Abstract
We introduce a class of spatial panel data models with correlated error components that can simultaneously handle cross-sectional and temporal correlation. These models are based on Gaussian Markov Random Fields with a Kronecker product of separable error covariance matrices, which allows capturing correlations both in time and space while reducing the number of parameters being estimated. We then propose a unified approach for estimating these models using a novel Bayesian approach, known as integrated nested Laplace approximations. An empirical illustration using U.S. cigarette consumption data is given, and we find that the most general model outperforms its competitors in both in-sample fit and forecast performance.
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Notes
The pattern of strong cross-sectional dependence can be traced back to stochastic processes that are common to all panel members.
Gibbs sampling may become inefficient when handling a high-dimensional parameter space. The number of parameters to be sampled is: \(\left[N\left(N+1\right)+T\left(T+1\right)\right]/2\) for Model 1, \(1+\left[N\left(N+1\right)\right]/2\) for Model 2 and \(1+\left[T\left(T+1\right)\right]/2\) for Model 3.
R code for the simulation is available from the authors upon request.
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Acknowledgements
The authors appreciate the anonymous reviewers and editors for their constructive comments and suggestions that have significantly improved the quality of this manuscript. Yuheng LING would like thank for the financial support of Hainan Provincial Natural Science Foundation (423QN208), the Talent Project of Hainan Provincial Natural Science Foundation (422RC666).
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Ling, Y., Le Gallo, J. Bayesian spatial panel models: a flexible Kronecker error component approach. Lett Spat Resour Sci 16, 39 (2023). https://doi.org/10.1007/s12076-023-00362-8
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DOI: https://doi.org/10.1007/s12076-023-00362-8
Keywords
- Panel data
- Spatial error component models
- Kronecker product
- Bayesian inference
- INLA
- Gaussian Markov random fields