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Local weighting or the necessity of flexibility

  • Jesus Mur

    ()

  • Antonio Paez

    ()

The local estimation algorithms are well-known techniques in the current spatial econometric literature. The Geographically Weighted Regressions are very popular to estimate, locally, static models, whereas the SALE or the Zoom approaches are useful solutions in the case of dynamic models. These techniques are well founded from a methodological point of view and present interesting properties. However, Farber and Paez (2008) detect some inconsistencies in the behavior of some of these algorithms that claim for a further analysis. The point that we want to study in this paper refers to the role of the bandwith. This measure defines how many neighbors will be used in the estimation of the local parameters corresponding to each observation. The cross-validation is the most popular criteria to fix the bandwith, although there are several other criteria in the literature. We think that there is a basic problem with this approach. The objective of these algorithms is to relax the restriction of homogeneity of the parameters of the model allowing for local peculiarities; however the definition of local neighborhood is the same. It does not matter if the observation corresponds to an isolated and poorly communicated region or it belongs to a central and highly connected point. According to our view, this is a very restrictive decision that should be avoided. Specifically, we discuss the procedure of specifying the sequence of local weighting matrices that will be used in the analysis. Our purpose is to achieve that these matrices also reflect the local surrounding of each observation. We examine two different strategies in order to construct the local weighting matrices. The first is a parametric approach which involves the J test, as presented by Kelejian (2008), and the second is a nonparametric approach that uses the guidance of the symbolic entropy measures. The first part of the paper presents the overall problem, including a review of the literature; we discuss the solutions in the second part and the third part consists of a Monte Carlo simulation.

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Paper provided by European Regional Science Association in its series ERSA conference papers with number ersa11p942.

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Date of creation: Sep 2011
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Handle: RePEc:wiw:wiwrsa:ersa11p942
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  1. Henk Folmer & Johan Oud, 2008. "How to get rid of W: a latent variables approach to modelling spatially lagged variables," Environment and Planning A, Pion Ltd, London, vol. 40(10), pages 2526-2538, October.
  2. Raffaele Paci & Stefano Usai, 2009. "Knowledge flows across European regions," The Annals of Regional Science, Springer, vol. 43(3), pages 669-690, September.
  3. Luisa Corrado & Bernard Fingleton, 2011. "Where is the economics in spatial econometrics?," LSE Research Online Documents on Economics 33581, London School of Economics and Political Science, LSE Library.
  4. Peter Burridge & Bernard Fingleton, 2010. "Bootstrap Inference in Spatial Econometrics: the J-test," Spatial Economic Analysis, Taylor & Francis Journals, vol. 5(1), pages 93-119.
  5. Conley, Timothy G. & Molinari, Francesca, 2007. "Spatial correlation robust inference with errors in location or distance," Journal of Econometrics, Elsevier, vol. 140(1), pages 76-96, September.
  6. Matilla-Garci­a, Mariano & Ruiz Mari­n, Manuel, 2008. "A non-parametric independence test using permutation entropy," Journal of Econometrics, Elsevier, vol. 144(1), pages 139-155, May.
  7. Esteban Fernández-Vázquez & Matías Mayor-Fernández & Jorge Rodríguez-Vález, 2009. "Estimating Spatial Autoregressive Models by GME-GCE Techniques," International Regional Science Review, , vol. 32(2), pages 148-172, April.
  8. Peter Burridge, 2012. "Improving the J Test in the SARAR Model by Likelihood-based Estimation," Spatial Economic Analysis, Taylor & Francis Journals, vol. 7(1), pages 75-107, March.
  9. P Bodson & D Peeters, 1975. "Estimation of the coefficients of a linear regression in the presence of spatial autocorrelation. An application to a Belgian labour-demand function," Environment and Planning A, Pion Ltd, London, vol. 7(4), pages 455-472, April.
  10. Hansen, Bruce E. & Racine, Jeffrey S., 2012. "Jackknife model averaging," Journal of Econometrics, Elsevier, vol. 167(1), pages 38-46.
  11. Olivier Parent & James P. Lesage, 2007. "Bayesian Model Averaging for Spatial Econometric Models ," University of Cincinnati, Economics Working Papers Series 2007-02, University of Cincinnati, Department of Economics.
  12. Bruce E. Hansen, 2007. "Least Squares Model Averaging," Econometrica, Econometric Society, vol. 75(4), pages 1175-1189, 07.
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