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Convergence analysis for hierarchical longitudinal data

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  • Fazio, Giorgio
  • Piacentino, Davide

Abstract

Convergence analysis is typically envisaged either from a macro or a micro perspective. However, empirical tests tend to ignore that the two levels are often “nested” in a hierarchy. Building on hierarchical growth curve modelling, we propose an approach to convergence analysis that allows contemporaneous inference on macro and micro-convergence. Compared to the classic linear convergence analysis, the suggested methodology provides a more flexible alternative to model heterogeneity and validate the results for possible Galton's fallacy. We illustrate the approach in two empirical examples, one considering convergence across European regions and countries and the other across Italian firms and regions. In the European case, we find that the evidence of convergence depends on the choice of cross-sectional sample. Evidence on convergence in Italy applies only to part of the temporal sample and, therefore, is not robust to Galton's fallacy. Our analysis returns more robust results on the convergence process and allows better inference for policy intervention. We can envisage that this approach will find increasing applications in the future, as disaggregated data becomes available and heterogeneity becomes an increasingly prominent feature in economic modelling.

Suggested Citation

  • Fazio, Giorgio & Piacentino, Davide, 2018. "Convergence analysis for hierarchical longitudinal data," Economic Modelling, Elsevier, vol. 73(C), pages 89-99.
  • Handle: RePEc:eee:ecmode:v:73:y:2018:i:c:p:89-99
    DOI: 10.1016/j.econmod.2018.03.009
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    as
    1. Avi J. Cohen, 2003. "Retrospectives: Whatever Happened to the Cambridge Capital Theory Controversies?," Journal of Economic Perspectives, American Economic Association, vol. 17(1), pages 199-214, Winter.
    2. Durlauf, Steven N. & Kourtellos, Andros & Minkin, Artur, 2001. "The local Solow growth model," European Economic Review, Elsevier, vol. 45(4-6), pages 928-940, May.
    3. Jean H.P. Paelinck, 2000. "On aggregation in spatial econometric modelling," Journal of Geographical Systems, Springer, vol. 2(2), pages 157-165, July.
    4. Phillips, Peter C.B. & Sul, Donggyu, 2007. "Some empirics on economic growth under heterogeneous technology," Journal of Macroeconomics, Elsevier, vol. 29(3), pages 455-469, September.
    5. Sala-i-Martin, Xavier X., 1996. "Regional cohesion: Evidence and theories of regional growth and convergence," European Economic Review, Elsevier, vol. 40(6), pages 1325-1352, June.
    6. Steele, Fiona, 2008. "Multilevel models for longitudinal data," LSE Research Online Documents on Economics 52203, London School of Economics and Political Science, LSE Library.
    7. Sergio J. Rey & Mark V. Janikas, 2005. "Regional convergence, inequality, and space," Journal of Economic Geography, Oxford University Press, vol. 5(2), pages 155-176, April.
    8. Barro, Robert J & Sala-i-Martin, Xavier, 1992. "Convergence," Journal of Political Economy, University of Chicago Press, vol. 100(2), pages 223-251, April.
      • Barro, R.J. & Sala-I-Martin, X., 1991. "Convergence," Papers 645, Yale - Economic Growth Center.
      • Barro, Robert J. & Sala-i-Martin, Xavier, 1992. "Convergence," Scholarly Articles 3451299, Harvard University Department of Economics.
    9. Harry Garretsen & Ron Martin, 2011. "The Journal of Economic Geography a decade on: where do we go from here?," Journal of Economic Geography, Oxford University Press, vol. 11(2), pages 207-213, March.
    10. J. Felipe & J.S.L. McCombie, 2014. "The Aggregate Production Function: 'Not Even Wrong'," Review of Political Economy, Taylor & Francis Journals, vol. 26(1), pages 60-84, January.
    11. Bernard, Andrew B. & Durlauf, Steven N., 1996. "Interpreting tests of the convergence hypothesis," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 161-173.
