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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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  1. Aghion, P. & Howitt, P., 1990. "A Model Of Growth Through Creative Destruction," DELTA Working Papers, DELTA (Ecole normale supérieure) 90-12, DELTA (Ecole normale supérieure).
  2. Chincarini, Ludwig & Asherie, Neer, 2008. "An analytical model for the formation of economic clusters," Regional Science and Urban Economics, Elsevier, Elsevier, vol. 38(3), pages 252-270, May.
  3. Ottaviano, Gianmarco I. P., 2001. "Monopolistic competition, trade, and endogenous spatial fluctuations," Regional Science and Urban Economics, Elsevier, Elsevier, vol. 31(1), pages 51-77, February.
  4. Romer, Paul M, 1986. "Increasing Returns and Long-run Growth," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 94(5), pages 1002-37, October.
  5. Yannis Ioannides & Henry G. Overman, 2004. "Spatial evolution of the US urban system," LSE Research Online Documents on Economics, London School of Economics and Political Science, LSE Library 600, London School of Economics and Political Science, LSE Library.
  6. 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.
  7. Grossman, Gene M & Helpman, Elhanan, 1991. "Quality Ladders and Product Cycles," The Quarterly Journal of Economics, MIT Press, MIT Press, vol. 106(2), pages 557-86, May.
  8. Paul M Romer, 1999. "Endogenous Technological Change," Levine's Working Paper Archive 2135, David K. Levine.
  9. Jones, Charles I, 1995. "R&D-Based Models of Economic Growth," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 103(4), pages 759-84, August.
  10. 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, Cambridge University Press, vol. 13(01), pages 20-45, February.
  11. Klaus Desmet & Esteban Rossi-Hansberg, 2007. "Spatial Growth and Industry Age," NBER Working Papers 13302, National Bureau of Economic Research, Inc.
  12. Baldwin, Richard E. & Martin, Philippe, 2004. "Agglomeration and regional growth," Handbook of Regional and Urban Economics, Elsevier, in: J. V. Henderson & J. F. Thisse (ed.), Handbook of Regional and Urban Economics, edition 1, volume 4, chapter 60, pages 2671-2711 Elsevier.
  13. Aghion, Philippe & Howitt, Peter, 1992. "A Model of Growth Through Creative Destruction," Scholarly Articles 12490578, Harvard University Department of Economics.
  14. Quah, Danny, 2002. "Spatial Agglomeration Dynamics," CEPR Discussion Papers, C.E.P.R. Discussion Papers 3208, C.E.P.R. Discussion Papers.
  15. Baldwin, Richard E., 2001. "Core-periphery model with forward-looking expectations," Regional Science and Urban Economics, Elsevier, Elsevier, vol. 31(1), pages 21-49, February.
  16. Brock, William & Xepapadeas, Anastasios, 2008. "Diffusion-induced instability and pattern formation in infinite horizon recursive optimal control," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 32(9), pages 2745-2787, September.
  17. Robert E. Lucas & Esteban Rossi-Hansberg, 2002. "On the Internal Structure of Cities," Econometrica, Econometric Society, Econometric Society, vol. 70(4), pages 1445-1476, July.
  18. McKenzie, Lionel W., 1979. "Optimal Economic Growth and Turnpike Theorems," Working Papers, California Institute of Technology, Division of the Humanities and Social Sciences 267, California Institute of Technology, Division of the Humanities and Social Sciences.
  19. Brock, William & Xepapadeas, Anastasios, 2010. "Pattern formation, spatial externalities and regulation in coupled economic-ecological systems," Journal of Environmental Economics and Management, Elsevier, vol. 59(2), pages 149-164, March.
  20. Ron Martin & Peter Sunley, 2003. "Deconstructing clusters: chaotic concept or policy panacea?," Journal of Economic Geography, Oxford University Press, Oxford University Press, vol. 3(1), pages 5-35, January.
  21. Lucas, Robert Jr., 1988. "On the mechanics of economic development," Journal of Monetary Economics, Elsevier, Elsevier, vol. 22(1), pages 3-42, July.
  22. Alexandre Scheinkman, Jose, 1976. "On optimal steady states of n-sector growth models when utility is discounted," Journal of Economic Theory, Elsevier, Elsevier, vol. 12(1), pages 11-30, February.
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Cited by:
  1. Carmen Camacho & Agustín Pérez-Barahona, 2012. "Land use dynamics and the environment," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00674020, HAL.
  2. Holger Breinlich & Gianmarco I. P. Ottaviano & Jonathan R. W. Temple, 2013. "Regional Growth and Regional Decline," CEP Discussion Papers dp1232, Centre for Economic Performance, LSE.
  3. Raouf Boucekkine & Carmen Camacho & Giorgio Fabbri, 2013. "Spatial dynamics and convergence: The spatial AK model," Documents de recherche, Centre d'Études des Politiques Économiques (EPEE), Université d'Evry Val d'Essonne 13-09, Centre d'Études des Politiques Économiques (EPEE), Université d'Evry Val d'Essonne.
  4. repec:hal:journl:halshs-00674020 is not listed on IDEAS

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