Do Households Substitute Intertemporally? 10 Structural Shocks That Suggest Not

Finance and Economics Discussion Series Federal Reserve Board, Washington, D.C. ISSN 1936-2854 (Print) ISSN 2767-3898 (Online) Do Households Substitute Intertemporally? 10 Structural Shocks That Suggest Not Edmund Crawley 2025-021 Please cite this paper as: Crawley, Edmund (2025). “Do Households Substitute Intertemporally? 10 Structural Shocks That Suggest Not,” Finance and Economics Discussion Series 2025-021. Washington: Board of Governors of the Federal Reserve System, https://doi.org/10.17016/FEDS.2025.021. NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the Finance and Economics Discussion Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.

Do Households Substitute Intertemporally? 10 Structural Shocks That Suggest Not* Edmund Crawley March 2025 Abstract I combine microdata on the intertemporal marginal propensity to consume with 10 structuralmacroshockstoidentifytheroleofintertemporalsubstitutioninconsumptionbehavior. AlthoughsomeofthestructuralshocksthatIexamineleadtolargeand persistentchangesinrealinterestrates—whichinmanymodelswouldinducealarge ff intertemporalsubstitutione ect—Ifindnoevidencethathouseholdsshiftthetiming of their consumption in response to these interest rate changes. Indeed, changes to the expected path of income explain almost all the aggregate consumption response, leavingnoroleforintertemporalsubstitution. JEL:E21,E32,E52 Keywords: IntertemporalSubstitution,HANK,MonetaryPolicy,Consumption *Viewpointsandconclusionsstatedinthispaperaretheresponsibilityoftheauthoraloneanddonot necessarilyreflecttheviewpointsoftheFederalReserveBoard. Crawley: FederalReserveBoard,edmund.s.crawley@frb.gov. 1

1 Introduction Inmostmacroeconomicmodels,householdswanttosmoothconsumptionovertimeand adjusttheirconsumptionpathsinresponsetochangesinrealinterestrates. However,there islittleempiricalevidence—microormacro—thathouseholdconsumptionissensitiveto real interest rates. For example, in his seminar paper, Hall (1988) found no relationship between interest rates and consumption growth in aggregate data. This lack of evidence maystemfromthefactthatrealinterestratesco-movewithotherfeaturesoftheeconomy thatgointothehouseholdconsumptiondecision;therefore,identifyingtheroleplayedby realinterestratesischallenging. Mypaperaimstoovercomesomeoftheseidentification challenges. ff The key insight of this paper is recognizing that the e ect of real interest rates on consumption can be calculated as a residual after accounting for the other inputs to the consumption-saving decision. Furthermore, in light of recent advances, economists now have good empirical evidence on how households respond to changes in the other main drivers of consumption, namely the expected paths for labor income, stock prices, and real estate prices. As a result, it is possible to infer the role of interest rates following ff ten di erent structural shocks that I select from Ramey (2016). I find that none of the 10 structural shocks I examine suggest a role for intertemporal substitution in household decisionmaking,and,takentogether,theyprovideatightestimateclosetozero. This paper is closely related to Auclert et al. (2020) who estimate the consumption behavior of households by combining micro evidence on how households respond to income shocks with macro evidence from monetary policy shocks. Relative to Auclert et al.(2020),whoestimateafully-specifiedgeneralequilibriummodel,thispapercontributes to the literature by narrowing the scope to the consumption “block” of a model. This narrower scope allows me two advantages: 1) I can be agnostic about the rest of the model; and 2) I can use a much wider range of structural shocks to estimate household behavior. Regardingthefirstadvantage,becauseIamagnosticabouttherestofthemodel, 2

ff myfindingsareconsistentwithmodelsthatincludefirm-sidefinancialfrictions,di erent mechanisms for sticky prices, international trade, time-to-build and other investment frictions, as well as modeling features that are yet to be discovered, so long as they are independent of the consumption block of the model. The second advantage arises as a consequenceofthefirst: IamabletouseamuchwiderrangeofstructuralshocksbecauseI donotneedtomodeleachoneexplicitly. Forastructuralshocktobeusedforestimationin ff myframework,Ionlyneedtoimposetheconditionthatthewayinwhichtheshocka ects household consumption decisions is mediated through the expected paths of aggregate laborincome,therealfedfundsrate,andassetprices. Asasimpleexample,productivity and monetary policy shocks in the standard three-equation New Keynesian model both fit into this paradigm. But more complex structural shocks from the empirical literature, suchasinvestment-specifictechnologynewsshocks,canbeusedwithoutmakingspecific modelingchoicesabouttheexactnatureoftheseshocks. I impose two structures on the consumption block but allow for enough flexibility to spanmostempiricallyplausiblehouseholdbehavior. First,Ifixtheinput-outputstructure oftheconsumptionblock. Theinputstotheconsumptiondecisionaretheexpectedpaths for: aggregate labor income; the real fed funds rate; the real return on the stock market; and the real return on real estate. The output must include aggregate consumption but can also include aggregate savings in each asset. With this input-output structure, the dynamics of the linearized version of the consumption block in sequence space are fully describedbyhowaggregateconsumptionrespondsattimettoamarginalchangeineach ofthefourinputsattimes. Thatis,fourconsumptionJacobians—oneforeachinput—are ffi su cientstatisticsforconsumptiondynamics. ThesecondstructureIimposeontheconsumptionblockistoreducethedimensionality oftheseJacobians,eachofwhichisaninfinite-dimensionalobject. TodothisIusemicroempiricalevidencealongwiththeory. FortheincomeJacobian—howconsumptionattime tchangesinresponsetonewsofashocktoincomeattimes—IuseevidencefromFagereng 3

et al. (2021) to fit a one-asset heterogenous agent model to the marginal propensities to consume (MPC) for each of the first five years following a lottery win. In the model, I allow for the possibility of sticky expectations, following Carroll et al. (2020), because thecurrentmicro-empiricalliteraturelacksstrongevidenceonhouseholds’consumption responsestonewsaboutfutureincome. Stickyexpectationsareonewayofgeneratingthe humpshapeoftenobservedinmacroeconomicimpulseresponsefunctions. The real fed funds rate Jacobian—how consumption at time t changes in response to news of a shock to the short-term interest rate at time s—is of most interest in this paper. First,IdecomposetherealinterestrateJacobianfromtheoneassetmodelintoanintertemff poral substitution Jacobian and an income e ect Jacobian, following Farhi et al. (2022). ff The income e ect Jacobian in the one-asset model does not do a good job of capturing ff thetrueincomee ectsbecausethemainassetshouseholdshold—namelystocksandreal estate—are not well approximated by the short-term bonds of the model. As a result, I ff ff keeponlytheintertemporalsubstitutione ectJacobianandassumethattheincomee ect is captured by the stock market and real estate Jacobians. The resulting intertemporal substitution Jacobian shows that, in response to a future increase in the real interest rate, householdsreduceconsumptionupuntiltheincrease,collectthehigherinterestrate,and ff then spend down their savings following the change. The magnitude of this e ect may depend on households’ elasticity of intertemporal substitution and the degree to which they pay attention to changes in the interest rate among many other possibly rational or behavioral factors. I again introduce sticky expectations, and this single parameter allows the intertemporal substitution Jacobian to span most of the empirically plausible intertemporal substitution behaviors—from nothing at all to full rational expectations withhighelasticityofintertemporalsubstitution. Incorporating sticky expectations into the model is essential not only because it helps generate the hump-shaped impulse responses observed in macroeconomic data, but also becauseitallowsforamorerigoroustestofintertemporalsubstitution. Akeyconcernin 4

estimating the response of consumption to real interest rates using Euler equation-based approaches is the possibility that households appear unresponsive simply because they areslowtoadjusttheirbehavior. Byexplicitlyallowingforstickyexpectations,mymodel ensuresthattheabsenceofaconsumptionresponsetointerestratechangesisnotmerely anartifactofsluggishbeliefupdating. Inotherwords,ifhouseholdsweresimplyslowto ff processnewinformation,theestimatedintertemporalsubstitutione ectmightbebiased toward zero due to delayed reactions rather than an actual lack of substitution. The fact that my results hold even when accounting for sticky expectations strongly suggests that the near-zero response of consumption to real interest rates is not due to frictions in expectation updating, but rather reflects a genuine lack of intertemporal substitution in householdbehavior. Overall,Iimposeenoughstructurefromthemicro-empiricalevidencecombinedwith aheterogeneousagentmodelthatIamleftwithjusttwoparameterstoestimateusingthe macrostructuralshocks—stickyexpectationsparametersforlaborincomeandforthefed funds rate. To estimate these parameters, I first run local projections on each of the four inputs to the consumption decision—the federal funds rate, labor income, stock and real estatereturns. TheselocalprojectionsgivemewhatIwillcalltheempiricalimpulseresponse function to the shock for every input to the consumption block. These impulse response functionstellmehowmucheachofthefourinputstotheconsumptionblockisexpected to deviate from its expected value before the arrival of the shock at every quarter s after the shock hits. If I know the consumption Jacobians with respect to each of these inputs, I can then calculate how much I expect consumption to deviate t periods after the shock hits—I will call this the Jacobian-implied impulse response function for consumption. This Jacobian-implied impulse response function for consumption is simply the sum of each of the four Jacobians multiplied by the empirical impulse response for their respective input. Finally, I can compare the Jacobian-implied impulse response function for consumption 5

