Output Persistence, Economic Structure, and the Choice of Stabilization Policy

STEVEN N. DURLAUF Stanford University Output Persistence, Economic Structure, and the Choice of Stabilization Policy A STRIKINGchange in empiricalmacroeconomics in the 1980s has been the developmentof an alternativeway to think about aggregatetrends andcycles. Traditionally,aggregate series such as gross nationalproduct have been modeled as stationaryprocesses about a deterministictrend. All aggregate fluctuations were thus short-run phenomena with no bearingon the long-runbehavior of the economy. Startingwith the work of Charles Nelson and Charles Plosser, however, empirical workers have developed considerableevidence that suggests that some component of aggregateactivity follows a stochastic trend-the long-runpath of the macroeconomyis permanentlyaffected by contemporaryevents. I This perspective means that not only are trend-cycle decompositions extremelydifficult, in thatthe same structuralstochastic elements affect both underlyingtime series, but that, in addition, the feedback mecha- nisms from current activity to long-rungrowth render the traditional distinctionmeaningless. The identificationof unitroots has become a veritablecottage industry amongempirical workers. On the other hand, there has been compara- tively little work on the economics of unit roots. Most theoreticalwork on the subject has treated unit roots exclusively as a manifestationof I thankAndrew Bernard, Robert Hall, DavidRomer, John Shoven, ChristopherSims, GavinWright, and membersof the BrookingsPanel for helpfuldiscussions. Outstanding researchassistance by AndrewBernard and SuzanneCooper is gratefullyacknowledged. LauraDolly has suppliedsuperb secretarial support. All errorsare mine. 1. Nelson and Plosser (1982). 69 70 Brookings Papers on Economic Activity, 2:1989 technology or supply shocks. Robert King and others assume that the persistentcomponent of GNP is generatedby a randomwalk in technology.2 Jones and Manuellishow that if the marginalproduct of capitalis bounded sufficientlyabove zero, stationaryinnovations to wealth will be spreadover an infinitehorizon.3 This idea is of course the basis of the random walk theory of consumption, which requires that the gross marginalproduct of capital is a constant equal to the inverse of the discount rate. These examples, however, require very specialized as- sumptions on technology. Typically, macroeconomistsemploy repre- sentative agent models to explain the behaviorof aggregatetime series. This class of models represents the equilibriumsample path for the economy as the solutionto some sort of dynamicprogramming problem. Dynamic programmingproblems in turn generate unit roots in control variables only for isolated parametervalues unless one assumes that some of the exogenous state variablesalready contain unit roots. From the representativeagent perspective, unit roots are rare phenomena. ChristopherSims has gone so far as to conclude that the theoretical justificationfor looking for unit roots follows from "algebraicconven- ience and professionalinertia, not by experimentalevidence or intuitive plausibility."4 Interestin the existence of unit roots has been matchedby interestin assessing the role of permanentshocks in explainingtotal fluctuations. Aggregatefluctuations may be conceptualizedas generatedby a com- binationof persistentand mean-revertingcomponents. The importance of the unit root as a contributorto the variance of output changes has engendered considerable controversy. John Campbell, N. Gregory Mankiw, and John Cochrane have developed substantially different perspectiveson the magnitudeof the unit root componentof GNP.' The unit root has furtherbeen treatedby numerousauthors as a measureof the componentof aggregateinnovations induced by supply-sidefactors. OlivierBlanchard and Danny Quah perform trend-cycle decompositions by assumingthat demand shocks are transitory.6J. BradfordDe Long and LawrenceSummers go so far as to arguethat the greaterpersistence 2. Kingand others (1987). 3. Jones and Manuelli(1987). 4. Sims (1988,p. 464). 5. Campbelland Mankiw(1987a); Cochrane (1988). 