The Evolution of Macro Models at the Federal Reserve Board

The Evolution of Macro Models at the Federal Reserve Board Flint Brayton,AndrewLevin,RalphTryon,andJohnC.Williams (cid:3) Federal Reserve Board Washington,D.C.20551 Revised: February7,1997 (cid:3) This paper was prepared for the Carnegie-Rochester Conference on Public Policy, November 22-23, 1996.TheauthorsgratefullyacknowledgethecommentsofRobertKingandBenMcCallumandparticipants attheconference.ThemacroeconomicmodelsattheFederalReserveBoarddescribedinthispaperrepresent the work of many individuals at the Fed. Brayton and Williams participated in the project to build the FRB/US model, along with other membersof the Macroeconomicsand QuantitativeStudiessection in the DivisionofResearchandStatistics. TheywouldliketoacknowledgethevaluableassistanceofSteveSumner in preparing this paper. The FRB/MCM was developed in the Trade and Financial Studies section of the DivisionofInternationalFinance. LevinandTryonacknowledgevaluablediscussionswithDavidBowman, Chris Erceg, Dale Henderson, and John Rogers, and the excellentresearch assistance of Asim Husain and Jon Otting. Views presented arethose of theauthorsand do notnecessarily representthoseof the Federal ReserveBoard.

1 Introduction Large-scalemacroeconometricmodelshavebeenusedforforecastingandquantitativepolicyandmacroeconomicanalysisattheFederalReserveBoardforthepast30years.1 Model design and development efforts at the Fed have been divided into two complementary research programs. One project, undertaken in the Division of Research and Statistics, focusesontheU.S.economy,andtheother,residingintheDivisionofInternationalFinance, is oriented toward the global economy. For some applications, the macro models maintainedbythetwodivisionsare combinedtoform asingleworldmodel. The first-generation Fed models—MPSandMCM—were developedinthe 1960'sand 1970's and based on the then-reigning IS/LM/Phillips curve paradigm. During the 1970's and1980's,thetheoreticalunderpinningsofmodelsofthistypewereseriouslychallenged. Thesecriticisms,aswellasimprovementsineconometricmethodologyandcomputational capabilities, led to a basic redesign of the Fed macro models in the 1990's. These secondgenerationmodelsrepresentasignificantimprovementovertheirpredecessorsinthetreatment of expectations, intertemporal budget constraints, and household and firm decisionmaking,whileat thesametimeholdingtoahighstandardofgoodnessoffit. ThispaperdescribestheevolutionofmacromodelsattheFed,withanemphasisonthe structureandpropertiesofthesecond-generationmodelscurrentlyinuse. Thenextsection summarizesthehistoryoftheinitialpairofmodelsusedattheFed—MPSandMCM—and section 3 presents the new ones, focusing on the combined FRB/WORLD model. Section 4describesthesystempropertiesofthisnewmodel,andthelastsectionprovidesexamples ofhowitmaybeusedforpolicyanalysis. Conclusionsthenfollow. 2 The First Generation of Macro Models at the Fed Theinitialphaseofmacromodelingat theFederal Reserve Board beganinthelate1960's with the construction of the MPS model of the U.S. economy and continued in the 1970's with the building of the Multi-Country Model (MCM). The decisions to develop these models were made at a time when interest in large-scale macroeconomic models was widespread—intheacademiccommunityandelsewhere—andadvancesincomputertech- 1Reifschneider,Stockton,andWilcox(1997)discusstheusesoftheseandothereconomicmodelsatthe FederalReserveBoard. 1

nology were making the use of such models feasible, as demonstrated by the Brookings Model, work on which had started in the early 1960's. This favorable climate for model buildingfosteredprojectstodevelopotherlarge-scalemodelsoftheU.S.economy,including the MPS model. Soon thereafter, modeling efforts expanded from the development of isolated national models to ones having a more international perspective. The MCM was oneofthefirst majoreffortsinthisdirection. 2.1 1966-1975: Focus on the U.S. Economy Work on the MPS model began in 1966 as a joint effort among a group of academic economists and staff members of the Division of Research and Statistics at the Federal Reserve Board. Leading the project were Franco Modigliani of MIT, Albert Ando of the UniversityofPennsylvania,andFrankdeLeeuwoftheFed.2 ThemodelenteredintooperationalusebyBoardstaffin1970forforecastingandpolicyanalysis. Theinitialoperational version of MPS contained about 60 behavioral equations, making it considerably smaller thantheBrookingsmodel,versionsofwhichcontained200ormorebehavioralequations. Much of the basic structure of the first versionof MPS was retained throughoutits periodofuseattheFed,whichendedin1995. Inthatstructure,short-rundynamicsfollowed the IS/LM paradigm, augmented with a Phillips curve specification of wage inflation and a markup equation for the price level. Underlying these dynamics were a long-run neoclassical growthmodel of productionand factor demands and the life-cycle model of consumption. In this structure, the long-runlevel of output was determinedby supplyfactors. Careful attention was paid to imposing homogeneity conditions, such as those needed to ensuretheneutralityofmoneyinthelongrun,andtoincludingsectoralbudgetconstraints. The role of expectations was recognized; however, in practice expectations were characterized as adaptiveor implicitlysubsumed in the lags of explanatory variables included in variousequations. Because MPS was designed for use in the analysis of stabilization policies, close attention was given to the inclusion of a wide range of monetary and fiscal policy “levers” and to the delineation of the mechanisms throughwhich movementsin policyinstruments 2FordescriptionsofearlyversionsofMPS,seeAndoandModigliani(1969),RascheandShapiro(1968), de Leeuw and Gramlich (1968, 1969), and Ando and Rasche (1971). The 1985 version is presented in Brayton and Mauskopf (1985). MPS is an abbreviation of MIT, University of Pennsylvania, and Social ScienceResearchCouncil. 2

affected the macro economy. The attention paid to fiscal policy reflected, in part, the optimistic view of the time that discretionary fiscal actions could be an important ingredient in countercyclical macro policies. With regard to monetary policy, the model contained threeprimarytransmissionchannels: effects oftheusercostofcapitaloninvestment,nonhumanwealthonconsumption,andcreditrationingonhousingconstruction(deLeeuwand Gramlich,1969). Thesechannelsalloperatedthroughinterestratesandincludedequations linkinglong-terminterestratestoshort-termratesandthestockmarkettobondrates. Aside from their influence on short-term interest rates, monetary quantities had virtually no effectsoutsideofthemonetarysectoritself. Amonetaryrealbalanceeffectoperatedthrough theinfluenceofwealthonconsumption,but itsquantitativesignificancewas minimal. Up until the early 1970's, most modelers interpreted the inflation experience of the postwar period as supporting the presence of a long-run tradeoff between inflation and unemployment, and in this respect the properties of the first operational version of MPS were no different thanthose of other large-scale models (de Menil and Enzler, 1972). The increases in inflation of the late 1960's and very early 1970's, however, suggested that the long-run Phillips curve was vertical, and this was incorporated into the model's structure (Enzler and Pierce, 1974). The wage-price block in MPS remained little-changed for the next 20 years and came to be regarded as one of the more stable parts of the model (Ando andBrayton,1995). The first oil-price shock motivated additional work on the supply side of MPS. In an article written in early 1974, soon after the initial jump in world oil prices, Enzler and Pierce (1974) used the MPS model to provide a reasonably accurate assessment of the “stagflationary” consequences of a sustained increase in the relative price of energy. At the time, the model did not formally contain many of the linkages from oil prices to other macroeconomic variables needed to carry out the experiment, and Enzler and Pierce had to deal with omitted effects in ad hoc ways. Later, as an outgrowth of their work, the model's supply structure was revised to include energy as a factor of production and to permit differential effects of energy and food prices on the prices for components of final demand. Anothermajorshiftintheeconomicclimateintheearly1970'swas thecollapseofthe Bretton-Woodssystemoffixedexchangerates,followingontheexchangeratecrisesofthe 1960's. Atthetime,MPShadonlyaveryrudimentaryforeigntradesectorinwhichexports 3

wereexogenous;moreover,theexchangeratedidnotappearinthemodelatall. Inresponse tothefloatingofexchangeratesandthegrowingimportanceoftradeflows,thetradesector was significantly enlarged. A set of portfolio-balance equations for international financial capitalstockswereincludedtoendogenizetheexchangerate. Still,MPSremainedasinglecountrymodelwithjustafewequationsrepresentingforeigneconomicdevelopments. 2.2 1975-1980: An International Focus The experience of the first oil shock and the floating of exchange rates, along with other events, combined to raise interest in global macroeconomic modeling. The increasing opennessoftheU.S.economyandgrowthinotherindustrialcountriesincreasedtheimportance of foreign economic developments and trade on the domestic economy. The OPEC oil shock of 1974 underscored the dramatic effects that external supplyshocks could have ontheU.S.economy. Against this background, the Division of International Finance at the Federal Reserve Board began in 1975 to develop a multi-country econometric model that could be used to model the external sector of the U.S. economy more completely than existing models and to provide an empirical framework for modeling interactions among the major industrial countries. This project was one of the first efforts to build a multi-country econometric model,followingonthepioneeringworkbyLawrenceKleinonProject LINK. ThefirstversionoftheMulti-CountryModel(MCM)modeledtheeconomiesofCanada, Germany, Japan, the U.K., the U.S., and a rest-of-world (ROW) sector. In total, the MCM contained over 200 behavioral equations. Like the MPS model, the basic framework for the MCM model combined the short-run dynamics of the IS/LM/Phillips curve paradigm andimplicitexpectationswithalong-runneoclassical growthmodel. The MCM built upon extensive empirical research in two areas of international economics. One was the modeling of international capital flows, which had received a great deal of attention in the fixed exchange rate regime of the 1960's, and the other the modeling of bilateral trade flows. In its original incarnation, the MCM used bilateral equations tomodelgoodstradeamongtheindividualcountries,andmultilateralequationstoexplain gross inflows and outflows of both direct and portfolio claims and liabilities. Reaction functions were used to describe official exchange market interventions, and the nominal exchangeratewasdeterminedimplicitly,asthepricethatclearedthebalanceofpayments. 4

