NBER WORKING PAPER SERIES

ON DSGE MODELS

Lawrence J. ChristianoMartin S. Eichenbaum

Mathias Trabandt

Working Paper 24811http://www.nber.org/papers/w24811

NATIONAL BUREAU OF ECONOMIC RESEARCH1050 Massachusetts Avenue

Cambridge, MA 02138July 2018

Prepared for the Journal of Economic Perspectives. We are grateful for the comments of Olivier Blanchard, Robert Gordon, Narayana Kocherlakota, Douglas Laxton, Edward Nelson, Giorgio Primiceri and Sergio Rebelo on an earlier draft of this paper. The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research.

At least one co-author has disclosed a financial relationship of potential relevance for this research. Further information is available online at http://www.nber.org/papers/w24811.ack

NBER working papers are circulated for discussion and comment purposes. They have not been peer-reviewed or been subject to the review by the NBER Board of Directors that accompanies official NBER publications.

© 2018 by Lawrence J. Christiano, Martin S. Eichenbaum, and Mathias Trabandt. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source.

On DSGE ModelsLawrence J. Christiano, Martin S. Eichenbaum, and Mathias TrabandtNBER Working Paper No. 24811July 2018JEL No. E0,E3

ABSTRACT

The outcome of any important macroeconomic policy change is the net effect of forces operating on different parts of the economy. A central challenge facing policy makers is how to assess the relative strength of those forces. Dynamic Stochastic General Equilibrium (DSGE) models are the leading framework that macroeconomists have for dealing with this challenge in an open and transparent manner. This paper reviews the state of DSGE models before the financial crisis and how DSGE modelers responded to the crisis and its aftermath. In addition, we discuss the role of DSGE models in the policy process.

Lawrence J. ChristianoDepartment of EconomicsNorthwestern University2001 Sheridan RoadEvanston, IL 60208and NBERl-christiano@northwestern.edu

Martin S. EichenbaumDepartment of EconomicsNorthwestern University2003 Sheridan RoadEvanston, IL 60208and NBEReich@northwestern.edu

Mathias TrabandtFreie Universität BerlinDepartment of EconomicsBoltzmannstrasse 2014195 BerlinGermanymathias.trabandt@gmail.com

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1 IntroductionThe outcome of any important macroeconomic policy change is the net effect of forcesoperatingondifferentpartsoftheeconomy.Acentralchallengefacingpolicymakersishowtoassesstherelativestrengthofthoseforces.Economistshavearangeoftoolsthatcanbeusedtomakesuchassessments.Dynamicstochasticgeneralequilibrium(DSGE)modelsaretheleadingtoolformakingsuchassessmentsinanopenandtransparentmanner.

To be concrete, suppose we are interested in understanding the effects of a systematicchange in policy, like switching from inflation targeting to price-level targeting. Themostcompellingstrategywouldbetodorandomizedcontroltrialsonactualeconomies.But,thatcourseofactionisnotavailabletous.So,whatarethealternatives?Itiscertainlyusefultostudyhistoricalepisodesinwhichsuchasimilarpolicyswitchoccurredortousereduced-formtimeseriesmethods.But,thereareobviouslimitationstoeachoftheseapproaches.Inthehistorical approach, the fact that no two episodes are exactly the same always raisesquestions about the relevance of a past episode for the current situation. In the case ofreduced-formmethods,itisnotalwaysclearwhichparametersshouldbechangedandwhichshouldbekeptconstantacrosspolicyoptions.Inevitably,assessingtheeffectsofasystematicpolicychangehastoinvolvetheuseofamodel.

To be useful for policy analysis, DSGEmodelsmust be data based. As a practicalmatter,macroeconomicdataaren’t sufficient fordiscriminatingbetweenmanyalternativemodelsthat offer different answers to policy questions. Put differently, many DSGE models areobservationallyequivalentwithrespecttomacrodata.ButmodernDSGEmodelsarebasedon microeconomic foundations. So, microeconomic data and institutional facts can bebroughttobearonthedesign,constructionandevaluationofDSGEmodels.Microdatabreaktheobservationalequivalencethatwasthebaneofmacroeconomists.

TheopennessandtransparencyofDSGEmodelsisavirtue.Butitalsomakesthemeasytocriticize. Suspiciousassumptionscanbehighlighted. Inconsistencieswith theevidencecaneasilybespotted.Forcesthataremissingfromthemodelcanbeidentified.Theprocessofresponding to informed criticisms is a critical part of the process of building better DSGEmodels.Indeed,thetransparentnatureofDSGEmodelsisexactlywhatmakesitpossiblefordiversegroupsofresearchers-includingthosewhodon’tworkonDSGEmodels-tobepartoftheDSGEproject.

SomeanalystsobjecttoworkingwithDSGEmodelsandprefertoinsteadthinkaboutpolicybyworkingwithsmallequilibriummodelsthatemphasizedifferentsubsetsoftheeconomy,labor or financial markets. This approach has a vital contribution to make because smallmodels help us build intuition about the mechanisms at work in DSGE models. But, thisapproach cannot be a substitute for DSGEmodels itself because quantitative conclusionsabouttheoveralleconomicimpactofapolicyrequiresinformaljudgmentasoneintegratesacross individual small-scale models. The small-model approach to policy thus involvesimplicitassumptionsandlacksthetransparencyoftheDSGEapproach.

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Tobeclear,policydecisionsaremadebyrealpeopleusingtheirbestjudgment.Usedwisely,DSGEmodelscanimproveandsharpenthatjudgment.Inanidealworld,wewillhavebothwisepolicymakersandempiricallyplausiblemodels.But,torephraseFischer(2017)’squotingof Samuelson on Solow: “We’d rather have Stanley Fischer than aDSGEmodel, butwe’dratherhaveStanleyFischerwithaDSGEmodelthanwithoutone.”Insection2wereviewthestateofmainstreamDSGEmodelsbeforethefinancialcrisisandtheGreatRecession.Insection3wedescribehowDSGEmodelsareestimatedandevaluated.Section4addressesthequestionofwhyDSGEmodelers– likemostothereconomistsandpolicy makers – failed to predict the financial crisis and the Great Recession. Section 5discusseshowDSGEmodelersrespondedtothefinancialcrisisanditsaftermath.Section6discusseshowcurrentDSGEmodelsareactuallyusedbypolicymakers.Section7providesabriefresponsetocriticismofDSGEmodels,withspecialemphasisonStiglitz(2017).Section7offersconcludingremarks.

2BeforetheStorm

InthissectionwedescribeearlyDSGEmodelsandhowtheyevolvedpriortothecrisis.

2.1 Early DSGEModels

Asapracticalmatter,peopleoftenusethetermDSGEmodelstorefertoquantitativemodelsofgrowthorbusinesscyclefluctuations.AclassicexampleofaquantitativeDSGEmodel istheRealBusinessCycle(RBC)modelassociatedwithKydlandandPrescott(1982)andLongandPlosser(1983).TheseearlyRBCmodelsimaginedaneconomypopulatedbyhouseholdswhoparticipateinperfectlycompetitivegoods,factorandassetmarkets.Thesemodelstookthepositionthatfluctuationsinaggregateeconomicactivityareanefficientresponseoftheeconomy to theone sourceof uncertainty in agents’ environment, exogenous technologyshocks. The associated policy implications are clear: there is no need for any form ofgovernmentintervention.Infact,governmentpoliciesaimedatstabilizingthebusinesscyclearewelfare-reducing.

ExcitementaboutRBCmodelscrumbledunderthe impactofthreeforces.First,microdatacast doubt on someof the key assumptions of themodel. These assumptions include, forexample,perfectcreditandinsurancemarkets,aswellasperfectlyfrictionlesslabormarketsinwhichfluctuationsinhoursworkedreflectmovementsalongagivenlaborsupplycurveoroptimalmovementsofagentsinandoutofthelaborforce(seeChettyetal.(2011)).Second,themodelshaddifficultyinaccountingforsomekeypropertiesoftheaggregatedata,suchastheobserved volatility in hours worked,the equity premium,the low co-movement ofrealwages and hoursworked (see ChristianoandEichenbaum(1992)andKing and Rebelo(1999)).Open-economy versionsofthesemodelsalsofailedtoaccountforkeyobservationssuchasthecyclicalco-movement of consumption and output across countries (see Backus

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et al. (1992)) and theextremelyhighcorrelationbetweennominalandrealexchangerates(seeMussa(1986)).

Third, becausemoney plays no role in RBCmodels, thosemodels seem inconsistent withmainstream interpretations of various historical episodes. One example is Hume (1742)’sdescriptionofhowmoneyfromtheNewWorldaffectedtheEuropeaneconomy.AdifferentexampleistheviewthattheearlieracountryabandonedtheGoldStandardduringtheGreatDepression,thesooneritsrecoverybegan(seeBernanke(1995)).AfinalexampleistheviewthattheseverityoftheU.S.recessionintheearly1980swasinlargepartcausedbymonetarypolicy.Finally,thesimpleRBCmodeliseffectivelymuteonahostofpolicy-relatedquestionsthatareofvital importancetomacroeconomistsandpolicymakers.Examples include:whataretheconsequencesofdifferentmonetarypolicyrulesforaggregateeconomicactivity,whataretheeffectsofalternativeexchangerateregimes,andwhatregulationsshouldweimposeonthefinancialsector?

2.2 NewKeynesianModels

Prototypical pre-crisis DSGEmodels built upon the chassis of the RBCmodel to allow fornominalfrictions,bothinlaborandgoodsmarkets.ThesemodelsareoftenreferredtoasNewKeynesianDSGEmodels.But,itwouldbejustasappropriatetorefertothemasFriedmaniteDSGEmodels. The reason is that they embody the fundamental world view articulated inFriedman’s seminal Presidential Address (see Friedman (1968)). According to this view,hyperinflationsaside,monetarypolicyhasessentiallynoimpactonrealvariableslikeoutputandtherealinterestrateinthelongrun.However,duetostickypricesandwagesmonetarypolicymatters in the short run.1 Specifically, apolicy-induced transitory fall in thenominalinterestrateisassociatedwithadeclineinthereal interestrate,anexpansionineconomicactivityandamoderateriseininflation.

