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General Pattern Formation in Recursive Dynamical Systems Models in Economics

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  • Anastasios Xepapadeas

    (Athens University of Economics and Business and Beijer Fellow)

  • William Brock

    (University of Wisconsin and Beijer Fellow)

Abstract

This paper presents a fairly general treatment of recursive infinite horizon forward looking optimizing systems on infinite dimensional spatial domains. It includes optimal control, an analysis of local stability of spatially flat optimal steady states and development of techniques to compute spatially heterogeneous optimal steady states. The paper also develops a concept of rational expectations equilibrium, a local stability analysis for spatially homogeneous rational expectations steady states, and computational techniques for spatially heterogeneous rational expectations steady states.

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Bibliographic Info

Paper provided by Fondazione Eni Enrico Mattei in its series Working Papers with number 2009.49.

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Date of creation: Jun 2009
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Handle: RePEc:fem:femwpa:2009.49

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Keywords: Pattern Formation; Spatial Spillovers; Optimal Control; Spillover Induced Instability; Growth Models;

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References

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  1. Boucekkine, Raouf & Camacho, Carmen & Zou, Benteng, 2009. "Bridging The Gap Between Growth Theory And The New Economic Geography: The Spatial Ramsey Model," Macroeconomic Dynamics, Cambridge University Press, vol. 13(01), pages 20-45, February.
  2. Robert E. Lucas, Jr., 2001. "Externalities and Cities," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 4(2), pages 245-274, April.
  3. Aghion, Philippe & Howitt, Peter, 1992. "A Model of Growth Through Creative Destruction," Scholarly Articles 12490578, Harvard University Department of Economics.
  4. Brock, William & Xepapadeas, Anastasios, 2008. "Diffusion-induced instability and pattern formation in infinite horizon recursive optimal control," Journal of Economic Dynamics and Control, Elsevier, vol. 32(9), pages 2745-2787, September.
  5. Jones, Charles I, 1995. "R&D-Based Models of Economic Growth," Journal of Political Economy, University of Chicago Press, vol. 103(4), pages 759-84, August.
  6. Aghion, P. & Howitt, P., 1989. "A Model Of Growth Through Creative Destruction," Working papers 527, Massachusetts Institute of Technology (MIT), Department of Economics.
  7. Paul Romer, 1989. "Endogenous Technological Change," NBER Working Papers 3210, National Bureau of Economic Research, Inc.
  8. Danny Quah, 2002. "Spatial Agglomeration Dynamics," American Economic Review, American Economic Association, vol. 92(2), pages 247-252, May.
  9. Lucas, Robert Jr., 1988. "On the mechanics of economic development," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 3-42, July.
  10. Baldwin, Richard & Martin, Philippe, 2003. "Agglomeration and Regional Growth," CEPR Discussion Papers 3960, C.E.P.R. Discussion Papers.
  11. Ron Martin & Peter Sunley, 2003. "Deconstructing clusters: chaotic concept or policy panacea?," Journal of Economic Geography, Oxford University Press, vol. 3(1), pages 5-35, January.
  12. Romer, Paul M, 1986. "Increasing Returns and Long-run Growth," Journal of Political Economy, University of Chicago Press, vol. 94(5), pages 1002-37, October.
  13. Yannis Ioannides & Henry G. Overman, 2000. "Spatial evolution of the US urban system," LSE Research Online Documents on Economics 20138, London School of Economics and Political Science, LSE Library.
  14. Gianmarco Ottaviano, 1996. "Monopolistic Competition, Trade and Endogenous Spatial Fluctuations," Working Papers 240, Dipartimento Scienze Economiche, Universita' di Bologna.
  15. Alexandre Scheinkman, Jose, 1976. "On optimal steady states of n-sector growth models when utility is discounted," Journal of Economic Theory, Elsevier, vol. 12(1), pages 11-30, February.
  16. Brock, William & Xepapadeas, Anastasios, 2008. "Pattern Formation, Spatial Externalities and Regulation in Coupled Economic-Ecological Systems," MPRA Paper 9105, University Library of Munich, Germany.
  17. Grossman, G.M. & Helpman, E., 1989. "Quality Ladders And Product Cycles," Papers 39-89, Tel Aviv.
  18. Desmet, Klaus & Rossi-Hansberg, Esteban, 2009. "Spatial growth and industry age," Journal of Economic Theory, Elsevier, vol. 144(6), pages 2477-2502, November.
  19. Baldwin, Richard E., 2001. "Core-periphery model with forward-looking expectations," Regional Science and Urban Economics, Elsevier, vol. 31(1), pages 21-49, February.
  20. Chincarini, Ludwig & Asherie, Neer, 2008. "An analytical model for the formation of economic clusters," Regional Science and Urban Economics, Elsevier, vol. 38(3), pages 252-270, May.
  21. McKenzie, Lionel W., 1979. "Optimal Economic Growth and Turnpike Theorems," Working Papers 267, California Institute of Technology, Division of the Humanities and Social Sciences.
  22. Robert E. Lucas & Esteban Rossi-Hansberg, 2002. "On the Internal Structure of Cities," Econometrica, Econometric Society, vol. 70(4), pages 1445-1476, July.
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Cited by:
  1. Raouf Boucekkine & Carmen Camacho & Giorgio Fabbri, 2013. "Spatial dynamics and convergence: The spatial AK model," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00827641, HAL.
  2. Breinlich, Holger & Ottaviano, Gianmarco I.P. & Temple, Jonathan R.W., 2014. "Regional Growth and Regional Decline," Handbook of Economic Growth, in: Handbook of Economic Growth, edition 1, volume 2, chapter 4, pages 683-779 Elsevier.
  3. Carmen Camacho & Agustín Pérez-Barahona, 2012. "Land use dynamics and the environment," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00674020, HAL.
  4. repec:hal:journl:halshs-00674020 is not listed on IDEAS

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