Thedomesticfinancialsectorofeachcountrywasmodeledinkeepingwiththisportfoliobalanceapproachtothebalanceofpayments. Theprivatebankingsectorwasmodeledexplicitly,withthe demand for the monetarybase derivedfrom banks' desired reserves. The authoritiescontrolledthemonetarybase,andtheshort-terminterestrateclearedthemoney market. Thedemandforbondswasalsomodeledexplicitly,andthelong-terminterestrate clearedthebondmarketratherthanbeingdeterminedinanexplicitterm-structurerelation. Guy Stevens led the effort to develop the original MCM, which was completed and brought into regular use at the Board in 1979. Stevens et al. (1984) describes the first version of the MCM in detail. Its primary use was to simulate the effects of alternative policy scenarios and external shocks. The MCM was not used directly for forecasting, although simulations of alternative scenarios provided an input into forecasts of foreign activityandtheU.S.externalsector. 2.3 1980-1990: Incremental Changes After their initial development, changes to MPS and MCM came about in response to economic events, changes in institutional and regulatory structure, and, to a lesser extent, developmentsontheacademicfront. Forthemostpart,revisionswereincrementalthrough the 1980's and very early 1990's. In the current decade, resources were redirected to the designandconstructionofnewmodelsthatincorporatedmorefullyinnovationsinmacroeconomictheoryand econometrics. Onthedomesticside,financialinnovationandderegulationresultedinchangesincredit and moneymarkets that necessitated significant revisions to the MPS model. Almost onethirdof thebehavioral equationsinthefirst versionofMPS were inthehousingand mortgagesectors. Atthetime,therationingofmortgagecreditthataccompaniedariseinmarket interest rates was a key mechanism through which monetary policy actions influenced the economy. In the late 1970's and early 1980's, the factors responsible for the rationing of mortgage funds—legislated ceilings on interest rates paid on deposits and the lack of integration between mortgage markets and other capital markets—disappeared, leading to a dramatic simplification of the financial block of the model. Because mortgage quantities were no longer needed in the equations for residential construction, the detailed mortgage sector was replaced witha singleequationin which the mortgagerate was related toother market interest rates. Thischange, inturn,eliminatedtheneed tohavea detailedmodelof 5

depositflowsandinterestrates at thriftinstitutions. Financial innovationand deregulation, and associated shifts over time in the emphasis placed by policymakers on various shorter-term monetary instruments and targets, led to further revisions to the monetary sector of MPS. In the initial version of the model, the reserves market received considerable attention, and early presentations of the model's system properties were usually based on the assumption that nonborrowed reserves was theexogenousinstrumentofpolicy. Asthe1970'sprogressed,however,policysimulations werebasedmostfrequentlyontheassumptionthatM1wasexogenous,makingthereserves equationslargelysuperfluous. Later,theinstabilityofM1demandequationsledtoagreater emphasis on M2, which was mirrored in an expansion of the monetary sector to include interest rate and quantityequations for components of M2. More recently, attentionto the model's monetary sector diminishedas instabilityof the demand equations for M2 caused short-runcharacterizations ofpolicytobestatedinterms ofthefederal fundsrate. On the international side, several trends in academic economics contributed to an important change in the modeling of the international accounts in the MCM. In its original version,thebalance ofpayments was modeledusinga structural,portfolio-balanceframework. But, the assumptions required to specify and estimate equations for capital flows led to dissatisfaction with this approach. The overshooting model of Dornbusch (1976) provided an attractive alternative that offered an open-economy model of exchange rate determinationinarisk-neutralframework. Theseandotherfactorsledtotheuseofamodified interest parity relationship in the MCM to determine exchange rates, in place of the capital flow equations. Similar considerations led to the elimination of the banking sector fromthecountrymodels. Instead,theauthoritieswereassumedtocontroleitherthemoney stockortheshort-terminterestrate. ThesecondoilshockgaverisetotheexplicitinclusionofoilintheMCM,anon-trivial extensionbecausethebilateraltradeequationsusedinthemodelatthetimeexplainedtotal goodstrade. Themodel was alsoreestimated,andmanyequationsrespecified, usingsome of the error-correction specifications and methods of residual analysis suggested by David HendryandotherLSEeconometricians. Edison,Marquez,andTryon(1989)describethese andotherchanges totheMCM. The final restructuring and reestimation of MCM came in 1991-1992 when it was extendedto12regions(individualmodelsfor theG-7andMexico,plusaggregateblocksfor 6

other OECD countries, the newly industrialized economies, OPEC, and ROW). The other significant modification made at this time was replacing the bilateral trade structure with a multilateral one. This change greatly simplified the model's data requirements and the analysisofsimulationresultsfor agivencountry. 3 FRB Policy Models Today Amongacademics,interestinlarge-scalemacroeconomicmodelsstartedtodiminishinthe 1970's, and subsequently a large gulf emerged between applied macroeconomics as practicedbyacademicsandthatcontainedinlarge-scalemodels. Thebasicunderpinningsofthe traditional IS/LM/Phillips curve model were challenged on a number of fronts, including identification, treatment of expectations,and econometric methodology. This led to a fundamentaloverhaulofboththeMPSandMCMmodels,culminatinginasetofreplacement models—FRB/US,FRB/MCM,andthecombinedFRB/WORLD.Fromthebeginning,the new models were designed to incorporate explicit specifications of expectation formation and intertemporal decisionmaking. In thisway, the criticismsof the first-generation models wereat leastpartiallyaddressed. 3.1 Motivations for Fundamental Changes Some academic reviews of the macroeconomic models of the 1970s were, if nothing else, blunt: Lucas and Sargent (1978) described the “spectacular failure” of Keynesian macro models and Sims (1980) characterized the identification restrictions in these models as “incredible.” Underlying these and other criticisms was the general theme that economic theory had to be relied on more heavily for guidance in specifying structural equations. In particular, applied macroeconomic analysis needed to give more attentionto the role of expectationsineconomicdecisions. Several specific developments in applied macroeconomics that grew out of these concerns were important in the decision to builda new set of macro models at the Fed, rather thantocontinuetheapproachofincrementalrevisions. Onewas theburgeoninguseofthe rationalexpectationsassumptioninappliedresearchsubsequenttoLucas's(1976)critique that policyanalysis couldnot be conductedusingmodels that failedtoidentifyfundamentalstructuralparameters. Anotherwasthedevelopmentofmodelsofdynamicoptimization 7

andtheiruseinmanymacroeconomicapplications. A related issue concerned methods by which a model's system properties could be evaluated. The vast literature on atheortic VARs initiated by Sims (1980) provided useful benchmarks against which structural models could be gauged. On the econometric front, theworkofEngleandGranger(1987)andothers provideda frameworkfortheestimation andtestingoflong-runrelationships. The decisiontoconstruct newmacro modelswas alsomotivatedbya desiretoaddress issues that could not be analyzed adequately given the treatment of expectations in the existingmodels. Onesetofsuchissuesconcernedeffectsofexpectedshiftsinfiscalpolicy on the level of long-term interest rates. Could a long-term fiscal consolidation induce a reduction of long-term interest rates large enough to offset its direct negative effects on aggregate demand? The first attempt to address this question with the MPS model was undertaken in the early 1980's by Jared Enzler and Eileen Mauskopf. Simulations were conducted with a version of the model in which the standard term structure and stock market equations, which contained adaptive expectations, were replaced with alternatives incorporatingrationalexpectations. A second issue of interest to policymakers was the cost, in terms of foregone output, of reducing the rate of inflation. In the MPS and MCM models, the (nearly) linear structure and assumptionof adaptiveexpectations made the standard measure of this cost—the output sacrifice ratio—independent of such factors as the speed with which a disinflation tookplace and the degree to which the publicunderstoodor believedin a policytoreduce inflation. Althoughthese models providedan estimate of the sacrifice ratio, they were not useful in analyzing the determinants of the costs of disinflation and how policy could be designedtominimizethesecosts. Evenwiththesestimulantsforthedevelopmentofnewmacromodelsfeaturingrational expectations, their construction did not take place overnight. The technical requirements forestimatingandsimulatinglarge-scalemodelswithrationalexpectationsaresubstantial. And the standard rational expectations assumption is not necessarily the superior choice, givencostsofacquiringandprocessinginformation. 8

3.2 1990-1996: The Development of New Macro Models Projectstodevelopanewpairofmacroeconomicmodelswereinitiatedintheearly1990's. Work onthe successor toMPS started in1991,while developmentof a new versionof the MCMbeganin1993. FRB/USandFRB/MCM officiallyreplacedtheearliergenerationof models in 1996, and a versionwhich links the foreign country models of FRB/MCM with FRB/US, called FRB/WORLD, is now the main policy model at the Board. FRB/US is alsousedforshort-runforecasting. FRB/WORLDcontainsover250behavioralequations, of which 40 describe the U.S. economy and the rest describe the 11 other countries and regions. The large size and degree of disaggregation in the models is due, in part, to the requirement that they be able to execute a wide range of types of simulations and provide estimates of outcomes for a large set of variables of interest. Equations are estimatedwith single-equation techniques; model size precludes full-system estimation at this time, but simultaneousestimationofblocksofequationsis planned. In terms of basic structure, the new models share several features with the old. In the short run prices are sticky and output is determined by aggregate demand. In the long run prices adjust fullyandtheequilibriumis determinedbysupplyfactors. Thedifferences lie primarilyinthespecificationofexpectationsandtheprocessofdynamicadjustmenttothe long-runequilibrium. The three basic building blocks of FRB/WORLD are equilibrium conditions, expectation formation, and dynamic adjustments. Equilibrium conditions describe the relationships between macroeconomic variables when adjustment dynamics are fully worked out. Among the fundamentals that shape the long-run equilibrium allocation of resources in each country/regionare three-factor (labor, capital, and energy) Cobb-Douglas production functionswhichdetermineaggregatesupplyandequilibriumfactordemands. FRB/WORLD ascribes an important role to expectations. Anticipated values of future variables directly influence interest and exchange rates, various components of aggregate demand, and wages and prices. Recognizing that no single assumption regarding the formation of expectations is likely to be appropriate in all circumstances and that it may be useful to see how different specifications in this regard affect system properties, the new model has been designed to have the flexibility to be simulated under alternative assumptionsabouthowexpectationsareformed. Atpresent,twooptions(orcombinationsthereof) are available: backward-looking, or adaptive, expectations and model-consistent, or ratio- 9