Modelsinwhichpermanentchangesinmonetarypolicyinduceroughlyone-to-onechangesininflationandthenominalrateofinterestaresaidtosatisfytheFisherianproperty.Modelsinwhichtransitorychangesinmonetarypolicyinducemovementsinnominalinterestratesandinflationoftheoppositesignaresaidtosatisfytheanti-Fisherianproperty.ThecanonicalNewKeynesianmodelsofYun(1996)andClaridaetal.(1999)andWoodford(2003)satisfybothproperties.

The basic intuition behind the anti-Fisherian property of the New Keynesian model is as

1Forexample,Friedman(1968,p. 10)writesthatafterthemonetaryauthority increasesmoneygrowth,“... muchormostoftheriseinincomewilltaketheformofanincreaseinoutputandemploymentratherthan inprices. Peoplehavebeenexpectingprices tobe stable, andpricesandwageshavebeen set forsome time in the future on that basis. It takes time for people to adjust to a new state of demand.Producers willtendtoreacttotheinitialexpansioninaggregatedemandbyincreasingoutput,employeesbyworking longerhours,andtheunemployed,bytakingjobsnowofferedatformernominalwages.”

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follows.Firmsset theirpricesonthebasisofcurrentandfuturemarginalcosts.Thefuturestateoftheeconomyisrelativelyunaffectedbyatransitorymonetarypolicyshock.So,actualinflationrespondsrelativelylittletoapolicyinducedtransitoryfallinthenominalinterestrate.As a result, the real interest rate declines. Intertemporal substitution by households theninduces a rise in current consumption, leading to a rise in labor income. That increasereinforces the contemporaneous rise in consumption and employment. The expansion inemploymentdriveswagesandmarginalcostsup.Thelattereffectdrives inflationup.Sinceinflation and the nominal interest move in opposite directions, the model has the anti-Fisherian property. Less surprisingly, standardNew Keynesianmodels satisfy the Fisherianpropertybecauseitslong-runpropertiesareroughlythesameastheunderlyingRBCchassis.

ManyresearchersfoundNewKeynesianmodelsattractivebecausetheyseemedsensibleandtheyallowedresearcherstoengageinthetypesofpolicydebatesthatRBCmodelshadbeensilentabout.Acriticalquestionwas: whatpropertiesshouldquantitativeversionsofthesemodelshave?Toaddress thisquestion, theempirical literature focusedonquantifying thedynamiceffectsofashocktomonetarypolicy.Thistypeofshockhaslongbeenofinteresttomacroeconomists for a variety of reasons. For example, Friedman and Schwartz (1963)attributedthemajorportionofbusinesscyclevariationstoexogenousshocksinthemoneysupply.Therecentliteraturefindstheseshocksinterestingbecausetheyprovideapotentiallypowerfuldiagnosticfor discriminatingbetweenmodels.Perhapsthemostextremeexampleisthatarealbusinesscyclemodelimpliesnothinghappenstorealvariablesafteramonetarypolicyshock.Incontrast,simpleNewKeynesianmodelsimplythatrealvariablesdorespondtoamonetarypolicyshock.

Amonetarypolicyshockcanreflectavarietyoffactorsincludingmeasurementerrorinthereal-timedatathatpolicymakersconditiontheiractionsonandthebasicrandomnessthatisinherentingroupdecisions.InaseminalpaperSims(1986)arguedthatoneshouldidentifymonetarypolicyshockswithdisturbancestoamonetarypolicyreactionfunctioninwhichthepolicyinstrumentisashort-terminterestrate.BernankeandBlinder(1992)andChristianoetal. (1996,1999) identifymonetarypolicyshocksusingtheassumptionthatmonetarypolicyshocks have no contemporaneous impact on inflation and output.2 This set of identifyingrestrictions, like theentireNewKeynesianenterprise, falls squarely in the Friedmanworldview.Forexample,intestimonybeforeCongress,Friedman(1959)said:

“Monetaryandfiscalpolicyisratherlikeawatertapthatyouturnonnowandthatthenonlystartstorun6,9,12,16monthsfromnow.”

In practice, this Friedman-style identifying strategy is implemented using a vectorautoregression representation (VAR) with a large set of variables. Figure 1, taken fromChristiano,TrabandtandWalentin(2010),displaystheeffectsof identifiedmonetarypolicyshocksestimatedusingdatacoveringtheperiod1951Q1to2008Q4.Forconvenienceweonlyshow the response functions for a subset of the variables in the VAR. The dashed linescorrespondto95%confidenceintervalsaboutthepointestimates(solidblackline).

2Christiano,EichenbaumandEvans(1999)showthattheresultsfromimposingthisassumptiononmonthlyorquarterlydataarequalitativelysimilar.Theassumptionisobviouslymorecompellingformonthlydata.

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Overall,theresultsareconsistentwiththeviewthatanexpansionarymonetarypolicyshockhas the effects that Friedman (1968) asserted in his Presidential Address. Specifically, anexpansionarymonetarypolicyshockcorrespondingtoadeclineintheU.S.federalfundsrateleadstohump-shapedexpansionsinconsumption,investmentandoutput,aswellasrelativelysmallrisesinrealwagesandinflation.Sincetheinflationratemovesverylittleinresponsetoamonetarypolicyshock,theresponsesintherealinterestrateandthefederalfundsrateareroughlythesame.

AnaturalquestionishowrobusttheresultsinFigure1aretothevarioustechnicalassumptionsunderlyingthestatisticalanalysis.Here,wefocusonsensitivitytothenumberoflagsintheVARandtothestartofthesampleperiod.AVARrepresentseachvariableasafunctionofthelaggedvaluesofallthevariablesinthesystem.Denotethenumberoflagsbyn.ThebaselinespecificationinFigure1assumesn=2.TheFigurereportstheresultsofredoingtheanalysisforn=1,…,5.Foreachvalueofn,theFigurereportstheresultsbasedonstartingthesampleperiodineachofthedates1951Q1,1951Q2,…,1985Q4.Inthisway,wegenerate700setsofresults,eachofwhichisdisplayedbyathinsolidgreylineinFigure1.Notethatthebasicqualitativeproperties of the benchmark analysis are remarkably robust, although there are of course

Notes: All data are expressed in deviations from what would have happened in the absence of the shock. The units are given in the titles of the subplots. % means percent deviation from unshocked path. APR means annualized percentage rate deviation from unshocked path.

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specificationsofnandthesampleperiodthatyielddifferentimplications.Itisinterestinghowsimilartheshapeoftheconfidenceandsensitivityintervalsare.

Inrecentyearsresearchershavedevelopedalternativeproceduresforidentifyingmonetarypolicyshocks.Theseprocedures focusonmovements inthefederal funds futuresrate inatight window of time around announcements made by monetary policy makers. See, forexample,GertlerandKaradi(2015)whobuildontheworkofKuttner(2001)andGürkaynak,SackandSwanson(2005).Broadlyspeaking,thisliteraturereachesthesameconclusionsabouttheeffectsofmonetarypolicy shocksdisplayed in Figure1. Inour view, these conclusionssummarizetheconventionalviewabouttheeffectsofamonetarypolicyshock.

2.3 Christiano,EichenbaumandEvans’Model

Akeychallengewas todevelopan empirically plausibleversionof theNew Keynesianmodel that could account quantitatively for the type of impulse response functionsdisplayedinFigure1.Christiano et al. (2005)developed a version of the NewKeynesianmodelthatmet thischallenge.Wegointosomedetaildescribingthebasicfeaturesofthatmodel because they form the core of leading pre-crisis DSGEmodels, such as Smets andWouters (2003, 2007).

2.3.1 ConsumptionandInvestmentDecisionsConsistentwithalongtraditioninmacroeconomics,themodeleconomyinChristianoetal.(2005) is populatedbya representativehousehold.At eachdate, thehouseholdallocatesmoneytopurchasesoffinancialassets,aswellasconsumptionandinvestmentgoods.Thehousehold receives income from wages, from renting capital to firms and from financialassets,allnetoftaxes.AsinthesimpleNewKeynesianmodel,Christianoetal.(2005)makeassumptionsthatimplythehousehold’sborrowingconstraintsarenotbinding.So,theinterestratedeterminestheintertemporal time pattern of consumption. Of course, the present value of incomedetermines the level of consumption. Holding interest rates constant, the solution to thehousehold problem is consistent with a key prediction of Friedman’s permanent incomehypothesis: persistent changes in income have a much bigger impact on householdconsumptionthantransitorychanges.

Tobeconsistentwiththeresponseofconsumptionandtheinterestratetoamonetarypolicyshock observed in Figure 1, Christiano et al. (2005) had to depart from the standardassumption that utility is time-separable in consumption. Generally speaking, thatassumption implies that after a policy-induced decline in the interest rate, consumptionjumpsimmediatelyandthenfalls.But,thisisaverydifferentpatternthanthehump-shaperesponse thatwe see in Figure1. To remedy this problem,Christianoet al. (2005) followFuhrer (2000) by adopting the assumption of habit-formation in consumption.Under thisspecification,themarginalutilityofcurrentconsumptiondependspositivelyonthelevelof

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thehousehold’spastconsumption.Householdsthenchoosetoraiseconsumptionslowlyovertime, generating a hump-shape response-pattern as in Figure 1. As it turns out, there issubstantialsupportforhabitpersistenceinthefinance,growthandpsychologyliteratures.3

Tobeconsistentwiththehump-shaperesponseofinvestmenttoamonetarypolicyshock,Christiano et al. (2005) had to assume households face costs of changing the rate ofinvestment.Toseewhy,notethatabsentuncertainty,arbitrageimpliesthattheone-periodreturnoncapitalisequaltotherealrateofinterestonbonds.Absentanyadjustmentcosts,theone-periodreturnoncapitalisthesumofthemarginalproductofcapitalplusoneminusthe depreciation rate. Suppose that there is an expansionarymonetary policy shock thatdrivesdowntherealinterestrate,withthemaximalimpactoccurringcontemporaneously,asin the data (see Figure 1). Absent adjustment costs, arbitrage requires that themarginalproductofcapitalfollowapatternidenticaltotherealinterestrate.Forthattohappenboththecapitalstockandinvestmentmusthaveexactlytheoppositepatternthanthemarginalproduct of capital. With the biggest surge in investment occurring in the period of themonetarypolicyshockthesimplemodelcannotreproducethehump-shapepatterninFigure1.Whenitiscostlytoadjusttherateofinvestment,householdschoosetoraiseinvestmentslowlyovertime,generatingahump-shaperesponse-patternasinFigure1.

