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Policy Analysis with Econometric Models

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CHRISTOPHER A. SIMS University of Minnesota Policy Analysis with Econometric Models RECENTLY the rationalexpectations school has mountedan attackon the conventionaluse of simultaneousequations models for policy analysis. One might go furtherand say that among academic macroeconomists the conventionalmethods have not just been attacked, they have been discredited. The practice of using econometric models to project the likely effects of different policy choices, then choosing the best from amongthe projectedoutcomes, is widely believed to be unjustifiableor even the primarysource of recent problemsof combined high inflation and low economic activity. Instead, it is claimed, policy analysis should be formulatedas choice amongrules of behaviorfor the policy authorities andestimates shouldbe madeof the stochasticproperties of the economy undereach proposed rule to choose the best. This point of view has gained such wide acceptance in part because of its association with Lucas's theoreticaldemonstration that a Phillips curve could emergein an economy in which such an associationbetween inflation and real activity was not a usable menu for policy choice. Because users of conventional simultaneousequations models some- times presented the Phillips curve as just such a menu, and because it became apparentin the 1970sthat this menu was not helpful,an analysis thatprovided a cogent explanationfor why the menuwas chimericalhad greatappeal. As in most revolutions, the old regime toppled by the rational expectationsrevolution was corruptand in some sense deserved its fate. However, as is often the case, the revolutionitself has had its excesses, destroyingor discardingmuch that was valuablein the name of utopian 0007-230318210002-0107$1 .00/0 ?3BrAookings Inistitlutioni 107 108 Brookings Papers on Economic Activity, 1:1982 ideology. This papertries to assess where the revolutionitself could use revision.I In this paper I argue that it is a mistake to think that decisions about policy can only be described, or even often be described, as choice amongpermanent rules of behaviorfor the policy authorities.A policy actionis betterportrayed as implementationof a fixed or slowly changing rule. I also argue that explicit identificationof expectation-formation mechanisms is not necessary for policy analysis, concluding that the rationalexpectations critique of econometric policy analysis is a cau- tionary footnote to such analysis rather than a deep objection to its foundations.From this perspective,the conventionaluse of econometric models to aid in policy choice is neitherself-contradictory nor meaning- less. Applying Decision Theory to Economic Policymaking Formalquantitative analysis of policy choice must begin with a model of the effects of policy. The modelmust describethe "outcome," usually in the formof a probabilitydistribution over futureevents in the economy, for each possible "setting of policy." To choose policy optimally, one evaluatesthe outcomesaccording to some objectivefunction and chooses the best. Although this description appears static, in the sense that it refers to a single decision ratherthan to a time sequence of them, it can also be appliedto dynamicproblems. In the conventionaldescription of a dynamicproblem there is at each date, t, a measure,y,, of the current state of the economy (which may include informationon the history of the economy and of policy), and a value must be chosen for the policy action at t, c,. The model gives a conditional distribution for y, , the state of the economy in the next period, as a function of y, and c,. If the objective function includedonly y, 1, one would simply choose c, so as 1. The senses in which the "old regime" was in my view "corrupt"are discussed in moredetail in my "Macroeconomicsand Reality," Econometrica, vol. 48 (January1980), pp. 1-48. ThereI arguethat the identifyingrestrictions used to obtainequation-by-equation interpretationsof these models are incredible.They are mainly simplifications,chosen empiricallyso that they do not conflictwith the data. Such simplificationsmay be a useful partof estimatinga forecastingmodel, but they do not representa prioriknowledge and thereforecannot help in identifyingthe model. Christopher A. Sims 109 to obtain the best probabilitydistribution of y, 1. In general, however, the objectivefunction will dependon y,,? (andperhaps also c,,?) at many or all dates beyond t + 1. Then, in orderto set ct optimallyin the current period, one must determine a set of optimal contingency plans for all future dates, describinghow each ct,+ will be chosen as a function of informationavailable at t + s. Definingthe outcome as the conditional distribution of all future yt, and ct,+ given yt, ct and