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Interaction matrix selection in spatial econometrics with an application to growth theory

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  • Nicolas DEBARSY

    ()

  • Cem ERTUR

    ()

Abstract

The interaction matrix, or spatial weight matrix, is the fundamental tool to model cross-sectional interdependence between observations in spatial econometric models. However, it is most of the time not derived from theory, as it should be ideally, but chosen on an ad hoc basis. In this paper, we propose a modified version of the J test to formally select the interaction matrix. Our methodology is based on the application of the robust against unknown heteroskedasticity GMM estimation method, developed by Lin & Lee (2010). We then implement the testing procedure developed by Hagemann (2012) to overcome the decision problem inherent to non-nested models tests. An application is presented for the Schumpeterian growth model with worldwide interactions (Ertur & Koch 2011) using three different types of interaction matrix: genetic distance, linguistic distance and bilateral trade flows and we find that the interaction matrix based on trade flows is the most adequate. Furthermore, we propose a network based innovative representation of spatial econometric results.
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Suggested Citation

  • Nicolas DEBARSY & Cem ERTUR, 2016. "Interaction matrix selection in spatial econometrics with an application to growth theory," LEO Working Papers / DR LEO 2172, Orleans Economics Laboratory / Laboratoire d'Economie d'Orleans (LEO), University of Orleans.
  • Handle: RePEc:leo:wpaper:2172
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    1. Kelejian, Harry H & Prucha, Ingmar R, 1999. "A Generalized Moments Estimator for the Autoregressive Parameter in a Spatial Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(2), pages 509-533, May.
    2. Caselli, Francesco, 2005. "Accounting for Cross-Country Income Differences," Handbook of Economic Growth,in: Philippe Aghion & Steven Durlauf (ed.), Handbook of Economic Growth, edition 1, volume 1, chapter 9, pages 679-741 Elsevier.
    3. Debarsy, Nicolas & Ertur, Cem, 2010. "Testing for spatial autocorrelation in a fixed effects panel data model," Regional Science and Urban Economics, Elsevier, vol. 40(6), pages 453-470, November.
    4. MacKinnon, James G. & White, Halbert & Davidson, Russell, 1983. "Tests for model specification in the presence of alternative hypotheses : Some further results," Journal of Econometrics, Elsevier, vol. 21(1), pages 53-70, January.
    5. Kelejian, Harry H & Prucha, Ingmar R, 1998. "A Generalized Spatial Two-Stage Least Squares Procedure for Estimating a Spatial Autoregressive Model with Autoregressive Disturbances," The Journal of Real Estate Finance and Economics, Springer, vol. 17(1), pages 99-121, July.
    6. Cem Ertur & Wilfried Koch, 2007. "Growth, technological interdependence and spatial externalities: theory and evidence," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(6), pages 1033-1062.
    7. N. Gregory Mankiw & David Romer & David N. Weil, 1992. "A Contribution to the Empirics of Economic Growth," The Quarterly Journal of Economics, Oxford University Press, vol. 107(2), pages 407-437.
    8. Jin, Fei & Lee, Lung-fei, 2013. "Cox-type tests for competing spatial autoregressive models with spatial autoregressive disturbances," Regional Science and Urban Economics, Elsevier, vol. 43(4), pages 590-616.
    9. Cem Ertur & Wilfried Koch, 2011. "A contribution to the theory and empirics of Schumpeterian growth with worldwide interactions," Journal of Economic Growth, Springer, vol. 16(3), pages 215-255, September.
    10. Robert E. Hall & Charles I. Jones, 1999. "Why do Some Countries Produce So Much More Output Per Worker than Others?," The Quarterly Journal of Economics, Oxford University Press, vol. 114(1), pages 83-116.
    11. 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.
    12. Lin, Xu & Lee, Lung-fei, 2010. "GMM estimation of spatial autoregressive models with unknown heteroskedasticity," Journal of Econometrics, Elsevier, vol. 157(1), pages 34-52, July.
    13. Kelejian, Harry H. & Prucha, Ingmar R., 2007. "The relative efficiencies of various predictors in spatial econometric models containing spatial lags," Regional Science and Urban Economics, Elsevier, vol. 37(3), pages 363-374, May.
    14. Davidson, Russell & MacKinnon, James G, 1981. "Several Tests for Model Specification in the Presence of Alternative Hypotheses," Econometrica, Econometric Society, vol. 49(3), pages 781-793, May.
    15. Kelejian, Harry H. & Piras, Gianfranco, 2011. "An extension of Kelejian's J-test for non-nested spatial models," Regional Science and Urban Economics, Elsevier, vol. 41(3), pages 281-292, May.
    16. Caselli, Francesco, 2005. "Accounting for cross-country income differences," LSE Research Online Documents on Economics 3567, London School of Economics and Political Science, LSE Library.
    17. Hagemann, Andreas, 2012. "A simple test for regression specification with non-nested alternatives," Journal of Econometrics, Elsevier, vol. 166(2), pages 247-254.
    18. Liu, Xiaodong & Lee, Lung-fei & Bollinger, Christopher R., 2010. "An efficient GMM estimator of spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 159(2), pages 303-319, December.
    19. Lung-fei Lee, 2003. "Best Spatial Two-Stage Least Squares Estimators for a Spatial Autoregressive Model with Autoregressive Disturbances," Econometric Reviews, Taylor & Francis Journals, vol. 22(4), pages 307-335.
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    Cited by:

    1. repec:eee:regeco:v:69:y:2018:i:c:p:48-68 is not listed on IDEAS
    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. Debarsy, Nicolas & LeSage, James, 2018. "Flexible dependence modeling using convex combinations of different types of connectivity structures," Regional Science and Urban Economics, Elsevier, vol. 69(C), pages 48-68.

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