nal,expectations. For the U.S. component of FRB/WORLD, adaptive expectations is implemented by assuming that all agents share a common small vector autoregression (VAR) model of the economy that includes past observations of inflation, interest rates, output, and long-run expectations of inflation and interest rates. Firms and households use this small model, augmentedwithadditionalequationsforvariablesspecifictoaparticularsector,toforecast future values of quantities of interest. In the other countries, adaptive expectations are representedbyunivariateprocesses. VAR-based or adaptive expectations limit the information set that is assumed to be available. At the other extreme is the model-consistent, or rational, assumption in which expectationsaregeneratedusingthepredictedvaluesfromthemodelitself. Solutionsunder model-consistentexpectationsareimplementedusingavariantoftheextendedpathmethod introduced by Fair and Taylor (1983). The future path of exogenous variables is assumed tobeknowninadvance. Duetothecomputationalcostsassociatedwiththismethod,aloglinearized version of the U.S. model has been created that can be solved efficiently using the AIM implementation (Anderson and Moore, 1985) of the Blanchard-Kahn solution method. Thefocus onexpectationsformationingeneral,andrational expectationsinparticular, necessitated that even more attention be given to equilibrium properties than was the case in the first-generation models. For example, budget constraints on the present discounted value of fiscal and external deficits are necessary for rational expectations solutions to exist. Long-run fiscal solvency is maintained by an endogenous tax rate reaction function, which adjusts the income or sales tax rate when the ratio of nominal government debt to GDP deviates from a specified target. Similarly, changes in the ratio of net external debt to GDP lead to corresponding movements in the sovereign risk premium. Thus, through uncovered interest parity, a deterioration of the current account induces an increase in the domesticrealinterestrateand/oradepreciationoftherealexchangerate. Areasonabledegreeofsovereignriskpremiumadjustmentensuresthatimprovednetexportsofgoodsand non-factor services will outweigh the higher net factor payments resulting from the initial increase in external debt, and thereby prevents an explosive path for the current account andnetexternal debt. The final building block is dynamic adjustments. A clear distinction is made between 10

the behavior of financial variables—bonds, equity, and the exchange rate—where adjustment tofundamentalsis assumedtobeinstantaneous,andnonfinancial variables—suchas demand components, prices, and wages—which adjust gradually. In the U.S. sector, decision rules based on a generalized model of adjustment costs are used for many key nonfinancial equations, and error correction specifications are used elsewhere. The non-U.S. sectors employ Taylor's (1980) staggered contracts model for wages, and error correction orpartialadjustmentspecificationsotherwise. 3.3 The U.S. Sector Not surprisingly for a Fed macro model, considerable attention was given to depicting as realistically as possible the implications of U.S. monetary policy actions on the U.S. economy. Amainconcerninthisregardwas thespecificationofdynamicsassociatedwith real and nominal rigidities and the role of expectations in intertemporal decision making. ForamoredetaileddescriptionofFRB/US, seeBraytonandTinsley(1996). A distinguishing feature of the U.S. sector is the use of a new model of generalized adjustment costs developed by Tinsley (1993). As is well known, the standard linearquadratic (LQ) model of adjustment costs frequently does a poor job in characterizing the dynamicbehaviorofmacroeconomicvariables. Thegeneralizedmodelofadjustmentcosts employed here, named PAC for “polynomial adjustment costs,” permits richer dynamics withinatheoretically-basedframeworkthatisparsimoniouswithregardtocoefficientsand contains testable restrictions. Because of its central role in the U.S. sector, as well as its generally successful application as gauged by the goodness of fit of equations and their performance on misspecification tests, we describe the derivation and implementation of PAC beforepresentingthestructureofthesectormorebroadly. AdjustmentDynamics. Theadjustmentdynamicsofmostmajornonfinancialvariables, including consumption, investment, hours and the price and wage levels, are based on the PACapproach. (Inthefollowingequations,allfuture-datedvariablesshouldbeinterpreted as expected values even when the expectations operator has been suppressed.) Several observationally-equivalentcostfunctionscanbeusedtoderivethePAC specification. One suchcostfunction, C t , C t = 1 = Xi 0 (cid:12) i [ ( y +t i (cid:0) y (cid:3) +t i ) 2 + Xk m = 1 b k ( ( 1 (cid:0) L ) k y +t i ) 2 ] ; (1) 11

penalizes both deviations of a variable y from its desired value y (cid:3) —as determined by an equilibrium condition—and movements in the level and m (cid:0) 1 time derivatives of the variable y . (cid:12) (= .98) is a discount factor, and b k ; k = 1 ; : : : ; m ; are cost parameters. A specialcaseofthecostfunction,popularintheappliedmacroliterature,isthatofquadratic adjustment costs on changes in the level of y ( m = 1 ). (Inventory research frequently uses specifications that are similar to the case m = 2 .) As will be shown, the form of generalized adjustment costs in equation (1) leads to a closed-form decision rule that is well-suited for empirical work.3 We will use the terms equilibrium, target, and desired valueinterchangeablytodescribe y (cid:3) . MinimizationofcostsyieldstheEulerequation, ( y t (cid:0) y (cid:3) t ) + Xk m = 1 b k [ ( 1 (cid:0) L ) ( 1 (cid:0) (cid:12) F ) ] k y t = 0 ; (2) where L is the lag operator and F ( (cid:17) L (cid:0) 1 ) is the lead operator. This expression can be writtenmorecompactlyas A ( (cid:12) F ) A ( L ) y t (cid:0) c y (cid:3) t = 0 ; (3) where A is a polynomial in the lag and lead operators of order m , e.g., a 1 L (cid:0) : : : (cid:0) a m L m A ( L ) = 1 (cid:0) and A ( (cid:12) F ) = 1 (cid:0) a 1 (cid:12) F (cid:0) : : : (cid:0) a m (cid:12) m F m , and c = A ( 1 ) A ( (cid:12) ) is a constant. The m parameters in A are transformationsof the m cost parameters inequation (1). Becausethedynamicstructureof y t isfactoredintoseparateleadandlagpolynomials, multiplicationofequation(3)by A ( (cid:12) F ) (cid:0) 1 yields,aftersimplification,thedecisionrule (cid:1) y t = A ( 1 ) ( y (cid:3) (cid:0)t 1 (cid:0) y (cid:0)t 1 ) + A (cid:3) ( L ) (cid:1) y (cid:0)t 1 + D ( F ) (cid:1) y (cid:3) t e : (4) According to this equation, (cid:1) y responds to the lagged gap between the level of y and its equilibrium value, to lagged values of (cid:1) y , and to future values of (cid:1) y (cid:3) , which here are explicitly indicated to be expected values. Note that the decision rule takes an error correctionformaugmentedwithterms associatedwithexpectedgrowthinthetarget. Theterm A (cid:3) ( L ) (cid:1) y (cid:0)t 1 representsthe m (cid:0) 1 lagsofthedependentvariablethatenterbe- 3Incontrast,thegeneralizedmodelofadjustmentcostsanalyzedbyHansenandSargent(1980)doesnot haveaclosed-formanalyticsolution. 12

causeofhigher-orderadjustmentfrictionsthatareabsentinthestandardLQspecification,4 while the expression D ( F ) (cid:1) y (cid:3) t e (cid:17) P 1 =i 0 d i (cid:1) y (cid:3) e +t i is an infinite forward sum which has a meanleadthatincreases withthemagnitudeofadjustmentfrictions. Theforward weights, d i , are nonlinear functions of (cid:12) and the parameters of the polynomial A .5 The advantage of thisapproach is clear: The presence of multiplelags of thedependent variableprovides a much better match to the dynamic behavior of major macroeconomic time series. At the same time, this framework imposes a testable set of nonlinear restrictions among the coefficients onthelagandleadterms. Estimationofequation(4)isathree-stepprocess. Coefficientsintheconstructionof y (cid:3) are estimatedorimposedonthebasisoftheoreticalpriors inthefirst step. Inthesecond,a forecasting model for (cid:1) y (cid:3) is estimated, and the adjustment coefficients, A ( 1 ) and A (cid:3) ( L ) , are estimatedinthelast step. To model expectations,a VAR approach is usedin which a “core” VAR for five macro variables—thefederalfundsrate,consumerpriceinflation,theoutputgap(thedeviationbetween output and an estimateof potential),long-runinflationexpectations (survey-based), and long-runinterest rate expectations (forward rates)—is common to expectations across all sectors, and “auxiliary” VAR equations are added for sector-specific variables. Equationsforsector-specificvariablescontainlagsofboththecorevariablesandofthemselves, whereas the equations for the first three core variables contain only lags of the core variables themselves. Long-run inflation and interest rate expectations, which are included to anchor the VAR projections, are assumed to follow random walks (Kozicki, Reifschneider, and Tinsley, 1996; and Kozicki and Tinsley, 1996). The underlying principle of the VAR approach is that, at a minimum,agents understand the mainfeatures of the economy as represented by a a small-scale model, and use this information to form the necessary expectations. The adjustmentequation is linear in variables,and its nonlinear coefficient restrictions canbeimposedwithaniterativeOLSprocedurethat,ateachiteration,restrictstheforward 4 A (cid:3) ( L ) isimplicitlydefinedbytheidentity A ( L ) = A ( 1 ) L + [1 (cid:0) A (cid:3) ( L ) L ]( 1 (cid:0) L ) . 5AsshowninTinsley(1993), d i = c (cid:19) 0 m I[ m (cid:0) G (cid:0) ] 1 G i (cid:19) m ,where (cid:19) m isa 1 (cid:2) m vectorwithaoneinthe m t h elementandzeroeselsewhere,and G isthe m (cid:2) m matrix G = (cid:20) (cid:0) a 0 m (cid:12) m (cid:0) a m (cid:0) 1 (cid:12) m (cid:0) 1 I m : (cid:0) : : 1 (cid:0) a 1 (cid:12) (cid:21) : 13

weights to values determined by estimates of the adjustment coefficients from the prior iteration. Implementation of nonlinear least squares estimation is also straightforward. In most cases, the order of adjustment costs ( m ) is determined empirically by testing to see how many lags of the dependent variable are significant, and then including all lags up throughthelast significantone. For some nonfinancial variables in the U.S. model, the PAC framework is modified to take account of factors such as the presence of agents that are unable to optimize (e.g., liquidity-constrained consumers and firms) and particular institutional aspects of markets or features of data measurement. To illustrate how the adjustment-cost framework outlined above is applied and, in many cases, augmented, equations in three U.S. sectors— inventories, the wage-price block, and investment in producers' durable equipment—are presented in some detail. In the following, symbol definitions, which are given in table 1, generally use uppercase characters for levels (or rates) and lowercase characters for logarithms. Inventories. The equation for the logarithm of the stock of manufacturing and trade inventories, h , closely follows the adjustment-cost framework described above. Because theinventory-outputratioisstationary,theequilibriumconditionimposesaconstanttarget inventory-outputratio, h (cid:3) t = x b ;t : (5) Notethatinthisequationandtheonesthatfollow,constantterms aresuppressed. The dynamic adjustment equation for inventories contains a highly significant errorcorrectiontermandthreelags ofinventorygrowth, (cid:1) h t = 0 : 1 5 0 ( h (cid:3) (cid:0) h ) (cid:0)t 1 + 0 : 2 3 1 (cid:1) h (cid:0)t 1 + 0 : 1 1 8 (cid:1) h (cid:0)t 2 (6) + ( 0 6 : : 1 ( 1 4 ) 2 2 : 6 ) (cid:1) h (cid:0)t 3 + 0 : 5 3 ( 3 2 : E 7 ) (cid:0)t 1 1 = Xi 0 f h ;i (cid:1) h ( 1 (cid:3) +t : 4 : i ) span: 62q3-94q4 R 2 : .42 SEE: .0065 The forward expectations term is written with the dating of expectations (t-1) and the 14

