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Autoregressions, Expectations, and Advice Author(s): Thomas J. Sargent Reviewed work(s): Source: The American Economic Review, Vol. 74, No. 2, Papers and Proceedings of the Ninety- Sixth Annual Meeting of the American Economic Association (May, 1984), pp. 408-415 Published by: American Economic Association Stable URL: http://www.jstor.org/stable/1816394 . Accessed: 05/03/2012 13:34

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http://www.jstor.org Autoregressions, Expectations, and Advice

By THOMAS J. SARGENT*

Macroeconomistshave long spent most of the context of concretemodels. Therefore, in their time observingand interpretingaggre- advancing the arguments,I have taken the gative economic time-series.Recent progress risk that I mightmiss what Sims has in mind. has involved formalizingand standardizing In fact, in oral remarks,Sims has told me this activityinto one of estimatingand inter- that my interpretationfails to capture his preting vector autoregressions.Vector auto- thoughts,and should be labeled as my own regressionsprovide a convenientway of sum- argument.Nevertheless, I continue to attri- marizingthe second momentsof time-series bute to Sims a line of argumentwhich he , and conform naturallywith the recur- disowns.2I do so because the argumentthat sive that is associated with I attribute to him was gatheredduring my dynamic reading of Sims' work and is not my own models. In interpreting vector autoregres- creation. Sims has told me that he agrees sions, fundamentaldifferences exist between that the argumentin the text has the virtue users of rational expectationseconometrics of disposingof often-encounteredarguments and users of "atheoretical"or "uninterpret- to the effect that users of vector autoregres- ed" vector autoregressionsin the style of sions in the style of Sims and Litterman ChristopherSims (1980, 1982) and Robert must be regardedas ignoring dynamic eco- Litterman (1980, 1981).' This paper de- nomic theory. scribes these differences,and uses dynamic rational expectations theory to describe 1. VectorAutoregressions and Dynamic strong points of each approach.That theory can be used as forcefully to support Sims' style of more or less uninterpretedvector Robert Lucas' (1976) critique of econo- autoregressiveempirical work as it can be to metric policy evaluation procedures con- justify the "fully interpreted"or structural cerned proper ways of interpreting and vector autoregressiveempirical work prac- manipulatingvector autoregressions.Lucas ticed by rational expectations econometri- observed that it violated dynamic economic cians. theory with purposeful agents, as standard My purposeis to allude to specificformal proceduresthen did, to changeone equation models that exist in the literatureon rational representinggovernment policy actions in a expectationsmodels, and that can be used to support Sims' actual econometric practices 2In constructingmy unauthorizedinterpretation of and many of his remarks.To date, Sims' Sims, I have selected and emphasizedsome themes in argumentson the points in this paper have his writings,and have deemphasizedand deletedothers. been informal, and have not been made in My intention in doing so has been explicitly to use dynamic rationalexpectations theory to present a de- fense of Sims' actual econometricpractices. Among * Department of Economics, University of Min- Sims' words with which my interpretationmight be nesota, Minneapolis,MN 55455 and Federal Reserve inconsistentare such statementsas those found in his Bank of Minneapolis.I thank Neil Wallace, Bennett 1982 article:lines 7-13, p. 108; lines 27-29, p. 123; and McCallum,Robert Townsend, Robert E. Lucas, Jr., lines 3-13, p. 151. Whethermy interpretationis con- Robert Litterman,Bruce Smith, and ChristopherSims sistent with Sims' words hinges on the meaningof the for helpfulcomments. terms "policy analysis"and "useful." If they refer to 'The philosophyof rationalexpectations economet- givingadvice in choosinggovernment policy actions,my rics is describedin the introductoryessay of Robert interpretationdoes not apply.It does applyif the terms Lucas and myself (1981) and by my 1981 article.The referto makingprobability statements about the conse- approachof Sims and Littermanis describedin Sims quencesof alternativerealizations of policy actions on (1980), Litterman(1980, 1981),and ThomasDoan et al. the basis of the historicallyestimated probability struc- (1983). ture. 408 VOL. 74 NO. 2 CURRENT STA TE OF MACROECONOMIC THEORY 409 vector autoregressionwhile holding fixed the The most telling criticismof rational