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Necessity of the Transversality Condition for Stochastic Models with CRRA Utility

Author

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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 constant-relative-risk-aversion (CRRA) utility under 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 and CRRA utility. We establish two results. The first result is that the STVC is necessary in the case of logarithmic utility. The second result is that 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 (RBC) models with endogenous labor supply. Our results make it clear that there is practically no issue about necessity of the STVC for stochastic models with CRRA utility.

Suggested Citation

  • Takashi Kamihigashi, 2003. "Necessity of the Transversality Condition for Stochastic Models with CRRA Utility," Discussion Paper Series 137, Research Institute for Economics & Business Administration, Kobe University.
    • Handle: RePEc:kob:dpaper:137
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    File URL: https://www.rieb.kobe-u.ac.jp/academic/ra/dp/English/dp137.pdf
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    References listed on IDEAS

    as
    1. Kamihigashi, Takashi, 2003. "Necessity of transversality conditions for stochastic problems," Journal of Economic Theory, Elsevier, vol. 109(1), pages 140-149, March.
    2. William A. Brock & Leonard J. Mirman, 2001. "Optimal Economic Growth And Uncertainty: The Discounted Case," Chapters, in: W. D. Dechert (ed.), Growth Theory, Nonlinear Dynamics and Economic Modelling, chapter 1, pages 3-37, Edward Elgar Publishing.
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    7. Kamihigashi, Takashi, 2001. "Necessity of Transversality Conditions for Infinite Horizon Problems," Econometrica, Econometric Society, vol. 69(4), pages 995-1012, July.
    8. 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.
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    Citations

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    Cited by:

    1. Benhabib, Jess & Evans, George W. & Honkapohja, Seppo, 2014. "Liquidity traps and expectation dynamics: Fiscal stimulus or fiscal austerity?," Journal of Economic Dynamics and Control, Elsevier, vol. 45(C), pages 220-238.
    2. 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.
    3. Marco Bassetto & Thomas J. Sargent, 2020. "Shotgun Wedding: Fiscal and Monetary Policy," Annual Review of Economics, Annual Reviews, vol. 12(1), pages 659-690, August.
    4. 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.
    5. Takashi Kamihigashi, 2017. "Regime-Switching Sunspot Equilibria in a One-Sector Growth Model with Aggregate Decreasing Returns and Small Externalities," Studies in Economic Theory, in: Kazuo Nishimura & Alain Venditti & Nicholas C. Yannelis (ed.), Sunspots and Non-Linear Dynamics, chapter 0, pages 125-146, Springer.
    6. 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.
    7. Masataka Eguchi & Toshiya Hatano, 2023. "What is fiscal sustainability?―Transversality condition, Domar condition, the fiscal theory of the price level―," Public Policy Review, Policy Research Institute, Ministry of Finance Japan, vol. 19(3), pages 1-29, September.
    8. Marco Bassetto & Wei Cui, 2018. "The Fiscal Theory of the Price Level in an Environment of Low Interest Rates," 2018 Meeting Papers 574, Society for Economic Dynamics.
    9. Tapan Mitra & Santanu Roy, 2022. "Propensity to consume and the optimality of Ramsey–Euler policies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(1), pages 55-89, February.
    10. Ravi Kashyap, 2016. "Solving the Equity Risk Premium Puzzle and Inching Towards a Theory of Everything," Papers 1604.04872, arXiv.org, revised Sep 2019.
    11. Bassetto, Marco & Cui, Wei, 2018. "The fiscal theory of the price level in a world of low interest rates," Journal of Economic Dynamics and Control, Elsevier, vol. 89(C), pages 5-22.
    12. 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.
    13. Plantin, Guillaume & Barthélemy, Jean & Mengus, Eric, 2019. "Public Liquidity Demand and Central Bank Independence," CEPR Discussion Papers 14160, C.E.P.R. Discussion Papers.
    14. Takashi Kamihigashi, 2015. "A Simple No-Bubble Theorem," Discussion Paper Series DP2015-03, Research Institute for Economics & Business Administration, Kobe University.
    15. 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.
    16. Benhabib, Jess & Evans, George W. & Honkapohja, Seppo, 2014. "Liquidity traps and expectation dynamics: Fiscal stimulus or fiscal austerity?," Journal of Economic Dynamics and Control, Elsevier, vol. 45(C), pages 220-238.
    17. Mitra, Tapan & Roy, Santanu, 2017. "Optimality of Ramsey–Euler policy in the stochastic growth model," Journal of Economic Theory, Elsevier, vol. 172(C), pages 1-25.

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    More about this item

    Keywords

    Transversality condition; Stochastic optimization; Stochastic growth; CRRA; Real business cycle;
    All these keywords.

    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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