weight sum (0.533) indicated explicitly. No t-statistic was calculated for the weight sum; this parameter is constrained in the adjustment model to be a function of (cid:12) and the coefficientsontheerror-correctiontermandthelagsofthedependentvariable,asistheprofileof theforwardweights, f h ;i . Themeanleadoftheforwardtermsintheproduct A ( L ) A ( B F ) , the lead/lag polynomial which multiplies the decision variable in equation (3), provides a compact measure of how far ahead agents look as well as how quickly a variable adjusts toitstargetlevel. Becausethelead/lagpolynomialisnearlysymmetric,themeanresponse lagis similartothe meanexpectationslead. Forinventories,the meanlead is 2.6quarters, indicatingthat theexpectationshorizonisshort andadjustmentisrapid. Prices andWages. The price-wage block contains two features not present for inventories: The targets include a stationary cyclical component, and variables appear in the dynamicequationsthat lieoutsidethePAC framework. The mixingof stationaryandnonstationary variables in the equilibrium condition requires that the dividing line between the first and third estimation steps be modified. Rather than separating the estimation of coefficients on the basis of whether they are part of equilibrium condition or adjustment dynamics, in this case the split is made on the basis of whether they are associated with nonstationary or stationary variables. The price-wage system contains a single long-run condition among nonstationary variables—based on a three-factor Cobb-Douglas productiontechnology—inwhichtheequilibriumpricelevelisaconstantmarkupoverminimized cost, p (cid:3) g ;t = : 9 8 ( w t (cid:0) (cid:26) t ) + : 0 2 p e ;t ; (7) where p g isapriceindexforadjustednonfarmbusinessoutput, w (cid:0) (cid:26) unitlaborcosts,and p e a price of crude energy. The estimated cointegrating relationship underlying equation (7)isrenormalizedtodefine theequilibriumwage, w (cid:3) t = (cid:26) t + ( 1 = : 9 8 ) p g ;t (cid:0) ( : 0 2 = : 9 8 ) p e ;t : (8) Intheseequilibriumequationsthepricelevelis indeterminate,and,outofequilibrium,the pricegapis simplythe(scaled)negativeofthewagegap, p (cid:3) g ;t (cid:0) p g ;t = (cid:0) ( 1 = : 9 8 ) ( w (cid:3) t (cid:0) w t ) ; (9) 15

Table1: DefinitionsofSymbols Symbol Definition C F L O W Corporateafter-tax cashflow C C Costofcapital D Dividends D w p c Dummyvariable forwageandpricecontrols (cid:14) Depreciation rate f j + ;t i Forwardweightinequation j forexpectation ofnonstationary variable g j + ;t i Forwardweightinequation j forexpectation ofstationary variable H Stockofmanufacturing andtradeinventories K Capitalstock P Absorptionpriceindex(GDP+imports-gov'tlabor-inventories) P b Priceindexforbusiness output P g Priceindexfornonfarm business outputlesshousing +oilimports P e Priceindexforcrudeenergy P f Relativepriceofimports P i = P Relativepricelevel P o Priceof (cid:25) e X o Expectedinflation (cid:5) After-taxprofits R s Short-terminterest rate R L Corporatebondrate (cid:26) Trendproductivity S I T A X Weightedgrowthrateofemployersocialinsurance taxes T Timetrend T O T Termsoftrade U Unemploymentrate V Tangiblewealth W Compensation perhour W m in Minimumwage(relativetolagged4-quarter averageof W ) ! e Scaledratioof P e to X P b GDP(actualorpotential) X b Businesssectoroutput (cid:1) (cid:22)x b Averagerateofgrowthof X g X b Nonfarmbusiness outputlesshousingplusoilimports X o Outputofnon-business sectorsplusnonoil importsless government laborandinventories X s Domesticsales Y Householdordisposable income ~y Outputgap(actual -potential) Z Optimalcapital-output ratio Notes: 1. Lowercaselettersareusedtodenotelogarithms. 2. An“e”superscript denotesanexpectation. 2. A“*”superscript denotesanequilibrium value. 16

with the individual contributions of wage and price adjustments to reestablishing equilibriumtobedeterminedbycoefficient valuesinthedynamicequations. The main price variable in the U.S. model is a type of absorption index, P . The domestic production price, P g , is a value-added measure that can be quite volatile at high frequencies, making it a poor indicator of the sluggishness of price adjustment. The application of an adjustment cost approach to price setting follows Rotemberg (1982), who specifies a quadratic cost in changing the price level. Unlike that model, which leads only to sticky adjustment of the price level, the PAC framework also generates gradual adjustmentoftheinflationrate. Thischaracteristicofpricedataisalsocapturedbythevariantof staggeredpricesettingdevelopedbyFuhrer andMoore(1995). The equilibrium and dynamic adjustment equations for P are given by equations (10) and(11). P (cid:3) t = ( P (cid:3) g ;t X g ;t + P o ;t X o ;t ) = X t (10) (cid:1) p t = 0 : 1 0 1 ( p (cid:3) (cid:0) p ) (cid:0)t 1 + 0 : 3 7 6 (cid:1) p (cid:0)t 1 + 0 : 1 9 1 (cid:1) p (cid:0)t 2 (11) + + ( 0 0 ( 3 : : 5 : 4 2 : 7 3 7 4 ) 3 1 ) E ! (cid:0) 1 t (cid:0) e ;t 1 = Xi 1 (cid:1) 0 ( f p p e (cid:1) ;i = ;t p p b (cid:3) +t ;t ( 5 i ) : 0 (cid:0) (cid:0) ) : 0 ( 0 : 0 0 0 0 ( 1 : 6 0 4 7 : 9 ) 3 ) ! E e (cid:0)t (cid:0) ;t ( 1 2 (cid:1) 2 : 1 = Xi ( 5 0 p ) g U p ;i (cid:0) 1 e ;t = +t p i (cid:0) b ;t 1 ) span: 63q1-94q4 R 2 : .88 SEE: .0025 Thedynamicpriceequationgivesabitmoreweighttopastpriceinflationthantoexpected cost increases. A vertical long-run Phillips curve is imposed—the coefficients on lagged and future inflation jointly sum to one—by requiring that b 1 = 0 in the cost equations (1) for both prices and wages. The target price level is permitted to vary with the cyclical state of the economy, which results in the inclusion of the expected unemployment rate in equation (11). The target price is estimated to vary procyclically.6 The equation also 6Theforwardweightson expectationsof stationaryvariables, g p ;i , havea slightly differentprofilethan the weights on the expectationsof differencesof nonstationaryvariables, f p ;i ; both sets are normalizedto sumtoone. 17

contains the growth rate of the real price of energy whose contemporaneous value enters highly significantly. This variable lies outside the PAC framework, and its significance likelyindicates that thespeedof adjustmentofprices of energy-intensiveproducts suchas retail gasolineisfaster thanthatofmanyothergoods. The wage adjustment equation (12) shows wages to be more inertial than prices. The error-correction coefficient is smaller, and the weights on lagged and expected inflation are shifted more toward the former. These coefficient differences are reflected in a mean expectations lead that is more than twice as long for wages (8.7 quarters) than for prices (3.3quarters). (cid:1) w t = 0 : 0 3 0 ( w (cid:3) (cid:0) w ) (cid:0)t 1 + 0 : 2 3 1 (cid:1) w (cid:0)t 1 + 0 : 2 1 0 (cid:1) w (cid:0)t 2 + 0 : 2 1 0 (cid:1) w (cid:0)t 3 (12) + (cid:0) ( 0 0 ( 3 : : 3 : 2 0 : 1 8 0 8 ) 9 9 ) E D (cid:0)t w 1 p c 1 = Xi ;t 0 + f w (cid:1) ;i 1 : 4 ( 7 : w 0 8 ) ( 3 : (cid:3) +t i S I T 6 ) (cid:0) A X : 0 0 ( 1 t 0 : 4 + 0 ) 3 0 ( E : 0 3 : (cid:0)t 2 8 4 ) ( 1 (cid:1) 3 : 5 1 = 0 Xi w m ) g w in ;i ;t U +t i ( 4 : 8 ) span: 63q1-94q4 R 2 : .82 SEE: .0028 The target wage also varies procyclically, but the coefficient on the expected unemployment rate is estimatedwithless precisionthan is the correspondingcoefficient in the price equation. Theequationforhourlycompensationcontainsthreenon-PACvariables,eachof which is highly significant—a dummy for wage and price controls, the rate of growth of employersocial insurancetaxes,andtherateofincreaseofthereal minimumwage. The presence of higher-order adjustment costs in the price and wage equations—as indicatedbytheeconomicallysignificantcoefficients onthelaggeddependentvariables— implies that both price and wage inflation are sticky. One consequence of this property is that policy actions to lower the rate of inflation require that the unemployment rate rise aboveits equilibriumfor some period of time, evenif firms and householdsform expectationsrationallyandare awareofthepolicyshift. Investment. The final sector presented is investment in producers' durable equipment. The equilibrium condition (13) is the standard first-order condition for capital given a 18

