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The Inverse Optimal Problem: A Dynamic Programming Approach

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  • Chang, Fwu-Ranq

Abstract

This paper solves the stochastic inverse optimal problem. Dynamic programming is used to transform the origina l problem into a differential equation. A solution exists for any pro duction function with a finite slope at the origin provided the savin gs function, starting from the origin, is steep initially and flat ev entually. Three consumption functions-linear, Keynes-ian, and Cantabr igian-are also studied with a Cobb-Douglas production technology. A w ell-known result in discrete time models-that a logarithmic utility f unction and a Cobb-Douglas production function imply a Keynesian cons umption function-does not carry through to the continuous time case. Copyright 1988 by The Econometric Society.

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  • Chang, Fwu-Ranq, 1988. "The Inverse Optimal Problem: A Dynamic Programming Approach," Econometrica, Econometric Society, vol. 56(1), pages 147-172, January.
    • Handle: RePEc:ecm:emetrp:v:56:y:1988:i:1:p:147-72
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    Cited by:

    1. Josa-Fombellida, Ricardo & Rincón-Zapatero, Juan Pablo, 2008. "Markov Perfect Nash Equilibrium in stochastic differential games as solution of a generalized Euler Equations System," UC3M Working papers. Economics we086731, Universidad Carlos III de Madrid. Departamento de Economía.
    2. Posch, Olaf, 2009. "Structural estimation of jump-diffusion processes in macroeconomics," Journal of Econometrics, Elsevier, vol. 153(2), pages 196-210, December.
    3. Cassou, Steven P. & Lansing, Kevin J., 1998. "Optimal fiscal policy, public capital, and the productivity slowdown," Journal of Economic Dynamics and Control, Elsevier, vol. 22(6), pages 911-935, June.
    4. Danyang Xie, 2002. "Explicit Transitional Dynamics in Growth Models," GE, Growth, Math methods 0207003, University Library of Munich, Germany.
    5. Fiaschi, Davide & Marsili, Matteo, 2012. "Distribution of wealth and incomplete markets: Theory and empirical evidence," Journal of Economic Behavior & Organization, Elsevier, vol. 81(1), pages 243-267.
    6. Fwu‐Ranq Chang, 2009. "Optimal growth and impatience: A phase diagram analysis," International Journal of Economic Theory, The International Society for Economic Theory, vol. 5(2), pages 245-255, June.
    7. Joshi, Sumit, 1998. "A framework to analyze comparative dynamics in a continuous time stochastic growth model," Economic Modelling, Elsevier, vol. 15(1), pages 125-134, January.
    8. Antoniadou, Elena & Koulovatianos, Christos & Mirman, Leonard J., 2013. "Strategic exploitation of a common-property resource under uncertainty," Journal of Environmental Economics and Management, Elsevier, vol. 65(1), pages 28-39.
    9. Posch, Olaf & Trimborn, Timo, 2013. "Numerical solution of dynamic equilibrium models under Poisson uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2602-2622.
    10. Olaf Posch & Klaus Wälde, 2011. "On the link between volatility and growth," Journal of Economic Growth, Springer, vol. 16(4), pages 285-308, December.
    11. Ngo Long & Gerhard Sorger, 2010. "A dynamic principal-agent problem as a feedback Stackelberg differential game," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 18(4), pages 491-509, December.
    12. Posch, Olaf & Trimborn, Timo, 2010. "Numerical solution of continuous-time DSGE models under Poisson uncertainty," Hannover Economic Papers (HEP) dp-450, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    13. Kehoe, Timothy J & Levine, David K & Romer, Paul M, 1992. "On Characterizing Equilibria of Economies with Externalities and Taxes as Solutions to Optimization Problems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 2(1), pages 43-68, January.
    14. Robert Feicht & Wolfgang Stummer, 2010. "Complete Closed-form Solution to a Stochastic Growth Model and Corresponding Speed of Economic Recovery preliminary," DEGIT Conference Papers c015_041, DEGIT, Dynamics, Economic Growth, and International Trade.
    15. Guo Jang-Ting & Lansing Kevin J, 2003. "Globally-Stabilizing Fiscal Policy Rules," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 7(2), pages 1-15, July.
    16. Ricardo Josa-Fombellida & Juan Rincón-Zapatero, 2015. "Euler–Lagrange equations of stochastic differential games: application to a game of a productive asset," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 59(1), pages 61-108, May.
    17. Posch, Olaf, 2011. "Explaining output volatility: The case of taxation," Journal of Public Economics, Elsevier, vol. 95(11), pages 1589-1606.
    18. Rebelo, Sergio & Xie, Danyang, 1999. "On the optimality of interest rate smoothing," Journal of Monetary Economics, Elsevier, vol. 43(2), pages 263-282, April.
    19. Lansing, Kevin J., 1999. "Optimal redistributive capital taxation in a neoclassical growth model," Journal of Public Economics, Elsevier, vol. 73(3), pages 423-453, September.
    20. Christensen, Bent Jesper & Posch, Olaf & van der Wel, Michel, 2016. "Estimating dynamic equilibrium models using mixed frequency macro and financial data," Journal of Econometrics, Elsevier, vol. 194(1), pages 116-137.

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