with the empirical impulse response function for consumption calculated from local projections using a distance metric. I choose the two sticky expectations parameters for the Jacobians in order to minimize the sum over all ten shocks of the distance between the Jacobian-implied impulse response for consumption and the empirical impulse response function for consumption.1 A robust finding is that the sticky expectations parameter implies the intertemporal substitution Jacobian is close to zero everywhere. That is, householdsdonotsubstituteintertemporally. Shouldthereaderbesurprisedthathouseholdsdonotappeartosubstituteintertemporally? Iwouldarguenot. First,itiswellknownfromthenearrationalityliterature,starting with Akerlof and Yellen (1985), that the consumption-saving behavior that comes from standard models is not robust to either small deviations in rationality or other frictions. Forexample,Cochrane(1989)findsthataconsumerwhobasestheirconsumption-saving decision on the 10-year moving average of the real interest rate in place of the forward ff short-term real rate will su er a utility loss equivalent to between $0.08 and $1.45 per quarter—small enough that we might expect a rational consumer to not pay attention at all. He suggests the result “implies that the theory as it stands provides few predictionsabouttherelationshipbetweenaggregateconsumptionandassetpriceoraggregate quantityfluctuationsthatarerobustto$1“mistakes”ormisspecifications.”2 Furthermore, thereisawealthofempiricalevidenceonconsumptionbehaviorthatsuggestshouseholds do not behave according to standard models in other respects. More anecdotally, Choi (2022) compares the advice of popular financial advice books with the advice that comes from models in the household finance literature. He finds many ways in which popular ff adviceontheconsumption-savingdecisiondi ersfromthatofacademicmodels. Healso finds a complete lack of advice on how households should change consumption-saving behaviorinresponsetointerestrates,stronglysuggestingthatthisisnotaquestionmany 1ThemethodissimilartothoselaidoutinBarnichonandMesters(2020)andLewisandMertens(2022) andtothatusedinCai(2024) 2Morerecently,Andreetal.(2025)findevidenceofnearrationalbehaviorinresponsetolargeandsmall incomeshocks. 6

households even ask. To the extent that there is any link between interest rates and consumption choices in Choi’s review of the popular finance literature, it is through the advicetosaveenoughtocontinuetospendafixedfractionofyourincomeinretirement, advicethatwouldsuggestanegativeintertemporalelasticityofsubstitution. The second reason it may not be surprising that households do not intertemporally substitute is that little evidence of such behavior has been found in previous studies. Hall (1988) provides a seminal contribution showing no relationship between interest rates and consumption growth in aggregate data. He states, “A detailed study of data for the twentieth-century United States shows no strong evidence that the elasticity of intertemporalsubstitutionispositive,”and,furthermore,hestatesofhisestimates“most of them are also quite precise, supporting the strong conclusion that the elasticity is unlikely to be much above 0.1, and may well be zero.” Hall (1988) inspired a large literaturethatusedtheEulerequationtofindmicroevidenceonthesizeofintertemporal substitution—many such papers are reviewed in Browning and Lusardi (1996). These papers contained a wide array of estimates, with little in the way of consensus, and the methodsusedhavesincebeenbroughtintoquestionbyCarroll(1997). More recently there has been mixed evidence on intertemporal substitution. Best et al. (2019) makes use of the unusual notching characteristics of the U.K. mortgage market to gain identification of the elasticity of intertemporal substitution under some reasonable assumptions and finds, like this paper, that it is close to zero. By contrast, Crumpetal.(2022)useidiosyncraticinflationexpectationsfromtheNewYorkSurveyof expectationsandfindasubstantiallypositiveelasticityofintertemporalsubstitution. The decompositionofconsumptionbehaviorinresponsetomonetarypolicyshocksisstudied byHolmetal.(2021)whouseofNorwegianadministrativedatatouncoverheterogenous behavior. ThispaperisalsocloselyrelatedtoMcKayandWolf(Forthcoming),whoshowhowto usethesequencespaceJacobians,alongwithimpulseresponsefunctions(IRFs)identified 7

ff from several di erent types of monetary policy shocks, to estimate economic dynamics that are robust to the Lucas critique. Hebden and Winkler (2021), Beraja (2023), and BarnichonandMesters(2023)allhaverecenttheoreticalpaperswithsimilarideas. The paper is structured as follows. The pedagogical material in section 2 explains the key ideas of the paper in the context of a simple endowment economy with two agents. Section 3 details the exact methodology that I use to estimate the intertemporal substitution Jacobian. Section 4 presents the results, section 5 examines the robustness of theresultstosomeunderlyingassumptions,andsection6concludes. = 2 Example: ATwo-AgentEndowmentEconomywithC Y Itisusefultoseehowthemethodologyworksinasimpletwo-agentendowmenteconomy model in which consumption is equal to income. In this economy, all households receive λ an exogenous stream of income, Y . A fraction of households, , are hand to mouth and t = − λ spend all their income each period: C htm,t Y t . The remaining fraction, 1 , optimize Exogneous Y Y, β Y, β Market Clearing C Household Block Unknowns r r Figure1: Directedacyclicalgraphforasimpleendowmenteconomy 8

theirconsumptionaccordingtotheconsumptionproblem: maximize E (cid:88) ∞ (cid:16) Πt β (cid:17)C1 op − t σ ,t (1) {Copt,t } 0 t=0 i=0 i 1 −σ subjectto: + ≤ + + . C opt,t A t (1 r t )A t−1 Y t (2) β Here, is the exogenously given discount factor for each period i, while the real interest i rate, r , is taken as given by the optimizing household but will be endogenously detert = λ + − λ = mined in equilibrium to clear the market such that C t C htm,t (1 )C opt,t Y t . A directedacyclicalgraphrepresentationofthemodelisshowninfigure1,inwhichthetwo β agentshavebeenaggregatedtoahouseholdblockwithinputpathsforY, ,andrandan = output path for C. Assuming A−1 0, the household block is described by the following function: { }∞ = C { }∞ ,{ }∞ ,{β}∞ . C ( Y r ) (3) t=0 t=0 t=0 t=0 Iwilllinearizethismodelaroundsteady-statevalues. Consequently,thedynamicsofthe householdblockarefullydescribedbythreeJacobians: C C C JC,Y = d t, JC,r = d t, JC,β = d t. t,s dY t,s dr t,s d β s s s Economists are particularly interested in the first two Jacobians: how consumption changes with income and with interest rates. In the case of our two-agent model, these Jacobians are graphically represented in figure 2. The left-hand panel of 2 shows the impulseresponseofconsumptionovertimetoanexpectedoneunitincreaseinincomein zero, four, and eight quarters’ time, holding interest rates and discount factors constant. ThisJacobianisalsoknownastheintertemporalmarginalpropensitytoconsume(iMPC). In this example, I have set the hand-to-mouth share to be 0.25 and the behavior of these 9

households shows through in the large spikes in the consumption response at the time theincomeisreceived. Theoptimizingagentsincreasetheirconsumptionineveryperiod / + by r (1 r ) multiplied by the present value of the expected increase in income—this ss ss increasecanonlyjustbemadeoutinthefigure. The right-hand panel of figure 2 shows the impulse response of consumption over time to an expected one unit increase in the realized interest rate in 0, 4, and 8 quarters’ time, holding income and discount rates constant. While hand-to-mouth households do notchangetheirconsumptioninresponsetoachangeininterestrates,optimizingagents choose to save up to the quarter of the higher interest rate and then—after they have receivedthehigherinterestrateontheirsavings—consumethereafterataslightlyhigher levelthanbefore. 2.1 Two steps to find the consumption-interest rate Jacobian The thought experiment I want to entertain is one in which an economist is able to directlymeasuretheconsumption-incomeJacobian,saybyrunningexperimentsinwhich householdsaregivenincomesperiodsinthefuture,butcannotrunasimilarrandomized experiment for interest rates. Nevertheless, the economist has aggregate data on income andinterestrates(andconsumption,thoughthisisequaltoincomebyconstruction)and wishes to estimate the consumption-interest rate Jacobian. My approach is to follow two steps. β Step 1: Identify a shock in which does not move. In many macroeconomic models, including the simple one presented here, households may change their consumption decision for reasons unrelated to income or interest rates. In this case, I have modeled this possibility as a shock to the discount factor. The existence of such shocks makes it ffi di cult to measure the Jacobian of the interest rate because in equilibrium the interest ff ratewillmovetoo setchangestothediscountfactor. Intheabsenceofshockstoincome, 10

0.25 0.20 0.15 0.10 0.05 0.00 0 1 2 3 4 5 6 7 8 9 10 11 Quarter noitpmusnoC Consumption-Income Jacobian 0.0 0.1 0.2 0.3 0 1 2 3 4 5 6 7 8 9 10 11 Quarter noitpmusnoC Consumption-Interest rate Jacobian s=0 s=4 s=8 Figure2: ConsumptionJacobiansforthesimpletwo-agentmodel = thesediscountfactorshockswouldresultinaconstantlevelofconsumption,sinceC Y, despite a changing interest rate. A naive economist might be led to the conclusion that consumptionisinsensitivetochangesintheinterestrate. My strategy to overcome this problem, in the context of this example, is to identify shocks that are orthogonal to changes in household preferences and therefore have an ff e ectonconsumptiononlythroughchangestothepathforexpectedincomeandinterest rates. In this simple model with only two exogenous variables, these identified shocks are exogenous shocks to the path of income. Such shocks to income can, however, vary intimingandpersistence. Infigure3,Ishowtheimpulseresponsesforincome,realinterestrates,andconsumption to an exogenous shock to income that takes the form of an AR(1) decaying at a rate of 0.5. Because these IRFs are a result of general equilibrium, the IRF for consumption is equal to that for income. However, from the point of view of individual households, their consumption choice isa functionof the IRFsfor bothincome andreal interest rates, whichtheytakeasgiven. Step 2: Find the consumption-interest rate Jacobian that explains the residual consumption IRF. The consumption IRF in figure 3 can be further decomposed into two 11

