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Optimal Buffer Stocks and Precautionary Savings with Disappointment Aversion

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  • Joshua Aizenman

Abstract

Developing countries use various risk reduction schemes, ranging from active management of buffer stocks and international reserves to commodity stabilization funds. The purpose of this paper is to reexamine the design of these schemes in a generalized expected utility maximization model where agents are disappointment averse. We derive first the generalized risk premium, showing that disappointment aversion increases the conventional risk premium by a term proportional to the standard deviation times the degree of disappointment aversion. Next, we show that disappointment aversion modifies the characteristics of precautionary saving. The concavity of the marginal utility continues to determine precautionary saving, but its effect is of a second order magnitude (proportional to the variance) compared to the first order effect (proportional to the standard deviation) induced by disappointment aversion. Hence, higher volatility increases the precautionary saving of a disappointment averse agent. This result applies even if the income process approaches a random walk. Finally, we reexamine the optimal size of buffer stocks, showing that disappointment aversion increases its size by a first order magnitude. A buffer stock that is rather small when agents are maximizing the conventional expected utility is rather large when agents are disappointment averse.

Suggested Citation

  • Joshua Aizenman, 1995. "Optimal Buffer Stocks and Precautionary Savings with Disappointment Aversion," NBER Working Papers 5361, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:5361
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    References listed on IDEAS

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    1. Aizenman, Joshua, 1997. "Investment in new activities and the welfare cost of uncertainty," Journal of Development Economics, Elsevier, vol. 52(2), pages 259-277, April.
    2. Segal, Uzi & Spivak, Avia, 1990. "First order versus second order risk aversion," Journal of Economic Theory, Elsevier, vol. 51(1), pages 111-125, June.
    3. Harless, David W & Camerer, Colin F, 1994. "The Predictive Utility of Generalized Expected Utility Theories," Econometrica, Econometric Society, vol. 62(6), pages 1251-1289, November.
    4. Arrau, Patricio & Claessens, Stijn, 1992. "Commodity stabilization funds," Policy Research Working Paper Series 835, The World Bank.
    5. A. Sandmo, 1970. "The Effect of Uncertainty on Saving Decisions," Review of Economic Studies, Oxford University Press, vol. 37(3), pages 353-360.
    6. Epstein, Larry G & Zin, Stanley E, 1991. "Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: An Empirical Analysis," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 263-286, April.
    7. Gul, Faruk, 1991. "A Theory of Disappointment Aversion," Econometrica, Econometric Society, vol. 59(3), pages 667-686, May.
    8. Epstein, Larry G & Wang, Tan, 1994. "Intertemporal Asset Pricing Under Knightian Uncertainty," Econometrica, Econometric Society, vol. 62(2), pages 283-322, March.
    9. Gilboa, Itzhak, 1987. "Expected utility with purely subjective non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 65-88, February.
    10. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    11. Newbery, David M, 1989. "The Theory of Food Price Stabilisation," Economic Journal, Royal Economic Society, vol. 99(398), pages 1065-1082, December.
    12. Kreps, David M & Porteus, Evan L, 1978. "Temporal Resolution of Uncertainty and Dynamic Choice Theory," Econometrica, Econometric Society, vol. 46(1), pages 185-200, January.
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    Cited by:

    1. Joshua Aizenman, 1999. "International Portfolio Diversification with Generalized Expected Utility Preferences," Canadian Journal of Economics, Canadian Economics Association, vol. 32(4), pages 995-1008, August.
    2. Aizenman, Joshua & Marion, Nancy, 2003. "The high demand for international reserves in the Far East: What is going on?," Journal of the Japanese and International Economies, Elsevier, vol. 17(3), pages 370-400, September.
    3. Hideaki Tamura & Yoichi Matsubayashi, 2014. "A New Solution to the Equity Premium Puzzle and the Risk-Free Rate Puzzle: Theory and Evidence," Discussion Papers 1422, Graduate School of Economics, Kobe University.

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    JEL classification:

    • F1 - International Economics - - Trade

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