ex- remainingequations, many of whichdescribe pectationseconometrics has come from Sims private agents' decisions. Of the procedures (1980, 1982) in a sequenceof remarksabout that Lucas criticized,the most sophisticated appropriateways of estimatingand utilizing explicitlyposed an optimal control problem vector autoregressions.While accepting the for the governmentas the way of findingthe theoretical observation underlying Lucas' best equation for governmentpolicy vari- critique, Sims challenges rational expecta- ables, holding fixed the remainingequations tions ,and does so by appealing in an estimatedvector autoregression. In such to the very same general body of dynamic a control problem, the object of choice is a economic theory that Lucas used. Sims' vi- rule or regime for the government,and the sion and rational expectationseconometrics predicted outcome of that choice is a new are based on differentmodels of the econ- and improved probabilitystructure for the omy. To begin, it is necessaryto clarifywhat . Lucas observedthat dynamiceco- is meant by a model economy. nomic theory implies that in general all of A model economy consists of a collection the equations in the of agents arrangedin a particularway over can be expectedto changewith such a change time and space; a descriptionof agents' en- in regime,not just the equations describing dowments of and preferencesfor ; a the governmentpolicy. technology for converting goods into one One constructiveresponse to Lucas' ob- another,possibly at differentpoints in time servation has been an ambitious research and space; and a mechanismfor arranging programto build workabledynamic rational agents into coalitionsor institutions,and for expectationsmodels and methodsof estima- coordinatingdecisions both withinand across tion that can be used to predict how all of coalitions.This conceptionof an economyis the other equations of a vector autoregres- so broad that it leaves open whether the sion will change when one equationdescrib- coordinationmechanism is a Walrasianone, ing a governmentpolicy variableis hypothet- or an alternativeone that, when compared ically altered.3 The goal of this rational with a Walrasianmechanism, seems to con- expectations econometric program remains stitute a "disequilibrium."5 ultimatelyto searchfor rules for government With a given mechanism,the economycan policy variablesthat are predictedto imply be viewedas the solutionof a dynamicgame. the most desirablevector autoregressionfor the economy. The intention is thereby to obtain good practicalquantitative advice for formulatingnew strategies for government pectations equilibrium and the solution of the social actions in the years beyond the sample planning problem, which Lucas and Prescott (1971) period.4 have fruitfully exploited, fails to occur. Such nonoptimal rational expectations equilibria must be computed by methods other than those used by Lucas and Prescott 3Contributions that share this goal, while differing in (see Kydland and Prescott, 1977; Dennis Epple et al., some technical details, are represented by John Taylor 1984; Paul Romer, 1982; and Charles Whiteman (1983)). (1979, 1980, 1982) and and myself Notice that Willem Buiter's (1980) characterization of (1980), by Finn Kydland and Edward Prescott (1982), some rational expectations work in macroeconomics as and by Hansen and Kenneth Singleton (1982). being "the economics of Dr. Pangloss" does not apply 4In the brand of rational expectations econometrics to the line of work that I am summarizing under the that I am describing, the historical time-series are sup- category of rational expectations econometrics. Rather, posed to have been generated as the solution of a it is Sims' criticism of rational expectations economet- dynamic game whose outcome can be improved upon. rics that comes closer to resting on the view that "we This can occur in a variety of rational expectations live in the best of all possible stochastic processes." equilibria in which suboptimal government behavior in 5Robert Townsend (1983a) describes a model econ- conjunction with nonneutralities prevent rational expec- omy with purposeful -setting agents. For a particu- tations equilibria from being Pareto optimal. Some use- lar game that he sets out, a Walrasian equilibrium is a ful examples are studied by Zvi Eckstein and Martin solution. Presumably, settings exist in which games Eichenbaum (1984a, b). In such contexts, the computa- specified in terms of the same primitive objects as tionally convenient equivalence between a rational ex- Townsend's have non-Walrasian solutions. 410 AEA PAPERS AND PROCEEDINGS MA Y 1984

