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Selecting the W Matrix. Parametric vs Nonparametric Approaches

  • Jesus Mur

    ()

  • Marcos Herrera
  • Manuel Ruiz

In spatial econometrics, it is customary to specify a weighting matrix, the so-called W matrix, just choosing one matrix from the different types of matrices a user is considering (Anselin, 2002). In general, this selection is made a priori, depending on the user’s judgment. This decision is extremely important because if matrix W is miss-specified in some way, parameter estimates are likely to be biased and they will be inconsistent in models that contain some spatial lag. Also, for models without spatial lags but where the random terms are spatially autocorrelated, the obtaining of robust standard estimates of the errors will be incorrect if W is miss-specified. Goodness-of-fit tests may be used to chose between alternative specifications of W. Although, in practice, most users impose a certain W matrix without testing for the restrictions that the selected spatial operator implies. In this paper, we aim to establish a nonparametric procedure where the chosen by objective criteria. Our proposal is directly related with the Theory of Information. Specifically, the selection criterion that we propose is based on objective information existing in the data, which does not depend on the investigator’s subjectivity: it is a measure of conditional entropy. We compare the performance of our criteria against some other alternative like the J test of Davidson and McKinnon or a likelihood ratio obtained in a maximum likelihood framework.

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Paper provided by European Regional Science Association in its series ERSA conference papers with number ersa11p1055.

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Date of creation: Sep 2011
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Handle: RePEc:wiw:wiwrsa:ersa11p1055
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  1. Hansen, Bruce E. & Racine, Jeffrey S., 2012. "Jackknife model averaging," Journal of Econometrics, Elsevier, vol. 167(1), pages 38-46.
  2. J. Barkley Rosser, 2009. "Introduction," Chapters, in: Handbook of Research on Complexity, chapter 1 Edward Elgar.
  3. 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.
  4. Raffaele Paci & Stefano Usai, 2009. "Knowledge flows across European regions," The Annals of Regional Science, Springer, vol. 43(3), pages 669-690, September.
  5. 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.
  6. Luisa Corrado & Bernard Fingleton, 2011. "Where is the Economics in Spatial Econometrics?," Working Papers 1101, University of Strathclyde Business School, Department of Economics.
  7. 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.
  8. 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.
  9. Conley, Timothy G. & Molinari, Francesca, 2005. "Spatial Correlation Robust Inference with Errors in Location or Distance," Working Papers 05-12, Cornell University, Center for Analytic Economics.
  10. Bruce E. Hansen, 2007. "Least Squares Model Averaging," Econometrica, Econometric Society, vol. 75(4), pages 1175-1189, 07.
  11. 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.
  12. 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.
  13. 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.
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