Lucca (2006) and Matsuyama (1984) provide interesting theoretical foundations for theinvestment adjustment cost in Christiano et al. (2005). In addition, there is substantialempiricalevidence insupportofthespecification(seeEberlyetal. (2012)andMatsuyama(1984)).An importantalternative specificationofadjustment costspenalizeschanges in thecapitalstock. Thisspecificationhasalonghistoryinmacroeconomics,goingbackatleasttoLucasand Prescott (1971). Christiano, Eichenbaum and Evans show that with this type ofadjustment cost, investment jumps afteranexpansionarymonetarypolicyshockandthenconverges monotonically back to its pre-shock level from above. This response pattern isinconsistentwiththeVARevidence.

2.3.2NominalRigidities

IncontrasttoRBCmodels,goodsandlabormarketsinChristianoetal.(2005)arenotperfectlycompetitive.Thisdepartureisnecessarytoallowforstickypricesandstickynominalwages–ifapriceorwageissticky,someonehastosetit.

In Christiano et al. (2005), nominal rigidities arise from Calvo (1983) style frictions. Inparticular, firms and households can change prices or wages with some exogenous

3 Inthefinanceliteraturesee,forexample,EichenbaumandHansen(1990),Constantinides(1990)andBoldrinetal.(2001).InthegrowthliteratureseeCarrolletal.(1997,2000).Inthepsychologyliterature,seeGremeletal.(2016).

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probability.Inaddition,theymustsatisfywhateverdemandmaterializesatthosepricesandwages.

Calvo-stylefrictionsmakesenseonly inenvironmentswhereinflationismoderate.Eveninmoderateinflationenvironments,Calvo-stylefrictionshaveimplicationsthatareinconsistentwithaspectsofmicrodata(seeforexampleNakamuraandSteinsson(2008)orEichenbaumet al. (2011)). Still, its continued use reflects two factors. First, Calvo-style frictions allowmodelstocapture,inanelegantandtractablemanner,whatmanyresearchersbelieveisanessential feature of business cycles: for moderate inflation economies, firms and laborsupplierstypicallyrespondtovariationsindemandbyvaryingquantitiesratherthanprices.Second,authorslikeEichenbaumetal.(2011)arguethat,formoderateinflationeconomies,theCalvomodelprovidesagoodapproximationtomoreplausiblemodelsinwhichfirmsfacecostsofchangingtheirpricingstrategies.

2.3.3A-cyclicalMarginalCosts

Christianoetal.(2005)buildfeaturesintothemodelwhichensurethatfirms’marginalcostsarenearlya-cyclical.Theydosoforthreereasons.First,thereissubstantialempiricalevidenceinfavorofthisview(seeforexample,Andersonetal. (2018)).Second,themorea-cyclicalmarginalcostis,themoreplausibleistheassumptionthatfirmssatisfydemand.Third,asinstandardNewKeynesianmodels,inflationisanincreasingfunctionofcurrentandexpectedfuture marginal costs. So, relatively a-cyclical marginal costs are critical for dampeningmovementsintheinflationrate.

ThemodelinChristianoetal.(2005)incorporatestwomechanismstoensurethatmarginalcostsarerelatively a-cyclical. The first is the sticky nominal wage assumption mentionedabove.The secondmechanism is that the rateatwhich capital is utilized canbe varied inresponse toshocks.

2.3.4QuantitativePropertiesToillustratethemodel’squantitativeproperties,weworkwiththevariantofthemodelofChristianoetal. (2005)estimatedbyChristiano,EichenbaumandTrabandt (2016).Were-estimated the model using a Bayesian procedure that treats the VAR-based impulseresponsestoamonetarypolicyshockasdata.Theappendixtothispaperprovidesdetailsaboutthepriorandposteriordistributionsofmodelparameters.Herewehighlightsomeofthekeyestimatedparameters.Theposteriormodeestimatesimplythatfirmschangepricesonaverageonceevery2.3quarters,thehouseholdchangesnominalwagesaboutonceayear,pastconsumptionenterswithacoefficientof0.75inthehousehold’sutilityfunction,andtheelasticityofinvestmentwithrespecttoaonepercenttemporaryincreaseinthecurrentpriceofinstalledcapitalisequalto0.16.ThethinsolidblacklinesinFigure2aretheVAR-basedimpulseresponsefunctionestimatesreproducedfromFigure1.Thegreyareadepictsthe95%confidenceintervalsassociatedwith

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thoseestimates.ThesolidbluelinedepictstheimpulseresponsefunctionoftheestimatedDSGE model to a monetary policy shock, calculated using the mode of the posteriordistributionofthemodel’sparameters.Fourkeyfeaturesoftheresultsareworthnoting.First,themodelsucceedsinaccountingforthehump-shaperiseinconsumption,investmentandrealGDPafterapolicy-inducedfallinthefederalfundsrate.Second,themodelsucceedsinaccountingforthesmallriseininflationaftertheshock.Third,themodelhasthepropertythatrealwagesareessentiallyunaffectedby the policy shock. Finally, the model has the anti-Fisherian property that the nominalinterestandinflationmoveintheoppositedirectionafteratransitorymonetarypolicyshock.

Weemphasizethatthemodel’spropertiesdependcriticallyonstickywages.Thereddashedline in Figure 2 depicts themodel’s implications if we recalculate the impulse responsesassumingthatnominalwagesarefullyflexible(holdingothermodelparametersfixedatthemode of the posterior distribution). Note that the model’s performance deterioratesdrastically.

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Notes: All data are expressed in deviations from what would have happened in the absence of the shock. The units are given in the titles of the subplots. % means percent deviation from unshocked path. APR means annualized percentage rate deviation from unshocked path.

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In Christiano, Eichenbaum and Evans (2005), sticky wages are sticky by assumption.Christiano,EichenbaumandTrabandt(2016)showthatwagestickinessarisesendogenouslyinaversionofChristiano,EichenbaumandEvans(2005),wheretherearelabormarketsearchandmatchingfrictions.Thekeyfeatureofthemodelisthatworkersandfirmsbargaininawaythatreducesthesensitivityofthewagetomacroeconomicaggregates.Oneadvantageof endogenously generating sticky wages in this way is that Christiano, Eichenbaum andTrabandt (2016) can analyze the aggregate effects of various policies like unemploymentinsurance.

Finally,we note that habit formation and investment adjustment costs are critical to themodel’ssuccess.Absentthosefeatures,itwouldbeverydifficulttogeneratehump-shapedresponseswithreasonabledegreesofnominalrigidities.

3 HowDSGEModelsAreEstimatedandEvaluated

Priortothefinancialcrisis,researchersgenerallyworkedwithlog-linearapproximationstotheequilibriaofDSGEmodels.Therewerethreereasonsforthischoice.First,forthemodelsbeingconsideredandforthesizeofshocksthatseemedrelevantforthepost-warU.S.data,linear approximations are very accurate (see for example the papers in Taylor and Uhlig(1990)).Second, linearapproximationsallowresearcherstoexploitthelargearrayoftoolsfor forecasting, filtering and estimation provided in the literature on linear time seriesanalysis. Third, it was simply not computationally feasible to solve and estimate large,nonlinearDSGEmodels.Thetechnologicalconstraintswererealandbinding.

Researchers choose values for the key parameters of their models using a variety ofstrategies. In some cases, researchers choose parameter values to match unconditionalmodelanddatamoments,ortheyreferencefindingsintheempiricalmicroliterature.Thisprocedureiscalledcalibrationanddoesnotuseformalsamplingtheory.Calibrationwasthedefault procedure in the early RBC literature and it is also sometimes used in the DSGEliterature.MostofthemodernDSGEliteratureconductsinferenceaboutparametervaluesandmodel fit using one of two strategies thatmake use of formal econometric samplingtheory.

The first strategy is limited information because it does not exploit all of the model’simplications formomentsof thedata.One variantof the strategyminimizes thedistancebetweenasubsetofmodel-impliedsecondmomentsandtheiranalogsinthedata.Amoreinfluentialvariantofthisfirststrategyestimatesparametersbyminimizingthedistancebe-tween model and data impulse responses to economic shocks (examples of the impulseresponsematching approach includeChristianoet al. (2005), Altig et al. (2011), Iacoviello(2005)andRotembergandWoodford(1991)).

Oneway to estimate the data impulse response functions is based on partially identifiedVARs. Another variant of this strategy, sometimes referred to as themethod of externalinstruments, involves using historical or narrativemethods to obtain instruments for the

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underlying shocks (see, Mertens and Ravn (2013)). Finally, researchers have exploitedmovementsinassetpricesimmediatelyaftercentralbankpolicyannouncementstoidentifymonetary policy shocks and their consequences. This approach is referred to as highfrequencyidentification(earlycontributionsincludee.g.Kuttner(2001)andGürkaynaketal.(2005)).

TheinitiallimitedinformationapplicationsintheDSGEliteratureusedgeneralizedmethodofmomentsestimatorsandclassicalsamplingtheory(seeHansen(1982)).Buildingontheworkof Chernozhukov and Hong (2003), Christiano et al. (2010) showed how the Bayesianapproachcanbeappliedinlimitedinformationcontexts.