Cobb-Douglasproductionfunction,translatedintoasteady-stateconditionforinvestment.7 i (cid:3) t = x b ;t + z t + l o g ( (cid:1) (cid:22)x b ;t + (cid:14) t ) (13) (cid:1) i t = 0 : 0 6 6 ( i (cid:3) (cid:0) i ) (cid:0)t 2 + 0 : 0 0 8 (cid:1) i (cid:0)t 1 + : 2 5 4 (cid:1) i (cid:0)t 2 (14) + + ( 0 ( 0 ( 2 : 8 : 2 : 4 : 1 : 9 9 2 5 3 ) 9 ) 2 ) E (cid:1) (cid:0)t c f 2 l 1 =X j o w (cid:0) 1 t f + i;j (cid:1) 0 ( ( i : 0 1 0 +t 6 : 0 : 9 j 6 ) ) (cid:1) + c f 1 : 2 ( 2 l o 7 : 2 w 5 ) (cid:0)t E 1 ( 3 (cid:0)t : 2 2 ) j 1 =X (cid:0) 1 g i;j (cid:1) x b + ;t j span: 64q1-94q4 R 2 : .40 SEE: .0224 Two aspects of the dynamic investment equation (14) are noteworthy. First, firms are heterogeneous, with some following the optimizing specification and others constrained by cash flow. According tothe equation,22 percent of investmentis undertaken by firms that are constrained—as indicated by the sum of coefficients on cash flow growth—and the remaining 78 percent by firms that optimize. The optimizingshare is embodied in the coefficients onthe adjustment andexpectations variables. Second, the optimizingfirms have aone-quarterdeliverylag,indicatedbythetimedatingoftheerror-correctiontermandthe expectationsvariables. OverviewoftheU.S.Equations. The U.S. sector contains about 40 behavioral equationsofwhichaboutone-thirdhavebeenestimatedwiththecostofadjustmentspecification oraspresentvaluesandthuscontainexplicitexpectations. Inadditiontothefourequations discussedabove,thePACframeworkisusedforconsumption,twocategoriesofconsumer durables,aggregatelaborhours,anddividends. Equationsforthreelong-terminterestrates and the value of corporate stock use a present value specification. Equations for exports, imports, labor supply, hours per worker, nonresidential structures, and a number of other variablesare estimatedusingtraditionalmethodswithoutexplicitexpectations. LookingfirstatthePACequations,whicharesummarizedintheupperblockoftable2, 7Because BEA has yet to publish data for real capital stocks that are consistent with the new chainweightedmeasuresofrealinvestment,theequilibriumconditionsforbusinessandhouseholdinvestmenttake thisflowform. 19

Table2: SummaryofKeyFRB/US Equations Equation Equilibrium Component AdjustmentCost Additional Variables Mean Component Dynamic Nonstationary Stationary Lead 1 Order MeanLead 2 Terms (1) (2) (3) (4) (5) (6) Agg. consumption Y e ; V ~y 16.0 2 3.8 Liq. constr. Motorvehicles Y e ; V ; P i = P ; T ~y ; C C 16.0 2 2.5 Accel. Otherdurables Y e ; V ; P i = P ; T ~y ; C C 16.0 2 3.7 Accel. Housing Y e ; V ; T C C 16.0 2 4.7 Accel. Equip. inv. X b ; C C ; (cid:14) (cid:1) x 3 8.6 Cashflow Inventory inv. X b 4 2.6 Agg. hours X g ; T 2 2.9 Price W ; (cid:26) ; P e U 3 3.3 Wage P ; (cid:26) ; P e U 4 8.7 Dividends (cid:5) 2 4.4 FundamentalVariables 5-yr. bondrate R e s ; ~y e 8.9 0 10-yr. bondrate R e s ; ~y e 17.1 0 Corp. bondrate R e s ; ~y e 39.2 0 StockMarket R L ; (cid:25) e ; (cid:1) d e 49.0 0 Notes: 1. Meanlead(quarters) oftargetvariables thatareexpectedvalues( Y e ; R e s ; (cid:25) e ; etc.). 2. Meanlead(quarters) ofexpectations oftargetvariables fromadjustment dynamics. 20

the estimated order of adjustmentcosts, which is reported in column4 and corresponds to the value of m , ranges from 2 to 4. Thus, compared with the standard LQ specification ( m = 1 ), all nonfinancial equations contain added adjustment parameters—or “higherorder”adjustmentcosts.8 Meanleadsofexpectationsassociatedwithadjustmentdynamics (column 5) range up to 8 quarters. Mean adjustment lags (not shown) are similar to the mean leads. Not surprisingly, adjustment dynamics are most rapid for aggregate hours andinventories. Motorvehiclepurchases alsorespondquickly. Equipmentinvestmentand wages displaythemostsluggishdynamics. Themagnitudesofadjustmentcostsasmeasuredbythemeanadjustmentlagsaresomewhat smallerthancomparableresultsreported intheliterature(Rotemberg, 1982;Blinder, 1986;andSchuh,1996). TwoothergeneralcharacteristicsofthePACequationsareimportant tonote(BraytonandTinsley,1996). Onlyabout one-quarteroftheequationsfail tests ofrationalexpectationsoveridentifyingrestrictionsatconventionalsignificancelevels,and anequally smallpercentage showsignificantevidenceofseriallycorrelated residuals. The generallyfavorablenatureofthetestoutcomesisaconsequenceoftheinclusionofhigherorderadjustmentcosts. Several of the nonfinancial equations combine optimizing behavior, subject to adjustment frictions, with other types of behavior. The case of equipment investment, in which some firms are constrained by available cash flow, has been discussed. Similarly, in the spirit of Campbell and Mankiw (1989), the equation for aggregate consumption, which includes the service flow from the stock of durables, allows for the presence of both optimizing and rule-of-thumb or liquidity-constrained households. The estimated shares of consumption by the two groups are .90 and .10, respectively. Abstracting from the existence of rule-of-thumb consumers, the consumption sector would still violate Ricardian equivalence, because optimizinghouseholds use a high 25 percent annual discount rate in calculating expected income.9 Another aspect of the consumer's optimization problem is that labor supply is taken as exogenous, so there is no explicit substitution between labor andleisure. 8In the case of other consumer durables, however, the single extra cost parameter is not statistically significant. 9Thediscountrateof25percentcorrespondstoameanleadof16quartersinthecalculationofexpected income,asindicatedincolumn3oftable2. Estimationresultsdeterioratesignificantlyatlowvaluesofthe discountrate. AsshownbyMuelbrauerandLattimore(1995),atheoreticalrationaleforahighdiscountrate isthepresenceofriskaversioninthefaceofidiosyncraticincomeuncertainty. 21

Equationsforthreelong-termbondratesarespecifiedaccordingtotheexpectationstheoryofthetermstructure. Ineachequation,theprincipalexplanatoryvariableisaweighted average of short-term interest rates expected to prevail over the maturity of the bond, with weights given by the maturity of the bond and the sample mean of its yield, as in Shiller (1979). Eachbondyieldisestimatedtohaveatime-varyingtermpremiumthat iscountercyclical. The equation for the value of the stock market is based on the Campbell-Shiller (1989)loglinearizationofthediscountedvalueofexpecteddividends,assumingaconstant equitypremium. The residuals of the bondand stock market equations contain substantial serial correlation. As in the case of nonfinancial equations, expectations required to estimatethefinancial equationsare generatedbyVARs. 3.4 The Non-U.S. Countries The design and specification of the foreign sectors of FRB/WORLD follows from two research projects at the International Finance Divisionat the Fed. The first was the developmentofasmallmulti-countrymodel,alongthelinesofthemodelsofTaylor(1993b)and theIMF'sMultimod(Massonetal.,1988). Thisfour-regionmodel(U.S.,Germany,Japan, andROW),namedMX-3,wasconstructedwithforward-lookingexpectationsinequations for prices, interest rates, and exchange rates (Gagnon, 1991). The second was the direct incorporationofforward-lookingbehaviorintoaversionoftheMCMmodel. Levin(1996) discussesthestructureandpropertiesofFRB/MCM. For the G7 countries excluding the United States (Canada, France, Germany, Italy, Japan, and the United Kingdom), a consistent set of dynamic specifications is employed, as summarizedinTable3. Except fortheconsumptionandinvestmentequations,equation coefficients are calibrated, not estimated. The level of aggregationis about the same or, in some cases, somewhat greater than that for the U.S. economy. For example, consumption expenditures are not disaggregated. Expectations enter explicitly in the definition of real interestrates,thepricingoflongbonds,andthedeterminationofexchangerates. Componentsofaggregatedemandareassumedtofollowerror-correction orpartial adjustment dynamic models. The equilibrium ratio of consumption to either disposable or total income depends on the real interest rate. Equations for residential, non residential, andinventoryinvestmentreflectdynamicadjustmenttowardsdesiredstocks,whichdepend onthecost ofcapital. Equilibriumlevelsofnon-fuelgoodsandnon-factorservice imports 22

Table3: SummaryofNon-U.S.Sectors Equation Equilibrium Component Dynamics Nonstationary Stationary OwnLags Otherfactors (1) (2) (3) (4) Consumption Y or X C C 0 (cid:1) x Housinginvestment/GDP K = X C C 1-4 (cid:1) x Privatefixedinvestment/GDP K = X C C 1-8 (cid:1) x Inventory investment/GDP K = X s C C 1-8 (cid:1) x s Nonfuelgoodsimports X P f 1 NFGexports/foreign NFGimports T O T 1 Price(totaloutput) W ; P e ~y 1 Contractwage W U 0 Realmoneydemand X R s 1 Longbondrate R e s 0 depend on relative prices and domestic absorption. To ensure balanced global trade, each country's exports are determined by its share of world imports,with the equilibrium share dependingonthetermsoftrade. Wage setting is based on Taylor's (1980) staggered contracts model, with the contract wageafunctionofexpectedfuturemarketwagesandlabormarkettightness,asrepresented by deviations of the unemploymentrate from the NAIRU. The market wage is a weighted average of current and past contract wages. The markup of the output price deflator over thewagerateandthedomesticoilpricevariesprocyclically. Real interestratesaredefined using expectations of changes in the domestic absorption deflator, constructed from the outputdeflatorandrelativeenergyandimportprices. Equationsforlong-terminterestrates are based on the expectations model of the term structure with a fixed term premium, and those for nominal exchange rates are uncoveredinterest parity conditions augmented with atimevaryingsovereignriskpremium. For the three sectors representing Mexico, the newly industrializing economies, and other OECD countries, a somewhat more simplified and stylized specification is used. Investment is not disaggregated, and calibration is used instead of econometric estimation forallequationcoefficients. Finally,forthesectorsrepresentingOPECmembersandother developingandtransitioneconomies,themodelis simplifiedfurther. 23