1.0 0.8 0.6 0.4 0.2 0.0 0 1 2 3 4 5 6 7 8 9 10 11 Quarter Y Exogenous Income Shock 0.0 0.2 0.4 0.6 0.8 1.0 0 1 2 3 4 5 6 7 8 9 10 11 Quarter R Real Interest Rate IRF 1.0 0.8 0.6 0.4 0.2 0.0 0 1 2 3 4 5 6 7 8 9 10 11 Quarter C Consumption IRF Total Income Component Interest Rate Component Figure3: Impulseresponsetoanexogenousincomeshock components: the household response to the expected income path and the household responsetotheexpectedrealinterestratepath: ∞ ∞ (cid:88) (cid:88) dC = JC,YdY + JC,rdr . (4) t t,s s t,s s s= (cid:32)(cid:32)0(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32) (cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32) s= (cid:32)(cid:32)0(cid:32)(cid:32)(cid:32)(cid:32) (cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32) (cid:124) (cid:123)(cid:122) (cid:125) (cid:124) (cid:123)(cid:122) (cid:125) Incomecomponent Interestratecomponent In my setup, I can observe the following IRFs: dC , dY , and dr . Furthermore, I have t t t assumed that the consumption-income Jacobian, JC,Y, is observable, say from natural t,s experiments or randomized control trials. Under these assumptions, I can calculate the 12

interestratecomponentoftheconsumptionIRF: ∞ ∞ (cid:88) (cid:88) Interestratecomponent = JC,rdr = dC − JC,YdY . (5) t,s s t t,s s s=0 s=0 This calculation allows me to identify the partial equilibrium consumption response to a particular path for the real interest rate. However, there are many consumption-interest rate Jacobians that are consistent with any one particular path. In order to identify the entireconsumption-interestrateJacobian,itwillbenecessarytoparameterizetheJacobian with a finite set of parameters. I can then find the set of parameters that best fits the IRF, or IFRs, that I have observed. This set of parameters allows me to calculate the entire consumption-interestrateJacobian. 3 Methodology The core identification ideas are outlined in the specific example of a simple two-agent modelinsection2. Inthissection,Ibuildonthoseideasandshowhowthemethodology canbeappliedtomuchrichermodelsthatincluderichhouseholdheterogeneity,firmsthat make investment decisions, sticky prices and wages, international trade, and firm-side financial frictions. I will also show some of the limitations of the methodology, both in theoryandinpractice. After I have set up the theory, I show how I choose to parameterize the consumption Jacobiansofinterest. Ithenexplainmymethodologyforestimatingtheimpulseresponses tostructuralshocks. Finally,IdetailthemethodIusetoestimatetheJacobianparameters and,hence,thefullconsumptionJacobians. 13

w Labor N,T Y l r l ,r s ,r re ConsumptionSaving C,S l ,S s ,S re Figure4: Thehouseholdblockseparatedintolaborandconsumptionblocks 3.1 The Consumption Choice Embedded in a Rich Model β The household block structure—inputs Y, r, and and output C—shown in figure 1 appearsasasub-blockofmanystandardandnot-so-standardDSGEmodelsoftheeconomy. For example, this block is embedded in the textbook three-equation model from chapter 3 of Gal´ı (2015). However, the household block is often described as both a consumption and labor decision, with wages as an input place of income, and hours worked included in outputs. Figure 4 shows how, in many models, this household block can be further separated into a labor decision and a consumption decision (the figure also allows for three asset types—liquid assets, stocks, and real estate—and includes savings in these threeassetsasoutputsoftheconsumption-savingblock). Theabilitytoseparatethelabor choice from the consumption-saving decision through aggregate labor income is my key assumption: Key assumption: The impulse response function for aggregate consumption is a functionoftheexpectedpathsforaggregatelaborincome,thereturnsonavailableassets,and otherinputsthatareindependentoftheaggregateshocksanalyzed. Figure 4 is useful in demonstrating when this key assumption will not be valid. For example,ifleisureandconsumptionarenotseparableintheutilityfunctionofthehousehold, then it is not possible to separate the labor and consumption decisions in this way. Furthermore, in a two-agent or heterogenous agent model in which households make 14

ff ff their own labor decisions, di erent aggregate shocks may be associated with di erent labor income distributions. As a consequence, the consumption block is not separable from the labor block through aggregate labor income alone. Instead, the whole distributionofincomeisneededtoseparatethelaborandconsumptionblocks. Mymethodology cannot strictly apply to such models. However, the method can be applied to a model in which household labor is allocated by a union and the distribution of this allocation is independentoftheoriginofthechangeinaggregatehoursworked,suchasisthecasein many heterogeneous agent models with sticky wages. Furthermore, empirical evidence ff does not point to clear di erences in how aggregate income fluctuations are distributed exceptinthecaseofprogressiveorregressivechangesintaxes.3 Mymethodologyisalsolimitedtoanalyzingsmalldeviationsaroundasteadystate. As such,featuressuchastime-varyingriskpremiumsorstate-dependentimpulseresponses arenotcurrentlyaccountedforintheanalysis. As long as the key assumption above is satisfied, the consumption-saving block can be envisaged as part of a far more complex model and the methodology for identifying households’responsestointerestrateshockswillremainvalid. Forexample,suchablock canformpartofamodelwithmanyofthefeaturesthatresearchershaveaddedtoboththe real business cycle and New Keynesian models: investment, firm-side financial frictions, heterogenous firms, international trade, sticky prices or menu costs, and labor market frictions. A key advantage of the methodology presented here is that it is not necessary ff tospecifytherestofthemodel—eventhoughashockmaya ecteveryotherblockinthe model,itisenoughtoknowtheinputsandoutputsoftheconsumptionblocktoestimate householdconsumptionbehavior. 3Foradetailedanalysisofhowlaborincomevariesheterogeneouslyoverthebusinesscycle,seePatterson (2023). 15

3.2 Parameterizing the Consumption Jacobians Underthekeyassumptionfromsection3.1andassumingalinearizedmodel,thedynamics of aggregate consumption are determined by the Jacobian of aggregate consumption to aggregate labor income, JC,Y l, to the federal funds rate JC,R, as well as to stock and real estate returns, JC,stocks, and JC,realestate. Because each of these objects has an infinite dimension,itisnecessarytodisciplinetheseJacobianstoreducethenumberofparameters required for estimation. In this section, I will show how I use a mixture of theory and microdatatoleavejusttwoparameterstobeestimatedwithmacrodata. The Consumption-to-Labor-Income Jacobian The consumption-to-labor-income Jacobian is also known as the interterporal marginal propensity to consume, or iMPC. It measures the amount by which aggregate consumption t periods from now increases whenanewsshockarrivesthatindicatesthataggregatelaborincomewillincreasebyone = dollar s periods from now. The first column, s 0, is the impulse response of aggregate consumption to an instantaneous increase in labor income. There is a fair amount of empirical evidence that I will use to fit this first column. There is less empirical evidence on consumption responses to news shocks, and I will use a mixture of theory and empirics to reduce the number of parameters for this Jacobian to just one sticky expectations parameter. In order to parameterize the consumption-to-labor-income Jacobian, I will make use of a one-asset heterogeneous agent model with sticky expectations. The resulting oneparameterJacobianfitstheempiricalevidenceavailableforthefirstcolumnoftheJacobian whileallowingforavarietyofpossibilitiesfornewsshocks. Themodelitselfitnotmeant to be taken too seriously but instead should be thought of as a way to span the space of reasonableJacobiansgiventheempiricalandtheoreticalevidenceavailable. Intheone-assetmodel,infinitelylivedhouseholdsmaximizetheirutilityinthefaceof idiosyncraticincomeuncertainty,alongwithaninabilitytoborrow. Thevaluefunctionis 16

afunctionofthecurrentwagestate,e,andstockofassets,a,ofthehousehold. Inorderto ff match the first column of the Jacobian, I allow for six di erent types of households that ff β di eronlyintheirdiscountfactor . Foreachtype,thehouseholdproblemcanbewritten i inBellmanformasfollows: , = +βE (cid:48), (cid:48) | V(e a) maxu(c) [V(e a )e] i i i c,a(cid:48) (cid:48) + = + + s.t. a c (1 R)a y(e) (cid:48) ≥ a 0 TheincomeprocesscomesfromKaplanetal.(2018)alongwithaprogressivetaxstructure and is identical across each of the six household types. I choose power utility with a ffi coe cient of relative risk aversion of 1 and a real interest rate of 3 percent. Note that ff withadi erentincomeprocessandparameters,thespacespannedbytheone-parameter Jacobian will be similar—that is, all my results are robust to the specific specifications here. β With this model, I then estimate the values of ’s that best fit the evidence from i Fagereng et al. (2021) about the spending pattern over the 5 years following a shock to income. = = The solid lines in figure 5 show the resulting iMPC columns for s 0 and s 6, assumingallhouseholdsintheeconomyarehitwithanequalpercentageincreaseintheir before-taxincome—notethattheprogressivetaxmeansthatafter-taxincomewillincrease relativelymoreforlow-incomehouseholds. ThefirstcolumnoftheJacobianthatcomesoutofthiscalibratedmodel,shownasthe = s 0 solid line in figure 5, shows an MPC of around 0.3 in the first quarter. Marginal spending drops rapidly in the second quarter to below 0.1 and then declines more graduallyinthequartersfollowing. TheMPCof0.3inthefirstquarterisinlinewiththenow 17

0.30 0.25 0.20 0.15 0.10 0.05 0.00 0 2 4 6 8 10 Quarter noitpmusnoC s=0 shock s=6 shock sticky expecations Figure 5: Columns of the consumption-to-income Jacobian, with and without sticky expectations largeliteratureonMPCs. Thereislessempiricalevidenceontheresponseofconsumptiontoanewsshockabout future income—the columns after the first column in the income Jacobian—and I use the one-asset model to determine the impulse response to news shocks. Encouragingly, Auclertetal.(2018)experimentwithavarietyofmodelsandfindthat“modelswithvery ff di erentprimitives,oncecalibratedtotheexistingevidenceoniMPCsoutofunexpected incomeshocks,predictsimilartent-shapediMPCsoutofexpectedincomeshocks. Given thelackofgoodempiricalevidenceontheseiMPCs,thisisreassuring.” The solid line with a peak in the sixth quarter in figure 5 shows the model-implied consumption response to an increase in income in six quarters’ time. It more or less fits ff the evidence available: There seems to be little di erence in the consumption response to anticipated and unanticipated income shocks. However, there is some evidence that the consumption response to a news shock may not be as symmetric around the arrival dateofincomeasimpliedbyastandardheterogenousagentmodel. Forexample,Kueng (2018), using the announcement and arrival of Alaska oil payments, and Ganong and Noel (2019), using the known expiration of unemployment benefits, both find much less anticipatorybehaviorthanastandardmodelwouldsuggest. 18

