Stochastic Trends and Economic Fluctuations By ROBERT G. KING, CHARLES I. PLOSSER, JAMES H. STOCK, AND MARK W. WATSON* Are business cycles mainly the result of permanent shocks to productivity? This paper uses a long-run restriction implied by a large class of real-business-cycle models -identifying permanent productivity shocks as shocks to the common stochastic trend in output, consumption, and investment-to provide new evidence on this question. Econometric tests indicate that this common-stochas- tic-trend/ cointegration implication is consistent with postwar U.S. data. How- ever, in systems with nominal variables, the estimates of this common stochastic trend indicate that permanent productivity shocks typically explain less than half of the business-cycle variability in output, consumption, and investment. (JEL E32, C32) A central, surprising, and controversial tent with the presence of a common result of some currentresearch on real busi- stochastic productivitytrend. Such a trend ness cycles is the claim that a common is capable of explainingimportant compo- stochastic trend-the cumulative effect of nents of fluctuationsin consumption,invest- permanent shocks to productivity-under- ment, and output in a three-variablere- lies the bulk of economic fluctuations. If duced-formsystem. However, the common confirmed, this finding would imply that trend's explanatorypower drops off sharply many other forces have been relatively when measures of money, the price level, unimportantover historicalbusiness cycles, and the nominal interest rate are added to including the monetary and fiscal policy the system.The key implicationof the stan- shocks stressed in traditional macroeco- dard real-business-cyclemodel, that perma- nomic analysis. This paper shows that the nent productivityshocks are the dominant hypothesisof a common stochastic produc- source of economic fluctuations,is not sup- tivity trend has a set of econometricimpli- ported by these data. Moreover,our empiri- cations that allows us to test for its pres- cal results cast doubt on other explanations ence, measure its importance, and extract of the business cycle: estimates of perma- estimates of its realized value. Applying nent nominalshocks, which are constrained these procedures to consumption, invest- to be neutral in the long run, explain little ment, and output for the postwar United real activity. States,we find resultsthat both supportand Our econometricmethodology can deter- contradict this claim in the real-business- mine the importanceof productivityshocks cycle literature. The U.S. data are consis- within a wide class of real-business-cycle (RBC) models with permanentproductivity disturbances.To explain why this is so, we *University of Rochester, University of Rochester, begin by discussing three features of the University of California-Berkeley, and Northwestern researchon which our analysisbuilds. First, University, respectively. The authors thank Ben Bernanke, C. W. J. Granger, Robert Hall, Gary there is a long tradition of empirical sup- Hansen, Thomas Sargent, James Wilcox, and two ref- port for balanced growth in which output, erees for helpful discussions and comments and thank investment, and consumption all display Craig Burnside and Gustavo Gonzaga for valuable positive trend growthbut the consumption: research assistance. This research was supported in output and investment:output"great ratios" part by the National Science Foundation, the Sloan Foundation, and the John M. Olin Foundation at the do not (see e.g., Robert Kosobud and University of Rochester. LawrenceKlein, 1961).Second, in large part 819 820 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 1991 because of this ratio stability, most RBC ond, in a three-variablemodel incorporating models are one-sectormodels which restrict output, consumption, and investment, the preferences and production possibilities so balanced-growthshock explains 60-75 per- that "balanced growth" occurs asymptoti- cent of the variationof output at business- cally when there is a constant rate of cycle horizons (4-20 quarters). Moreover, technological progress. Third, these RBC the estimatedresponse of the real variables models imply that permanentshifts in pro- to the balanced-growthshock is similar to ductivity will induce (i) long-run equipro- the dynamic multipliersimplied by simple portionate shifts in the paths of output, RBC models driven by random-walkpro- consumption, and investment and (ii) dy- ductivity.Third, these results change signif- namic adjustmentswith differential move- icantly when nominal variables are added ments in consumption,investment, and out- to the empirical model. When money, put. prices, and interest rates are added, the The econometric procedures developed balanced-growthshock