4 Full-System Properties As mentioned above, the single-equation approach to estimating FRB/WORLD leads to equationswhichindividuallyhavegoodstatisticalproperties intermsof fit andabsence of misspecification. Theestimationproceduredoes notensurethattheresultingsystemproperties will resemble those of the data, however. Tests of system dynamics are important, notonlybecausethemainusesofthemodelinvolvedynamicsimulationsbutalsobecause such tests may lead to a reexamination of the specifications of particular equations. Not surprisingly, the process of developing FRB/WORLD involved some iterating back and forthbetweenevaluationofsystemcharacteristics andrevisionofspecificequations. A traditional approach to characterizing a model's properties is to examine responses totransitoryshocks, and several sets of such responses are presented below. In additionto describingsystemproperties,thesesimulationsareusedtoevaluatetheeffectsofswitching betweenlimited-andfull-informationassumptionsregardingexpectationsformationandto compareimpulseresponsesofanestimatedVARwiththoseobtainedfromFRB/WORLD. To provide another view of the model's goodness of fit, moments of historical data are comparedwiththosegeneratedbystochasticsimulation. 4.1 System Responses to Transitory Shocks Forthesimulationsinthissection,theU.S.monetaryauthorityisassumedtosetthefederal funds rate according to the equation for that variable in the core part of the expectations VAR used in the U.S. sector, while other central banks set short-term rates according to a Taylor-type(1993a) rule in whichthe real short rate responds to deviationsof outputfrom potential and inflation from its target. The U.S. funds rate equation was estimated over 1963:Q1-1994:Q4. Figure1showstheresponsesofinflation,output,thefederalfundsrate, andthe10-yeargovernmentbondratetoaone-quarter,100-basispointpositiveshocktothe U.S.policyrule. Inordertosimplifythedesignofthissimulationandtheotherexperiments involvingtransitoryshocks,eachsimulationofthistypeisbasedontheassumptionthatthe long-runinflation objectiveof monetary policyis unchanged, as are privateperceptions of theobjective. TheU.S.economy'sresponseundermodel-consistentexpectationsisshown as the solid line, while the dashed line represents the results under VAR expectations.10 10In this and other simulations of FRB/WORLD, “VAR” expectations denotes the case of limitedinformationexpectationsbasedonVARsintheU.S.sectorandautoregressionsintheothersectors. 24

Figure1: One-quarter,100basispointshocktofunds rate Inflation rate Output Gap 0.05 0.2 0.00 0.0 -0.05 -0.2 -0.10 -0.15 -0.4 -0.20 -0.6 -0.25 -0.30 -0.8 0 10 20 30 40 0 10 20 30 40 Quarters Quarters Federal funds rate 10 year government bond rate 1.5 0.3 1.0 0.2 0.5 0.1 0.0 0.0 -0.5 -0.1 0 10 20 30 40 0 10 20 30 40 Quarters Quarters Model-Consistent Exp. VAR Exp. Resultsinallinstancesare displayedas deviationsfrombaseline. Theincreaseinthenominalfederalfundsrategeneratestheexpectationofhigherfunds ratesinthefuture,drivingupbondrates. Giventhesluggishadjustmentofprices,thecosts of capital for consumer durables, housing, and business investment rise and the real exchange rate appreciates, causing aggregate demand and output to decline and unemployment to increase. The rise in actual and expected unemployment drives wage and price inflation down. The hump-shaped pattern of the output response is a consequence of the interaction of sluggish adjustment of demand components, the evolution of expectations of future quantities and prices, and the endogenous response of monetary policy after the initialshock. 25

Figure2: Four-quarter,1%ofGDPIncrease inGovernmentPurchases Inflation rate Output Gap 0.2 1.5 0.1 1.0 0.0 0.5 -0.1 0.0 -0.2 -0.5 -0.3 -1.0 0 10 20 30 40 0 10 20 30 40 Quarters Quarters Federal funds rate 10 year government bond rate 0.8 0.20 0.6 0.15 0.4 0.10 0.2 0.05 0.0 0.00 -0.2 -0.05 -0.4 -0.10 0 10 20 30 40 0 10 20 30 40 Quarters Quarters Model-Consistent Exp. VAR Exp. Our prior was that this experiment should result in outcomes under model-consistent and VAR expectations which are similar. The shock is not unusual in any way, and so the responses of the expectations VAR should mimic those of the full model. In other words, expectationsbasedonthefull structureshouldbeabout thesameas expectationsbasedon thesmall VAR.Lookingat thefigure, the simulatedoutcomes forthe outputgapand short and long interest rates are in fact quite similar under the two expectations assumptions. However, the peak reduction in inflation under VAR expectations is about three times that undermodel-consistentexpectations. Wewillreturntothisissuelater. Figure 2shows the responseto an increase ingovernmentpurchases, equal to one percentofGDP,lastingoneyear. Theexogenousriseinaggregatedemandisinitiallyreflected 26

one-for-one in output. Sluggishadjustment of hours implies that muchof this initial surge in activity is generated by a temporary up-tick in productivity. The high level of activity leadstoanincreaseininterestrates. Thecessationofthespendingshockthendrivesoutput significantlybelow baseline as the effects of the rise in interest and exchange rates start to takehold. Thisovershootingofoutputis thencorrected overtime. The larger movementin the governmentbondrate under VAR expectations,relativeto that under model-consistent expectations, can be traced to differences between the “typical” behavior of output as represented in the expectations VAR and the unusual pattern inducedby this particularshock. The four-quarter nature of thespendingshockrepresents an atypical pattern for demand shocks; thus, under VAR expectations agents misinterpret the information contained in the output gap and forecast a rise in output that is more sustained than that which occurs, leading to more dramatic movements in prices and interest rates. As in the previous experiment, the behavior of inflation is dissimilar under the two expectationsassumptions. Infact,theinflationresponseunderrationalexpectationsisnegative in response to the boom in spending. This is due to the forward-looking nature of price and wage setting. Although unemployment falls below baseline during the year of the shock, and rises above baseline thereafter, the weighted sum is positive. Thus, a small transitoryreductionininflationresults. Iftheshockweretolastlonger,theinitialresponse of inflation would in fact be positive because the weighted sum of future unemployment wouldbenegative. TheprocyclicalpatternofinflationobservedinthecaseofVARexpectationscanbetracedtoexpectationserrors. 4.2 Comparison with VAR Models One test of a properlyspecified model is its abilitytomimicthe behaviorof data as represented by VAR models. For this purpose, we compare the system response to a funds rate shock under VAR expectations tothe impulseresponse from the VAR used in formulating expectations in the U.S. sector. In order for an experiment of this type to be consistent, one needs to apply the same shock to the two models. This is straightforward to do for a funds rate shock, if we use an ordering assumption to make it orthogonal to other shocks. To extend the comparison to demand and supply disturbances, however, aggregates of the manydemandandsupplyshocks inFRB/US wouldhavetobeconstructed. 27

InFigure3,theimpulseresponsesofthecoreexpectationalVARarerepresentedbythe dashed lines and one standard error bands by the dotted and dash-dotted lines. The solid lines represent the response of FRB/WORLD under VAR expectations; these are taken from Figure1. Ingeneral, theimpulseresponsesof FRB/WORLD for inflationandoutput are fairly close to those of the VAR. Inflation declines more rapidly in the former, but this difference should be viewed in a positivelight. The VAR displays a “price puzzle”— inflation initially rises in response to the positive interest rate shock. FRB/WORLD does notcontainastructuralmechanismforsuchaneffect tooccur,thoughsuchaneffect could enter as a result of the use of the VAR for expectations. Adjusting for this discrepancy, the two paths are very similar. Also included in the figure is a time representation of the movementsinthe level and slope of the yieldcurve. This provides a graphical description ofhowapolicyactionaffects short-andlong-terminterestrates overtime. 4.3 Comparison of Moments Thepreviousexperimentsusedtraditionalmethodstocharacterizethesystempropertiesof theFRB/WORLDmodel,emphasizingtheresponsesofinflation,output,andinterestrates to transitory policy shocks. We now turn to a more general approach to studying system dynamics—onefrequentlyusedintheequilibriumbusinesscycleliterature—thatcompares simulated standard deviations and cross correlations for key endogenous variables with comparablestatisticscalculatedusinghistoricaldata. Forcomputationalreasons,thisexerciseiscarriedoutwithFRB/USonly. Theforeignsectorsarereplacedbysimpleequations for the levels of foreign price and output aggregates. Each stochastic simulation lasts 30 yearsandisbasedonabootstrapprocedurethatdrawsshocksrandomlyfromthesetofhistorical equation error vectors over 1966:Q1-1995:Q4.11 Simulated moments are based on 300replications. Monetarypolicyischaracterizedbytheestimatedequationforthefederal funds rate that is inthe expectational VAR.Historical and simulatedmomentswere calculated after low-frequency movements in the actual and simulated data had been removed withtheHodrick-Prescott(HP) filter. Historicalstandarddeviationsofkeyvariablesandtheircorrelationswithreal GDPare 11Atotalof50equationsareshocked,includinganumberoftimeseriesequationsspeciallyaddedinthis exerciseforvariables,suchasthepriceofoil,thatarenormallyexogenous;remainingexogenousvariables areheldconstant. Shocksaredrawnfromthesetofhistoricalequationresidualsobtainedfromestimationof eachequationwiththeVAR-basedproxiesforexpectations. 28

Figure3: VAR Estimated: 1963-1994 Inflation rate Output Gap 0.4 0.4 0.2 0.2 0.0 0.0 -0.2 -0.2 -0.4 -0.4 -0.6 -0.6 -0.8 0 10 20 0 10 20 Quarters Quarters Federal funds rate 1.5 0.8 0.6 1.0 0.4 0.5 0.2 0.0 0.0 -0.5 -0.2 0 10 20 Quarters 90-day 5-year 10-year 30-year Yield Curve 1 Quarter 4 Quarter 8 Quarter 12 Quarter FRB/WORLD VAR upper band lower band shownintable4,asarecorrespondingsimulatedstatisticsunderVARandmodel-consistent expectations. Thesamesetofshockswereusedforeachexpectationalassumption. Forthe simulated moments, two asterisks denote instances where the historical statistic is more than two standard deviations from the simulated value, while a single asterisk indicates differences that are between one and two standard deviations. The standard deviationsare basedonthedistributionofstatisticsovertheset ofsimulations. The results in the table provide considerable information about the ability of FRB/US to match the dynamic properties of historical data, and about the effects of different expectations assumptions on simulateddynamics. Under both expectations assumptions,the model matches the historical correlations of output with leads and lags of key variables 29

