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QML Estimation of the Spatial Weight Matrix in the MR-SAR Model

Author

Listed:
  • Saruta Benjanuvatra
  • Peter Burridge

Abstract

We investigate QML estimation of a parametric form for the spatial weight matrix, W, appearing in the mixed regressive, spatial autoregressive (MR-SAR) model and extend the identifiability, consistency, and asymptotic Normality results given by Lee (2004, 2007) to the case when W depends on an unknown parameter, y, that is to be estimated from a single cross-section. Numerical experiments illustrate that the QML estimator works quite well inmoderate sized samples, yielding well-behaved parameter estimates and t-statistics with approximately correct size in most cases. These findings should open the door to a much more flexible approach to the construction of spatial regression models. Finally, the QML estimator using two types of sub-models for the spatial weights is applied to the cross-sectional dataset used in Ertur and Koch (2007), to illustrate the utility of the approach.

Suggested Citation

  • Saruta Benjanuvatra & Peter Burridge, 2015. "QML Estimation of the Spatial Weight Matrix in the MR-SAR Model," Discussion Papers 15/24, Department of Economics, University of York.
    • Handle: RePEc:yor:yorken:15/24
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    Citations

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    Cited by:

    1. Angulo, Ana & Burridge, Peter & Mur, Jesús, 2018. "Testing for breaks in the weighting matrix," Regional Science and Urban Economics, Elsevier, vol. 68(C), pages 115-129.
    2. Marcos Herrera & Jesus Mur & Manuel Ruiz-Marin, 2017. "A Comparison Study on Criteria to Select the Most Adequate Weighting Matrix," Working Papers 18, Instituto de Estudios Laborales y del Desarrollo Económico (IELDE) - Universidad Nacional de Salta - Facultad de Ciencias Económicas, Jurídicas y Sociales.
    3. Elżbieta Antczak, 2018. "Building W Matrices Using Selected Geostatistical Tools: Empirical Examination and Application," Stats, MDPI, vol. 1(1), pages 1-22, September.
    4. Quintaba Pablo Aníbal & Herrera Gómez Marcos, 2023. "Spatial Weighting Matrix Estimation through Statistical Learning: Analyzing Argentinean Salary Dynamics under Structural Breaks," Asociación Argentina de Economía Política: Working Papers 4688, Asociación Argentina de Economía Política.
    5. Bełej, Mirosław & Cellmer, Radosław & Foryś, Iwona & Głuszak, Michał, 2023. "Airports in the urban landscape: externalities, stigmatization and housing market," Land Use Policy, Elsevier, vol. 126(C).

    More about this item

    Keywords

    Spatial autoregressive model; estimated spatial weight matrix; quasi-maximum likelihood estimator; growth spillovers.;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • R15 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Econometric and Input-Output Models; Other Methods

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