AcriticaladvantageoftheBayesianapproachisthatonecanformallyandtransparentlybringtobear information fromavarietyofsourcesonwhatconstitutes“reasonable”values formodelparameters.Suppose,forexample,thatonecouldonlymatchthedynamicresponsetoamonetarypolicyshockformodelparametervaluesimplyingthatfirmschangetheirpricesonaverageeverytwoyears.Thisimplicationisstronglyatvariancewithevidencefrommicrodata.IntheBayesianapproach,theanalystwouldimposepriorsthatsharplypenalizesuchparametervaluessothatthoseparametervalueswouldbeassignedlowprobabilitiesintheanalyst’s posterior distribution. Best practice compares priors and posteriors for modelparameters.Thiscomparisonallowstheanalysttomakecleartheroleofpriorsandthedataingeneratingtheresults.AswejuststressedtheBayesianapproachallowsonetobringtobearinformationculledfrommicro data onmodel parameters. This approach allows one to bring to bear informationculledfrommicrodataonmodelparameters.Atadeeperlevel,microdatainfluences,inacriticalbutslow-movingmanner,theclassofmodelsthatweworkwith.Ourdiscussionofthedemise of the pure RBCmodel is one illustration of this process. Themodels of financialfrictions and heterogeneous agents discussed below are an additional illustration of howDSGEmodelsevolveovertimeinresponsetomicrodata(seesections5.1and5.3).ThesecondstrategyforestimatingDSGEmodelsinvolvesfull-informationmethods.Inmanyapplications,thedatausedforestimationisrelativelyuninformativeaboutthevalueofsomeoftheparametersinDSGEmodels(seeCanovaandSala(2009)).Anaturalwaytodealwiththisfactistobringotherinformationtobearontheanalysis.Bayesianpriorsareavehiclefordoingexactly that. This is an important reasonwhy theBayesianapproachhasbeenveryinfluentialinfull-informationapplications.StartingfromSmetsandWouters(2003),alargeeconometricliteraturehasexpandedtheBayesiantoolkittoincludebetterwaystoconductinference about model parameters and to analyze model fit. For a recent survey seeFernandez-Villaverdeetal.(2016).

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4 Why Didn’t DSGE Models Predict the FinancialCrisis?

Pre-crisisDSGEmodelsdidn’tpredictthe increasingvulnerabilityoftheU.S.economytoafinancial crisis. They have also been criticized for not placingmore emphasis on financialfrictions.Here,wegiveourperspectiveonthesefailures.

Thereisstillanongoingdebateaboutthecausesofthefinancialcrisis.Ourview,sharedbyBernanke(2009)andmanyothers, isthatthefinancialcrisiswasprecipitatedbyarollovercrisisinaverylargeandhighlyleveredshadow-bankingsectorthatreliedonshort-termdebttofundlong-termassets.ByshadowbankswemeanfinancialinstitutionsnotcoveredbytheprotectiveumbrellaoftheFederalReserveandFederalDeposit InsuranceCorporation(forfurtherdiscussion,seeBernanke(2010)).

Rollover crisiswas triggeredbya setofdevelopments in thehousing sector.U.S.housingpricesbegantoriserapidlyinthe1990’s.TheS&P/Case-ShillerU.S.NationalHomePriceIndexrose by a factor of roughly 2.5 between 1991 and 2006. The precise role played byexpectations, the subprimemarket,declining lending standards inmortgagemarkets, andoverly-loosemonetarypolicyisnotcriticalforourpurposes.Whatiscriticalisthathousingpricesbegantodeclineinmid-2006,causingafallinthevalueoftheassetsofshadowbanksthathadheavilyinvestedinmortgage-backedsecurities.TheFed’swillingnesstoprovideasafetynetfortheshadowbankingsystemwasatbestimplicit,creatingtheconditionsunderwhicharoll-overcrisiswaspossible.Infact,arollovercrisisdidoccurandshadowbankshadtoselltheirasset-backedsecuritiesatfire-saleprices,precipitatingthefinancialcrisisandtheGreatRecession.Againstthisbackground,weturntothefirstofthetwocriticismsofDSGEmodelsmentionedabove,namely their failure to signal the increasing vulnerabilityof theU.S. economy toafinancialcrisis.Thiscriticismiscorrect.Thefailurereflectedabroaderfailureoftheeconomicscommunity.Theoverwhelmingmajorityofacademics,regulatorsandpractitionersdidnotrealize that a small shadow-banking system had metastasized into a massive, poorly-regulated,wildwest-likesectorthatwasnotprotectedbydepositinsuranceorlender-of-last-resortbackstops.

WenowturntothesecondcriticismofDSGEmodels,namelythattheydidnotsufficientlyemphasizefinancialfrictions.Inpracticemodelershavetomakechoicesaboutwhichfrictionstoemphasize.OnereasonwhymodelersdidnotemphasizefinancialfrictionsinDSGEmodelsisthatuntiltheGreatRecession,post-warrecessionsintheU.S.andWesternEuropedidnotseemcloselytiedtodisturbancesinfinancialmarkets.TheSavingsandLoanscrisisintheUSwasalocalizedaffairthatdidnotgrowintoanythingliketheGreatRecession.Similarly,thestockmarketmeltdownin1987andtheburstingofthetech-bubblein2001onlyhadminoreffectsonaggregateeconomicactivity.

Atthesametime,thefinancialfrictionsthatwereincludedinDSGEmodelsdidnotseemto

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haveverybigeffects.Consider,forexample,Bernankeetal.(1999)’sinfluentialmodelofthefinancialaccelerator.Thatmodelisarguablythemostinfluentialpre-crisisDSGEmodelwithfinancialfrictions.Itturnsoutthatthefinancialacceleratorhasonlyamodestquantitativeeffectonthewaythemodeleconomyrespondstoshocks,seee.g.Lindéetal.(2016).Inthesamespirit, Kocherlakota (2000)argues thatmodelswithKiyotaki andMoore (1997) typecreditconstraintshaveonlynegligibleeffectsondynamicresponsestoshocks.Finally,Brzoza-Brzezina and Kolasa (2013) compare the empirical performance of the standard NewKeynesian DSGE model with variants that incorporate Kiyotaki and Moore (1997) andBernankeetal.(1999)typeconstraints.Theirkeyfindingisthatneithermodelsubstantiallyimprovesontheperformanceofthebenchmarkmodel,eitherintermsofmarginallikelihoodsorimpulseresponsefunctions.So,guidedbythepost-wardatafromtheU.S.andWesternEurope, and experience with existing models of financial frictions, DSGE modelersemphasizedotherfrictions.

5 After theStorm

Giventhedata-drivennatureofDSGEenterprise,itisnotsurprisingthatthefinancialcrisisanditsaftermathhadanenormousimpactonDSGEmodels.Inthissectionwediscussthemajorstrandsofworkinpost-financialcrisisDSGEmodels.

5.1 Financial Frictions

The literature on financial frictions can loosely be divided between papers that focus onfrictionsoriginatinginsidefinancialinstitutionsandthosethatarisefromthecharacteristicsofthepeoplewhoborrowfromfinancialinstitutions.Theoriesofbankrunsandrollovercrisisfocusonthefirstclassoffrictions.Theoriesofcollateralconstrainedborrowersfocusonthesecondclassoffrictions. WedonothavespacetosystematicallyreviewtheDSGEmodelsthatdealwithbothtypesoffinancialfrictions.Instead,wediscussexamplesofeach.

Frictions That Originate Inside Financial Institutions

Motivated by events associated with the financial crisis, Gertler and Kiyotaki (2015) andGertler,KiyotakiandPrestipino(2016)developaDSGEmodelofarollovercrisisintheshadowbankingsector,whichtriggersfiresales.Theresultingdeclineinassetvaluestightensbalancesheetconstraintsintherestofthefinancialsectorandthroughouttheeconomy.4

IntheGertlerandKiyotaki(2015)model,shadowbanksfinancethepurchaseof long-termassetsbyissuingshort-term(one-period)debt.Bankshavetwowaystodealwithshort-termdebtthatiscomingdue.Thefirstistoissuenewshort-termdebt(thisiscalledrollingover

4 ThekeytheoreticalantecedentisthebankrunmodelofDiamondandDybvig(1983)andthesovereigndebtrollovercrisismodelofColeandKehoe(2000).

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thedebt).Thesecondistosellassets.Thecreditor’sonlydecisioniswhetherornottobuynewshort-termdebt.There isnothingthecreditorcandotoaffectpaymentsreceivedonpastshort-termdebt.Unlike intheclassicbankrunmodelofDiamondandDybvig (1983),thereisnoreasontoimposeasequentialdebtserviceconstraint.

There is always an equilibrium in theGertler and Kiyotaki (2015)model inwhich shadowbankscanrollovertheshort-termdebtwithoutincident.But,therecanalsobeanequilibriuminwhicheachcreditorchoosesnottorolloverthedebt.Supposethatanindividualcreditorbelievesthatallothercreditorswon’textendnewcredittobanks.Inthatcase,therewillbeasystem-widefailureofthebanks,asattemptstopayoffbankdebtleadtofiresalesofassetsthatwipesoutbankequity. The individual creditorwouldprefer tobuyassetsat fire saleprices rather than extend credit to a bank that has zero networth.With every potentialcreditor thinking thisway, it is aNash equilibrium for each creditor to not purchase newliabilitiesfrombanks.Suchanequilibriumisreferredtoasarollovercrisis.

Arollovercrisisleadstofiresalesbecause,withallbanksselling,theonlypotentialbuyersareotheragentswhohavelittleexperienceevaluatingthebanks’assets.Inthisstateoftheworld,agencyproblemsassociatedwithasymmetricinformationbecomeimportant.5

Figure 3: Balance Sheet of the Shadow-Banking Sector Before and After theHousingMarketCorrection:AnIllustrativeExample

Note:Figure3capturesinahighlystylizedwaythekeyfeaturesoftheshadow-bankingsystembefore(leftside)andafter(rightside)thehousingcrisis.Thenumberswithoutparenthesesarebaselinevalues,whilethenumbersinparenthesesshowwhatthevalueswouldbeifthereweretobearollovercrisisandfires-saleofassets.Inthepre-housingmarketcorrectionperiod,thebankswouldstaysolventinarollovercrisis;thereforenorollovercrisiscanoccuraccordingtheanalysisofGertlerandKiyotaki(2015).Inthepost-housingmarketcorrectionperiod,thevalueoftheassetsinthecaseofarollovercrisisis95andthenetworthofthebankisnegative.Inthisscenarioarollovercrisiscanoccur.As part of the specification of the model, Gertler and Kiyotaki (2015) assume that theprobabilityofarollovercrisisisproportionaltothelossesdepositorswouldexperienceintheeventthatarollovercrisisoccurs.So,ifbankcreditorsthinkthatbanks’networthwouldbepositiveinacrisis,thenarollovercrisisisimpossible.However,ifbanks’networthisnegativeinthisscenariothenarollovercrisiscanoccur.