Table4: MomentComparison CrossCorrelationofGDPwith Std. Variablesx dev. x(t-4) x(t-2) x(t-1) x(t) x(t+1) x(t+2) x(t+4) Historical Data(1966-95) GDP 1.70 0.24 0.68 0.87 1.00 0.87 0.68 0.24 Nondurables&Services 0.89 0.43 0.76 0.85 0.84 0.72 0.55 0.14 DurableConsumption 5.08 0.51 0.76 0.83 0.82 0.60 0.39 -0.07 BusinessFixedInvest. 4.88 -0.14 0.32 0.58 0.80 0.88 0.86 0.57 InventoryStock 1.53 -0.22 0.08 0.30 0.57 0.76 0.85 0.75 Hours 1.91 0.04 0.49 0.72 0.89 0.90 0.82 0.49 InflationRate 1.40 -0.37 -0.07 0.09 0.27 0.39 0.47 0.64 RealWage 0.50 0.36 0.55 0.58 0.60 0.50 0.36 -0.04 FederalFundsRate 2.10 -0.57 -0.23 0.08 0.35 0.50 0.56 0.55 10YearBondRate 0.94 -0.50 -0.36 -0.19 -0.02 0.06 0.10 0.13 SimulatedData: VARExpectations GDP 1.29** 0.14 0.60* 0.80* 1.00 0.80* 0.60* 0.14 Nondurables&Services 0.92 0.21* 0.56* 0.69* 0.75* 0.63 0.46 0.10 DurableConsumption 4.53 0.28* 0.59* 0.68* 0.73* 0.48* 0.24* -0.21* BusinessFixedInvest. 4.18 -0.04 0.25 0.43 0.63* 0.70* 0.67* 0.38* InventoryStock 1.30* -0.25 -0.10 0.05* 0.31* 0.49* 0.58** 0.54* Hours 1.35** 0.02 0.34 0.53* 0.74* 0.72* 0.64* 0.30* InflationRate 1.48 -0.12* 0.03 0.16 0.28 0.34 0.35 0.26** RealWage 0.65* 0.06* 0.23* 0.27* 0.31* 0.25* 0.15* -0.03 FederalFundsRate 1.68* -0.45* -0.30 -0.11* 0.18* 0.40 0.45 0.45 10YearBondRate 0.75* -0.39 -0.35 -0.24 -0.06 0.04 0.12 0.20 SimulatedData: Model-ConsistentExpectations GDP 2.09* 0.17 0.67 0.86 1.00 0.86 0.67 0.17 Nondurables&Services 1.43** 0.18* 0.66* 0.84 0.92** 0.82* 0.64 0.21 DurableConsumption 6.54* 0.21** 0.66* 0.82 0.91** 0.74** 0.52* 0.04 BusinessFixedInvest. 4.05* -0.07 0.26 0.45 0.64* 0.71* 0.67* 0.37* InventoryStock 1.60 -0.16 0.17 0.36 0.59 0.72 0.76 0.60* Hours 2.10 0.08 0.55 0.75 0.90 0.86 0.74* 0.32* InflationRate 1.20* -0.30 -0.26* -0.15* 0.01** 0.13* 0.17** 0.16** RealWage 0.65* -0.07* -0.08** -0.08** -0.05** -0.06** -0.06* -0.04 FederalFundsRate 2.21 -0.34* -0.37 -0.30** -0.17** 0.03** 0.20* 0.31* 10YearBondRate 0.75* -0.52 -0.60* -0.51** -0.31* -0.08 0.10 0.31* 30

relatively well. However, the simulated standard deviations of most series are somewhat largerundermodel-consistentexpectationsthanunderVARexpectations. Among the correlations, a few differences do stand out and may suggest aspects of equationspecification that are inconsistent withthe data. In the historical data, the pattern of correlations of lags and leads of consumptionof nondurables and services with GDP is skewedtowardthelags. Thatis,preceedingconsumptionvaluesaremorehighlycorrelated withGDPthanthosethatsucceed. Thisasymmetricpatternisabsentinthesimulatedcorrelationsundermodel-consistentexpectationsandpresenttoonlyaminordegreeunderVAR expectations. Forbusinessfixedinvestment,thepatternofhistoricalcorrelationswithGDP is the reverse of that of consumption, with correlations being stronger for leads of investment thanfor lags. AlthoughFRB/US matches the qualitativenature of this asymmetry,it understatesthemagnitudeoftheskewnessforbothexpectationsassumptions. The most strikingcontrast between expectations assumptionsis foundin the wage and price sector. Recall that disparities between the simulated behavior of inflation under the twoexpectationsassumptionswerealsofoundinthesimulationsofthetwotransitorypolicy shocks. Under VAR expectations, the match between the simulated moments of price inflation and those from historical data is close. The simulatedreal product wage is, however, slightly less procyclical than it is historically. On the other hand, the outcome under model-consistent expectations is far less favorable. In this case, the real wage is slightly countercyclicaland thecorrelationsacrosstimeofpriceinflationwithoutputaregenerally inconsistent with the historical correlations. These differences suggest two conclusions: The wage-price block under model-consistent expectations does not fully capture the dynamicsof wages andprices; andtheVAR-based measuresof expectationsinthewageand priceblockdifferfrom thereduced-form behaviorofthefull structureofFRB/US. 5 Policy Evaluation To the extent that the specifications of intertemporal decision making and expectations formationinthe newmodelare accurate depictionsofreality,itis not subject to theLucas critique and can be legitimately used to analyze the consequences of shifts in policy. In addition,theflexible approach toexpectations formationand the incorporationof learning intothe expectations process makes it possibleto analyze more fullypolicyissues such as 31

the costs of disinflationand the effects of fiscal consolidation. Two sets of simulationsare used toillustratethesecapabilities.12 5.1 Disinflation and Policy Credibility Wefirst consideramonetarypolicyshiftthat aimstopermanentlyreduce theinflationrate byonepercentagepoint. Anynumberof pathsforinterest rates can achievethisobjective; inthesimulationsthatfollow,monetarypolicyfollowsaruleforthefederal fundsratethat is consistentwith the plannedreduction ininflation, but responds to transitorymovements in output and inflation using an equation estimated for the period since late 1979. We consider two cases of policy credibility as reflected in the behavior of long-run inflation expectations. Inthefirstcaseof“perfectcredibility,”theprivatesectorrecognizesandfully believesthattheannounceddisinflationarypolicywilloccurasplanned. Inthesecondcase of “learning,”the privatesector onlyslowlyadjustsits views about theprobabilitythat the full disinflationary program will be carried out. In the latter case, the rate of adjustment is 5% per quarter, so that long-run inflation expectations have fallen by one-half of one percentage point after 3-1/2 years. This rate of “learning” is consistent with the fall in long-runexpectationsas measuredbysurveysduringthedisinflationofthe1980's. Figure 4 shows the consequences of a credible policy of disinflation. Higher-order costs of adjustmentin wages and prices implythat inflationis stickyand that loweringthe inflation rate necessitates opening up an unemployment gap. Still, in the case of perfect credibilitypolicy,thecostcanbereducedtoatrivialamountiftheactiontoreducetherate of inflationis carried out very graduallyorannounced far inadvance. For the experiments consideredhere, however,thepolicychangeis carried out rather aggressively—withinflationfallingbytheintendedamountinabouttwoyears—andthesacrificeratio(cumulative annual increase in the unemployment rate divided by the percentage point decrease in the inflation rate, computed at the end of the tenth year) under model-consistent expectations (2.0) is in fact a bit higher than that under VAR expectations (1.6). For this particular experiment, the forecasting errors that agents make under VAR expectations actually help to reducethecostofdisinflation. Theresultsofrelaxingtheassumptionofperfectcredibilityofthedisinflationarypolicy 12Inanotherapplication,Williams(1997)studiesthestabilizationcharacteristicsofmonetarypolicyrules usingFRB/USundermodel-consistentexpectations. 32

Figure4: Disinflation, with and without learning Estimated Policy (1979-1995) (deviations from baseline, per cent) consumption price inflation output gap 0.2 0.2 0.0 0.0 -0.2 -0.2 -0.4 -0.6 -0.4 -0.8 -0.6 -1.0 -0.8 -1.2 -1.4 -1.0 0 2 4 6 8 years 0 2 4 6 8 years real federal funds rate 10-year government bond rate 1.2 0.2 1.0 0.0 0.8 -0.2 0.6 -0.4 0.4 -0.6 0.2 -0.8 0.0 -1.0 -0.2 -1.2 -0.4 -1.4 0 2 4 6 8 years 0 2 4 6 8 years Model-consistent expectations, instantaneous recognition (thick solid) Model-consistent expectations, learning, 5% rate (dashed) VAR expectations, instantaneous recognition (dotted) VAR expectations, learning, 5% rate (thin solid) are also shown in Figure 4. Inflation declines more gradually in this case. Also, the rapid declineinbondrates inthecaseofperfect credibilityis absentunderimperfect credibility. Bondtraders,likeotheragents intheeconomy,onlygraduallyadjusttheirviewsaboutthe long-runobjectivesofpolicy. Thehigherrealinterestratesgeneratedbythedisinflationary policyleadtolossesofoutputthataresignificantlygreaterthanthoseunderperfectcredibility. Intermsofthesacrificeratio,theeffectofimperfectcredibilityistoincreasethecostof disinflationfrom 1.6to2.9 forVAR expectationsand from 2.0 to2.5for model-consistent expectations. Underimperfectcredibilityofmonetarypolicy,theextraleveragefromafull and immediate reduction in long-run inflationary expectations is absent. Thus, the monetaryauthoritymustdampenaggregatedemandandlowerobservedinflationthroughhigher 33

real interestrates inordertoconvincetheprivatesectorofitsdeterminationtodisinflate. 5.2 Shifts in Foreign Macroeconomic Policy We consider a scenario of current policy interest, fiscal consolidation in the foreign G-7 economies, toillustratethe operational use of the FRB/WORLD model.13 Compared with abaselineinwhichspendingreductionswouldbeimplementedgraduallyoversevenyears startingin1999,thescenarioassumesthatthereductionsstartin1997andarecompletedin onlytwoyears tohelp ensurethat the E.U.members meet theMaastricht criteria for monetary union, and to reflect similar actions under considerationin Canada and Japan. Thus, this experiment measures the impact on the U.S. economy of a tighteningin foreign fiscal policy that commences in 1997, reaches its peak in 1998, and after gradually diminishing ends in2005. The peak cuts in government spending are 1 percent of GDP in Canada, France, the U.K., and Germany; 1-1/2 percent in Japan; and 4 percent in Italy. We assume that the monetary authorities in the U.S., Canada, Germany and Japan set interest rates according toTaylor's(1993a)rule,andthattheFrenchfranc,Italianlira,andBritishpoundarepegged totheDeutschmark. Thesimulationresultsforthisexperimentareshowninfigure5. Asseeninthebottom left panel, the government spending cuts cause foreign GDP (aggregated by U.S. trade weights) to drop about 3/4 percent relative to baseline toward the end of the second year of the simulation, before gradually returning to baseline. The decline in foreign output is similar under VAR and model-consistent expectations. In contrast, the contraction of U.S. GDP and reduction in U.S. inflation is sensitiveto the expectations assumption, with the effects being larger in magnitude in the limitedinformation case, though still far short of the decline abroad. U.S. monetary policy dampens the impact of falling net exports through a reduction of about 20-25 basis points in the federal funds rate. Foreign interest rates decline by a larger amount, in response to the larger decline in foreign output, and hencetheforeignexchangevalueofthedollarappreciates. 13BowmanandRogers(1997)providea detailedanalysisofFRB/WORLD modelsimulationsrelatedto foreignfiscalconsolidation. 34

