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General Pattern Formation in Recursive Dynamical Systems Models in Economics

Author

Listed:
  • 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.

Suggested Citation

  • Anastasios Xepapadeas & William Brock, 2009. "General Pattern Formation in Recursive Dynamical Systems Models in Economics," Working Papers 2009.49, Fondazione Eni Enrico Mattei.
  • Handle: RePEc:fem:femwpa:2009.49
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    References listed on IDEAS

    as
    1. Romer, Paul M, 1986. "Increasing Returns and Long-run Growth," Journal of Political Economy, University of Chicago Press, vol. 94(5), pages 1002-1037, October.
    2. M. Kurz, 1968. "The General Instability of a Class of Competitive Growth Processes," Review of Economic Studies, Oxford University Press, vol. 35(2), pages 155-174.
    3. Danny Quah, 2002. "Spatial Agglomeration Dynamics," American Economic Review, American Economic Association, vol. 92(2), pages 247-252, May.
    4. Ottaviano, Gianmarco I. P., 2001. "Monopolistic competition, trade, and endogenous spatial fluctuations," Regional Science and Urban Economics, Elsevier, vol. 31(1), pages 51-77, February.
    5. Gene M. Grossman & Elhanan Helpman, 1991. "Quality Ladders and Product Cycles," The Quarterly Journal of Economics, Oxford University Press, vol. 106(2), pages 557-586.
    6. 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.
    7. 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.
    8. Yannis M. Ioannides & Henry G. Overman, 2004. "Spatial evolution of the US urban system," Journal of Economic Geography, Oxford University Press, vol. 4(2), pages 131-156, April.
    9. Aghion, Philippe & Howitt, Peter, 1992. "A Model of Growth through Creative Destruction," Econometrica, Econometric Society, vol. 60(2), pages 323-351, March.
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    11. Romer, Paul M, 1990. "Endogenous Technological Change," Journal of Political Economy, University of Chicago Press, vol. 98(5), pages 71-102, October.
    12. Robert E. Lucas & Esteban Rossi-Hansberg, 2002. "On the Internal Structure of Cities," Econometrica, Econometric Society, vol. 70(4), pages 1445-1476, July.
    13. Baldwin, Richard E. & Martin, Philippe, 2004. "Agglomeration and regional growth," Handbook of Regional and Urban Economics,in: J. V. Henderson & J. F. Thisse (ed.), Handbook of Regional and Urban Economics, edition 1, volume 4, chapter 60, pages 2671-2711 Elsevier.
    14. 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.
    15. Jones, Charles I, 1995. "R&D-Based Models of Economic Growth," Journal of Political Economy, University of Chicago Press, vol. 103(4), pages 759-784, August.
    16. McKenzie, Lionel W., 1979. "Optimal Economic Growth and Turnpike Theorems," Working Papers 267, California Institute of Technology, Division of the Humanities and Social Sciences.
    17. 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.
    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.
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    21. 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.
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    Cited by:

    1. repec:hal:journl:halshs-00674020 is not listed on IDEAS
    2. Boucekkine, R. & Camacho, C. & Fabbri, G., 2013. "Spatial dynamics and convergence: The spatial AK model," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2719-2736.
    3. 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.
    4. Javier de Frutos & Guiomar Martín-Herrán, 2016. "Pollution control in a multiregional setting: a differential game with spatially distributed controls," Gecomplexity Discussion Paper Series 201601, Action IS1104 "The EU in the new complex geography of economic systems: models, tools and policy evaluation", revised Jan 2016.
    5. Camacho, Carmen & Pérez-Barahona, Agustín, 2015. "Land use dynamics and the environment," Journal of Economic Dynamics and Control, Elsevier, vol. 52(C), pages 96-118.

    More about this item

    Keywords

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

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

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