the optimal contingencyplans, the dynamicproblem becomes analogousto the static problem.A policy setting is a complete set of contingencyplans for the futurecourse of policy, and one chooses amongsuch settings to achieve the best outcome. However, this abstract description of the problem of policy choice appearsat first glance not to match the problemspolicymakers actually face. Decision theoryportrays optimal policy choice in a dynamicsetting as a single analytical exercise. One has to produce contingency plans specifyingpolicy actions at all futuredates underall conceivablecircum- stances in orderto findthe best currentpolicy action. Once this has been done, there should be no need for new analysis at future dates. Yet in practice macroeconomicpolicymaking does not seem to be this sort of once-for-all analysis and decision. Policymakers ordinarily consider what actions to take in the next few quartersor years, reconsidertheir plans every few months, and repeatedly use econometric models to project the likely effects of alternativeactions. Furthermore,optimal policy should be a deterministicfunction of informationavailable to the policymaker,but actual policy seems to include a large componentthat is unpredictableeven to observers with the same informationset as the policymaker. On closer examination, these difficulties with decision theory as a descriptionof actualpolicy choice are probablynot important.It is likely that policymakers' objective functions discount the future, so that actionsand consequences farenough ahead receive little weight. Precise contingencyplans for dates far in the future will thereforebe relatively unimportantin solvingthe currentproblem. A good approximatesolution will thus concentrate on determinationof the currentpolicy action, ct, and the contingency plans for policy actions in the near future, but will toleratecruder approximations for contingencyplans in the increasingly distantfuture. This is more likely because the state of the economy in the distant future is relatively unpredictable, so that the range of 110 Brookings Papers on Economic Activity, 1:1982 contingenciesthat would have to be considered in formulatingprecise contingency plans for that time period is great. The cost of precise analysisof such wide rangesof contingenciesis high, while the value of such accurateanalysis of the distantfuture in improvingthe choice of c, is relativelylow. It is perfectly reasonable,therefore, for even a nearly optimalprocedure for choosing policy to involve reconsideringpolicy plans at regularintervals.2 Policy is not made by a single maximizingpolicymaker, but through the political interactionof a numberof institutionsand individuals.The people involved in the process, the nature of the institutions, and the views and values of the public shift over time in imperfectlypredictable ways. Thus even if each individualwho has some power over the choice of policy has a coherent view of his or her objectives and of a dynamic model of the economy, leading that policymaker to believe in the appropriatenessof a particularvalue for c, as a functionof the state, the actual setting of c, will be partly randomfrom the point of view of the public. The observed unpredictabilityof policy need not, therefore, implythat any individualpolicymaker is randomizinghis or her actions. Rational Expectations Controltheory's dynamicversion of the problemof optimaldecision theory rests on the following apparentlyreasonable assumptions: At each date t there is a list of numbers, the vector describingthe state of the economy, y,, which summarizesall aspects of the history of the system being controlledthat are relevantto its futureevolution. At each t thereis a function,f, determiningthe probabilitydistribution of the next period's state Yt+1, from the currentstate, yt, and the current policy action, ct, where f, is taken as given when policy choice is optimized. Policy actions, c, (the vector of values for the control variablesat t in 2. In textbook dynamiccontrol problems, the form of the functionrelating optimal c, to the currentstate often tends to be a fixed form over time. If economic policy choice werelike these textbookproblems, the needfor reanalysiswould steadily diminish through time as one refinedthe knowledge of the function describingthe optimal choice of c,. However, in economics the form of the model relatingthe state and policy to the next period'sstate inevitablydrifts in time so thatthere is no reliabletendency for c, to become a fixedfunction of the state of the economy. Christopher A. Sims 111 control theory), can depend on informationavailable at t, but not on informationavailable only later than t. In engineering applications the f, functions and the state of the economy and control vectors, y, and c, are determinedby the physical causal
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