Journal of Geographical Systems

, Volume 9, Issue 4, pp 311–344 | Cite as

Nonlinear regional economic dynamics: continuous-time specification, estimation and stability analysis

  • Gianfranco Piras
  • Kieran P. Donaghy
  • Giuseppe Arbia
Original Article

Abstract

This paper presents an innovative approach to the study of regional economic dynamics within a nonlinear continuous-time econometric framework—a generalized specification of the Lotka–Volterra system of equations. This specification, which accounts for interdependent behavior of three industrial sectors and spillover effects of activities in neighboring regions, is employed in an analysis of five Italian regions between 1980 and 2003. For these regions, we report estimation results, characterize the varying systems dynamics, analyze the models’ local and global stability properties, and determine via sensitivity analyses which structural features appear to exert the greatest influence on these properties.

Keywords

Regional dynamics Continuous-time econometrics Generalized Lotka–Volterra system Local and global stability analysis 

JEL Classification

O18 O41 C31 C33 C61 C62 

Notes

Acknowledgments

We are grateful to Jean Paelinck and two anonymous referees for their constructive comments, criticisms, and suggestions for improvement. The usual disclaimers apply.

References

  1. Arbia G, Paelinck JHP (2003) Economic convergence or divergence? Modeling the interregional dynamics of EU regions, 1985–1999. J Geogr Syst 5:291–314CrossRefGoogle Scholar
  2. Barro RJ, Sala-I-Martin X (1995) Economic growth. McGraw-Hill, New YorkGoogle Scholar
  3. Carlberg M (1980) A Leontief model of interregional economic growth. J Reg Sci 20:30–40CrossRefGoogle Scholar
  4. Cramer JS (1986) Econometric applications of maximum likelihood methods. Cambridge University Press, CambridgeGoogle Scholar
  5. Dendrinos DS, Mullally H (1985) Studies in the mathematical ecology of cities. Oxford University Press, OxfordGoogle Scholar
  6. Dendrinos DS, Sonis M (1986) Variational principles and conservation conditions in Volterra’s ecology and in urban relative dynamics. J Reg Sci 26:359–377CrossRefGoogle Scholar
  7. Donaghy K (2000) General stability analysis of a non-linear dynamic model. In: Reggiani A (eds) Spatial economic science. Springer, Berlin, pp 243–257Google Scholar
  8. Donaghy K, Dall’erba S (2004) Structural and spatial aspects of regional inequality in Spain. Paper presented at the North American Meetings of the Regional Science Association International, November, Seattle WashingtonGoogle Scholar
  9. Fingleton B (2001) Equilibrium and economic growth: spatial econometric models and simulations. J Reg Sci 41:117–147CrossRefGoogle Scholar
  10. Fisher FM (1966) The identification problem in econometrics. McGraw-Hill, New YorkGoogle Scholar
  11. Frisch R (1933) Editorial. Econometrica 1:2CrossRefGoogle Scholar
  12. Gandolfo G (1980) Economic dynamics: methods and models, 2nd Revised edn. North-Holland Publishing Company, AmsterdamGoogle Scholar
  13. Hahn W (1963) Theory and applications of Lyapunov’s direct method. Prentice-Hall, Englewood CliffsGoogle Scholar
  14. La Salle J, Lefschetz S (1961) Stability analysis by Lyapunov’s direct methods. Academic, New YorkGoogle Scholar
  15. Lotka A (1932) The Growth of mixed populations: Two species competing for a common food supply. In: Scudo F, Ziegler J (eds) The golden age of theoretical ecology: 1923–1940. Lecture Notes in Biomathematics, vol 22. Springer, Heidelberg, (1978) 274–286Google Scholar
  16. Medio A (1992) Chaotic dynamics: theory and applications to economics. Cambridge University Press, CambridgeGoogle Scholar
  17. Paelinck JHP (1992) De l’économètrie spatiale aux nouvelles dynamiques spatialisées. In: Derycke PH (ed) Espace et dynamiques territoriales. Economica, Paris, pp 137–154Google Scholar
  18. Paelinck JHP (2005) Lotka–Volterra models revisited: A mixed specification with endogenous generated SDLS-variables, and a finite automaton version. Paper presented to the North American Meetings of the Regional Science Association International, November, Las VegasGoogle Scholar
  19. Piras G, Donaghy K, Arbia G (2005) Continuous-time regional convergence: A comparison of various estimation procedures. Paper presented to the North American Meetings of the Regional Science Association International, November, Las VegasGoogle Scholar
  20. Puga D (2001) European regional policies in light of recent location theories. CEPR Discussion Paper 2767Google Scholar
  21. Samuelson P (1971) Generalized predator–prey oscillations in ecological and economic equilibrium. Proc Natl Acad Sci 68:980–983CrossRefGoogle Scholar
  22. Sargan JD (1983) Identification of models with autoregressive errors. In: Karlin S, Amemya T, Goodman L (eds) Studies in econometric time series and multivariate statistics. Academic, New York, pp 169–205Google Scholar
  23. Sydsaeter K, Strøm A, Berck P (1999) Economists’ mathematical manual, 3rd edn. Springer, BerlinGoogle Scholar
  24. Volterra V (1926) Variations and fluctuations in the numbers of coexisting animal species. In: Scudo F, Ziegler J (eds) The golden age of theoretical ecology: 1923–1940. Lecture Notes in Biomathematics, vol 22. Springer, Berlin (1978), pp 11–17Google Scholar
  25. Wymer CR (1972) Econometric estimation of stochastic differential equation systems. Econometrica 40:565–577CrossRefGoogle Scholar
  26. Wymer CR (1982) Sensitivity analysis of economic policy. Presented at workshop on the application of sensitivity analysis to the evaluation of financial policies, World Bank, Washington. In: Gandolfo G, Marzano F (eds) (1987) Essays in memory of Vittorio Marrama. Giuffrè, Milano, pp 953–965Google Scholar
  27. Wymer CR (1993) Estimation of nonlinear continuous-time models from discrete data. In: Phillips PCB (ed) Models, methods, and applications of econometrics. Basil Blackwell, Cambridge, Mass, pp 91–114Google Scholar
  28. Wymer CR (1997) Structural non-linear continuous-time models in econometrics. Macroecon Dyn 1:518–548CrossRefGoogle Scholar
  29. Wymer CR (2004) WYSEA (Wymer System Estimation and Analysis) softwareGoogle Scholar

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • Gianfranco Piras
    • 1
  • Kieran P. Donaghy
    • 2
  • Giuseppe Arbia
    • 3
    • 4
  1. 1.REAL, UIUCUrbana-ChampaignUSA
  2. 2.Department of City and Regional PlanningCornell UniversityIthacaUSA
  3. 3.University of ChietiChietiItaly
  4. 4.LUISS University RomeRomeItaly

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