Journal of Geographical Systems

, Volume 10, Issue 2, pp 109–139 | Cite as

Income distribution dynamics and cross-region convergence in Europe

Spatial filtering and novel stochastic kernel representations
  • Manfred M. Fischer
  • Peter Stumpner
Original Article


This paper presents a continuous version of the model of distribution dynamics to analyse the transition dynamics and implied long-run behaviour of the EU-27 NUTS-2 regions over the period 1995–2003. It departs from previous research in two respects: first, by introducing kernel estimation and three-dimensional stacked conditional density plots as well as highest density regions plots for the visualisation of the transition function, based on Hyndman et al. (J Comput Graph Stat 5(4):315–336, 1996), and second, by combining Getis’ spatial filtering view with kernel estimation to explicitly account for the spatial dimension of the growth process. The results of the analysis indicate a very slow catching-up of the poorest regions with the richer ones, a process of shifting away of a small group of very rich regions, and highlight the importance of geography in understanding regional income distribution dynamics.


Regional income Distribution dynamics Stochastic kernel estimation Spatial filtering EU-27 

JEL Classification

C14 D30 O18 O47 R11 



The authors gratefully acknowledge the grant no. P19025-G11 provided by the Austrian Science Fund (FWF). They also thank two anonymous referees for their comments which improved the quality of the paper. The calculations were done using a combination of the R package HDRCDE, provided by Rob Hyndman, and the PPA package, provided by Arthur Getis. Special thanks to Roberto Basile for providing the original stimulus to carry out this study.