    12. Alberto Díaz Dapena & Fernando Rubiera Morollón & Mônica de Moura Pires & Andréa da Silva Gomes, 2017. "Convergence in Brazil: new evidence using a multilevel approach," Applied Economics, Taylor & Francis Journals, vol. 49(50), pages 5050-5062, October.
    13. Maximilian von Ehrlich & Tobias Seidel, 2012. "More Similar Firms - More Similar Regions? On the Role of Firm Heterogeneity for Agglomeration," CESifo Working Paper Series 4028, CESifo Group Munich.
    14. Robert M. Solow, 1956. "A Contribution to the Theory of Economic Growth," The Quarterly Journal of Economics, Oxford University Press, vol. 70(1), pages 65-94.
    15. Carlo Altomonte & Italo Colantone, 2008. "Firm heterogeneity and endogenous regional disparities," Journal of Economic Geography, Oxford University Press, vol. 8(6), pages 779-810, November.
    16. Stefano Magrini & Margherita Gerolimetto & Hasan Engin Duran, 2015. "Regional Convergence and Aggregate Business Cycle in the United States," Regional Studies, Taylor & Francis Journals, vol. 49(2), pages 251-272, February.
    17. von Ehrlich, Maximilian & Seidel, Tobias, 2013. "More similar firms — More similar regions? On the role of firm heterogeneity for agglomeration," Regional Science and Urban Economics, Elsevier, vol. 43(3), pages 539-548.
    18. Coro CHASCO & Ana Mª LÓPEZ, 2009. "Multilevel Models: An Application To The Beta-Convergence Model," Region et Developpement, Region et Developpement, LEAD, Universite du Sud - Toulon Var, vol. 30, pages 35-58.
    19. Ricardo Hausmann & Jason Hwang & Dani Rodrik, 2007. "What you export matters," Journal of Economic Growth, Springer, vol. 12(1), pages 1-25, March.
    20. Roberto Basile & Sergio de Nardis & Carmine Pappalardo, 2014. "Firm heterogeneity and regional business cycles differentials," Journal of Economic Geography, Oxford University Press, vol. 14(6), pages 1087-1115.
    21. Luisa Corrado & Bernard Fingleton, 2012. "Where Is The Economics In Spatial Econometrics?," Journal of Regional Science, Wiley Blackwell, vol. 52(2), pages 210-239, May.
    22. Durlauf, Steven N & Johnson, Paul A, 1995. "Multiple Regimes and Cross-Country Growth Behaviour," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 10(4), pages 365-384, Oct.-Dec..
    23. Bruno Pellegrino & Luigi Zingales, 2017. "Diagnosing the Italian Disease," NBER Working Papers 23964, National Bureau of Economic Research, Inc.
    24. Peter Huber & Michael Pfaffermayr, 2010. "Testing for Conditional Convergence in Variance and Skewness: The Firm Size Distribution Revisited," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 72(5), pages 648-668, October.
    25. Giorgio Fazio & Davide Piacentino, 2010. "A Spatial Multilevel Analysis of Italian SMEs' Productivity," Spatial Economic Analysis, Taylor & Francis Journals, vol. 5(3), pages 299-316.
    26. Li, Kui-Wai & Zhou, Xianbo & Pan, Zhewen, 2016. "Cross-country output convergence and growth: Evidence from varying coefficient nonparametric method," Economic Modelling, Elsevier, vol. 55(C), pages 32-41.
    27. Giorgio Fazio & Enza Maltese, 2015. "Agglomeration Externalities and the Productivity of Italian Firms," Growth and Change, Wiley Blackwell, vol. 46(3), pages 354-378, September.
    28. Bartelsman, Eric J & Haskel, Jonathan & Martin, Ralf, 2008. "Distance to Which Frontier? Evidence on Productivity Convergence from International Firm-level Data," CEPR Discussion Papers 7032, C.E.P.R. Discussion Papers.
    29. S. Calligaris & M. Del Gatto & F. Hassan & G.I.P. Ottaviano & F. Schivardi, 2016. "Italy’s Productivity Conundrum. A Study on Resource Misallocation in Italy," European Economy - Discussion Papers 2015 - 030, Directorate General Economic and Financial Affairs (DG ECFIN), European Commission.
    30. Nazrul Islam, 2003. "What have We Learnt from the Convergence Debate?," Journal of Economic Surveys, Wiley Blackwell, vol. 17(3), pages 309-362, July.