5 GertlerandKiyotaki (2015)capturetheseagencyproblemsbyassumingthatthebuyersof long-termassetsduringarollovercrisisarerelativelyinefficientatmanagingtheassets.

Figure 1: Balance Sheet of the Shadow-Banking Sector Before and After the Housing MarketCorrection

As part of the specification of the model, GK assume that the probability of a rollover crisisis proportional to the losses depositors would experience in the event that a rollover crisisoccurs. So, if bank creditors think that banks’ net worth would be positive in a crisis, thena rollover crisis is impossible. However, if banks’ net worth is negative in this scenario thena rollover crisis can occur.26

We use this model to illustrate how a relatively small shock can trigger a system-widerollover crisis in the shadow banking system. To this end, consider Figure 1, which capturesin a highly stylized way the key features of the shadow-banking system before (left side) andafter (right side) the crisis. In the left-side table the shadow banks’ assets and liabilities are120 and 100, respectively. So, their net worth is positive. The numbers in parentheses arethe value of the assets and net worth of the shadow banks in the case of a rollover crisis andfire-sale of assets. In this example, a rollover crisis cannot occur.

Now imagine that the assets of the shadow banks decline because of a small shift infundamentals. Here, we have in mind the events associated with the decline in housingprices that began in the summer of 2006. The right side of Figure 1 is the analog of the leftside, taking into account the lower value of the shadow banks’ assets. In the example, themarket value of assets has fallen by 10, from 120 to 110. In the absence of a rollover crisis,the system is solvent. However, the value of the assets in the case of a rollover crisis is 95and the net worth of the bank is negative in that scenario. So, a relatively small change inasset values can lead to a severe crisis.

The example illustrates two important potential uses of DSGE models. First, an esti-mated DSGE model can be used to calculate the probability of a roll over crisis, conditionalon the state of the economy. In principle, one could estimate this probability function usingreduced form methods. However, since financial crises are rare events, estimates emergingfrom reduced form methods would have enormous sampling uncertainty. Because of its gen-eral equilibrium structure, a credible DSGE model would address the sampling uncertaintyproblem by making use of a wider array of information drawn from non-crisis times to assessthe probability of a financial crisis. The second potential use of credible DSGE models is todesign policies that deal optimally with financial crises. For this task, structure is essential.

While we think that existing DSGE models of financial crisis such as GK yield valuable

26The probability function in GK’s model is an equilibrium selection device.

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Weusethismodeltoillustratehowarelativelysmallshockcantriggerasystem-widerollovercrisis in the shadow banking system. To this end, consider the example Figure 3, whichcapturesinahighlystylizedwaythekeyfeaturesoftheshadow-bankingsystembefore(leftside) and after (right side) the crisis. In the left-side table the shadow banks’ assets andliabilities are 120 and 100, respectively. So, their net worth is positive. The numbers inparenthesesshowthevalueoftheassetsandnetworthoftheshadowbanksifthereweretobearollovercrisisandfire-saleofassets.Sincenetworthremainspositive,theGertlerandKiyotakianalysisimpliesthatarollovercrisiscannotoccur.Now imagine that the assets of the shadow banks decline because of a small shift infundamentals.Here,wehaveinmindtheeventsassociatedwiththedeclineinhousingpricesthatbeganinthesummerof2006.TherightsideofFigure3 istheanalogoftheleftside,takingintoaccountthelowervalueoftheshadowbanks’assets.Intheexample,themarketvalueofassetshasfallenby10,from120to110.Intheabsenceofarollovercrisis,thesystemissolvent.However,thevalueoftheassetsinthecaseofarollovercrisisis95andthenetworthofthebankisnegativeinthatscenario.So,arelativelysmallchangeinassetvaluescouldleadtoaseverefinancialcrisis.

Theexample illustratestwo importantpotentialusesofDSGEmodels. First,anestimatedDSGEmodelcanbeusedtocalculatetheprobabilityofarollovercrisis,conditionalonthestateoftheeconomy.Inprinciple,onecouldestimatethisprobabilityfunctionusingreducedformmethods. However, since financial crises are rare events, estimates emerging fromreducedformmethodswouldhaveenormoussamplinguncertainty.Becauseof itsgeneralequilibrium structure, an empirically plausible DSGE model would address the samplinguncertaintyproblembymakinguseofawiderarrayof informationdrawn fromnon-crisistimestoassesstheprobabilityofafinancialcrisis.ThesecondpotentialuseofDSGEmodelsis to design policies that deal optimally with financial crises. For this task, structure isessential.Whilewe think that existingDSGEmodelsof financial crisis suchasGertler andKiyotakiyieldvaluableinsights,thesemodelsareclearlystillintheirinfancy.

Forexample,themodelassumesthatpeopleknowwhatcanhappeninacrisis,togetherwiththeassociatedprobabilities.Thisseemsimplausible,giventhefactthatafull-blowncrisisisatwoorthreetimesacenturyevent.Itseemssafetoconjecturethatfactorssuchasaversionto ‘Knightian uncertainty’ play an important role in driving fire sales in a crisis (see, forexample, Caballero andKrishnamurthy (2008)). Still, researchon various typesof crises isproceedingatarapidpace,andweexpecttoseesubstantialimprovementsinDSGEmodelsonthesubject.Foranexample,seeBianchietal.(2016)andthereferencestherein.

FrictionsAssociatedwith thePeople thatBorrow fromFinancial InstitutionsWe now turn to our second example, which focuses on frictions that arise from thecharacteristicsofthepeoplewhoborrowfromfinancial institutions.Oneofthethemesofthis paper is that data analysis lies at the heart of theDSGEproject. Elsewhere,we havestressedtheimportanceofmicroeconomicdata.Here,wealsostresstheroleoffinancialdataasasourceofinformationaboutthesourcesofeconomicfluctuations.Usinganestimated

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DSGEmodel,Christianoetal.(2014)arguethatthedominantsourceofU.S.businesscyclefluctuationsaredisturbancesintheriskinessofindividualfirms(whattheycallriskshocks).Amotivation for their analysis is that in recessions, firmspayapremium toborrowmoney,abovetherateatwhicharisk-freeentityliketheU.S.governmentborrows.Christianoetal.(2014)ineffectinterpretthispremiumasreflectingtheviewoflendersthatfirmsrepresenta riskier bet. Christiano et al. (2014) estimate their DSGEmodel using a large number ofmacroeconomicandfinancialvariablesandconcludethatfluctuationsinriskcanaccountforthebulkofGDPfluctuations.

Tounderstandtheunderlyingeconomics,considerarecessionthatistriggeredbyanincreaseintheriskinessoffirms.6Asthecostofborrowingrises,firmsborrowlessanddemandlesscapital.Thisdeclineinducesafallinboththequantityandpriceofcapital.InthepresenceofnominalrigiditiesandaTaylorruleformonetarypolicy,thedeclineininvestmentleadstoaneconomy-widerecession,includingafallinconsumptionandariseinfirmbankruptcies.Withthe decline in aggregate demand, inflation falls. Significantly, the risk shock leads to anincreaseinthecross-sectionaldispersionoftherateofreturnonfirmequity.Moreover,therecessionisalsoassociatedwithafallinthestockmarket,drivenprimarilybycapitallossesassociatedwith the fall in the price of capital. All these effects are observed in a typicalrecession.7ThispropertyofriskshocksiswhyChristianoetal.(2014)’sestimationprocedureattributes60percentofthevarianceofU.S.businesscyclestothem.

Thedynamiceffectsof riskshocks in theChristianoetal. (2014)model resemblebusinesscyclessowell,thatmanyofthestandardshocksthatappearinpreviousbusinesscyclemodelsarerenderedunimportantintheempiricalanalysis.Forexample,Christianoetal.(2014)findthataggregateshockstothetechnologyforproducingnewcapitalaccountforonly13percentofthebusinesscyclevariationinGDP.ThiscontrastssharplywiththeresultsinJustinianoetal. (2010), who argue that this shock accounts for roughly 50 percent of business cyclevariationofGDP.ThecriticaldifferenceisthatChristianoetal.(2014)includefinancialdatalike the stock market in their analysis. Shocks to the supply of capital give rise tocountercyclical movements in the stock market, so they cannot be the prime source ofbusinesscycles. FinancialfrictionshavealsobeenincorporatedintoagrowingliteraturethatintroducesthehousingmarketintoDSGEmodels.Onepartofthisliteraturefocusesontheimplicationsofhousingpricesforhouseholds’capacitytoborrow(seeIacovielloandNeri(2010)andBergeretal.(2017)).Anotherpartfocusesontheimplicationsoflandandhousingpricesonfirms’capacity to borrow (Liu et al. (2013)). Space constraints prevent us from surveying thisliteraturehere.

6InChristianoetal.(2014)ariseinriskcorrespondstoanincreaseinthevarianceofafirm-specificshocktotechnology.Absentfinancialfrictions,suchashockwouldhavenoimpactonaggregateoutput.Ariseinthevariancewouldleadtobigger-sizedshocksatthefirmlevelbuttheaverageacrossfirmsisonlyafunctionofthemean(lawoflargenumbers).7Toourknowledge, thefirstpapertoarticulatethe ideathatapositiveshockto idiosyncratic riskcouldproduceeffectsthatresemblearecessionisWilliamson(1987).

