Abstract
According to the static theory of decision-making under uncertainty, the policy maker will take that action that maximizes expected utility. In the dynamic theory several consecutive periods play a role, each of which is characterized by a certain action. The policy maker will then choose a maximizing strategy (i.e., a rule according to which all successive actions are determined by the information which is available at the time when the action has to be taken). This note is confined to the action in the first period of such a strategy. It is shown that, under certain conditions, the first-period action of the strategy which maximizes expected utility is identical with that of the strategy which neglects the uncertainty problem by maximizing utility under the condition that all uncertain elements are equal to their mean values.
This article first appeared in Econometrica, 25 (1957), 346–349. Reprinted with the permission of the Econometric Society.
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References
H.A. Simon, “Dynamic Programming under Uncertainty with a Quadratic Criterion Function,“ Econometrica, 24 (1956), 74–81.
H. Theil, “Econometric Models and Welfare Maximization,” Weltwirtschaftliches Archiv, 72 (1954), pp. 60–83. It is also of some interest to note that the maximization analysis considered here can be regarded as a generalization of consumer’s theory, where a utility function is maximized subject to one single budget constraint. Just as there, we can distinguish between substitution and complementarity among pairs of variables (i.e., between two instruments, or two noncontrolled variables, or an instrument and a noncontrolled variable). In the present dynamic analysis this should be further specialized according to subperiods; i.e., there may be substitution between x1(t) and x2(t) but complementarity between xx(t) and x2(t’). It is interesting that the square matrix K of (2.2) is the inverse of the matrix of substitution terms of the instruments of the various subperiods. Cf. my forthcoming Economic Forecasts and Policy, North Holland, Amsterdam, 1958, ch. VIII.
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© 1992 Springer Science+Business Media Dordrecht
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Theil, H. (1992). A Note on Certainty Equivalence in Dynamic Planning. In: Raj, B., Koerts, J. (eds) Henri Theil’s Contributions to Economics and Econometrics. Advanced Studies in Theoretical and Applied Econometrics, vol 24. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2410-2_3
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DOI: https://doi.org/10.1007/978-94-011-2410-2_3
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