閤 Rules rather than Discretion: The Inconsistency of Optimal Plans OR。 Finn e Kydland; Edward C. Prescott The Journal of political Economy, Vol. 85, No. 3. (Jun, 1977), pp. 473-492 Stable url: http://inksistor.org/sici?sic0022-3808%028197706%02985%3a3%03c473%03arrtdt3e2.0.co%3b2-a The Journal of political Economy is currently published by The University of Chicago Press Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/about/terms.htmlJstOr'sTermsandConditionsofUseprovidesinpartthatunlessyouhaveobtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the jsTOR archive only for your personal, non-commercial use Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.istor.org/iournals/ucpress.html Each copy of any part of a JSTOR transmission must contain the same copyright notice that ap on the screen or printed page of such transmission STOR is an independent not-for-profit organization dedicated to and preserving a digital archive of scholarly journals. For more information regarding JSTOR, please contact support @jstor. org Fri Mar 161202:072007
Rules Rather than Discretion: The Inconsistency of Optimal Plans Finn E. Kydland; Edward C. Prescott The Journal of Political Economy, Vol. 85, No. 3. (Jun., 1977), pp. 473-492. Stable URL: http://links.jstor.org/sici?sici=0022-3808%28197706%2985%3A3%3C473%3ARRTDTI%3E2.0.CO%3B2-A The Journal of Political Economy is currently published by The University of Chicago Press. Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/about/terms.html. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/journals/ucpress.html. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is an independent not-for-profit organization dedicated to and preserving a digital archive of scholarly journals. For more information regarding JSTOR, please contact support@jstor.org. http://www.jstor.org Fri Mar 16 12:02:07 2007
Rules Rather than Discretion The Inconsistency of Optimal plans Finn E Kydland Norwegian School of Economics and Business Administration Edward C. Prescott Even if there is an agreed-upon, fixed social objective function and policymakers know the timing and magnitude of the effects of their ctions, discretionary policy, namely, the selection of that decision which is best, given the current situation and a correct evaluation of the end of-period position, does not result in the social objective function being maximized. The reason for this apparent paradox is that economic planning is not a game against nature but, rather a game against ational economic agents. We conclude that there is no way control theory can be made applicable to economic are rationa I. Introduction Optimal control theory is a powerful and useful technique for analyzing dynamic systems. At each point in time, the decision selected is best, given the current situation and given that decisions will be similarly selected in the future. Many have proposed its application to dynamic economic planning. The thesis of this essay is that it is not the appro- priate tool for economic planning even when there is a well-defined and agreed-upon, fixed social objective function. We find that a discretionary policy for which policymakers select the We would like to thank Walter Dolde, Leif Johansen, Robert E. Lucas, Jr, Christopher would like to acknowledge the support of the Guggenheim Foundation, National Science Foundation, and the Bank of norway
474 JOURNAL OF POLITICAL ECONOMY best action, given the current situation, will not typically result in the social objective function being maximized. Rather, by relying on some policy rules, economic performance can be improved. In effect this is an argument for rules rather than discretion, but, unlike Friedmans(1948 argument, it does not depend upon ignorance of the timing and magnitude of the effects of policy The reasons for this nonintuitive result are as follows: optimal control theory is an appropriate planning device for situations in which curren outcomes and the movement of the system,'s state depend only upon current and past policy decisions and upon the current state. But,we argue, this is unlikely to be the case for dynamic economic systems. Cur- rent decisions of economic agents depend in part upon their expectations of future policy actions. Only if these expectations were invariant to the future policy plan selected would optimal control theory be appropriate In situations in which the structure is well understood, agents will surely surmise the way policy will be selected in the future. Changes in the social objective function reflected in, say, a change of administration do have an immediate effect upon agents'expectations of future policies and affect their current decisions. This is inconsistent with the assump tions of optimal control theory, This is not to say that agents can fore cast future policies perfectly. All that is needed for our argument is that agents have some knowledge of how policymakers'decisions will change as a result of changing economic