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5.2 Zero Lower Bound andOtherNonlinearities

The financial crisis and its aftermath was associated with two important nonlinearphenomena. The first phenomenon was the rollover crisis in the shadow-banking sectordiscussed above. The Gertler and Kiyotaki (2015) model illustrates the type of nonlinearmodelrequiredtoanalyzethistypeofcrisis.Thesecondphenomenonwasthatthenominalinterest ratehit the zero-lowerbound inDecember2008.Anearlier theoretical literatureassociatedwithKrugman(1998),Benhabibetal.(2001)andEggertssonandWoodford(2003)hadanalyzedtheimplicationsofthezero-lowerboundforthemacroeconomy.Buildingonthisliterature,DSGEmodelersquicklyincorporatedthezero-lowerboundintotheirmodelsandanalyzeditsimplications.

In what follows, we discuss one approach that DSGEmodelers took to understand whattriggeredtheGreatRecessionandwhyitpersistedforsolong.WethenreviewsomeofthepolicyadvicethatemergesfromrecentDSGEmodels.

TheCausesof theCrisisandSlowRecoveryOnesetofpapersusesdetailednonlinearDSGEmodelstoassesswhichshockstriggeredthefinancialcrisisandwhatpropagatedtheireffectsovertime.Wefocusonthreepaperstogivethe readera flavorof this literature.Christianoetal. (2015)analyze thepost-crisisperiodtakingintoaccountthatthezerolowerboundwasbinding.Inaddition,theytakeintoaccountthe Federal Reserve OpenMarket Committee’s (FOMC) guidance about future monetarypolicy.Thisguidancewashighlynonlinearinnature:itinvolvedaregimeswitchdependingontherealizationofendogenousvariables(e.g.theunemploymentrate).

Christianoetal.(2015)arguethatthebulkofmovementsinaggregaterealeconomicactivityduring the Great Recession was due to financial frictions interacting with the zero-lowerbound. At the same time, their analysis indicates that the observed fall in total factorproductivityandtheriseinthecostofworkingcapitalplayedimportantrolesinaccountingforthesurprisinglysmalldropininflationafterthefinancialcrisis.

Lindé and Trabandt (2018b) argue that nonlinearities in price and wage-setting are analternativereasonforthesmalldeclineininflationduringtheGreatRecession.Inparticular,they assume that the elasticity of demand of a goods-producing firm is increasing in itsrelativepricealongthelinesproposedinKimball(1995).So,duringarecessionwhenmarginalcostsarefalling,firmsthatcanchangetheirpriceshavelessofanincentivetodosorelativeto the case in which the elasticity of demand is constant. They show that this effect isquantitativelyimportantinthestandardnonlinearNewKeynesianDSGEmodel.

Gustetal. (2017)estimateafullynonlinearDSGEmodelwithanoccasionallybindingzerolower bound. Nonlinearities in themodel play an important role for inference about thesourceandpropagationofshocks.Accordingtotheiranalysis,shockstothedemandforrisk-freebondsand,toalesserextent,themarginalefficiencyofinvestmentproxyingforfinancialfrictions,playedacriticalroleinthecrisisanditsaftermath.

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Acommonfeatureofthepreviouspapersisthattheyprovideaquantitativelyplausiblemodelof thebehavior ofmajor economic aggregates during theGreat Recessionwhen the zerolowerboundwasabindingconstraint.Critically,thosepapersincludebothfinancialfrictionsandnominal rigidities. Amodel of the crisis and its aftermathwhich didn’t have financialfrictions just would not be plausible. At the same time, a model that included financialfrictionsbutdidn’tallowfornominalrigiditieswouldhavedifficultyaccountingforthebroad-based decline across all sectors of the economy. Such amodel would predict a boom insectorsoftheeconomythatarelessdependentonthefinancialsector.

The fact that DSGE models with nominal rigidities and financial frictions can providequantitativelyplausibleaccountsofthefinancialcrisisandtheGreatRecessionmakesthemobvious frameworkswithinwhich to analyze alternative fiscal andmonetary policies.Webeginwithadiscussionoffiscalpolicy.

FiscalPolicyInstandardDSGEmodels,anincreaseingovernmentspendingtriggersariseinoutputandinflation.WhenmonetarypolicyisconductedaccordingtoastandardTaylorrulethatobeystheTaylorprinciple,a rise in inflation triggersa rise in the real interest rate.Other thingsequal,thepolicy-inducedrise inthereal interestrate lowers investmentandconsumptiondemand.So,inthesemodelsthegovernmentspendingmultiplieristypicallylessthanone.Butwhen the zero lower boundbinds, the rise in inflation associatedwith an increase ingovernment spending does not trigger a rise in the real interest rate. With the nominalinterest rate stuck at zero, a rise in inflation lowers the real interest rate, crowdingconsumptionandinvestmentin,ratherthanout.Thisraisesthequantitativequestion:howdoesabindingzerolowerboundconstraintonthenominalinterestrateaffectthesizeofthegovernmentspendingmultiplier?

Christianoetal.(2011)addressthisquestioninaDSGEmodel,assumingalltaxesarelump-sum.Abasicprinciplethatemergesfromtheiranalysisisthatthemultiplierislargerthemorebindingisthezerolowerbound.Christianoetal.(2011)measurehowbindingthezerolowerboundisbyhowmuchapolicymakerwouldliketolowerthenominalinterestbelowzeroifheorshecould.Fortheirpreferredspecification,themultiplierismuchlargerthanone.WhentheZLBisnotbinding,thenthemultiplierwouldbesubstantiallybelowone.

ErcegandLindé(2014)examineamongotherthingstheimpactofdistortionarytaxationonthemagnitudeofgovernmentspendingmultiplierinthezerolowerbound.Theyfindthattheresultsbasedonlump-sumtaxationarerobustrelativetothesituationinwhichdistortionarytaxesareraisedgraduallytopayfortheincreaseingovernmentspending.

ThereisbynowalargeliteraturethatstudiesthefiscalmultiplierwhentheZLBbindsusingDSGEmodels that allow for financial frictions, open-economy considerations and liquidityconstrainedconsumers.Wecannotreviewthisliteraturebecauseofspaceconstraints.But,the crucial point is thatDSGEmodels are playing an important role in the debate amongacademics andpolicymakers aboutwhether andhow fiscal policy shouldbeused to fight

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recessions.We offer two examples in this regard. First, Coenen et al. (2012) analyze theimpactof different fiscal stimulus shocks in severalDSGEmodels that areusedbypolicy-makinginstitutions.ThesecondexampleisBlanchardetal.(2017)whoanalyzetheeffectsofafiscalexpansionbythecoreeuroareaeconomiesontheperipheryeuroareaeconomies.Finally,wenotethattheearlypapersonthesizeofthegovernmentspendingmultiplieruselog-linearized versions ofDSGEmodels. For example, Christiano et al. (2011)workwith alinearizedversionoftheirmodelwhileChristianoetal.(2015)workwithanonlinearversionofthemodel.Significantly,thereisnowaliteraturethatassessesthesensitivityofmultipliercalculationstolinearversusnonlinearsolutions.See,forexample,ChristianoandEichenbaum(2012),Bonevaetal.(2016),Christianoetal.(2017)andLindéandTrabandt(forthcoming).

ForwardGuidance

Whenthezerolowerboundconstraintonthenominalinterestratebecamebinding,itwasnolongerpossibletofighttherecessionusingconventionalmonetarypolicy, i.e., loweringshort-terminterestrates.Monetarypolicymakersconsideredavarietyofalternatives.Here,wefocusonforwardguidanceasapolicyoptionanalyzedbyEggertssonandWoodford(2003)andWoodford(2012)insimpleNewKeynesianmodels.Byforwardguidancewemeanthatthemonetarypolicymakerkeepstheinterestratelowerforlongerthanheorsheordinarilywould.

As documented in Carlstrom et al. (2015), forward guidance is implausibly powerful instandard DSGE models like Christiano et al. (2005). Del Negro et al. (2012) refer to thisphenomenon as the forward guidance puzzle. This puzzle has fueled an active debate.Carlstrometal. (2015)andKiley (2016)showthatthemagnitudeof theforwardguidancepuzzleissubstantiallyreducedinastickyinformation(asopposedtoastickyprice)model.Otherresponsestotheforwardguidancepuzzleinvolvemorefundamentalchanges,suchasabandoning the representativeagent framework.Thesechangesarediscussed in thenextsubsection.Moreradicalresponsesinvolveabandoningstrongformsofrationalexpectations.SeeforexampleGabaix(2016),Woodford(2018)andAngeletosandLian(2018).

5.3 HeterogeneousAgentModels

The primary channel by which monetary-policy induced interest rate changes affectconsumption in the standard New Keynesian model is by causing the representativehousehold to reallocate consumptionover time. In fact, there is a great deal of empiricalmicroevidenceagainst the importanceof this reallocation channel, inpartbecausemanyhouseholdsfacebindingborrowingconstraints.8Motivated by these observations, macroeconomists are exploring DSGE models whereheterogeneousconsumersfaceidiosyncraticshocksandbindingborrowingconstraints.Given

8ThereisalsoimportantworkallowingforfirmheterogeneityinDSGEmodels.See,forexample,Gilchristetal.(2017)andOttonelloandWinberry(2017).

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spaceconstraints,wecannotreviewthisentirebodyofworkhere.SeeKaplanetal.(2017)andMcKayet al. (2016) forpapers that convey the flavorof the literature.Bothof thesepaperspresentDSGEmodelsinwhichhouseholdshaveuninsurable,idiosyncraticincomerisk.Inaddition,manyhouseholdsfaceborrowingconstraints.9

TheliteratureonheterogeneousagentDSGEmodelsisstillyoung.Butithasalreadyyieldedimportant insights into important policy issues like the impact of forward guidance (seeMcKayetal. (2016)andFarhiandWerning(2017)).Theliteraturehasalso leadtoaricherunderstandingofhowmonetarypolicyactionsaffecttheeconomy.Forexample,inKaplanetal.(2017)amonetarypolicyactioninitiallyaffectsthesmallsetofhouseholdswhoactivelyintertemporally adjust spending in response to an interest rate change. But,most of theimpactoccursthroughamultiplier-typeprocessthatoccursasotherfirmsandhouseholdsadjusttheirspendinginresponsetothechangeindemandbythe‘intertemporaladjusters’.ThisareaofresearchtypifiesthecuttingedgeofDSGEmodels:thekeyfeaturesaremotivatedbymicrodataandtheimplications(say,forthemultiplier-typeprocess)areassessedusingbothmicroandmacrodata.

