen, D. P.1992. Probit with spatial autocorrelation. Journal of Regional Science32: 335-348.
16.
Newley, W. K.
, and K. D. West. 1987. A simple positive semi-definite, heteroskedasticity and auto-correlation consistent covariance matrix. Econometrica55: 703-708.
17.
Raftery, A. E.
, and S. M. Lewis. 1992. How many iterations in the Gibbs sampler? In Bayesian statistics, Vol. 4, eds. J. M. Bernardo, J. O. Berger, A. P. Dawid, and A. F. M. Smith. London: Oxford University Press.
18.
Zellner, A.1984. Basic issues in econometrics. Chicago: University of Chicago Press.