Toaccountforthepossibilityoflessanticipation,Iallowforhouseholdstohavesticky expectations with respect to income. Under sticky expectations and following an income news shock, a fixed fraction of households who have yet to update their expectations, θ ,learnaboutthenewseachquarter.4 Oncetheincomearrivesonhouseholds’balance inc sheets, all households learn about the income change. The mechanism is similar to that describedinCarrolletal.(2020)andAuclertetal.(2020)butisappliedonlytotheincome ff Jacobian. Thee ectofstickyexpectationsistoreducethesizeoftheconsumptionresponse in anticipation of future income and increase the consumption response once the income hasarrived. Thedottedlineinfigure5showstheconsumptionresponsetoanewsshock sixquartersfromnowwithstickyexpectations—inthisexample,15percentofhouseholds updatetheirexpectationseachquarter. θ The resulting income Jacobian is described by one parameter, , which adjusts inc the degree to which households anticipate income news shocks. The first column of the Jacobianispinneddownbymicrodata,whilethecolumnsthatfollowhavesomeflexibility θ remaining. I will estimate using macrodata. My reading of the empirical literature inc θ ∈ , is that the possible Jacobians spanned by [0 1] cover most empirically plausible inc estimatesoftheincomeJacobian.5 The Consumption-to-Real-Interest-Rate Jacobian The response of consumption to a ff real interest rate news shock can be broken down into a substitution and income e ect. Farhi et al. (2022) lays out the theory in the context of an incomplete market with uncertainty. IntheheterogeneousagentmodelusedasastartingpointfortheJacobiansinthis ff paper, the substitution e ect can be calculated by changing the interest rate in the Euler ff equation—a ecting the marginal utility of spending in each period—while keeping the interestrateusedinthebudgetconstraintfixed. Keepingtheratefixedinthebudgetcon- 4In this paper, θ and θ denote the fraction of households that update each quarter. Some other inc sub papers,suchasCarrolletal.(2020),labelthefractionthatdonotupdate. 5Analternativetostickyexpectationsisfinitehorizonplanning—Iexploresuchapossibilityinsection 5.2. ThereissomeevidencethattheiMPChasafattail,asresultofmanytwo-assetmodels,butthisfeature oftheiMPCisnotmaterialtomyanalysis—seesection5.3. 19

0.2 0.0 0.2 0.4 0 2 4 6 8 10 Quarter noitpmusnoC Intertemporal Substitution Income Effect 0.2 0.0 0.2 s=0 shock 0.4 s=6 shock sticky expecations 0 2 4 6 8 10 Quarter Figure 6: Columns of the consumption-to-interest-rate Jacobian, divided into the substiff tutionandincomee ect,withandwithoutstickyexpectations straint ensures that the feasible set of consumption plans does not change and therefore that a change in consumption is solely the result of intertemporal substitution. Similarly, ff the income e ect can be calculated by fixing the interest rate in the Euler equation and changingtheinterestratethatappearsinthebudgetconstraint,ensuringthatanychange inbehaviorisderivedfromachangeinthefeasiblesetofconsumptionplansandnotfrom intertemporalsubstitution. Figure 6 plots the first and sixth columns of both the substitution Jacobian (left-hand ff panel) and the income-e ect Jacobian (right-hand panel) in solid black. The dotted lines show the respective sixth columns that assume households have sticky expectations to newsshocksaboutfutureinterestrates. The basic shape of the substitution Jacobian is similar across many models: News of a future interest rate increase causes households to save more before the rate increase in order to spend more after the rate increase. Overall, this substitution is budget neutral by construction. In theory, the shape of this Jacobian will depend on the elasticity of intertemporal substitution, the degree of precautionary saving, and other features of ffi the model. In practice, I find that a single parameter for sticky expectations su ces to approximately span a wide range of possible model Jacobians. In order to allow for the possibility of negative intertemporal substitution, and so as to avoid corner solutions, 20

0.020 0.015 0.010 0.005 0.000 0 2 4 6 8 10 Quarter noitpmusnoC Real Estate Stocks 0.020 0.015 0.010 s=0 shock 0.005 s=3 shock s=6 shock 0.000 0 2 4 6 8 10 Quarter Figure 7: Columns of the consumption-to-stock-market and consumption-to-real-estate Jacobians J θ = −J −θ θ < I set ( ) ( ) when 0 for the intertemporal substitution Jacobian. sub sub sub This formulation allows the parameters to smoothly move from the standard sign for θ > θ = intertemporal substitution, 0, through no intertemporal substitution, 0, to sub sub θ < intertemporalsubstitutionintheoppositedirectionofstandardtheory, 0. sub The income Jacobian, shown in the right-hand panel of figure 6, shows a positive ff income e ect consumption response to an increase in interest rates. Although the shape ofthesubstitutionJacobian—theleft-handpanel—isrelativelyrobusttomodelmisspecification, the shape of the income Jacobian from the model is derived from the unrealistic model assumption that households hold only short-term liquid real bonds. In practice, ff theincomee ectisgovernedbythetypesofassetsandliabilitieshouseholdshold: stocks, bonds,realestate,andfixedandfloatingmortgages,tonamejustafew. Amodelthatfully captures all of these, along with their use as borrowing collateral, is beyond the scope of ff thispaper. However,CrawleyandKuchler(2023)showthattheincomee ectfromassets ff and liabilities is small in the US. Accordingly, I discard the income-e ect Jacobian from themodelandreplaceitwithempiricalestimatesoftheconsumptionresponsetochanges instocksandrealestate,thetwolargestassetclassesheldbyhouseholds. 21

The Consumption-to-Stocks and Consumption-to-Real-Estate Jacobians I set the Jacobians for both the stock market and real estate such that households increase their consumption permanently, but without anticipating when the value of each asset goes up. I calibrate the MPC to both the stock market and real estate to be 0.03, in line with the existing literature, and set the stock of each asset owned by households to be about halfofGDPtomatchthehistoricalaveragesince1970. Selectedcolumnsoftherealestate (left-handpanel)andstockmarket(right-handpanel)Jacobiansareshowninfigure7. 3.3 Estimating Empirical Impulse Response Functions Foreachstructuralshockseries,Ineedtocalculatetheempiricalimpulsefunctionsforthe following outcomes: consumption, income, the real federal funds rate, the real return to thestockmarket,andtherealreturntorealestateassets. Toobtaintheseimpulseresponse functions,Iuselocalprojections. Thatis,foreachoftheseoutcomesO,Irunthefollowing regressionsforshockseriesq: q = O,q(cid:15)q +βO,q q +εO,q. O J X (6) t,t+h h t h t t,h q HereO istheoutcomevariable. Forconsumption,income,thestockmarket,andreal t−1,t+h − estate, this outcome is the percent change from period t 1. The real federal funds rate outcomeismeasuredasthefederalfundsrateminusthemedianexpectedone-year-ahead inflation from the Survey of Professional Forecasters. Consumption is total real personal consumption expenditure (PCE), and my measure of income captures the portion of real disposable income that is not derived from investments.6 This measure of income is chosen to align with the income Jacobian that is calibrated to match the MPC literature. By contrast to shocks to labor income and government transfers, it is well known that 6Specifically,thedefinitionofincomeIuseisthesumofcompensationofemployees,proprietors’income withinventoryvaluationandcapitalconsumptionadjustments,andtransfersminuscontributionstoSocial Security and 80 percent of personal taxes. The taxes are chosen to align with the proportion of personal taxespaidonnon-capitalincome. 22

shockstocapitalincome,whicharehighlyskewedtotheverywealthy,haveamuchlower MPC. The stock market measure uses prices from Fama French and is adjusted for PCE inflation,andtherealestatemeasurecomesfromtheCase-Shillerhousepriceindex,also adjustedforPCEinflation. O,q The object of interest that I wish to estimate is J , the impulse response for outcome h variable O after h periods following a structural shock of type q and magnitude one. (cid:15)q The structural shock series of type q takes the value at time t. Following Ramey t q (2016), I include in the set of controls X two lags each of log industrial production, the t unemployment rate, log of the consumer price index, log of a commodity price index, and the federal funds rate. I also include lags of the shock series itself, which is why the q controlsX areindexedbyqaswellast. t Foreachoutcome,Irunlocalprojectionsatamonthlyfrequencyforahorizonofupto 48 months.7 Following the advice in Montiel Olea and Plagborg-Møller (2021), I include (cid:99)O,q sixlagsoftheshockseriesandcalculatestandarderrorsfor J withoutNeweyandWest h (1987)adjustment. Choice of Structural Shocks The methodology in this paper allows me to use any ff ff structural shock series, so long as the shock only a ects consumption through its e ect on income and asset market returns. The recent pandemic is an example of a shock that clearly violates these assumptions—households chose, or were obliged, to cut back on their normal consumption activities in order to socially distance and limit the spread ff of disease. However, many of the shocks studied in the literature are thought to a ect consumption only indirectly. For example, a typical New Keynesian model will feature monetarypolicyshocks,totalfactorproductivity(TFP)shocks,andgovernmentspending ff shocks that only change consumption behavior through their e ect on income and asset returns. A large number of structural shocks have been proposed in the literature, along with 7Wheremonthlydataisnotavailable,Iinterpolatequarterlydatatoamonthlyfrequency. 23

ff di erentmethodstoidentifythem. However,foranyoneparticularstructuralshockthere isnoconsensusonwhetheritiswellidentified. Forexample,monetarypolicyshockshave ff been identified in a number of ways but each of these su ers from some limitations for ourpurposes. First,monetarypolicyshocksarethoughttoberesponsibleforonlyasmall fraction of the total forecast variance. Second, the identification methods used only pick up a further small fraction of total monetary policy shocks. Consequently, the estimated IRFshavelargestandarderrorsandaresensitivetotheexacttimeperiodoverwhichthey ff areestimated. Furthermore,theso-calledFedinformatione ect(NakamuraandSteinsson (2018))drawsintoquestionwhethertheseshocksaretrulyshockstomonetarypolicyorif theyareinreactiontoothermacroeconomicevents. Ithereforetaketheapproachofusing awidevarietyofstructuralshocks,includingbutnotonlymonetarypolicyshocks,inthe ffi hope that—while no single shock will be su cient to convince the reader of households’ consumptionbehavior—theaggregateevidencewillbeoverwhelming. Inordertolimitthenumberorshockseriestoamanageablenumberwhilenotcherrypicking series, I choose all 10 of the shock series for which local projections are plotted in the figures contained in Ramey (2016). This handbook chapter is an overview of the shock literature and includes monetary policy shocks, government spending shocks, tax ff shocks, and technology shocks. Furthermore, the chapter covers a variety of di erent identification methodologies such as high-frequency identification, Cholesky decomposition, maximum forecast error variance, and narrative methods. The aim of choosing a broad range of shock types and identification methods is to show the robustness of the results: ifthereaderhasadislikeforsomeparticularshock-identificationmethodologies, I hope she is able to find others to her taste. Ultimately, all the shock series used here pointinthesamedirectionoflittleintertemporalsubstitution. Detailsontheshockseries usedcanbefoundinappendixA. 24

