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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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  • 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. 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.
    5. Enrico Spolaore & Romain Wacziarg, 2013. "How Deep Are the Roots of Economic Development?," Journal of Economic Literature, American Economic Association, vol. 51(2), pages 325-369, June.
    6. 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.
    7. Kelejian, Harry H. & Prucha, Ingmar R., 2010. "Specification and estimation of spatial autoregressive models with autoregressive and heteroskedastic disturbances," Journal of Econometrics, Elsevier, vol. 157(1), pages 53-67, July.
    8. Daniel Cohen & Marcelo Soto, 2007. "Growth and human capital: good data, good results," Journal of Economic Growth, Springer, vol. 12(1), pages 51-76, March.
    9. N. Gregory Mankiw & David Romer & David N. Weil, 1992. "A Contribution to the Empirics of Economic Growth," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 107(2), pages 407-437.
    10. Yang, Zhenlin, 2015. "LM tests of spatial dependence based on bootstrap critical values," Journal of Econometrics, Elsevier, vol. 185(1), pages 33-59.
    11. 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.
    12. Diego Comin & William Easterly & Erick Gong, 2010. "Was the Wealth of Nations Determined in 1000 BC?," American Economic Journal: Macroeconomics, American Economic Association, vol. 2(3), pages 65-97, July.
    13. 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.
    14. James P. LeSage & R. Kelley Pace, 2014. "The Biggest Myth in Spatial Econometrics," Econometrics, MDPI, vol. 2(4), pages 1-33, December.
    15. Godfrey, Leslie G, 1983. "Testing Non-Nested Models after Estimation by Instrumental Variables or Least Squares," Econometrica, Econometric Society, vol. 51(2), pages 355-365, March.
    16. Liu, Shew Fan & Yang, Zhenlin, 2015. "Modified QML estimation of spatial autoregressive models with unknown heteroskedasticity and nonnormality," Regional Science and Urban Economics, Elsevier, vol. 52(C), pages 50-70.
    17. Caselli, Francesco, 2005. "Accounting for cross-country income differences," LSE Research Online Documents on Economics 5266, London School of Economics and Political Science, LSE Library.
    18. Flachaire, Emmanuel, 2005. "Bootstrapping heteroskedastic regression models: wild bootstrap vs. pairs bootstrap," Computational Statistics & Data Analysis, Elsevier, vol. 49(2), pages 361-376, April.
    19. 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.
    20. Godfrey, L. G. & Pesaran, M. H., 1983. "Tests of non-nested regression models: Small sample adjustments and Monte Carlo evidence," Journal of Econometrics, Elsevier, vol. 21(1), pages 133-154, January.
    21. 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.
    22. 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.
    23. 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.
    24. 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.
    25. Davidson, Russell & MacKinnon, James G., 2002. "Bootstrap J tests of nonnested linear regression models," Journal of Econometrics, Elsevier, vol. 109(1), pages 167-193, July.
    26. Godfrey, L. G., 1998. "Tests of non-nested regression models some results on small sample behaviour and the bootstrap," Journal of Econometrics, Elsevier, vol. 84(1), pages 59-74, May.
    27. 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.
    28. Hagemann, Andreas, 2012. "A simple test for regression specification with non-nested alternatives," Journal of Econometrics, Elsevier, vol. 166(2), pages 247-254.
    29. Liu, Xiaodong & Patacchini, Eleonora & Zenou, Yves, 2014. "Endogenous peer effects: local aggregate or local average?," Journal of Economic Behavior & Organization, Elsevier, vol. 103(C), pages 39-59.
    30. Elhorst, J. Paul & Lacombe, Donald J. & Piras, Gianfranco, 2012. "On model specification and parameter space definitions in higher order spatial econometric models," Regional Science and Urban Economics, Elsevier, vol. 42(1-2), pages 211-220.
    31. Cohen, Daniel & Leker, Laura, 2014. "Health and Education: Another Look with the Proper Data," CEPR Discussion Papers 9940, C.E.P.R. Discussion Papers.
    32. 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.
    33. 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.
    34. Lee, Lung-fei, 2007. "GMM and 2SLS estimation of mixed regressive, spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 137(2), pages 489-514, April.
    35. Liu, Xiaodong & Saraiva, Paulo, 2015. "GMM estimation of SAR models with endogenous regressors," Regional Science and Urban Economics, Elsevier, vol. 55(C), pages 68-79.
    36. Harry Kelejian, 2008. "A spatial J-test for model specification against a single or a set of non-nested alternatives," Letters in Spatial and Resource Sciences, Springer, vol. 1(1), pages 3-11, April.
    37. Lee, Lung-fei & Liu, Xiaodong, 2010. "Efficient Gmm Estimation Of High Order Spatial Autoregressive Models With Autoregressive Disturbances," Econometric Theory, Cambridge University Press, vol. 26(1), pages 187-230, February.
    38. 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.
    39. Howitt, Peter & Aghion, Philippe, 1998. "Capital Accumulation and Innovation as Complementary Factors in Long-Run Growth," Journal of Economic Growth, Springer, vol. 3(2), pages 111-130, June.
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    Cited by:

    1. 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.
    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.

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