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Necessity of the transversality condition for stochastic models with bounded or CRRA utility

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  • Kamihigashi, Takashi

Abstract

This paper shows that the standard transversality condition (STVC) is necessary for optimality for stochastic models with bounded or constant-relative-risk-aversion (CRRA) utility under fairly general conditions. We consider an infinite-horizon stochastic maximization problem that takes a general form of multi-sector growth model with a single consumption good. We establish three results: (i) the STVC is necessary if utility is bounded; (ii) the STVC is necessary if utility is logarithmic; and (iii) the STVC is necessary in the case of non-logarithmic CRRA utility as long as lifetime utility is finite at the optimum. These results apply to various stochastic growth models, including real business cycle models with endogenous labor supply. Since unbounded utility functions that do not belong to the CRRA class are rather rare in applications, our results provide a fairly complete set of solutions regarding necessity of the STVC in practice.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Dynamics and Control.

Volume (Year): 29 (2005)
Issue (Month): 8 (August)
Pages: 1313-1329

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Handle: RePEc:eee:dyncon:v:29:y:2005:i:8:p:1313-1329

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  1. Zilcha, Itzhak, 1976. "Characterization by prices of optimal programs under uncertainty," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 173-183, July.
  2. Brock, William A. & Mirman, Leonard J., 1972. "Optimal economic growth and uncertainty: The discounted case," Journal of Economic Theory, Elsevier, vol. 4(3), pages 479-513, June.
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  4. Foldes, Lucien, 1978. "Martingale conditions for optimal saving-discrete time," Journal of Mathematical Economics, Elsevier, vol. 5(1), pages 83-96, March.
  5. Takashi Kamihigashi, 2000. "A simple proof of Ekeland and Scheinkman's result on the necessity of a transversality condition," Economic Theory, Springer, vol. 15(2), pages 463-468.
  6. Benhabib, Jess & Farmer, Roger E.A., 1999. "Indeterminacy and sunspots in macroeconomics," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 6, pages 387-448 Elsevier.
  7. King, Robert G. & Rebelo, Sergio T., 1999. "Resuscitating real business cycles," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 14, pages 927-1007 Elsevier.
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  13. Takashi Kamihigashi, 2000. "Necessity of Transversality Conditions for Stochastic Problems," Discussion Paper Series 115, Research Institute for Economics & Business Administration, Kobe University.
  14. Takashi Kamihigashi, 2001. "A Simple Proof of the Necessity of the Transversality Condition," Discussion Paper Series 116, Research Institute for Economics & Business Administration, Kobe University.
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Cited by:
  1. Karim Azizi & Nicolas Canry & Jean-Bernard Chatelain & Bruno Tinel, 2012. "Are No-Ponzi Game and Transversality Conditions Relevant for Public Debt? A Keynesian Appraisal," Working Papers wp296, Political Economy Research Institute, University of Massachusetts at Amherst.
  2. repec:hal:journl:halshs-00706777 is not listed on IDEAS
  3. Takashi Kamihigashi, 2014. "Multiple Interior Steady States in the Ramsey Model with Elastic Labor Supply," Discussion Paper Series DP2014-11, Research Institute for Economics & Business Administration, Kobe University.
  4. Jean-Bernard Chatelain & Kirsten Ralf, 2012. "The Failure Of Financial Macroeconomics And What To Do About It," Manchester School, University of Manchester, vol. 80, pages 21-53, 09.
  5. repec:hal:cesptp:hal-00818474 is not listed on IDEAS
  6. Azizi, Karim & Canry, Nicolas & Chatelain, Jean-Bernard & Tinel, Bruno, 2013. "Government Solvency, Austerity and Fiscal Consolidation in the OECD: A Keynesian Appraisal of Transversality and No Ponzi Game Conditions," EconStor Preprints 72550, ZBW - German National Library of Economics.
  7. Takashi Kamihigashi, 2006. "Transversality Conditions and Dynamic Economic Behavior," Discussion Paper Series 180, Research Institute for Economics & Business Administration, Kobe University.
  8. repec:hal:wpaper:hal-00818474 is not listed on IDEAS
  9. Travis D. Nesmith, 2005. "Solving stochastic money-in-the-utility-function models," Finance and Economics Discussion Series 2005-52, Board of Governors of the Federal Reserve System (U.S.).

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