In a dynamic game, the strategy of each tive equilibriumis one tractable and com- agent depends on the strategieschosen by monly used such mechanism).It is then pos- "nature"and the other agentsin the system. sible to define a mapping from the free Such strategicinterdependence is the reason parametersof agents' preferencesand con- that when an equationin a vectorautoregres- straintsto the impliedtheoretical probability sion describingone agent's strategyis hypo- of all of the variables in the theticallyaltered, other equations should also model.The second momentsof this probabil- be expectedto change.The "rationalexpec- ity distribution can be completely sum- tations revolution"in macroeconomicscon- marized as a theoreticalvector autoregres- sists of a broad collectionof researchunited sion. Given this mapping, estimation can mainly by an aim to respectthe principleof proceed using the philosophy of maximum strategicinterdependence. likelihood or generalized method of mo- This principle is respected and heavily ments, each of which selects free parameters exploitedboth in rationalexpectations econ- of the model so that the theoreticalprobabil- ometrics and in Sims' criticismof that pro- ity distribution (or vector autoregression) gram. The differencebetween Sims and ra- matchesthe empiricalone as closely as possi- tional expectations econometrics involves ble. both the specificationof the dynamic game Once estimates of the free parametersof that was imaginedto have been played dur- agents' objectivesand constraintshave been ing the historicalsample period, and also the obtained, the aim is to use them to analyze dynamicgame that is imaginedto occurafter how the economywould behaveunder hypo- the sample period, when the analyst is con- thetical strategies for setting government templatingan intervention. policy variables that are differentfrom the one evident in the sample period. A sys- 11. Rational Expectationsand Fully Interpreted tematic search is to be conducted for the VectorAutoregressions governmentstrategy that optimizes the per- formance of the economy as a stochastic Rational expectations econometrics pro- processin the followingparticular sense. An ceeds on the supposition that the dynamic intertemporalobjective function is posited game that was being played during the esti- for the government,in some cases the mation periodis differentthan the one to be functionalof the representativeprivate agent analyzed,and whose playingis to be recom- in the model.A dynamicgame is formulated mended in the future.Rational expectations in which the governmentis dominantand is econometricstypically assumes that during imagined to choose a strategy to maximize the historicalsample period, private agents' its criterion,taking into accountthe reaction decisionssolved constrainedstochastic inter- of optimizingprivate agents' strategies to the temporaloptimization problems. Among pri- government'schoice of strategy.A solution vate agents' constraintsare of motion to this dynamic game will in general be a for government policy variables. Usually, stochasticprocess for the economy that dif- these governmentpolicy variablesare posited fers from the one in place duringthe sample to follow arbitrary,more or less general, period.6 stochastic processes. The econometrician The piece of this that specifies parametricforms for preferences, describes the government'spolicy decisions for technologies, and for stochastic pro- is what the rationalexpectations econometri- cesses for governmentpolicy variables and cian is preparedto recommendfor policy; other exogenous variables. The econome- the entire vector stochastic process is his trician next imposes the hypotheses that about how the economy would privateagents have rationalexpectations and behave were his policy recommendationsto behavepurposefully, and that thereis a given mechanismassuring consistency among viari- 6An exception to this statement occurs when the ous individuals'decision strategiesand their government policy rule was optimal during the sample perceptions(a rationalexpectations competi- period. VOL. 74 NO. 2 CURRENTSTATE OF MACROECONOMIC THEORY 411 be adopted.This hypotheticalstochastic pro- playedduring and afterthe estimationperiod, cess will have a vector autoregressiverepre- the presumptionis that the same stochastic sentation, which will generally differ from process will hold both during and after the the one in the sampleperiod. estimationperiod. It is then of no interestto This setup envisions that governmentbe- analyze a change in the governmentstrategy havior may have been guided by different or "cregime"because government behavior is principlesduring the