3.4 Estimating the Consumption Jacobians AfterparameterizingtheconsumptionJacobiansinsection3.2andestimatingtheempirical impulse responses to structural shocks in section 3.3, the last step is to estimate the parametersoftheJacobianstobestfittheempiricalimpulseresponsefunctions. Idothis withastandardminimum-distanceestimationmethod. Givenparametersfor θ = ( θ ,θ )andinput-estimatedIRFsJˆq = (JˆY,q, JˆR,q, Jˆstocks,q, Jˆrealestate,q), inc sub IcancalculatetheimpliedconsumptionIRFforastructuralshockoftypeq: (cid:88) C (Jˆq,θ ) = JC,O( θ )JˆO,q. O∈{Y,R,stocks,realestate} This consumption impulse response implied by the Jacobians and the empirical input IRFs can then be compared to the empirical IRF for consumption, Cˆq = JˆC,q. For each structuralshock,Icreatealossfunctionasafunctionoftheparameters, Lq( θ ). Lq( θ ) = ( C (Jˆq,θ ) −Cˆq) (cid:48)Σ−1( C (Jˆq,θ ) −Cˆq) (7) q Σ Here, is a diagonal matrix of estimated consumption IRF variances. Using a set of q structural shocks Q—which may consist of just one or up to all of the shocks described in section 3.3—my estimator for the Jacobian parameters is the parameter vector that minimizesthesumoflossesoverallstructuralshocksinQ. (cid:88) θˆ = argmin Lq( θ ) θ q∈Q 4 Results Table 1 shows the estimation results for the sticky expectations parameters for intertemporal substitution and income along with standard errors in parentheses below. The top row shows the result of estimation using all 10 structural shocks, and the following rows 25

SetofStructuralShocks(Q) θˆ θˆ sub inc All -0.02 0.22 (0.04) (0.17) RomerandRomer(2004) -0.81 0.76 (0.79) (1.18) GertlerandKaradi(2015) -0.13 0.00 (1.19) (0.25) RameyandZubairy(2018)militarynews 0.05 0.00 (0.19) (0.15) BenZeevandPappa(2017)defensespendingshocks -0.01 0.11 (0.10) (0.42) BlanchardandPerotti(2002)governmentspending -0.07 0.81 (0.32) (2.33) MertensandRavn(2011)taxnewsshocks 0.06 0.02 (0.13) (0.97) Leeperetal.(2012)expectedtaxesfromonetofiveyearsforward -0.00 1.00 (0.10) (5.78) BenZeevandKhan(2015)investmentspecificnewsshocks -0.14 0.09 (0.19) (0.13) Fernald(2014)utilization-adjustedTFP -0.36 0.00 (1.20) (0.48) Francisetal.(2014)unanticipatedTFPshocks -0.24 0.78 (4.06) (1.00) Table1: Parameterestimatesusingallstructuralshockstogetherandeachindividually showtheresultofestimationusingeachshockseriesindividually. The main result of the paper is that, in the estimation using all the structural shocks together, I find θˆ ≈ 0. This finding suggests that households do not intertemporally sub substitute—their consumption response to these structural shocks is best explained only ff throughtheirresponsetoincomeandwealthe ects. Whenestimatedindividuallyforeach selected structural shock, only 2 out of the 10 shocks result in positive estimates for θˆ sub intertemporalsubstitution. Futhermore, θˆ isestimatedtobestatisticallyindi ff erentfrom sub zeroforeachofthe10shocks,implyinganegligibleroleforintertemporalsubstitution. θ While all 10 estimates of are statistically indistinguishable from zero, some of the sub structural shocks are far more informative about the possible size of the intertemporal 26

ff substitutione ectthanothers. Forexample,thestandarderrorsfromtheestimatesusing Ben Zeev and Pappa (2017), Mertens and Ravn (2011), Leeper et al. (2012), and Ben Zeev and Khan (2015) are all below 0.15, while others such as those from Fernald (2014) ff and Francis et al. (2014) are above 1.0. These di erences come from the fact that some of the structural shocks feature real interest rate IRFs that are both large in magnitude and persistent, while in others the real interest rate barely moves. The standard errors from typical monetary policy shocks—Romer and Romer (2004) and Gertler and Karadi (2015)—aresomewhereinbetween,highlightingtheadvantagebeingabletouseawider rangeofstructuralshockstobetteridentifyintertemporalsubstitutionbehavior. The estimates for sticky expectations for income are less precise that those for intertemporalsubstitution. Somestructuralshockssuggestthathouseholdsdonotreactin anticipation of future income changes ( θˆ = 0), while others suggest households fully inc anticipate predictable income changes ( θˆ = 1). Estimation based on all 10 structural inc shocks leads to an estimate of 0.2. That is, each quarter, about 20 percent of households update their consumption based on the true expected income at a point in time in the future. Thewidearrayofestimatesandrelativelylargestandarderrorsforthisparameter θ θ reflectsthefactthat,incontrasttothevalueof ,thevalueof hasarelativelysmall sub inc ff e ectontheimpulseresponsefunctionandthereforeonthelossvalue. In the rest of this results section, I will examine the results in the context of the two shock series in detail: those from Romer and Romer (2004) and Ben Zeev and Pappa (2017). IwillthensummarizethedecompositionoftheconsumptionIRFsforall10shock series. ResultsusingRomerandRomer(2004)MonetaryPolicyShocks. Thetoprowoffigure 8 shows the empirical impulse response functions, along with 90 percent confidence intervals, for a Romer and Romer shock for each of the inputs to the consumption block: therealfedfundsrate,laborincome,thestockmarket,andrealestate. Followingashock ofthistype,therealfedfundsrateimmediatelydropsandthendissipatesoverarelatively 27

short period of one to two years. Labor income gradually rises over this period, peaking a little less than two years following the shock, before falling back to trend by the end of the period calculated. The stock market rises a little, and real estate prices oscillate, but thechangeinbothassetpricesisonlyjuststatisticallysignificantatthe90percentlevel. The larger lower panel shows the empirical impulse response of consumption along with detail on the impulse response estimated using the four inputs from the top row of the panel. The solid black line, the empirical impulse response, shows that, after a brief decline,consumptionrisesgraduallyoverayearandahalfbeforedecliningtosomewhat below trend four years after the shock. The 90 percent confidence intervals show the increase to be statistically significant. The bold dotted black line shows the impulse responsefunctioncalculatedbyapplyingtheestimatedJacobians—usingparametersfrom the estimation for all 10 shocks—for each of the four inputs in the top row of the panel.8 This estimated impulse response is close to the empirical impulse response, although it doesn’tcapturethefullextentsofthedeclineinconsumptionattheendoftheperiod. The blue, orange, and green bars in the lower panel of figure 8 show the contribution totheestimatedIRFforeachofthefollowinginputs: laborincome,stocks,andrealestate. These three bars add up to the bold dotted black line showing the estimated IRF. The contributionfromlaborincome,thebluebars,accountsforthebulkoftheestimatedIRF, withassetpricemovements—whichareonlyjuststatisticallysignificant—makingonlya smallcontributiontoconsumption. To illustrate why the contribution from intertemporal substitution is estimated to be zero, figure 8 also shows the size of this intertemporal substitution contribution that is implied by the model, assuming rational expectations—the hashed bars. These hashed bars push up consumption substantially over the first year following the shock, which ff then leads to a slight negative contribution to consumption after the shock’s e ect on the real fed funds rate has dissipated. These contributions from intertemporal substitution 8Thisestimationrestrictsθˆ tobepositive,whichinpracticemeansitisequaltozero. θˆ isestimated sub inc tobe0.22. 28

