The Speed of Income Convergence in Europe: A case for Bayesian Model Averaging with Eigenvector Filtering
The speed of income convergence in Europe remains one of the hot topics in regional economics. Recently Bayesian Model Averaging (BMA) applied to spatial autoregressive models seems to have gained more popularity. BMA averages over some predetermined number of so called top models, ranked by the model's posterior likelihood. We regard two approaches for especially noteworthy: First Crespo-Cuaresma and Feldkircher (2012) employ BMA to a spatial autoregressive model, where spatial eigenvector filtering is used in order to tackle the econometric problems caused by the spatial lag. However, spatial filtering has its drawbacks. It relies on a model approximation and no partial derivatives of interest associated with the model can be computed. This means, that it is impossible to derive direct and indirect effects. Second LeSage and Fischer (2008) rely on BMA applied to a Spatial Durbin Model (SDM), where the model posterior is calculated without any model approximation. Although it can be computationally burdensome, it allows for a proper model interpretation if the underlying data generating process (DGP) is of SDM form. One virtue of spatial filtering, as shown by Pace et al. (2011), is that it estimates some of the model coefficients efficiently for various spatial autocorrelated DGPs. Hence, the likelihoods associated with spatial filtering are more robust against model misspecification. Since our preliminary results show that the top models' (posterior) likelihoods obtained from a spatial filtering BMA exercise and (non spatial filtering) BMA applied to a Spatial Durbin Model differ, it is most likely that the DGP is not of SDM form, i.e. misspecified. This leads us to the conclusion that, even though the methodology employed by Crespo-Cuaresma and Feldkircher (2012) cannot be used for a proper model interpretation, the results obtained by spatial filtering BMA do not suffer from model misspecification. References: Crespo-Cuaresma, J., Feldkircher, M. (2012), `Spatial Filtering, Model Uncertainty and the Speed of Income Convergence in Europe', Journal of Applied Econometrics, forthcoming. LeSage, J., Fischer, M. (2008), `Spatial Growth Regressions, Model Specification, Estimation, and Interpretation', Spatial Economic Analysis 3, 275-304. Pace, R., LeSage, J., Zhu, S. (2011), `Interpretation and Computation of Estimates from Regression Models using Spatial Filtering', written for Spatial Econometrics Association 2011. Keywords: Model uncertainty, spatial ltering, determinants of economic growth, European regions. JEL Classi cations: C11, C21, O11, R11
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