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Spatial model selection strategies in a SUR framework. The case of regional productivity in EU

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Abstract

The purpose of the paper was to compare two well-known model selection strategies, the so-called Specific-to-General, Stge, and General-to-Specific, Gets, in a context of spatial SUR models. The two strategies use a battery of misspecification tests obtained in a maximum likelihood framework. The robust tests to local misspecification errors in the alternative hypothesis and the common factor test have been developed with this purpose. The paper includes a Monte Carlo experiment to compare their performance in a situation of small sample sizes. The results are mixed: Both alternatives work well under ideal conditions, but their efficiency deteriorates for different departures such as non-normality or endogeneity. All in all, Stge appears to be slightly preferable although our impression is that the two are complementary and can be used in common. The paper finishes with an application to the case of productivity for a large set of European regions.

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Notes

  1. The specification can be generalized by introducing weighting matrices, W, and interaction parameters, \(\lambda \) and \(\rho \), different for each cross section.

  2. In what follows, we will use a compact standard notation:

    $$\begin{aligned} \mathbf{LM}=\left[ {\mathbf{g}(\theta )_{\left| { H_0 } \right. } } \right] {^\prime } {\left[ {\mathbf{I}(\theta )_{\left| { H_0 } \right. } } \right] }^{-1} \left[ {\mathbf{g}(\theta )_{\left| { H_0 } \right. } } \right] {\mathop {\sim }\limits _{as}} \chi ^2 (df) \end{aligned}$$

    where \(\mathbf{g}(\theta )\) is the score (vector of first derivatives of the likelihood function), \(\mathbf{I}(\theta )\) the information matrix, df means degrees of freedom and ‘\({\vert }H_{0}\)’ means evaluated under the hypothesis \(H_{0}\).

  3. Results for other configurations, with greater G, T or R, are available from the authors.

  4. In fact, Angeriz et al. (2008) consider six different specifications for their regional productivity growth equation.

  5. Data on production and employment by regions and sectors of activity are obtained from EUROSTAT. Data on human capital proceed from EUROSTAT and from the UNESCO Institute for Statistics.

  6. We have used the predicted values of the productivity growth as proxies in the corresponding skedastic functions.

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Acknowledgments

The authors are grateful for the financial support of the Spanish Government’s Ministry of Economy and Competitiveness (ECO2012-36032-C03-01) and the Aragon Government’s Regional Ministry of Industry and Innovation.

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Authors and Affiliations

  1. Department of Quantitative Methods and Computing, Technical University of Cartagena, Cartagena, Spain

    Fernando A. López

  2. Department of Economic Analysis, University of Zaragoza, Zaragoza, Spain

    Jesús Mur & Ana Angulo

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  1. Fernando A. López
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  2. Jesús Mur
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Correspondence to Jesús Mur.

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López, F.A., Mur, J. & Angulo, A. Spatial model selection strategies in a SUR framework. The case of regional productivity in EU. Ann Reg Sci 53, 197–220 (2014). https://doi.org/10.1007/s00168-014-0624-2

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