6 Conclusions Large scale macro models are by their nature slow to evolve. This is both a blessing and a curse. Changes in models respond to shifts in the consensus view, as opposed to that of the latest cutting edge research. This helps avoid the pitfall of constantly changing policy advice and interpretation. On the other hand, models can easily become out of date and irrelevant. At the time of their original development, the Fed models reflected the received wisdom on macroeconomic and international linkages. This consensus started to shift in the 1970's towards a focus on rational expectations and intertemporal optimization. As a new consensus developed in the late 1980's and early 1990's, the Fed models were redesigned toincorporate,at leastpartially,theevolvingnewparadigm. By many measures this effort has been a success. The model fits the data well, yet retains a theoretical structure that can be used to investigate pertinent policy and general macroeconomic issues. The flexible treatment of expectations formation and learning opens a wide range of interesting issues for quantitativemonetary and fiscal policy analysis. Still, the new FRB model is not the stochastic general equilibrium model some have called for. For example, optimization and estimation is conducted on a single equation basis, ignoring some of the linkages between decisions by firms and households. Such an approach in a large-scale model is currently computationally prohibitive and must remain apart ofthethirdgenerationredesign. 35

Figure5: ForeignFiscal Consolidation Inflation rate Output Gap 0.1 0.1 0.0 0.0 -0.1 -0.1 -0.2 -0.2 -0.3 0 10 20 30 40 0 10 20 30 40 Quarters Quarters Federal funds rate 10 year government bond rate 0.0 0.00 -0.1 -0.05 -0.2 -0.10 -0.3 -0.15 -0.4 -0.20 0 10 20 30 40 0 10 20 30 40 Quarters Quarters Foreign GDP (%) Real Exchange Rate (Foreign/US) (%) 0.5 1.5 1.0 0.0 0.5 -0.5 0.0 -1.0 -0.5 0 10 20 30 40 0 10 20 30 40 Quarters Quarters Model-Consistent Exp. VAR Exp. 36

References Anderson, G. and Moore, G. (1985) A Linear Algebraic Procedure for Solving Linear Perfect ForesightModels. EconomicsLetters,17: 247-52. Ando, A. and Brayton F. (1995) Prices, Wages, and Employment in the US Economy: ATraditionalModelandTests ofSomeAlternatives. TheNaturalRateof Unemployment: Reflectionson25Years oftheHypothesis,ed. R. Cross. CambridgeUniversityPress. Ando, A. and Modigliani F. (1969) Econometric Evaluation of Stabilization Policies. AmericanEconomicReview,59: 296-314. Ando, A. and Rasche, R. (1971) Equations in the MIT-PENN-SSRC Econometric ModeloftheUnitedStates. Manuscript. UniversityofPennsylvania. Blinder,A.(1986)MoreontheSpeedofAdjustmentofInventories. JournalofMoney, Credit,andBanking,18: 355-65. Bowman,D.andRogers,J.(1997)AnAnalysisofFiscalPolicyintheFederal Reserve Board's Global Model. Manuscript. Division of International Finance, Federal Reserve Board. Brayton,F.andMauskopf,E.(1985)TheFederalReserveBoardMPSQuarterlyEconometricModeloftheU.S.Economy. EconomicModelling,2: 170-292. Brayton,F.andTinsley,P.(eds.) (1996)AGuidetoFRB/US:AMacroeconomicModel of the United States. Finance and Economics Discussion Series, 1996-42. Washington: Federal ReserveBoard. Campbell, J. and Mankiw, G. (1989) Consumption, Income and Interest Rates: Reinterpreting the Time Series Evidence. NBER Macroeconomics Annual. Cambridge: MIT Press. 37

Campbell, J. and Shiller, R. (1989) The Dividend-Price Ratio and Expectations of FutureDividendsandDiscountFactors. Reviewof FinancialStudies. 1: 195-228. de Leeuw, F. and Gramlich, E. (1968) The Federal Reserve-MIT Econometric Model. FederalReserve Bulletin,54: 11-40. de Leeuw, F. and Gramlich, E. (1969) The Channels of Monetary Policy: A Further Report on the Federal Reserve-MIT Econometric Model. Federal Reserve Bulletin, 55: 472-91. deMenil,G.andEnzler,J.(1972)PricesandWagesintheFR-MIT-PENNEconometric Model. The Econometrics of Price DeterminationConference, ed. O. Eckstein. Washington: BoardofGovernorsoftheFederal ReserveSystem. Dornbusch,R.(1976)ExpectationsandExchangeRate Dynamics. JournalofPolitical Economy,84: 1161-76. Edison,H.,Marquez,J.,andTryon,R.(1989)TheStructureandPropertiesoftheFederal Reserve BoardMulticountryModel. EconomicModelling,4: 115-315. Engle, R. and C. Granger (1985) Cointegration and Error Correction: Representation, Estimation,andTesting. Econometrica,55: 251-76. Enzler, J. and Pierce, J. (1974).The Effects of External Inflationary Shocks. Brookings PapersonEconomicActivity: 13-54. Fair, R. and Taylor, J. (1983) Solution and Maximum Likelihood Estimation of DynamicNonlinearRationalExpectationsModels. Econometrica51: 1169-85. Fuhrer,J.andMoore,G.(1995)InflationPersistence. QuarterlyJournalofEconomics, CX:127-59. 38

Gagnon,J.(1991)AForward-LookingMulti-CountryModelForPolicyAnalysis: MX- 3. EconomicandFinancialComputing,1: 311-61. Hansen, L. and Sargent, T. (1980) Linear Rational Expectations Models for Dynamically Interrelated Variables. Rational Expectations and Econometric Practice. eds. R. Lucas and T.Sargent. Minneapolis: UniversityofMinnesotaPress. Kozicki, S., Reifschneider, D., and Tinsley, P. (1996) The Behavior of Long-Term Interest Rates in the FRB/US Model. The Determinants of Long-Term Interest Rates and Exchange Rates and the Role of Expectations. Bank of International Settlements ConferencePapers,vol. 2,Basle: BankofInternationalSettlements. Kozicki, S. and Tinsley, P. (1996) Moving Endpoints and the Internal Consistency of Agents' ExAnteForecasts. FinanceandEconomicsDiscussionSeries,1996-47. Washington: Federal ReserveBoard. Levin, A. (1996) A Comparison of Alternative Monetary Policy Rules in the FRB Multi-CountryModel. TheDeterminantsofLong-TermInterestRatesandExchangeRates andtheRoleofExpectations. BankofInternationalSettlementsConferencePapers,vol. 2, Basle: BankofInternationalSettlements. Lucas, R. (1976) Econometric Policy Evaluation: A Critique. The Phillips Curve and Labor Markets, Carnegie-Rochester Conference Series on Public Policy, Amsterdam: North-Holland,19-46. Lucas, R., and Sargent, T.(1978)After KeynesianMacroeconomics. After thePhillips Curve: Persistence of High Inflation and High Unemployment, Federal Reserve Bank of Boston. Masson, P., Symansky, S., Haas, R., and Dooley, M. (1988) MULTIMOD: A Multi- Region Econometric Model. Staff Studies for the World Economic Outlook Washington, 39

DC: InternationalMonetaryFund. Muelbrauer,J.andLattimore,R.(1995)TheConsumptionFunction: ATheoreticaland Empirical Overview. Handbook of Applied Econometrics. eds. H. Pesaran and M. Wickens. Oxford: Blackwell. Rasche, R. and Shapiro, H. (1968) The F.R.B.-M.I.T. Econometric Model: Its Special Features. AmericanEconomicReview,58: 123-49. Reifschneider, D., Stockton, D., and Wilcox, D. (1997) Econometric Models and the Monetary Policy Process. Carnegie-Rochester Conference Series on Public Policy, 47, Amsterdam: North-Holland. Rotemberg,J.(1982)StickyPricesintheU.S.JournalofPoliticalEconomy,90: 1187- 211. Schuh, S. (1996) Evidence on the Link Between Firm-Level and Aggregate Inventory Behavior. Finance and Economics Discussion Series, 1996-46. Washington: Federal ReserveBoard. Shiller,R.(1979)TheVolatilityofLong-TermInterest Rates andExpectationsModels oftheTermStructure. JournalofPoliticalEconomy,87: 1190-1219. Sims,C.(1980)MacroeconomicsandReality. Econometrica,48: 1-48. Stevens,G.,Berner,R.,Clark,P.,Hernandez-Cata,E.,Howe,H.,andKwack,S.(1984) TheU.S.EconomyinanInterdependentWorld: AMulticountryModel. Washington: Board ofGovernorsoftheFederal ReserveSystem. Taylor, J. (1980) Aggregate Dynamics and Staggered Contracts. Journal of Political Economy,88: 1-24. 40

Taylor,J.(1993a)DiscretionVersusPolicyRulesinPractice. Carnegie-RochesterConferenceSeries onPublicPolicy,39: Amsterdam: NorthHolland. Taylor,J.(1993b)MacroeconomicPolicyinaWorldEconomy. NewYork: Norton. Tinsley, P. (1993) Fitting Both Data and Theories: Polynomial Adjustment Costs and Error-CorrectionDecisionRules. FinanceandEconomicsDiscussionSeries,93-21. Washington: Federal ReserveBoard. Williams, J. (1997) Simple Rules for Monetary Policy. Manuscript. Division of ResearchandStatistics,Federal Reserve Board. 41