6 HowareDSGEModelsUsedinPolicyInstitutions?InthissectionwediscusshowDSGEmodelsareusedinpolicyinstitutions.Asacasestudy,wefocusontheBoardofGovernorsof theFederalReserveSystem.Weareguided inourdiscussion by Stanley Fischer’s description of the policy-making process at the FederalReserveBoard(seeFischer(2017)).

Before theFederalReservesystemopenmarketcommittee (FOMC)meets tomakepolicydecisions,allparticipantsaregivencopiesoftheso-calledTealbook.10TealbookAcontainsasummaryandanalysisofrecenteconomicandfinancialdevelopmentsintheUnitedStatesandforeigneconomiesaswellastheBoardstaff’seconomicforecast.Thestaffalsoprovidesmodel-basedsimulationsofanumberofalternativescenarioshighlightingupsideanddown-sideriskstothebaselineforecast.Examplesofsuchscenariosincludeadeclineinthepriceofoil,ariseinthevalueofthedollarorwagegrowththatisstrongerthantheonebuiltintothebaseline forecast. These scenarios are generated using one or more of the Board’smacroeconomic models, including the DSGE models, SIGMA and EDO.11 Tealbook A alsocontainsestimatesoffutureoutcomesinwhichtheFederalReserveBoardusesalternativemonetarypolicyrulesaswellmodel-basedestimatesofoptimalmonetarypolicy.AccordingtoFischer(2017),DSGEmodelsplayacentral,thoughnotexclusive,roleinthisprocess.TealbookBprovidesananalysisofspecificpolicyoptionsfortheconsiderationoftheFOMCatitsmeeting.AccordingtoFischer(2017),“Typically,therearethreepolicyalternatives-A,

9 ImportantearlierpapersinthisliteratureincludeOhandReis(2012),GuerrieriandLorenzoni(2017),McKayandReis(2016),Gornemannetal.(2016)andAuclert(2017).10TheTealbooksareavailablewithafiveyearlagat https://www.federalreserve.gov/monetarypolicy/fomc_historical.htm.11ForadiscussionoftheSIGMAandEDOmodels,seeErcegetal. (2006) andhttps://www.federalreserve.gov/econres/edo-models-about.htm.

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B,andC-rangingfromdovishtohawkish,withacentristoneinbetween.”Thekeypointisthat DSGE models, along with other approaches, are used to generate the quantitativeimplicationsofthespecificpolicyalternativesconsidered.The Federal Reserve System is not the only policy institution that usesDSGEmodels. Forexample,theEuropeanCentralBank,theInternationalMonetaryFund,theBankofIsrael,theCzechNationalBank,theSverigesRiksbank,theBankofCanada,andtheSwissNationalBankallusesuchmodelsintheirpolicyprocess.12We just argued that DSGE models are used to run policy simulations in various policyinstitutions. The results of those simulations areuseful to theextent that themodels areempiricallyplausible.Oneimportantwaytoassesstheplausibilityofamodelistoconsideritsrealtimeforecastingperformance.Cai,DelNegro,Giannoni,Gupta,Li,andMoszkowski(2018)comparereal-timeforecastsoftheNewYorkFedDSGEmodelwiththoseofvariousprivate forecastersandwiththemedianforecastsof theFederalOpenMarketCommitteemembers.TheDSGEmodelthattheyconsiderisavariantofChristiano,MottoandRostagno(2014)thatallowsforshockstothedemandforgovernmentbonds.Caietal.findthatthemodel-basedreal time forecastsof inflationandoutputgrowtharecomparable to thatofprivateforecasters.Strikingly,theNewYorkFedDSGEmodeldoesabetterjobatforecastingtheslowrecoverythantheFederalOpenMarketCommittee,atleastasjudgedbytherootmeansquareerrorsoftheirmedianforecasts.Caietal.arguethatfinancialfrictionsplayacriticalroleinallowingthemodeltoanticipatetheslowgrowthinoutputafterthefinancialcrisis.

Insum,DSGEmodelsplayanimportantroleinthepolicymakingprocess.Tobeclear:theydonotsubstituteforjudgement,norshouldthey.Inanyevent,policymakershavevotedwiththeircollectivefeetontheusefulnessofDSGEmodels. Inthissense,theyaremeetingthemarkettest.

12For a review of the DSGEmodels used in the policy process at the ECB, see Smets et al. (2010).Carabenciovetal.(2013)andFreedmanetal.(2009)describeglobalDSGEmodelsusedforpolicyanalysisat the InternationalMonetary Fund (IMF),while Benes et al. (2014) describeMAPMOD, a DSGEmodelusedattheIMFfortheanalysisofmacroprudentialpolicies. Clintonetal.(2017)describetheroleofDSGEmodels in policy analysis at the CzechNational Bank andAdolfson et al. (2013) describe the RAMSES IIDSGE model used for policy analysis at the Sveriges Riksbank. Argov et al. (2012) describe the DSGEmodelusedforpolicyanalysisattheBankofIsrael,Dorichetal.(2013)describeToTEM,theDSGEmodelusedat theBankofCanadaforpolicyanalysisandAlpandaetal. (2014)describeMP2, theDSGEmodelusedattheBankofCanadatoanalyzemacroprudentialpolicies. RudolfandZurlinden(2014)andGerdrupetal.(2017)describetheDSGEmodelusedattheSwissNationalBankandtheNorgesbank,respectively, forpolicyanalysis.

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7 ABriefResponsetotheCritics

In this sectionwebriefly respond to some recent critiques ofDSGEmodels.We focus onStiglitz(2017)becausehiscritiqueiswell-knownandrepresentativeofpopularcriticisms.

EconometricMethods

Stiglitzclaimsthat“Standardstatisticalstandardsareshuntedaside[byDSGEmodelers].”Asevidence, he cites four points from what he refers to as Korinek (2017)’s “devastatingcritique”ofDSGEpractitioners.Thefirstpointis:

“...the time seriesemployedare typicallydetrendedusingmethods such

as theHP filter to focus the analysis on stationary fluctuations at businesscycle frequencies. Although this is useful in some applications, it risksthrowingthebabyoutwiththebathwaterasmanyimportantmacroeconomicphenomenaare non-stationaryoroccuratlowerfrequencies.” Stiglitz(2017,page3).

Neither Stiglitz nor Korinek offer any constructive advice on how to address the difficultproblemofdealingwithnonstationarydata.Insharpcontrast,theDSGEliteraturestrugglesmightilywiththisproblemandadoptsdifferentstrategies formodelingnon-stationarity inthedata.Asamatteroffact,StiglitzandKorinek’sfirstpointissimplyincorrect.ThevastbulkofthemodernDSGEliteraturedoesnotestimatemodelsusingHPfiltereddata.

DSGEmodelsofendogenousgrowthprovideaparticularlystarkcounterexampletoKorinekand Stiglitz’s claim thatmodelers focus the analysis on stationary fluctuations at businesscycle frequencies. See for example Comin and Gertler (2006)’s analysis of medium-termbusinesscycles.

Second,StiglitzreproducesKorinek(2017)’sassertion:

“.... for given detrended time series, the set of moments chosen to

evaluate themodelandcompare it to thedata is largelyarbitrary—there isno strong scientificbasis foroneparticular setofmomentsoveranother”.Stiglitz(2017,page3).

Third,StiglitzalsoreproducesthefollowingassertionbyKorinek(2017):

“... foragivensetofmoments,thereisnowell-definedstatistictomeasurethe goodness of fit of a DSGE model or to establish what constitutes animprovement insuchaframework”. Stiglitz(2017,page4).

Thesecriticismsmighthavebeenappropriateinthe1980s.But,theysimplydonotapplytomodernanalyses,whichusefullinformationmaximimumlikelihoodorgeneralizedmethodofmoments.

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FinancialFrictions

Stiglitz (2017) asserts that pre-crisis DSGE models did not allow for financial frictions orliquidity-constrained consumers. This claim is incorrect. Consider the following counterexamples.Galí etal. (2007) investigate the implicationsof theassumption that someconsumersareliquidityconstrained.Specifically,theyassumethatafractionofhouseholdscannotborrowatall.TheythenassesshowthischangeaffectstheimplicationsofDSGEmodelsfortheeffectsofashocktogovernmentconsumption.Notsurprisingly,theyfindthatliquidityconstraintssubstantiallymagnifytheimpactofgovernmentspendingonGDP.

CarlstromandFuerst(1997)andBernankeetal.(1999)developDSGEmodelsthatincorporatecreditmarket frictionswh i ch g i ve r i s e a “financial accelerator” inwhichcreditmarketsworktoamplifyandpropagateshocks tothemacroeconomy.

Christianoetal.(2003)addseveralfeaturestothemodelofChristianoetal.(2005)toallowforricherfinancialmarkets. First,theyincorporate thefractionalreservebankingmodel developed by Chari et al. (1995). Second, they allow for financial frictions asmodeledbyBernankeetal.(1999)andWilliamson(1987).Inaddition, theyassume thatagents can only borrow using nominal non-state contingent debt, so that the modelincorporatestheFisheriandebtdeflationchannel.

Finally,wenotethat Iacoviello (2005)developsandestimatesaDSGEmodelwithnominalloansandcollateralconstraintstiedtohousingvalues. Thispaperisanimportantantecedentto the large post-crisis DSGE literature on the aggregate implications of housing marketboomsandbusts.Stiglitz(2017,p.12)alsowrites:

“...anadequatemacromodelhas toexplainhowevenamoderate shockhaslargemacroeconomicconsequences.”

Thepost-crisis DSGE models cited in section5.1provideexplicit counterexamples to thisclaim.Stiglitz(2017)alsoassertsthatDSGEmodelsabstractfrominterestratespreads.Hewrites(p.10):“...instandardmodels...allthatmattersisthatsomehowthecentralbankis able tocontrol the interest rate. But, the interest rate is not the interestrate confrontinghouseholds and firms; the spread between the two is a criticalendogenous variable.”