sampleperiod than are posited to be determinedby the same pur- hypothesizedto guide it during the future. poses and constraints after the estimation During the sampleperiod, there is permitted period as beforeit.9 to be an asymmetrybetween the principle On the one hand, this view implies that, guiding the government'sstrategy, which is while it could be extendedto includeparam- arbitrarily(if generally) specified, and that eters for governmentagents, the rationalex- guiding private agents, which is purposeful. pectations econometricspursuit of the deep However,for computingthe optimalgovern- parametersof agents' preferencesand con- ment policy strategyfor the future,this pos- straintsis in itself of little .10Interven- sible asymmetryof behavioris removed,and tions in the form of changesin government both privateagents and the governmentare strategiesare supposednot to occur; but the supposed to be purposeful.(Some such dif- ability to analyze such interventions is a ferencein governmentbehavior between the majormotive of rationalexpectations econo- sample period and the hypothetical future metrics.On the other hand, this view implies must be posited by anyone recommendinga that for ,it is useful to estimate changein the government'sstrategy.) vector autoregressionsthat are left uninter- pretedin termsof parametersof agents'pref- III. Sims' Challenge erences and constraints.Such vector autore- gressionscan be used to producelinear least I interpret Sims as objecting to the as- squaresforecasts of the futurevector of vari- sumed asymmetry between private agents' ables given past values. They can also be behavior and government behavior during used to predictthe futureof some variables, the estimationperiod. Sims' view is that the conditionedon particularassumed paths over asymmetryshould be eliminatedby assum- part of the futurefor some governmentpolicy ing that governmentagents as well as private variables."' agentshave behavedas rationalexpectations intertemporaloptimizers during the sample period.7 This view has definite consequencesfor 9"Accurateprojections can be made from reduced in form models fit to historybecause it is not proposedto how the time-seriesare to be interpreted changethe policy rule,only to implementeffectively the terms of deep parametersof preferencesand existingrule" Sims (1980, p. 13). constraintsduring the estimationperiod, and l?lf the overidentifyingrestrictions imposed on a would requiremodifications of most existing vector autoregressionby a rational expectationsdy- methods of rational expectationseconomet- namic game are approximatelytrue, imposing them could be defended on the same instrumentalgrounds rics.8 Further, if the very same dominant that Doan et al. and Litterman(1980) give for imposing player dynamic game is imagined to be restrictionsnot based on expliciteconomic theories. "1Simsstates (1982): ".. . effects of policy actions that 7". . it is not clear that the existingpattern of policy affect expectation-formationmechanisms can be cor- in most countries,in which there is weight given to rectly evaluatedwith models that are reducedform in stabilizationof ,, and income dis- the sense that they do not explicitlydisplay parameters tribution,is very far from an optimal policy" (Sims, of the expectationformation mechanism" (pp. 115-16); 1980, p. 14). "They [theprocedures] take account of policyendogene- 8Manyof these modificationsare describedin Epple ity by generatingtrue conditional projections,given et al. Note that a rationalexpectations econometrician specifiedpaths for policy variables"(p. 150); "... a valid imposingone of their games E or F duringan estima- reduced form will make relativelyprecise conditional tion period would automaticallybe led to a position projectionsfor the effectsof policy actionsor sequences close to Sims' when it comes to giving advice for an of actions that are close in form to what has been improvedregime outside the sample. observedhistorically" (p. 118). 412 AEA PAPERS AND PROCEEDINGS MA Y 1984

