American Economic Association 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 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. American Economic Association is collaborating with JSTOR to digitize, preserve and extend access to The American Economic Review. 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 data, and conform naturallywith the recur- disowns.2I do so because the argumentthat sive decision theory that is associated with I attribute to him was gatheredduring my stochastic dynamic rational expectations 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 Macroeconomics 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 econometrics,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 economy. 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 vector autoregression 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 goods; 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 Lars Peter Hansen 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 price-setting agents. For a particu- tations equilibria from being Pareto optimal.