conditions. For example, agents may expect tax rates to be lowered in recessions and increased in booms The paradox also arises in situations in which the underlying economic structure is not well understood, which is surely now the case for aggre gate economic analyses, Standard practice is to estimate an econometric del and then, at least informally, to use optimal-control-theory techniques to determine policy. But as Lucas(1976) has argued, since optimal decision rules vary systematically with changes in the structure of series relevant to the decision maker, any change in policy will alt the structure of these rules, Thus cha policy induce changes in structure, which in turn necessitate reestimation and future changes in policy, and so on. We found for some not implausible structures that this iterative procedure does not converge, and, instead, stabilization efforts examples, however, it did converge, and the resulting policy was con- sistent but suboptimal. It was consistent in the sense that at each point in time the policy selected was best, given the current situation. In effect the policymaker is failing to take into account the effect of his policy rule upon the optimal decison rules of the economic agents In this paper, we first define consistent policy and explain for the is suboptimal. The implications of the analysis are then considered for patent policy and
RULES RATHER THAN DISCRETION 475 flood-control problems for which consistent policy procedures are not eriously considered. Then, for the aggregate demand management problem, it is shown that the application of optimal control theory is equally absurd, at least if expectations are rational. Doing what is best or price stability) were at the socially optimal rate. Consistency fo infinite-period recursive economic structures is then considered. In equili rium, optimizing agents follow rules which specify current decisions as a function of the current state 1 Methods are developed for computing these equilibrium decision rules for certain specialized structures.The methods are used to evaluate alternative investment-tax-credit policies designed both to stabilize and to yield optimal taxation. Among the policies evaluated is the suboptimal consistent policy. Within the class of feed back policy rules, we found that the optimal one depended upon the initial conditions. Thus it was not optimal to continue with the initial policy in subsequent periods; that is, the optimal policy was inconsistent. I. Consistent Policy Let I=(T1,T2,..., Tr)be a sequence of policies for periods (which may be infinite)and x =(*1, x2 r)be the corresponding sequence for economic agents'decisions. An agreed-upon social objective function is assumed to exist. 2 Further, agents'decisions in period\ depend. 7 S(a T) all policy decisions and their past decisions as follows xr=X(x1,…,x1-1,丌1,…,丌r),t=1 In such a framework an optimal policy, if it exists, is that feasible which maximizes(1) subject to constraints(2). The concept of consistency is less obvious and is defined as follows Definition: A policy r is consistent if, for each time period t, r maximizes(1), taking as given previous decisions, x I and that future policy decisions (s for s>t) are simila selected he original objective of this research was to demonstrate the applicability of consistent solution obtained by using control-theory techniques, but initially cons of our initial analyses, led us to the radical conclusions of this essay. 2 Uncertainty is not the central issue of this essay. As with Arrow- Debreu stat need only define the decision elements to be functions contingent upon observables to incorporate uncertainty as is done for the stabilization example in
The inconsistency of the optimal plan is easily demonstrated by a two-period example. For T= 2, I2 is selected so as to maximize (x1,x2,丌1,丌2), For a plan to be consistent, I, must maximize( 3), given the past decisions T1,*, and constraint (4). Assuming differentiability and an interior aS ax aS_0 The consi policy ignores the effects of decision rule, the first-order condition is CSax2SX1「 as aS aX2 ax2O2'aT2 aT2 Lax, ax2 ax, Only if either the effect of T2 upon x, is zero(i. e, aX,/aT,=0)or the effect of changes in x, upon S both directly and indirectly through xz is zero (ic, [aS/ax1 aS/ ax2 aX2/ax,]=0)would the consistent policy be optimal Pollak (1968)resolved a planning inconsistency which arose because different generations had different preference orderings by assuming at each stage that the policy selected was best (relative to that generation,s preferences), given the policies which will be followed in the future. For prol previous decisions T, and xu, is best ∏r( Once the functional relationship Ir is known, the determination of the 丌r-1=∏7-1(T1 T-2;x1 determined, and in general the consistent policy can be determined once future policy rules are known. With such a procedure, the policy decision at each stage is optimal, given the rules