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Differentiability and comparative analysis in discrete-time infinite-horizon optimization

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  • Santos, Manuel S.

Abstract

In this note I consider a family of discrete-time intertemporally separable optimization problems with unbounded horizon in which the objective is parameterized by a finite dimensional vector. Under standard assumptions, I show that optimal solutions vary smoothly with the initial state and the vector of parameters. These results provide a basic framework to develop the familiar methods of comparative analysis in a dynamic setting. Likewise, the local analysis of equilibria set out by Kehoe, Levine, and Romer [J. Econ. Theory50 (1990), 1–21] is extended here to economies with general equilibrium dynamics.

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  • Santos, Manuel S., 1992. "Differentiability and comparative analysis in discrete-time infinite-horizon optimization," Journal of Economic Theory, Elsevier, vol. 57(1), pages 222-229.
    • Handle: RePEc:eee:jetheo:v:57:y:1992:i:1:p:222-229
    DOI: 10.1016/S0022-0531(05)80049-3
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    1. Santos, Manuel S, 1991. "Smoothness of the Policy Function in Discrete Time Economic Models," Econometrica, Econometric Society, vol. 59(5), pages 1365-1382, September.
    2. Kehoe, Timothy J. & Levine, David K. & Romer, Paul M., 1990. "Determinacy of equilibria in dynamic models with finitely many consumers," Journal of Economic Theory, Elsevier, vol. 50(1), pages 1-21, February.
    3. Timothy J. Kehoe & David K. Levine & Paul Romer, 1989. "Steady States and Determinacy in Economies with Infinitely Lived Agents," Levine's Working Paper Archive 52, David K. Levine.
    4. Santos, M.S., 1989. "Differentiability And Comparative Analysis In Discrete-Time Infinite-Horizon Optimization Problems," UFAE and IAE Working Papers 127-89, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    5. Robert A. Becker, 1985. "Comparative Dynamics in Aggregate Models of Optimal Capital Accumulation," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 100(4), pages 1235-1256.
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    6. Cuong Le Van & Lisa Morhaim, 2006. "On optimal growth models when the discount factor is near 1 or equal to 1," International Journal of Economic Theory, The International Society for Economic Theory, vol. 2(1), pages 55-76, March.
    7. Fernández-Villaverde, J. & Rubio-Ramírez, J.F. & Schorfheide, F., 2016. "Solution and Estimation Methods for DSGE Models," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 527-724, Elsevier.
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    10. Christian Ghiglino & Marielle Olszak-Duquenne, 2005. "On The Impact Of Heterogeneity On Indeterminacy," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 46(1), pages 171-188, February.
    11. Joël Blot & Bertrand Crettez, 2004. "On the smoothness of optimal paths," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 27(1), pages 1-34, August.
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    14. Yu Chen & Thomas Cosimano & Alex Himonas, 2010. "Continuous time one-dimensional asset-pricing models with analytic price–dividend functions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(3), pages 461-503, March.
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