Both of these kinds of forecastsare to be are influenced by the public's speculation made in a way that respectsthe assumption about what successor"governments" will do. that the same stochasticprocess governsthe Typically,it is posited that each administra- vector of variables during and after the tion is followed by successorswith similar estimationperiod. In particular,both kinds objectivefunctions.13 of forecastingexercises are formulatedmath- In such a formulation,government agents ematically as projectionsof unknown vari- are imaginedto be dominantvis-a-vis private ables on known variables,using the estima- agents,and to takeinto accountthe effectsof tion-period vector autoregression as the their current actions on future actions of probabilitymodel. These are the only kinds private agents. However, because they can- of forecastingexercises that are of practical not commit their successors,in optimizing ,given Sims' conceptionof the game. they disregardthe effectson privateagents of These forecastingexercises respect the prin- those futuregovernment actions that are be- ciple of strategicinterdependence underlying yond the control of the currentadministra- Lucas's critique,because they never involve tion. This sequential setup is designed to hypothesizing an altered strategy for the reflect a reality in which governmentpolicy governmentoutside of the sampleperiod. emerges from a succession of personalities Closely related to his challenge of the within a successionof administrations,each estimationperiod-policy prescription period lacking power to commit its successors.14In asymmetryin rational expectations econo- such games, there is no sense in which a metrics, Sims has disputed the appropriate- policy regime is chosen once and for all. ness of the commonlyformulated dominant Instead, the stochastic process for govern- player dynamic game as one in which the ment policy is determinedby the purposeful governmentis imagined to search for a re- behaviorof a temporalhierarchy of agents, gime or strategyto be used into the indefinite each of whom influencesor controls only a future. In such a formulation, the gov- few periodsof actions. ernment is an infinitely lived agent that is imagined to attain beneficialoutcomes now IV. Contradictions by binding itself to state-contingentfuture actions.These beneficial effects come through Neither of the two above approachesis "expectations effects," or, more precisely, free of philosophicaldifficulties. The rational through the workings of the principle of expectations econometrics position is ex- strategicinterdependence. posed to the followinginternal contradiction. Sims doubts the applicabilityof a setup in Suppose that the free parametersof private which an infinitelylived governmentis imag- agents'preferences and constraintshave been ined to choose among infinitely lived "re- estimated during an estimationperiod, and gimes."" Instead, he can be interpretedas then are used to calculate a new and im- urgingthat the governmentbe thoughtof as consisting of an intertemporalsequence of 13Sims (1982): "Policyis not madeby a single maxi- finitely lived agents. There is a sequenceof mizing policymaker,but throughthe political interac- administrations,each of which cannot com- tion of a numberof institutionsand individuals.The mit its successoreven thoughcurrent options people involvedin the process,the natureof the institu- tions, and the views and valuesof the public shift over time in imperfectlypredictable ways" (p. 110); "...dis- putes about the optimalrule are no more importantin 12Sims (1982): "Yet in practice macroeconomic principle than disputes about how to implementthe policymakingdoes not seemto be thissort of once-for-all existing 'rule' as it emerges from existing institutions analysisand decision.Policymakers ordinarily consider and "(p. 139). what actions to take in the next few quartersor years, 14Such gameshave been analyzedby Abderrahmane reconsidertheir plans everyfew months,and repeatedly Alj and Haurie Alain (1983) and Epple et al. For a use econometricmodels to projectthe likely effects of generalreference on dynamicgames, see TamerBasar alternativeactions" (p. 109); "But permanentshifts in and GeertOlsder (1982). Epple et al.'s"game F" comes policy regime are by definition rare events. If they close to embodyingthe conceptionthat Sims seems to occurredoften they would not be permanent"(p. 118). have in mind. VOL. 74 NO. 2 CURRENT STA TE OF MA CROECONOMIC THEOR Y 413 provedstrategy for governmentpolicy in the ory of government behavior as a positive future. On the one hand, if this procedure theory of how the governmenthas actually were in fact likely to be persuasivein having behaved.This method of understandingpast the policy recommendationactually adopted governmentpolicy leaves no room for im- soon, it would that the originalecono- proving governmentpolicy in the future. In metric model with its arbitrarilyspecified economics and other social sciences, there rules for governmentpolicy had been mis- are many examples that exhibit the tension specified.A rationalexpectations model dur- between having a theory that, on the one ing the estimationperiod ought to reflectthe hand, can fully explain existing institutions procedureby whichpolicy is thoughtlater