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Dynamic spatial panels: models, methods, and inferences

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Abstract

This paper provides a survey of the existing literature on the specification and estimation of dynamic spatial panel data models, a collection of models for spatial panels extended to include one or more of the following variables and/or error terms: a dependent variable lagged in time, a dependent variable lagged in space, a dependent variable lagged in both space and time, independent variables lagged in time, independent variables lagged in space, serial error autocorrelation, spatial error autocorrelation, spatial-specific and time-period-specific effects. The survey also examines the reasoning behind different model specifications and the purposes for which they can be used, which should be useful for practitioners.

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Notes

  1. Recent surveys on static spatial panel data models are provided by Elhorst (2010a) and Lee and Yu (2010a). Lee and Yu's (2010a) overview also deals with dynamic spatial panel data models. We will come back to this paper several times.

  2. This remark through Balestra and Nerlove is striking especially since they are the devisers of the random effects model (Balestra and Nerlove 1966).

  3. The loss of degrees of freedom if N is large may be one of the main reasons to adopt the random effects model (Cressie and Wikle 2011). However, the number of observations in the cross-sectional domain of most empirical studies in spatial economics and economic geography is smaller than 1,000. Furthermore, methodological studies considering further extensions of the random effects models with spatial interaction effects also tend to present Monte Carlo simulation experiments for relatively small values of N (N < 500).

  4. To investigate this analytically, one should consider the expected value of the log-likelihood function and examine whether it is flat or almost flat. Alternatively, the algorithm that is used to find the optimum should be improved.

  5. As pointed out in Sects. 3.1 and 3.2, Hendry (1995) recommends to regress Y t on Y t−1, X t and X t−1 as a generalization of the first-order serial autocorrelation model for time-series data, while Burridge (1981) recommends to regress Y t on WY t , X t and WX t as a generalization of the first-order spatial autocorrelation model for cross-section data. Elhorst (2001) combines these two recommendations and suggests to regress Y t on Y t−1, WY t , WY t−1, X t , WX t , X t−1 and WX t−1 when having data in space and time. This extension of Eq. 7, however, worsens the identification problem. See also Beenstock and Felsenstein (2007) but then presented in the form of a spatial VAR model.

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Acknowledgments

The author would like to thank Jan Jacobs, three anonymous referees, the editor of this journal, and the participants of the 5th World Conference of the Spatial Econometrics Association in Toulouse 2011 for valuable comments on a previous version of this paper.

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Correspondence to J. Paul Elhorst.

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Elhorst, J.P. Dynamic spatial panels: models, methods, and inferences. J Geogr Syst 14, 5–28 (2012). https://doi.org/10.1007/s10109-011-0158-4

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