    31. Stefan P.T. Groot & Henri L.F. Groot & Martijn J. Smit, 2014. "Regional Wage Differences In The Netherlands: Micro Evidence On Agglomeration Externalities," Journal of Regional Science, Wiley Blackwell, vol. 54(3), pages 503-523, June.
    32. Chevalier, Paul-Antoine & Lecat, Rémy & Oulton, Nicholas, 2012. "Convergence of firm-level productivity, globalisation and information technology: Evidence from France," Economics Letters, Elsevier, vol. 116(2), pages 244-246.
    33. Fiona Steele, 2008. "Multilevel models for longitudinal data," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 171(1), pages 5-19, January.
    34. Robert J. Barro & Xavier Sala-i-Martin, 1991. "Convergence across States and Regions," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 22(1), pages 107-182.
    35. Francesco Aiello & Vincenzo Scoppa, 2000. "Uneven Regional Development in Italy: Explaining Differences in Productivity Levels," Giornale degli Economisti, GDE (Giornale degli Economisti e Annali di Economia), Bocconi University, vol. 59(2), pages 270-298, September.
    36. Azomahou, Théophile T. & El ouardighi, Jalal & Nguyen-Van, Phu & Pham, Thi Kim Cuong, 2011. "Testing convergence of European regions: A semiparametric approach," Economic Modelling, Elsevier, vol. 28(3), pages 1202-1210, May.
    37. Dani Rodrik, 2013. "Unconditional Convergence in Manufacturing," The Quarterly Journal of Economics, Oxford University Press, vol. 128(1), pages 165-204.
    38. Anthony J. Venables, 2011. "Productivity in cities: self-selection and sorting," Journal of Economic Geography, Oxford University Press, vol. 11(2), pages 241-251, March.
    39. Kremer, Kristen P. & Flower, Andrea & Huang, Jin & Vaughn, Michael G., 2016. "Behavior problems and children's academic achievement: A test of growth-curve models with gender and racial differences," Children and Youth Services Review, Elsevier, vol. 67(C), pages 95-104.
    40. Peter Egger & Michael Pfaffermayr, 2009. "On Testing Conditional Sigma – Convergence," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 71(4), pages 453-473, August.
    41. Alberto Díaz Dapena & Fernando Rubiera Morollón & Dusan Paredes Araya, 2017. "Are there different local patterns of convergence concealed beneath the regional level? An analysis for US states and counties using a multilevel approach," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 58(3), pages 623-640, May.
    42. Arbia, G. & Espa, G. & Giuliani, D. & Mazzitelli, A., 2012. "Clusters of firms in an inhomogeneous space: The high-tech industries in Milan," Economic Modelling, Elsevier, vol. 29(1), pages 3-11.
    43. Arbia, Giuseppe & Espa, Giuseppe & Giuliani, Diego & Mazzitelli, Andrea, 2010. "Detecting the existence of space-time clustering of firms," Regional Science and Urban Economics, Elsevier, vol. 40(5), pages 311-323, September.
    44. Stefan P.T. Groot & Henri L.F. Groot & Martijn J. Smit, 2014. "Regional Wage Differences In The Netherlands: Micro Evidence On Agglomeration Externalities," Journal of Regional Science, Wiley Blackwell, vol. 54(3), pages 503-523, June.
    45. Marian Rizov & Xufei Zhang, 2014. "Regional disparities and productivity in China: Evidence from manufacturing micro data," Papers in Regional Science, Wiley Blackwell, vol. 93(2), pages 321-339, June.
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    Cited by:

    1. Hałka, Aleksandra & Leszczyńska-Paczesna, Agnieszka, 2019. "Price convergence in the European Union – What has changed?," Economic Modelling, Elsevier, vol. 79(C), pages 226-241.

    More about this item

    Keywords

    Convergence analysis; Hierarchical longitudinal data; Growth curves; European convergence; Italian convergence;

    JEL classification:

    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models
    • O47 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - Empirical Studies of Economic Growth; Aggregate Productivity; Cross-Country Output Convergence
    • R11 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Regional Economic Activity: Growth, Development, Environmental Issues, and Changes

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