to and events in terms of purposefulbehavior, be influenced,for agents are posited to be and on the other hand, can be used to give speculatingabout governmentdecisions into advice for improving things. For example, the indefinite future. On the other hand, if this tension exists between the theory of the this procedureis not thought likely to be a firm and ."7The recent source of persuasive policy recommenda- work on vector autoregressionsand dynamic tions, most of its appealvanishes."5 rational expectations theory manifests this Sims' vision is subject to the observation tension in a new and dramaticcontext, but that, smackingof determinismas it does, it the tensionitself is an old one. lends limitedinterest not only to the estima- Sims has ample company among recent tion of "structural"or "fully interpreted" macroeconomistsin using the hypothesisof vector autoregressions,but to any vector au- optimizinggovernment agents to explain ob- toregressionwhatsoever.'6 In dynamic deci- servationson governmentbehavior. Two ex- sion and , the relevant choices ampleswill illustratethis. First,there is Lucas are among differentstochastic processes. In and Nancy Stokey's model (1983) of the these terms, an analysis that maintains the optimal time structureof governmentdef- assumptionof a fixed probabilisticstructure icits, and of the term structureof govern- permits no policy advice to be given or ment debt. Their model gives the prediction choices to be delineated.Vector autoregres- that in response to temporarylarge current sions become tools for passive,intervention- account government expenditures,such as free forecastingof varioustypes. those associatedwith wars, the government should run temporary deficits, issuing V. Positiveand Normative Economics state-contingentinterest-bearing securities to finance the deficit. The motive for running The view that I have attributedto Sims deficits is to minimize the distortions from subvertsnormative economics, and does so taxes by smoothing their occurrence over by embracinga normativeor optimizingthe- time. The Lucas-Stokeynormative results can be regardedas a positive theory of govern- ment financethat seems to work well for the '5In formal work, this contradiction is evaded by advancedcountries over much of the last 200 regarding analyses of policy interventions as descrip- tions of different , defined on different proba- years. Under the ,wars were bility spaces. The mental comparison is among econo- typicallyaccompanied by temporarysuspen- mies identical with respect to private agents' preferences sions of convertibilityinto specie of govern- and technologies, but differing in government policy ment notes, with the probabilityof subse- regime. The contradiction mentioned in the text surfaces at when attempts are made to put these formal results to quent resumption par dependingdirectly practical use by speaking of regime changes that are on the prospects for military victory. This imagined to occur suddenly in real time. My article with suspension pattern governs European and Neil Wallace (1976) described a version of this con- U.S. data from 1789 to 1928, and can be tradiction. regarded as a mechanism designed to ap- 16The issue here also concerns Gabriel Garcia Marquez (1971, 1983) and D. M. Thomas (1982), who describe settings in which individuals have access to more or less imperfect foresight, but exercise few effec- 17This example was suggested to me by Robert E. tive choices. Lucas, Jr. 414 AEA PAPERS AND PROCEEDINGS MA Y 1984 proximate a Lucas-Stokey optimal fiscal existing patterns of decentralization and policy.18 policy rules can be improved upon. This A second example is John Bryant and opinion comes from the perceptionthat un- Wallace'sthesis (1984) that the observedde- finished and imperfect theories have been nomination structure of government debt believed and acted upon in designing and (interest-bearingsecurities are typically is- operatinginstitutions. Dynamic rational ex- sued only in large denominations, while pectations models provide the main tools non-interest-bearingones are available in that we have for studyingthe operatingchar- small and large denominations)is to be un- acteristics of alternative schemes for de- derstood as the result of the government's centralizingdecisions across institutionsand effort to price discriminatebetween different across time. I believe that will classes of portfolio holders, so as to raise learn interestingand useful things by using seignorage and finance expendituresin an these tools. efficient way.9 20

VI. ConcludingRemarks REFERENCES

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