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Estimation of the Spatial Weights Matrix under Structural Constraints

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  • Arnab Bhattacharjee
  • Chris Jensen-Butler

Abstract

While estimates of models with spatial interaction are very sensitive to the choice of spatial weights, considerable uncertainty surrounds definition of spatial weights in most studies with cross-section dependence. We show that, in the spatial error model the spatial weights matrix is only partially identified, and is fully identified under the structural constraint of symmetry. For the spatial error model, we propose a new methodology for estimation of spatial weights under the assumption of symmetric spatial weights, with extensions to other important spatial models. The methodology is applied to regional housing markets in the UK, providing an estimated spatial weights matrix that generates several new hypotheses about the economic and socio-cultural drivers of spatial diffusion in housing demand.

Suggested Citation

  • Arnab Bhattacharjee & Chris Jensen-Butler, 2011. "Estimation of the Spatial Weights Matrix under Structural Constraints," Dundee Discussion Papers in Economics 254, Economic Studies, University of Dundee.
  • Handle: RePEc:dun:dpaper:254
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    Cited by:

    1. Achim Ahrens & Arnab Bhattacharjee, 2015. "Two-Step Lasso Estimation of the Spatial Weights Matrix," Econometrics, MDPI, Open Access Journal, vol. 3(1), pages 1-28, March.
    2. Paelinck, Jean & Mur, Jesús & Trivez, F. Javier, 2015. "Modelos para datos espaciales con estructura transversal o de panel. Una revisión/Models for Spatial Data with Panel or Cross-Sectional Structure. A Review," Estudios de Economía Aplicada, Estudios de Economía Aplicada, vol. 33, pages 7-30, Enero.
    3. Arnab Bhattacharjee & Taps Maiti & Dennis Petrie, 2014. "Spatial structures of health outcomes and health behaviours in Scotland: Evidence from the Scottish Health Survey," SEEC Discussion Papers 1401, Spatial Economics and Econometrics Centre, Heriot Watt University.
    4. Masayoshi Hayashi & Wataru Yamamoto, 2017. "Information sharing, neighborhood demarcation, and yardstick competition: an empirical analysis of intergovernmental expenditure interaction in Japan," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 24(1), pages 134-163, February.
    5. repec:esx:essedp:735 is not listed on IDEAS
    6. Antczak, El?Bieta & Lewandowska-Gwarda, Karolina, 2015. "Migration Processes in European Cities: A Spatio-Temporal Analysis Using Different Spatial Weights Matrices/Procesos migratorios entre ciudades europeas: Un análisis espacio-temporal usando diferentes," Estudios de Economía Aplicada, Estudios de Economía Aplicada, vol. 33, pages 53-80, Enero.
    7. Ana Angulo & Peter Burridge & Jesús Mur, 2017. "Testing for breaks in the weighting matrix," Documentos de Trabajo dt2017-01, Facultad de Ciencias Económicas y Empresariales, Universidad de Zaragoza.
    8. Arnab Bhattacharjee & Eduardo Castro & Taps Maiti & João Marques, 2014. "Endogenous spatial structure and delineation of submarkets: A new framework with application to housing markets," SEEC Discussion Papers 1403, Spatial Economics and Econometrics Centre, Heriot Watt University.
    9. repec:bla:presci:v:96:y:2017:i::p:s135-s153 is not listed on IDEAS
    10. 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.
    11. repec:eee:regeco:v:68:y:2018:i:c:p:115-129 is not listed on IDEAS
    12. Arnab Bhattacharjee & Sean Holly, 2015. "Influence, Interactions and Heterogeneity: Taking Personalities out of Monetary Policy Decision-making," Manchester School, University of Manchester, vol. 83(2), pages 153-182, March.
    13. Lam, Clifford & Souza, Pedro C.L., 2015. "Detection and estimation of block structure in spatial weight matrix," LSE Research Online Documents on Economics 59898, London School of Economics and Political Science, LSE Library.
    14. Solmaria Halleck Vega & J. Paul Elhorst, 2015. "The Slx Model," Journal of Regional Science, Wiley Blackwell, vol. 55(3), pages 339-363, June.
    15. Kelejian, Harry H. & Piras, Gianfranco, 2014. "Estimation of spatial models with endogenous weighting matrices, and an application to a demand model for cigarettes," Regional Science and Urban Economics, Elsevier, vol. 46(C), pages 140-149.
    16. Bhattacharjee, Arnab & Maiti, Taps & Petrie, Dennis, 2014. "General equilibrium effects of spatial structure: Health outcomes and health behaviours in Scotland," Regional Science and Urban Economics, Elsevier, vol. 49(C), pages 286-297.

    More about this item

    Keywords

    Spatial econometrics; Spatial autocorrelation; Spatial weights matrix; Spatial error model; Housing demand; Gradient projection;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - 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
    • R21 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - Household Analysis - - - Housing Demand
    • R31 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - Real Estate Markets, Spatial Production Analysis, and Firm Location - - - Housing Supply and Markets

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