Real Fed Funds Income Stock Market Real Estate 3 0.2 0.5 1.0 2 0.4 0.5 0.0 0.3 1 0.0 0.2 0.2 0 0.1 0.5 1 0.0 0.4 1.0 0.1 2 1.5 0 10 0 10 0 10 0 10 Quarter Quarter Quarter Quarter Consumption 0.4 Empirical IRF Estimated IRF 0.3 90 percent CI 0.2 0.1 0.0 Estimated IRF Contributions 0.1 Income Stocks 0.2 Real Estate Intertemporal substitution with rational expectations (Actual estimated int. subs. contribution is zero) 0.3 0 2 4 6 8 10 12 14 16 Quarter Figure8: InputsandoutputIRFstotheconsumptionblockfollowingaRomerandRomer (2004)shock. Source: Author’s calculations and data compiled from Federal Reserve Economic Data (FRED), Federal Reserve Bank of St. Louis; replication files for Ramey (2016), and the SurveyofProfessionalForecasters,FederalReserveBankofPhiladelphia. over the first year would act to pull the estimated IRF away from the empirical IRF and therefore increase the loss function. As a result, the sticky expectations parameter is ff estimated to be not significantly di erent from zero, equivalent to households paying no attentiontotherealfedfundsratewhenmakingtheirconsumption-savingdecisions. Overall, the Romer and Romer (2004) shocks provide some evidence that households do not substitute intertemporally. However, the point estimate of θˆ using this data is sub largeandnegative(-0.8)withverylargestandarderrors(0.76). Theselargestandarderrors 29

result from the fact the shock is relatively short lived—households that are slow to react will end up not reacting at all to these shocks even if they would eventually change their consumption behavior substantially in reaction to a more persistent shock. Furthermore, identification of monetary policy shocks (as with all macro shocks) is challenging and RomerandRomer(2004)isonlyonewayofdoingso. ResultsusingBenZeevandPappa(2017)DefenseSpendingShocks. Oneofthecontributionsofthemethodinthispaperoverothersthatrequirefullspecificationofageneral equilibrium model, for example Auclert et al. (2020), is that it allows a wide variety of structural shocks to be used for estimation. This can help reduce standard errors around estimates and increase the robustness of the results to one particular shock identification methodology. Here, I describe the results using the defense spending shocks from Ben Zeev and Pappa (2017) that overcome some of the limitations of the Romer and Romer (2004)shockseries. In contrast to the short-lived change in the real fed funds rate following a Romer and Romer (2004) shock, the change in the real fed funds rate following a defense spending shock as identified by Ben Zeev and Pappa (2017) is persistent. The top-left panel of 9 showsthattherealfedfundsrateimpulseresponsefunctionremainsnegativefor4years following the shock. The remaining three panels in the top row of figure 9 show the impulse response functions for income, the stock market, and real estate prices. Income increases gradually, reaching a maximum 2 to 3 years after the shock, while the stock marketshowsnosignificantchangeandrealestatepricesincrease. The lower panel of figure 9 shows the decomposition of the impulse response of consumption to a defense spending shock. The solid black line shows the empirical responseasestimatedbyalocalprojection. Thedottedblacklineshowstheconsumption IRF calculated from each of the four inputs multiplied by their respective Jacobians, wheretheJacobianparametershavebeenestimatedusingall10shocksandintertemporal substitution restricted to be positive (and hence estimated to be zero). The blue, orange, 30

andgreenbarsshowthedecompositionofthisIRFintocontributionsfromincome,stocks, andrealestate. The hashed white bars in the lower panel of 9 show the contribution to the consumption IRF that would be implied by the path of the real fed funds rate in the absence of ff sticky expectations. Under this shock, these intertemporal substitution e ects are large and positive and would push the Jacobian-implied consumption IRF well outside of the confidence intervals of the empirical consumption IRF. As such, it is clear that the Jacobian-implied IRF fits that data far better when there is no intertemporal substitution. Thisshock—assumingitiswellidentified—providesstrongevidencethathouseholdsdo littleinthewayofintertemporalsubstitution. Results for All 10 Structural Shocks. Figure 10 shows the empirical consumption IRFs forall10structuralshocksusedintheestimationwithintertemporalsubstitutionrestricted tobepositive,andthereforezeroinpractice.9 Thetop-leftpaneloffigure10isarepeatof the lowerpanel in figure8, except that thecontributions from stocksand real estate have been combined. Similarly, the second-row right panel is a repeat of figure 9. The other eight panels show the same elements of the consumption IRF and its decomposition for eachoftheothershocks. Therearethreekeytakeawaysfromfigure10. First, the estimated IRF from applying the Jacobians to the empirical IRFs for each of the four inputs does a good job at fitting the empirical consumption IRF for all 10 shock types. Indeed,theestimatedIRFrarelyescapesthe90percentconfidenceintervalbounds and often closely tracks the central estimate. Furthermore, the labor income contribution totheconsumptionIRFformsthebulkoftheresponse,withstocksandrealestateplaying a negligible role except in the “Tax News” shock panel. The small role played by stocks andrealestatecomespartlyfromthesmallmovementsoftheseassetpricesfollowingeach shockrelativetothesizeofassetpriceswingsoftenobservedinthemarket. TheJacobianI 9Appendix B shows the input IRFs (income, real federal funds, stocks, and real estate) as well as the consumptiondecompositionshowninfigure10forall10structuralshocks. 31

Real Fed Funds Income Stock Market Real Estate 0.2 2 0.6 3 1 0.0 0.4 0 2 0.2 0.2 1 2 1 0.4 0.0 3 0.6 0.2 4 0 0 10 0 10 0 10 0 10 Quarter Quarter Quarter Quarter Consumption 0.6 Empirical IRF Estimated IRF 0.4 90 percent CI 0.2 Estimated IRF Contributions 0.0 Income Stocks Real Estate 0.2 Intertemporal substitution with rational expectations (Actual estimated int. subs. contribution is zero) 0 2 4 6 8 10 12 14 16 Quarter Figure 9: Inputs and output IRFs to the consumption block following a Ben Zeev and Pappa(2017)shock. Source: Author’s calculations and data compiled from Federal Reserve Economic Data (FRED), Federal Reserve Bank of St. Louis; replication files for Ramey (2016), and the SurveyofProfessionalForecasters,FederalReserveBankofPhiladelphia. usedtocalculatetheseconsumptionresponsestoassetpricechangesassumeda3percent MPC—thefactthatthesepricechangesplaysuchasmallroleinthedecompositionshows that the main results of this paper are robust to replacing these Jacobians with any other reasonablecalibration. Second,foralltheshockseries,thecontributionofintertemporalsubstitution,ifitwere assumed households had rational expectations with an intertemporal elasticity equal to 1, would be to significantly increase the loss function. In almost all cases, adding the 32

0.4 0.2 0.0 0.2 0.4 0 2 4 6 8 10 12 14 16 noitpmusnoC Romer & Romer Gertler Karadi Empirical IRF 1.0 Estimated IRF 90 percent CI 0.5 0.0 Estimated IRF Contributions Income 0.5 Stocks and Real Estate Intertemporal substitution with rational expectations (Actual estimated int. subs. contribution is zero) 1.0 0 2 4 6 8 10 12 14 16 0.8 0.6 0.4 0.2 0.0 0.2 0.4 0 2 4 6 8 10 12 14 16 noitpmusnoC Ramey News (military spending) Ben Zeev and Pappa defense news 0.6 0.4 0.2 0.0 0.2 0 2 4 6 8 10 12 14 16 0.2 0.0 0.2 0.4 0 2 4 6 8 10 12 14 16 noitpmusnoC Blanchard-Perotti Tax News 0.3 0.2 0.1 0.0 0.1 0.2 0.3 0 2 4 6 8 10 12 14 16 0.2 0.0 0.2 0.4 0 2 4 6 8 10 12 14 16 noitpmusnoC Leeper, Richter and Walker (2011) Expected Tax Ben Zeev-Khan Investment-specific news 0.4 0.2 0.0 0.2 0.4 0.6 0.8 1.0 0 2 4 6 8 10 12 14 16 0.5 0.4 0.3 0.2 0.1 0.0 0.1 0.2 0 2 4 6 8 10 12 14 16 Quarter noitpmusnoC Fernald utilization-adjusted TFP FORD TFP 0.2 0.0 0.2 0.4 0.6 0 2 4 6 8 10 12 14 16 Quarter Figure10: TheconsumptionIRFsforall10shocks. Source: Author’s calculations and data compiled from Federal Reserve Economic Data (FRED), Federal Reserve Bank of St. Louis; replication files for Ramey (2016), and the 33 SurveyofProfessionalForecasters,FederalReserveBankofPhiladelphia.

contribution from intertemporal substitution would move the estimated consumption IRF well outside of the 90 percent confidence intervals of the empirical consumption IRF. In fact, only for the “Tax News” and “military news” shock series does a little bit of intertemporal substitution—sticky expectations parameter of around 0.05—even help move the estimated IRF toward the empirical IRF. For the other eight shock series, intertemporalsubstitutionisestimatedasnegative. Third,someoftheshockseriesfeatureIRFsfortherealfedfundsrate(notshown)that remain significantly negative for a prolonged period relative to the identified monetary policy shocks that are commonly studied. For example, the real fed funds rate remains negative throughout the period shown for the Ben Zeev and Pappa (2017) defense news shocksandtheexpectedtaxshocksfromLeeperetal.(2012). Theinvestment-specificnews shocks from Ben Zeev and Khan (2015) also result in a prolonged period of depressed real fed funds rates. The lack of an intertemporal substitution contribution from these shocks, despite a long period of lowered real fed funds rate, provides stronger evidence than the shorter-lived identified monetary policy shocks that households do not appear tosubstituteintertemporally. 5 Robustness For the baseline estimation, I took the consumption-income Jacobian from a one-asset ff bu er-stock model with an elasticity of substitution equal to 1 as the starting point. I then estimated the sticky-expectations parameter which best fit the impulse responses. I claim that this methodology spans the space of most reasonable-looking iMPCs and intertemporal substitution Jacobians. In this robustness section, I push that claim by consideringthreealternativeparameterizationsfortheseJacobians. 34