6. Blanchardand Quah(1988). Steven N. Durlauf 71 in postwar than pre-Depressionfluctuations is proof that stabilization policy has been a success, on the grounds that successful policy can eliminateonly mean-revertingfluctuations.i This paperconsiders the role of unit root findingsin the interpretation of economic fluctuationsand in the formulationof monetaryand fiscal policy rules. The papercomplements Sims's critiquein the sense that it emphasizes that what is importantabout output fluctuationsis persistence ratherthan the presence of an exact unit root. In several respects, exact unit root findingsmay not even matter. First, from the vantage point of a social planner, exact and near unit roots are equivalent. Intuitively, a social welfare function that discounts future utility is unaffectedby distant events, so that permanenceof innovationsis not necessarilyimportant. Second, unit roots provide little informationfor identifyingeconomic structure.This claim follows from several consid- erations. Empirically, cross-country data provide little evidence that permanentshocks eventually migrate internationally,whereas many sectors of the Americaneconomy seem to possess a common unit root despite differences in production functions. On the theoretical side, various business cycle models with fundamentally different policy implicationsmay be shown to be compatiblewith unit roots in economic time series. Although thus rejecting some previous interpretationsof the data, this paper argues that the unit root evidence is importantin several senses. Unit roots represent a parsimonious way of expressing the persistence of fluctuationsand as such are a significantstylized fact about the macroeconomy.This stylized fact is a naturalimplication of dynamic coordination failure and is therefore consistent with much currentmacroeconomic theory. Understandingthe degreeof persistence in aggregatefluctuations helps in assessing the potentialrole of coordi- nationfailure as a source of fluctuations. Further,understanding the degreeof persistencein economic fluctuations is essential for computingwelfare-maximizing policy rules. The dividedstate of empiricaland theoreticalmacroeconomics means that a policymakerought to be modeledas uncertainabout economic structure. Uncertaintyabout economic structureis equivalent in this context to uncertaintyabout policy effects-a question originally analyzed by 7. De Longand Summers(1988). 72 Brookings Papers on Economic Activity, 2:1989 William Brainard.8Brainard's work demonstrated that when policy multipliersare random,optimal policy constructionleads to a diversifi- cation of countercyclicalpolicy choices. Brainard'soriginal research concentratedon the role of multiplepolicy instrumentsin diversifying the uncertaintyof individualpolicies. In the case of uncertainstructure and one policy instrument,this idea can be exploited to demonstrate thatone chooses a rulethat weights the optimalrules under each structure based upon minimizingsome expected value function. The optimalrule diversifies in the sense that it constructs a weighting across different rules that are each optimal,conditional on a given regime. Persistencein fluctuationsmeans that if stabilizationpolicy success- fully reversesdownturns, then the social welfareimprovements are very large. As a result, the new empirical macroeconomics places a large weight on a countercyclical policy rule. Consequently, persistence in output leads to powerful policy implications even in the absence of strongimplications about economic structure.9 Welfare and Persistence The issue of unit roots and output persistence centers on long-run forecasts of log per capitaoutput Yt.In traditionalformulations cc (1) yt = Pt + E wjEt-j j=0 where t denotes time and the E's are white noise innovations. In this formulation, the y coefficients are square summable, j%=o-yj2 < X, which in turnimplies that the weights yj decline to zero. When output can be represented in this fashion, then long-run forecasts of GNP eventually become independentof the history of the process: (2) lim E(Yk- IkIEt)= 0. 8. Brainard(1967). 9. In fact, the "new macroeconomics"articulated by RobertHall and others, where the aggregateequilibrium is indeterminate,leads to similarpolicy conclusions. See Hall (1989)for an exampleof this type of model. Steven N. Durlauf 73 Likewise, (3) lim ELYk - 3kILY(t)]= O, k=>oc whereLy(t) represents total information contained in linearcombinations of Yt, Yt1-. In the traditional perspective, the deterministic trend, by proxyingfor technicalchange, capturesthe long-rundynamics of the economy. The new perspective on aggregate behavior treats the changes in outputas a stationaryprocess. The canonicalform for the time series of outputchanges is cc (4) A Yt + Oj Et j j= 0 where the a-coefficients are squaresummable and the innovationsE are uncorrelatedwith zero mean. Since one can think of YK,as Yt + EJ=1 A Y,+j, the long-runforecast of the economy is affected by the expecta- tions of all future changes in output. If there is no tendency for shocks to the economy to revertto zero, then it is apparentthat history matters for long-runpredictions about the economy. 10 Persistence in aggregate output reveals nothing about its relative importanceas a component of fluctuations.This is true in two senses. First, there is a statisticalquestion as to the magnitudeof persistence as a component of total fluctuations. For example, if 99 percent of the varianceof AYt

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