Pre-crisisDSGEmodelslikethoseinWilliamson(1987),CarlstromandFuerst(1997),Charietal. (1995) and Christiano et al. (2003) and post-crisis DSGEmodel like Gertler and Karadi(2011), Jermann and Quadrini (2012), Curdia and Woodford (2010) and Christiano et al.(2014)arecounterexamplestoStiglitz(2017)’sassertions.Inallthosepapers,whichareonly

25

asubsetoftherelevantliterature,creditandtheendogenousspreadbetweentheinterestratesconfrontinghouseholdsandfirmsplaycentralroles.

NonlinearitiesandLackofPolicyAdvice

Stiglitz(2017,p.7)writes:

“...thelargeDSGEmodelsthataccountforsomeofthemorerealisticfeaturesof themacroeconomy can only be ‘solved’ for linear approximations and smallshocks—precludingthebigshocksthattakeusfarawayfromthedomainoverwhich the linear approximation has validity.”

Stiglitz (2017,p. 1)alsowrites:

“...the inability of theDSGEmodel to...providepolicy guidanceonhow to dealwith the consequences [of the crisis], precipitated current dissatisfaction withthemodel.”

Thepaperscitedinsection5.2andtheassociatedliteraturesareclearcounterexamplestoStiglitz’sclaims.SotooisthesimplefactthatpolicyinstitutionscontinuetouseDSGEmodelsaspartoftheirpolicyprocess.

HeterogeneityStiglitz(2017)’scritiquethatDSGEmodelsdonotincludeheterogeneousagents.Hewrites:

“...DSGEmodelsseemtotakeitasareligioustenetthatconsumptionshouldbeexplainedbyamodelofarepresentativeagentmaximizinghisutilityoveraninfinitelifetimewithoutborrowingconstraints.”(Stiglitz,2017,page5).

Thisviewisobviouslyatvariancewiththecutting-edgeresearchinDSGEmodels(seesection5.3).DSGE models will become better as modelers respond to informed criticism. Stiglitz’scriticismsarenotinformed.8 Conclusion

TheDSGEenterpriseisanorganicprocessthatinvolvestheconstantinteractionofdataandtheory.Pre-crisisDSGEmodelshadshortcomingsthatwerehighlightedbythefinancialcrisisand itsaftermath.Substantialprogresshasoccurred since then.Wehaveemphasized theincorporationoffinancialfrictionsandheterogeneityintoDSGEmodels.Becauseof space considerations,wehavenot reviewedexcitingworkondeviations fromconventionalrationalexpectations.Thesedeviationsincludek-levelthinking,robustcontrol,

26

social learning, adaptive learning and relaxing the assumption of common knowledge.Frankly,wedonotknowwhichofthesecompetingapproacheswillplayaprominentroleinthenextgenerationofmainstreamDSGEmodels.Will the futuregenerationofDSGEmodelspredict the timeandnatureof thenextcrisis?Franklywedoubtit.Asfarasweknowthereisnosure,time-testedwayofforeseeingthefuture.Theproximatecauseofthefinancialcrisiswasaprofession-widefailuretoobservethegrowingsizeand leverageof theshadow-bankingsector.DSGEmodelsareevolving inresponsetothatfailureaswellastotheever-growingtreasuretroveofmicrodataavailabletoeconomists.Wedon’tknowyetexactlywherethatprocesswillleadto.Butwedoknowthat DSGE models will remain central to how macroeconomists think about aggregatephenomenaandpolicy.Thereissimplynocrediblealternativetopolicyanalysisinaworldofcompetingeconomicforcesoperatingondifferentpartsoftheeconomy. References

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Appendix

Table 1: Priors and Posteriors of Estimated Parameters inChristiano, Eichenbaum and Trabandt (2016) Model with Calvo Sticky Wages

Prior Distribution Posterior DistributionD,Mode,[2.5-97.5%] Mode,[2.5-97.5%]

Price and Wage Setting ParametersCalvo Price Stickiness, ξ B,0.68,[0.35 0.89] 0.565,[0.49 0.68]Calvo Wage Stickiness, ξw B,0.78,[0.41 0.95] 0.752,[0.69 0.76]Gross Price Markup, λ G,1.20,[1.06 1.35] 1.181,[1.09 1.27]

Monetary Authority ParametersTaylor Rule: Interest Rate Smoothing, ρR B,0.76,[0.22 0.96] 0.796,[0.76 0.83]Taylor Rule: Inflation Coe¢cient, rπ G,1.69,[1.30 2.18] 1.746,[1.51 2.06]Taylor Rule: GDP Gap Coe¢cient, ry G,0.08,[0.02 0.32] 0.012,[0.00 0.03]

Preferences and Technology ParametersConsumption Habit, b B,0.50,[0.12 0.88] 0.755,[0.69 0.78]Capacity Utilization Adjustment Cost, σa G,0.32,[0.08 1.90] 0.161,[0.05 0.47]Investment Adjustment Cost, S

00G,3.00,[0.74 12.7] 6.507,[4.43 9.97]

Exogenous Process ParameterStd. Deviation Monetary Policy Shock, 400σR G,0.65,[0.51 0.81] 0.673,[0.57 0.71]Notes: Posterior mode and parameter distributions based on a standard MCMC algorithm with a total of 1.2 million

draws (8 chains with each 150.000 draws, 1/3 of draws used for burn-in, draw acceptance rates about 0.22).

B and G denote beta and gamma distributions, respectively. Estimation of Christiano, Eichenbaum and Trabandt

(2016) model with Calvo sticky wages based on Bayesian impulse response matching to a VAR monetary policy

shock. See Christiano, Eichenbaum and Trabandt (2016) for details about the model and parameter notation.

Table 2: Non-Estimated Parameters and Calibrated Steady State Variables inChristiano, Eichenbaum and Trabandt (2016) Model with Calvo Sticky Wages

Parameter Value

Panel A: ParametersDepreciation rate of physical capital, δK 0.025Discount factor, β 0.9968Gross wage markup, λw 1.2Inverse Frisch labor supply elasticity, 1Annual output per capita growth rate, 400ln(µ) 1.7Annual investment per capita growth rate, 400ln(µ · µΨ) 2.9

Panel B: Steady State ValuesAnnual net inflation rate, 400(π − 1) 2.5Intermediate goods producers profits, profits 0Government consumption to gross output ratio, G/Y 0.2

Notes: see Christiano, Eichenbaum and Trabandt (2016) for details about the model and parameter notation.

Table 1: Priors and Posteriors of Estimated Parameters inChristiano, Eichenbaum and Trabandt (2016) Model with Calvo Sticky Wages

Prior Distribution Posterior DistributionD,Mode,[2.5-97.5%] Mode,[2.5-97.5%]

Price and Wage Setting ParametersCalvo Price Stickiness, ξ B,0.68,[0.35 0.89] 0.565,[0.49 0.68]Calvo Wage Stickiness, ξw B,0.78,[0.41 0.95] 0.752,[0.69 0.76]Gross Price Markup, λ G,1.20,[1.06 1.35] 1.181,[1.09 1.27]

Monetary Authority ParametersTaylor Rule: Interest Rate Smoothing, ρR B,0.76,[0.22 0.96] 0.796,[0.76 0.83]Taylor Rule: Inflation Coe¢cient, rπ G,1.69,[1.30 2.18] 1.746,[1.51 2.06]Taylor Rule: GDP Gap Coe¢cient, ry G,0.08,[0.02 0.32] 0.012,[0.00 0.03]

Preferences and Technology ParametersConsumption Habit, b B,0.50,[0.12 0.88] 0.755,[0.69 0.78]Capacity Utilization Adjustment Cost, σa G,0.32,[0.08 1.90] 0.161,[0.05 0.47]Investment Adjustment Cost, S

00G,3.00,[0.74 12.7] 6.507,[4.43 9.97]

Exogenous Process ParameterStd. Deviation Monetary Policy Shock, 400σR G,0.65,[0.51 0.81] 0.673,[0.57 0.71]Notes: Posterior mode and parameter distributions based on a standard MCMC algorithm with a total of 1.2 million

draws (8 chains with each 150.000 draws, 1/3 of draws used for burn-in, draw acceptance rates about 0.22).

B and G denote beta and gamma distributions, respectively. Estimation of Christiano, Eichenbaum and Trabandt

(2016) model with Calvo sticky wages based on Bayesian impulse response matching to a VAR monetary policy

shock. See Christiano, Eichenbaum and Trabandt (2016) for details about the model and parameter notation.

Table 2: Non-Estimated Parameters and Calibrated Steady State Variables inChristiano, Eichenbaum and Trabandt (2016) Model with Calvo Sticky Wages

Parameter Value

Panel A: ParametersDepreciation rate of physical capital, δK 0.025Discount factor, β 0.9968Gross wage markup, λw 1.2Inverse Frisch labor supply elasticity, 1Annual output per capita growth rate, 400ln(µ) 1.7Annual investment per capita growth rate, 400ln(µ · µΨ) 2.9

Panel B: Steady State ValuesAnnual net inflation rate, 400(π − 1) 2.5Intermediate goods producers profits, profits 0Government consumption to gross output ratio, G/Y 0.2

Notes: see Christiano, Eichenbaum and Trabandt (2016) for details about the model and parameter notation.

36

Table 3: Steady States and Implied Parameters at Estimated Posterior Modein Christiano, Eichenbaum and Trabandt (2016) Model with Calvo Sticky Wages

Variable Value

Capital to gross output ratio (quarterly), K/Y 6.71Consumption to gross output ratio, C/Y 0.58Investment to gross output ratio, I/Y 0.22Steady state labor input, l 0.945Gross nominal interest rate (quarterly), R 1.014Gross real interest rate (quarterly), Rreal 1.0075Marginal cost (inverse price markup), mc 0.85Capacity utilization cost parameter, σb 0.035Gross output, Y 1.38Real wage, w 1.10Inflation target (annual percent), π 2.5Fixed cost to gross output ratio, φ/Y 0.17

Notes: see Christiano, Eichenbaum and Trabandt (2016) for details about the model and parameter notation.