SetofStructuralShocks(Q) EIS=1 EIS=0.5 EIS=0.33 EIS=0.25 All -0.02 (0.05) -0.04 (0.09) -0.07 (0.18) -0.09 (0.26) RomerandRomer(2004) -0.81 (0.79) -1.00 (1.59) -1.00 (2.44) -1.00 (3.16) GertlerandKaradi(2015) -0.13 (1.19) -0.38 (7.61) -0.42 (12.68) -0.42 (17.18) RameyandZubairy(2018) 0.05 (0.19) -0.70 (2.03) -0.55 (2.63) -0.52 (3.16) BenZeevandPappa(2017) -0.01 (0.10) -0.02 (0.20) -0.04 (0.34) -0.07 (0.47) BlanchardandPerotti(2002) -0.07 (0.32) -0.13 (0.80) -0.16 (1.34) -0.16 (1.71) MertensandRavn(2011) 0.06 (0.13) 0.14 (0.40) 0.43 (1.47) 0.52 (2.17) Leeperetal.(2012) -0.00 (0.10) -0.01 (0.20) -0.02 (0.32) -0.04 (0.45) BenZeevandKhan(2015) -0.14 (0.19) -0.17 (0.39) -0.17 (0.60) -0.19 (0.81) Fernald(2014) -0.36 (1.20) -0.73 (3.18) -0.96 (5.09) -1.00 (6.57) Francisetal.(2014) -0.24 (4.06) -0.30 (12.94) -0.28 (17.01) -0.24 (15.89) Table 2: Estimates of θˆ starting with di ff erent values for the elasticity of intertemporal sub substitutionusingallstructuralshockstogetherandeachindividually. 5.1 Robustness to the model’s elasticity of substitution The one-asset model that I begin with in the main analysis uses an elasticity of substitution (EIS) equal to 1. I then estimate a sticky expectations parameter of zero, implying that households do not in practice substitute intertemporally. Here, I test whether that conclusionisrobusttostartingwithalowerEISintheinitialmodel. Table2showsestimatesfor θˆ startingwithdi ff erentvaluesfortheEISusingallstrucsub = tural shocks together and each individually. The EIS 1 column replicates the estimates inthebaselineanalysis. TheestimatesusingEISvalueslessthanonearealsostatistically insignificantwithnineoutoftenestimatesnegativeineachcolumn. However,relativeto thebaseline,themagnitudeofthepointestimatestendtobelarger—aconsequenceofthe fact that the size of the consumption response is approximately proportional to the EIS multiplied by the sticky expectations parameter when the sticky expectations parameter is small. Overall, these results confirm a negligible response of consumption to interest rates. 35

5.2 Finite horizon planning in place of sticky expectations Inthemainanalysis,Ihavechosentoexamineastickyexpectationsversionofastandard ff bu er-stockmodelinordertoallowforthehump-shapedresponsetoshocksthatshocks that are often observed in the data. A popular alternative deviation from rational expectationsisamodeloffinitehorizonplanning(FHP).Underfinitehorizonplanning,agents have fully rational expectations about the state of the economy in the current period, but their expectations about deviations from the steady state become increasingly biased towards zero the further into the future these expectations relate to. For example, with anFHPparameterof0.5,agents’expectationsaboutdeviationsfromthesteadystatetwo quarters from now are one quarter (0 . 52) of what a rational agent would expect. Finite horizonplanningisonewayforamodeltoavoidtheforwardguidancepuzzle. However, unlikeastickyexpectationsmodel,finitehorizonplanningdoesnotleadtohumpshaped impulseresponses. Table3showstheestimatesfortheFHPparametersassociatedwiththeintertemporal substitution Jacobian (FHˆP ) and the income Jacobian (FHˆP ). As with the sticky sub inc expectations estimates, all but one of the FHP estimates suggest negative intertemporal substitution,andnoneofthe10individual-shockestimates,northeestimatethatusesall 10 shocks together, are statistically significant. The point estimate using all 10 structural shocks is -0.45, which translates into only a small (and opposite-signed) intertemporal substitutionresponse. 5.3 Fatter tails and lower initial MPCs in the intertemporal MPC ff One concern is that the one-asset bu er-stock model that I start with has some known problems, and, in particular, the way I have calibrated it to match the one-year MPC for ff di erentwealthquintilesresultsinfartoolittleaggregatewealth. Atwo-assetmodelcan addresssomeoftheseconcerns. ff In Auclert et al. (2018), the authors examine the di erences between the iMPCs in a 36

SetofStructuralShocks(Q) FHˆP FHˆP sub inc All -0.45 0.87 (0.25) (0.12) RomerandRomer(2004) -0.56 0.80 (0.68) (0.49) GertlerandKaradi(2015) -0.63 0.14 (1.24) (8.62) RameyandZubairy(2018)militarynews -0.26 0.83 (2.04) (0.50) BenZeevandPappa(2017)defensespendingshocks -0.31 0.83 (0.80) (0.57) BlanchardandPerotti(2002)governmentspending -0.65 0.99 (0.77) (0.28) MertensandRavn(2011)taxnewsshocks 0.65 -0.08 (0.38) (11.32) Leeperetal.(2012)expectedtaxesfromonetofiveyearsforward -0.33 0.79 (0.82) (3.50) BenZeevandKhan(2015)investmentspecificnewsshocks -0.46 0.89 (0.49) (0.13) Fernald(2014)utilization-adjustedTFP -0.71 -0.16 (0.81) (11.26) Francisetal.(2014)unanticipatedTFPshocks -0.76 0.99 (1.54) (0.10) Table3: Finitehorizonplanningparameterestimatesusingallstructuralshockstogether andeachindividually. ff selection of models. Somewhat reassuringly, they find few material di erences in the columns of the iMPCs between the models they examine, conditional on matching the empirical evidence for the first column. The one exception is that, in their two-asset model, the marginal propensity to consume four or more years after an income shock decays more slowly than in the other models examined. This feature of the two-asset modelcanleadtofarlargerfiscalmultipliersintheirgeneralequilibriummodel. AfurtherconcernisthatMPCsmaybelowerthansuggestedbytheempiricalevidence I use to discipline my one-asset model. The MPC estimates I use are at the high end of thoseintheliterature,and,furthermore,HavranekandSokolova(2020)findsevidenceof publicationbiasinthisliterature. 37

1 2 3 4 5 6 7 0 20 40 60 80 100 Quarter CPM goL 1.0 Baseline 20% fully smoothing 0.8 Fully smoothing 0.6 0.4 0.2 0.0 0.2 0.0 0.2 0.4 0.6 0.8 1.0 Fraction fully smoothing etamitse noitatcepxe ykcitS 9 8 7 6 0.0 0.2 0.4 0.6 0.8 1.0 Fraction fully smoothing noitcnuf ssoL Figure 11: Log MPC out up to 40 years (left-hand panel), sticky-expectations parameter ff estimate (middle panel), and loss function (right-hand panel) for di erent fractions of fully-smoothingagentsinthemodel. ff To address these concerns, I examine the e ects of replacing the baseline iMPC I use with a linear combination of the baseline iMPC and the iMPC that comes from a fullysmoothing agent. The left-hand panel of figure 11 shows how introducing a fraction of fully-smoothing agents changes the tail behavior of MPCs. The solid line shows the log MPCs from my baseline one-asset model, the dashed line shows those from a model in which 80 percent of agents are similar to those of the baseline model and 20 percent are fully smoothing, and the dotted line shows the iMPC of a model in which all agents fully smooth consumption. Compared to the baseline model, the model with 20 percent fully-smoothingagentsdisplaysafarslowerdeclineintheMPCintheverylongtail. This ff behavior captures the main di erence that also exists between a two-asset model and a one-asset model. Note that, relative to the one-asset model in Auclert et al. (2018), my baselinemodelalreadyhasaslowerdeclineinMPCsbecausemybaselinemodelincludes heterogeneityindiscountfactors. The middle panel of figure 11 shows that the sticky expectations parameter estimate is not sensitive to variation in the model in this way—the estimate is close to zero (and slightly negative) for all versions of the underlying model up to 100 percent fullysmoothingagents. However,asshownintheright-handpaneloffigure11,increasingthe fraction of fully-smoothing agents beyond around 0.2 in the model diminishes the fit of 38

themodeltotheempiricalimpulseresponsefunctions. Thisexerciseshowsthatstructuralshocksidentifiedintheliteratureshownoevidence ofintertemporalsubstitution,evenwhenviewedthroughthelensofolderrepresentativeagentmodels. However,theiMPCsimpliedbyheterogenousagentmodelsdoabetterjob of matching the impulse response data than representative agent models. Furthermore, theslowdeclineinthetailMPCsthatareafeatureoftwo-assetmodels,whichcangreatly ff increasefiscalmultipliersinsomegeneralequilibriumsettings,donothavealargee ect ontheestimationofstickyexpectationsinmysetup. 6 Conclusion In this paper, I have presented a new way to estimate the size of the intertemporal subff stitutione ectonhouseholdbehavior. Despitethetraditionalemphasisonintertemporal substitution as a pivotal factor in macroeconomic models influencing household conff ff sumption, I find no evidence of such an e ect across ten di erent structural shocks. This evidenceisinlinewithotherrecentadvancesintheheterogenousagentliterature,butby isolating the consumption block of the model I have been able to bring to bear a much wider array of empirical evidence. The finding that intertemporal substitution has little bearing on consumption behavior invites further research on the transmission of monetarypolicy,withapossibilitythatinvestmentbehaviordrivestheresponseorthatoutput islessresponsivetomonetarypolicythanpreviouslythought. 39

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A Description of the 10 shock series used MonetaryPolicyShocks Monetary policy shocks are some of the most studied structural shocks because ff economists and central bankers are naturally interested in the e ects of monetary policyoneconomicoutcomes. Ramey(2016)examinesrepresentativeshockseriesfromthree ff di erent methods for identifying monetary policy shocks. The first, from Christiano et al. (1999), uses a recursive assumption in a SVAR model. My analysis in this paper is on local projections, and I will not examine this shock series. The next two monetary policy shockseriesareincludedinmyanalysis. 1. Romer and Romer (2004). In this method, monetary policy shocks are identified by regressing the federal funds target rate on the Greenbook forecasts at each FOMC meetingandtakingtheresidualtobetheshock. 2. Gertler and Karadi (2015). This high frequency identification method uses changes to the three-month-ahead fed funds futures around a window of FOMC announcementstofindsurprisechangestothepolicyrate. FiscalShocks The fiscal shocks series I examine include both shocks to government spending and shockstoanticipatedtaxes. 3. Ramey and Zubairy (2018) military news. This method identifies changes in the expectedpresentvalueofgovernmentpurchases,causedbymilitaryevents. Specifically, the method involves reading BusinessWeek for such spending events in an ff e ort to capture the news of the event, rather than relying on spending data that mayhavealreadybeenanticipated. 4. Ben Zeev and Pappa (2017) defense spending shocks. This paper identifies news aboutfuturedefensespendingfollowingthemethodologyofBarskyandSims(2011). 44

