Bayesian Techniques in Spatial and Network Econometrics: 1. Model Comparison and Posterior Odds

Abstract

In this paper the problems of specification and nonnested model comparison in spatial and network econometrics are examined, and the Bayesian posterior probabilities approach is developed. The theory is developed for the comparison of alternative spatial weights matrices in both the systematic and the disturbance components of models, and also for the comparison of alternative spatial disturbance processes. Several empirical illustrations are provided, and extensions of the Bayesian approach are discussed.

Heteroskedasticity of Unknown Form in Spatial Autoregressive Models with Moving Average Disturbance Term

“…The result in Equation (16) indicates that the average of the individual variances is asymptotically equivalent toσ 2 n (δ 0 ). Concentrating out β and σ 2 from the log-likelihood function in Equation (6) yields:…”

“…The third term vanishes by Lemma 1(4) and Equation (16). The probability limit of the remaining term can be found by the Chebyshev inequality.…”

“…In the literature, various estimation methods have been proposed [6][7][8][9][10][11][12][13][14][15][16]. The ML method is the best known and most common estimator used in the literature for both SARAR and SARMA specifications.…”

W-based versus latent variables spatial autoregressive models: evidence from Monte Carlo simulations

“…The approach is based on a spatial weights matrix, usually denoted W, that accounts for spatial dependence or spill-over effects among the spatial units of observation. The selection of a spatial weights matrix is a crucial step in spatial modelling because it a priori imposes a model structure which affects estimates (Bhattacharjee and Jensen-Butler 2006;Anselin 2002;Fingleton 2003) and the substantive interpretation of the research findings (Hepple 1995).…”

“…Much progress has been made with respect to the the construction and comparison of spatial weights matrices including estimation of spatial weights matrices that are consistent with an observed pattern of spatial dependence rather than assuming a priori the nature of spatial interaction dependence (Hepple 1995;Getis 2004, 2006). In spite of all these developments the most common procedure in applied research is still to assume a priori first-order contiguity, as expressed by a spatial weights matrix W with diagonal elements equal to zero and off-diagonal elements equal to one if two regions are first-order contiguous and zero elsewhere.…”