explains less of the here use the models' long-run balanced- fluctuationsin output, from 35 percent to 44 growthimplication to isolate the permanent percent depending on the particularspeci- shocks in productivityand then to trace out fication used. Permanent nominal shocks, the short-runeffects of these shocks. These identified by imposing long-run neutrality econometricprocedures rely on the fact that for output, explainlittle of the variabilityin balanced growth under uncertaintyimplies the real variables. Much of the short-run that consumption, investment, and output variabilityin output and investmentis asso- are cointegrated in the sense of Robert ciated with a shock that has a persistent Engle and Clive Granger (1987). In turn, effect on real interest rates. These results this means that a cointegrated vector au- suggest that models that rely solely on per- toregression(VAR) nests log-linearapprox- manent productivity or long-run neutral imations of all RBC models that generate nominalshocks are not capableof capturing long-run balanced growth. Our empirical importantfeatures of the postwar U.S. ex- analysis is based on such a cointegrated perience. VAR (or vector error-correctionmodel), The paper is organizedas follows.Section which is otherwise unrestrictedby prefer- I provides theoretical backgroundand re- ences or technology.Thus, our conclusions views recent work on real business cycles. can be interpretedas casting doubt on the Section II outlines the empiricalmodel and strong claims emergingfrom an entire class discusses identification.Sections III and IV of real-business-cyclemodels. present the empirical results. Our conclu- The empirical analysis is structured sions are presented in Section V. around three questions. First, what are the cointegration properties of postwar U.S. I. Growthand Fluctuations:Theoretical data, and are these properties consistent Background with the predictions of balanced growth? Second, how much of the cyclicalvariation To fix some ideas and notation, this sec- in the data can be attributedto innovations tion outlines a simple real-business-cycle in the common stochastic trends? Third, a model with permanent productivity shocks. naturalalternative to RBC models is one in The model is of the general class put for- which nominal variablesplay an important ward by Fynn Kydland and Edward Prescott role. Do innovationsassociated with nomi- (1982) and is detailed in King et al. (1988). nal variables explain important cyclical Output, Y, is produced via a constant- movementsin the real variables? returns-to-scale Cobb-Douglas production The empirical results provide robust an- function: swers to these questions. First, cointegra- tion tests and estimated cointegratingvec- wheK) ihYt =cAtal stokaNd e tors indicate that the data are consistent with the balanced-growthhypothesis. Sec- where Kt is the capital stock and Nt repre- VOL. 81 NO. 4 KING ETAL.: STOCHASTIC TRENDS 821 sents labor input. Total factor productivity, [I(O) or "stationary"]. In Engle and At, follows a logarithmicrandom walk: Granger's(1987) terminology,the two lin- early independent cointegratingvectors, a1 (2) log(At) = /LA +log(At_1) + et = (-11,0)' and a 2 = (- 1,0, 1) isolate sta- tionary linear combinations of Xt corre- where the innovations,{ft}, are independent spondingto the logarithmsof the balanced- and identicallydistributed with a mean of 0 growthgreat ratios. and a variance of o-2. The parameter LtA In this basic one-sector model and vari- represents the average rate of growth in ants of it, the precise dynamic adjustment productivity;et representsdeviations of ac- process to a permanent productivityshock tual growthfrom this average. depends on the details of preferences and Within the basic neoclassicalmodel with technology. For example, recent RBC re- deterministic trends, it is familiar (from search has studied alterationsin the invest- Robert Solow [1970]) that per capita con- ment technology(time-to-build, adjustment sumption, investment, and output all grow costs, and inventories),the productiontech- at the rate jLA /0 in steady state.1The com- nology (variable capacity utilization, labor mon deterministic trend implies that the indivisibilities,and employmentadjustment great ratios of investmentand consumption costs), preferences (nonseparabilities in to output are constantalong the steady-state leisure and durable consumption goods), growth path. When uncertainty is added, and serial correlation in the productivity realizations of et change the forecast of growth process. Two general properties trend productivityequally at all future dates: emerge from these investigations.First, the Et log(At+s) = Et1(At+s) + et. A positive productivityshock sets off transitionaldy- productivityshock