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Selecting the W Matrix. Parametric vs Nonparametric Approaches

Author

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  • Jesus Mur

    ()

  • Marcos Herrera
  • Manuel Ruiz

Abstract

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.

Suggested Citation

  • Jesus Mur & Marcos Herrera & Manuel Ruiz, 2011. "Selecting the W Matrix. Parametric vs Nonparametric Approaches," ERSA conference papers ersa11p1055, European Regional Science Association.
  • Handle: RePEc:wiw:wiwrsa:ersa11p1055
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    References listed on IDEAS

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    Cited by:

    1. Marasteanu, I. Julia & Jaenicke, Edward C., 2013. "Agglomeration and Spatial Dependence in Certified Organic Operations in the United States," 2013 Annual Meeting, August 4-6, 2013, Washington, D.C. 149551, Agricultural and Applied Economics Association.
    2. Marasteanu, I. Julia & Jaenicke, Edward C., 2014. "Clusters of Organic Operations and their Impact on Regional Economic Growth in the United States," 2014 Annual Meeting, July 27-29, 2014, Minneapolis, Minnesota 170336, Agricultural and Applied Economics Association.
    3. repec:bpj:jossai:v:3:y:2015:i:5:p:463-471:n:7 is not listed on IDEAS
    4. Solmaria Halleck Vega & J. Paul Elhorst, 2015. "The Slx Model," Journal of Regional Science, Wiley Blackwell, vol. 55(3), pages 339-363, June.

    More about this item

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • C50 - Mathematical and Quantitative Methods - - Econometric Modeling - - - General

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