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Necessity of the Transversality Condition for Stochastic Models with Bounded or CRRA Utility

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  • Takashi Kamihigashi

    (Research Institute for Economics & Business Administration (RIEB), Kobe University, Japan)

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.

Suggested Citation

  • Takashi Kamihigashi, 2004. "Necessity of the Transversality Condition for Stochastic Models with Bounded or CRRA Utility," Discussion Paper Series 152, Research Institute for Economics & Business Administration, Kobe University.
  • Handle: RePEc:kob:dpaper:152
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    File URL: http://www.rieb.kobe-u.ac.jp/academic/ra/dp/English/dp152.pdf
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    Citations

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    Cited by:

    1. Takashi Kamihigashi, 2015. "Multiple interior steady states in the Ramsey model with elastic labor supply," International Journal of Economic Theory, The International Society for Economic Theory, vol. 11(1), pages 25-37, March.
    2. 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, September.
    3. 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.
    4. Takashi Kamihigashi, 2015. "A Simple No-Bubble Theorem for Deterministic Sequential Economies," Discussion Paper Series DP2015-38, Research Institute for Economics & Business Administration, Kobe University.
    5. Takashi Kamihigashi, 2006. "Transversality Conditions and Dynamic Economic Behavior," Discussion Paper Series 180, Research Institute for Economics & Business Administration, Kobe University.
    6. Vasilev, Aleksandar, 2015. "The welfare effect of at income tax reform: the case of Bulgaria. Technical Appendix," EconStor Research Reports 124168, ZBW - German National Library of Economics.
    7. Karim Azizi & Nicolas Canry & Jean-Bernard Chatelain & Bruno Tinel, 2013. "Government Solvency, Austerity and Fiscal Consolidation in the OECD: A Keynesian Appraisal of Transversality and No Ponzi Game Conditions," Working Papers hal-00818474, HAL.
    8. Takashi Kamihigashi, 2016. "A Simple Optimality-Based No-Bubble Theorem for Deterministic Sequential Economies," Discussion Paper Series DP2016-22, Research Institute for Economics & Business Administration, Kobe University.
    9. Takashi Kamihigashi, 2015. "Regime-Switching Sunspot Equilibria in a One-Sector Growth Model with Aggregate Decreasing Returns and Small Externalities," Discussion Paper Series DP2015-42, Research Institute for Economics & Business Administration, Kobe University.
    10. Takashi Kamihigashi, 2016. "A Generalization of Fatou's Lemma for Extended Real-Valued Functions on σ-Finite Measure Spaces: With an Application to Infinite-Horizon Optimization in Discrete Time," Discussion Paper Series DP2016-37, Research Institute for Economics & Business Administration, Kobe University, revised Jan 2017.
    11. Takashi Kamihigashi, 2015. "A Simple No-Bubble Theorem," Discussion Paper Series DP2015-03, Research Institute for Economics & Business Administration, Kobe University.
    12. 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.
    13. Kamihigashi, Takashi, 2018. "A Simple optimality-based no-bubble theorem for deterministic sequential economies with strictly monotone preferences," Mathematical Social Sciences, Elsevier, vol. 91(C), pages 36-41.
    14. Takashi Kamihigashi, 2015. "A Simple No-Bubble Theorem for Deterministic Dynamic Economies," Discussion Paper Series DP2015-24, Research Institute for Economics & Business Administration, Kobe University.
    15. 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.).
    16. repec:eee:jetheo:v:172:y:2017:i:c:p:1-25 is not listed on IDEAS
    17. repec:hal:journl:halshs-00825446 is not listed on IDEAS

    More about this item

    Keywords

    Transversality condition; Stochastic optimization; Stochastic growth; CRRA; Real business cycle;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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