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Necessity of the Transversality Condition for Stochastic Models with 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 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.

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File URL: http://www.rieb.kobe-u.ac.jp/academic/ra/dp/English/dp137.pdf
File Function: First version, 2003
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Bibliographic Info

Paper provided by Research Institute for Economics & Business Administration, Kobe University in its series Discussion Paper Series with number 137.

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Length: 13 pages
Date of creation: May 2003
Date of revision:
Handle: RePEc:kob:dpaper:137

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Related research

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

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  1. 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.
  2. 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.
  3. Kamihigashi, Takashi, 2003. "Necessity of transversality conditions for stochastic problems," Journal of Economic Theory, Elsevier, vol. 109(1), pages 140-149, March.
  4. Halkin, Hubert, 1974. "Necessary Conditions for Optimal Control Problems with Infinite Horizons," Econometrica, Econometric Society, vol. 42(2), pages 267-72, March.
  5. Alvarez, Fernando & Stokey, Nancy L., 1998. "Dynamic Programming with Homogeneous Functions," Journal of Economic Theory, Elsevier, vol. 82(1), pages 167-189, September.
  6. Kamihigashi, Takashi, 2001. "Necessity of Transversality Conditions for Infinite Horizon Problems," Econometrica, Econometric Society, vol. 69(4), pages 995-1012, July.
  7. 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.
  8. Olson, Lars J., 1989. "Stochastic growth with irreversible investment," Journal of Economic Theory, Elsevier, vol. 47(1), pages 101-129, February.
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Cited by:
  1. Benhabib , Jess & Evans, George W. & Honkapohja, Seppo, 2012. "Liquidity traps and expectation dynamics: Fiscal stimulus or fiscal austerity?," Research Discussion Papers 27/2012, Bank of Finland.

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