  1. Abreu M, Groot HLF, Florax RJG (2004) Space and growth: a survey of empirical evidence and methods. Tinbergen Institute, Working Paper No TI04-129/3. Available at SSRN:
  2. Bashtannyk DM, Hyndman RJ (2001) Bandwidth selection for kernel conditional density estimation. Comput Stat Data Anal 36:279–298CrossRefGoogle Scholar
  3. Basile R (2006) Intra-distribution dynamics of regional per capita income in Europe: evidence from alternative conditional density estimators. Paper presented at the 53rd North-American meetings of the RSAI, November 2006, TorontoGoogle Scholar
  4. Bulli S (2001) Distribution dynamics and cross-country convergence: a new approach. Scottish J Polit Econ 48(2):226–243CrossRefGoogle Scholar
  5. Durlauf SN, Quah DT (1999) The new empirics of economic growth. In: Taylor JB, Woodford M (eds) Handbook of macroeconomics, vol 1. Elsevier, Amsterdam, pp 235–308Google Scholar
  6. Fan J, Yao Q, Tong H. (1996) Estimation of conditional densities and sensitivity measures in nonlinear dynamical systems. Biometrika 83(1): 189–206CrossRefGoogle Scholar
  7. Fingleton B (1997) Specification and testing of Markov chain models: an application to convergence in the European Union. Oxf Bull Econ Stat 59(3):385–403CrossRefGoogle Scholar
  8. Fingleton B (1999) Estimates of time to economic convergence: an analysis of regions of the European Union. Int Reg Sci Rev 22(1):5–34Google Scholar
  9. Fingleton B (ed) (2003) European regional growth. Springer, BerlinGoogle Scholar
  10. Fischer MM, Stirböck C (2006) Pan-European regional income growth and club-convergence. Ann Reg Sci 40(4):693–721CrossRefGoogle Scholar
  11. Friedman M (1992) Do old fallacies ever die? J Econ Literat 30(4):2129–2132Google Scholar
  12. Getis A (1990) Screening for spatial dependence in regression analysis. Pap Reg Sci Assoc 69:69–81CrossRefGoogle Scholar
  13. Getis A (1995) Spatial filtering in a regression framework: examples using data on urban crime, regional inequality, and government expenditures. In: Anselin L, Florax R (eds) New directions in spatial econometrics. Springer, Berlin, pp 172–188Google Scholar
  14. Getis A, Griffith DA (2002) Comparative spatial filtering in regression analysis. Geogr Anal 34(2):130–140CrossRefGoogle Scholar
  15. Getis A, Ord JK (1992) The analysis of spatial association by use of distance statistics. Geogr Anal 24(3):189–206Google Scholar
  16. Griffith DA (2006) Spatial autocorrelation and spatial filtering. Springer, BerlinGoogle Scholar
  17. Hall P, Wolff RC, Yao Q (1999) Methods for estimating a conditional distribution function. J Am Stat Assoc 94(445):154–163CrossRefGoogle Scholar
  18. Hyndman RJ (1996) Computing and graphing highest density regions. Am Stat 50(2):120–126CrossRefGoogle Scholar
  19. Hyndman RJ, Yao Q (2002) Nonparametric estimation and symmetry tests for conditional density functions. J Nonparam Stat 14(3):259–278CrossRefGoogle Scholar
  20. Hyndman RJ, Bashtannyk DM, Grunwald GK (1996) Estimating and visualizing conditional densities. J Comput Graph Stat 5(4):315–336CrossRefGoogle Scholar
  21. Islam N (2003) What have we learnt from the convergence debate? J Econ Surv 17(3):309–362CrossRefGoogle Scholar
  22. Johnson PA (2004) A continuous state space approach to “Convergence by parts”. Vassar College Economics Working Paper No. 54, Department of Economics, Vassar CollegeGoogle Scholar
  23. Jones CI (1997) On the evolution of the world income distribution. J Econ Perspect 11(3):19–36Google Scholar
  24. LeGallo J (2004) Space-time analysis of GDP disparities among European regions: a Markov chains approach. Int Reg Sci Rev 27(2):138–163CrossRefGoogle Scholar
  25. López-Bazo E, Vaya E, Mora AJ, Surinach J (1999) Regional economic dynamics and convergence in the European Union. Ann Reg Sci 33(3):343–370CrossRefGoogle Scholar
  26. Magrini S (1999) The evolution of income disparities among the regions of the European Union. Reg Sci Urban Econ 29(2):257–281CrossRefGoogle Scholar
  27. Magrini S (2004) Regional (di)convergence. In: Henderson JV, Thisse J-F (eds) Handbook of regional and urban economics. Elsevier, Amsterdam pp 2741–2796Google Scholar
  28. Ord JK, Getis A (1995) Local spatial autocorrelation statistics: distributional issues and an application. Geogr Anal 27(4):286–306Google Scholar
  29. Paap R, van Dijk HK (1998) Distribution and mobility of wealth of nations. Eur Econ Rev 42(7):1269–1293CrossRefGoogle Scholar
  30. Pittau MG, Zelli R (2006) Empirical evidence of income dynamics across EU regions. J Appl Econ 21:605–628CrossRefGoogle Scholar
  31. Quah DT (1993a) Empirical cross-section dynamics in economic-growth. Eur Econ Rev 37(2–3):426–434CrossRefGoogle Scholar
  32. Quah DT (1993b) Galtons fallacy and tests of the convergence hypothesis. Scand J Econ 95(4):427–443CrossRefGoogle Scholar
  33. Quah DT (1996a) Regional convergence clusters across Europe. Eur Econ Rev 40(3–5):951–958CrossRefGoogle Scholar
  34. Quah DT (1996b) Empirics for economic growth and convergence. Eur Econ Rev 40(6):1353–1375CrossRefGoogle Scholar
  35. Quah DT (1997a) Regional cohesion from local isolated actions: I Historical outcomes. Centre for Economic Performance, Discussion Paper No. 378, London School of EconomicsGoogle Scholar
  36. Quah DT (1997b) Regional cohesion from local isolated actions: II Conditioning. Centre for Economic Performance, Discussion Paper No. 379, London School of EconomicsGoogle Scholar
  37. Quah DT (1997c) Empirics for growth and distribution: stratification, polarization, and convergence clubs. J Econ Growth 2(1):27–59CrossRefGoogle Scholar
  38. Quah DT (1999) Regional cohesion from local isolated actions— historical outcomes, in study of the socio-economic impact of the projects financed by the cohesion fund—a modelling approach, vol 2. Office for Official Publications of the European Communities, LuxembourgGoogle Scholar
  39. Reichlin L (1999) Discussion of ‘Convergence as distribution dynamics’, by D Quah. In: Baldwin R, Cohen D, Sapir A, Venables A (eds) Market, integration, regionalism, and the global economy. Cambridge University Press, Cambridge, pp 328–335Google Scholar
  40. Rey SJ (2001) Spatial empirics for economic growth and convergence. Geogr Anal 33(3):195–214Google Scholar
  41. Rey SJ, Dev B (2006) σ-convergence in the presence of spatial effects. Pap Reg Sci 85(2):217–234CrossRefGoogle Scholar
  42. Rey SJ, Janikas MV (2005) Regional convergence, inequality and space. J Econ Geogr 5(2):155–176CrossRefGoogle Scholar
  43. Silverman BW (1986) Density estimation for statistics and data analysis. Chapman & Hall, London and New YorkGoogle Scholar
  44. Temple J (1999) The new growth evidence. J Econ Literat 37:112–156Google Scholar
  45. Wand MP, Jones MC (1995) Kernel smoothing. Chapman and Hall, LondonGoogle Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Institute for Economic Geography and GIScienceVienna University of Economics and Business AdministrationViennaAustria

Personalised recommendations