Theseshocksarethosethatbestexplainfuturemovementsindefensespendingover afiveyeartimehorizon,andthatareorthogonaltocurrentdefensespending. 5. Blanchard and Perotti (2002) government spending. Government spending shocks areidentifiedviaaCholeskydecompositionofaVARinwhichgovernmentspending isorderedfirst. 6. Mertens and Ravn (2011) tax news shocks. The shocks in the paper build upon the tax shock series from Romer and Romer (2010) by dividing that shock series into anticipated and unanticipated shocks based on the delay between the passing of the legislation and the implementation of the legislation. In turn, Romer and Romer(2010)useanarrativeapproachtoidentifytaxshocks,lookingatpresidential speechesandcongressionalreports. 7. Leeper et al. (2012) expected taxes from one to five years forward. This measure of expected tax changes is based on the spread between federal and municipal bonds. ffi Theinsighthereisthat,ifassetmarketsaree cient,thespreadbetweentax-exempt municipalbondsandtreasurybondswillreflectanticipatedchangestotaxes. TechnologyShocks 8. BenZeevandKhan(2015)investment-specific(IST)newsshocks. FollowingGreenwoodetal.(2000),thispaperidentifiesinvestment-specifictechnologyastheinverse of the real price of investment. Then, using an adapted version of the maximum forecast error variance identification approach of Barsky and Sims (2011), IST news shockareidentifiedbyfindingthelinearcombinationofreduced-forminnovations that are orthogonal to both current TFP and current IST that maximizes the sum of contributionstoISTforecasterrorvarianceoverafinitehorizon. 9. Fernald (2014) utilization-adjusted TFP. This paper begins by measuring the Solow residual using inputs, including capital, to create a TFP series. This series is then 45

adjustedtoaccountforvariationsinfactorutilizationfollowingthemethodinBasu etal.(2006). TheshockseriesiscalculatedasthequarterlychangestothisutilizationadjustedTFPseries. 10. Francis et al. (2014) unanticipated TFP shocks. This paper identifies technology shocks by maximizing the contribution to the forecast-error variance of labor productivityatalonghorizon. B Input and output IRFs for the 10 structural shocks. Figures A.1 through A.10 show the four input IRFs along with the consumption IRF decomposed into its various components for all 10 shocks used in the paper. The Jacobians used in each decomposition are estimated using all 10 shocks with intertemporal substitutionrestrictedtobepositive(andinpracticeequaltozero). Ineachcase,author’scalculationsareperformedondatacompiledbytheauthorfrom Federal Reserve Economic Data (FRED), Federal Reserve Bank of St. Louis; replication files for Ramey (2016), ”Macroeconomic Shocks and Their Propagation”; and the Survey ofProfessionalForecasters,FederalReserveBankofPhiladelphia. 46

Real Fed Funds Income Stock Market Real Estate 3 0.2 0.5 1.0 2 0.4 0.5 0.0 0.3 1 0.0 0.2 0.2 0 0.1 0.5 1 0.0 0.4 1.0 0.1 2 1.5 0 10 0 10 0 10 0 10 Quarter Quarter Quarter Quarter Consumption 0.4 Empirical IRF Estimated IRF 0.3 90 percent CI 0.2 0.1 0.0 Estimated IRF Contributions 0.1 Income Stocks 0.2 Real Estate Intertemporal substitution with rational expectations (Actual estimated int. subs. contribution is zero) 0.3 0 2 4 6 8 10 12 14 16 Quarter FigureA.1: InputsandoutputIRFstotheconsumptionblockfollowingRomerandRomer (2004)monetarypolicyshock. Source: Author’s calculations and data compiled from Federal Reserve Economic Data (FRED), Federal Reserve Bank of St. Louis; replication files for Ramey (2016), and the SurveyofProfessionalForecasters,FederalReserveBankofPhiladelphia. 47

Real Fed Funds Income Stock Market Real Estate 0.4 0.5 2 5 0.2 0 0.0 0 0.0 2 0.5 0.2 5 4 1.0 0.4 10 0 10 0 10 0 10 0 10 Quarter Quarter Quarter Quarter Consumption 1.0 Empirical IRF Estimated IRF 90 percent CI 0.5 0.0 Estimated IRF Contributions Income 0.5 Stocks Real Estate Intertemporal substitution with rational expectations (Actual estimated int. subs. contribution is zero) 1.0 0 2 4 6 8 10 12 14 16 Quarter Figure A.2: Inputs and output IRFs to the consumption block following Gertler and Karadi(2015)monetarypolicyshock. Source: Author’s calculations and data compiled from Federal Reserve Economic Data (FRED), Federal Reserve Bank of St. Louis; replication files for Ramey (2016), and the SurveyofProfessionalForecasters,FederalReserveBankofPhiladelphia. 48

Real Fed Funds Income Stock Market Real Estate 4 0.2 0.8 4 0.6 2 3 0.0 0.4 0 2 0.2 0.2 2 0.4 1 0.0 4 0.6 0 0.2 6 0 10 0 10 0 10 0 10 Quarter Quarter Quarter Quarter Consumption Empirical IRF 0.8 Estimated IRF 0.6 90 percent CI 0.4 0.2 Estimated IRF Contributions 0.0 Income Stocks 0.2 Real Estate Intertemporal substitution with rational expectations 0.4 (Actual estimated int. subs. contribution is zero) 0 2 4 6 8 10 12 14 16 Quarter Figure A.3: Inputs and output IRFs to the consumption block following Ramey and Zubairy(2018)militarynewsshock. Source: Author’s calculations and data compiled from Federal Reserve Economic Data (FRED), Federal Reserve Bank of St. Louis; replication files for Ramey (2016), and the SurveyofProfessionalForecasters,FederalReserveBankofPhiladelphia. 49

Real Fed Funds Income Stock Market Real Estate 0.2 2 0.6 3 1 0.0 0.4 0 2 0.2 0.2 1 2 1 0.4 0.0 3 0.6 0.2 4 0 0 10 0 10 0 10 0 10 Quarter Quarter Quarter Quarter Consumption 0.6 Empirical IRF Estimated IRF 0.4 90 percent CI 0.2 Estimated IRF Contributions 0.0 Income Stocks Real Estate 0.2 Intertemporal substitution with rational expectations (Actual estimated int. subs. contribution is zero) 0 2 4 6 8 10 12 14 16 Quarter Figure A.4: Inputs and output IRFs to the consumption block following Ben Zeev and Pappa(2017)defensespendingshock. Source: Author’s calculations and data compiled from Federal Reserve Economic Data (FRED), Federal Reserve Bank of St. Louis; replication files for Ramey (2016), and the SurveyofProfessionalForecasters,FederalReserveBankofPhiladelphia. 50

Real Fed Funds Income Stock Market Real Estate 2 0.2 0.4 0 0 0.0 0.2 1 2 0.0 0.2 2 4 0.2 0.4 3 6 0 10 0 10 0 10 0 10 Quarter Quarter Quarter Quarter Consumption Empirical IRF 0.2 Estimated IRF 90 percent CI 0.0 0.2 Estimated IRF Contributions Income Stocks 0.4 Real Estate Intertemporal substitution with rational expectations (Actual estimated int. subs. contribution is zero) 0 2 4 6 8 10 12 14 16 Quarter Figure A.5: Inputs and output IRFs to the consumption block following Blanchard and Perotti(2002)governmentspendingshock. Source: Author’s calculations and data compiled from Federal Reserve Economic Data (FRED), Federal Reserve Bank of St. Louis; replication files for Ramey (2016), and the SurveyofProfessionalForecasters,FederalReserveBankofPhiladelphia. 51

Real Fed Funds Income Stock Market Real Estate 0.2 0.4 1 0.0 0 0.0 0.2 1 0.5 2 1.0 0.0 0.2 3 1.5 4 0.2 0.4 5 2.0 0.4 6 0 10 0 10 0 10 0 10 Quarter Quarter Quarter Quarter Consumption Empirical IRF 0.3 Estimated IRF 0.2 90 percent CI 0.1 0.0 Estimated IRF Contributions 0.1 Income Stocks 0.2 Real Estate Intertemporal substitution with rational expectations 0.3 (Actual estimated int. subs. contribution is zero) 0 2 4 6 8 10 12 14 16 Quarter Figure A.6: Inputs and output IRFs to the consumption block following Mertens and Ravn(2012)taxnewsshock. Source: Author’s calculations and data compiled from Federal Reserve Economic Data (FRED), Federal Reserve Bank of St. Louis; replication files for Ramey (2016), and the SurveyofProfessionalForecasters,FederalReserveBankofPhiladelphia. 52

Real Fed Funds Income Stock Market Real Estate 0.4 0.2 0 1.0 0.2 0.0 0.5 2 0.0 0.0 0.2 0.2 4 0.5 0.4 0.4 1.0 6 0.6 0 10 0 10 0 10 0 10 Quarter Quarter Quarter Quarter Consumption Empirical IRF Estimated IRF 0.2 90 percent CI 0.0 Estimated IRF Contributions 0.2 Income Stocks Real Estate Intertemporal substitution with rational expectations 0.4 (Actual estimated int. subs. contribution is zero) 0 2 4 6 8 10 12 14 16 Quarter Figure A.7: Inputs and output IRFs to the consumption block following Leeper et al. (2012)expectedtaxesshock. Source: Author’s calculations and data compiled from Federal Reserve Economic Data (FRED), Federal Reserve Bank of St. Louis; replication files for Ramey (2016), and the SurveyofProfessionalForecasters,FederalReserveBankofPhiladelphia. 53

Real Fed Funds Income Stock Market Real Estate 0.2 0 0.0 2 0.2 1 0.0 0.4 0 2 0.2 0.6 2 3 0.8 0.4 1.0 4 4 1.2 0.6 5 0 10 0 10 0 10 0 10 Quarter Quarter Quarter Quarter Consumption 0.4 Empirical IRF 0.2 Estimated IRF 90 percent CI 0.0 0.2 0.4 Estimated IRF Contributions 0.6 Income Stocks 0.8 Real Estate Intertemporal substitution with rational expectations (Actual estimated int. subs. contribution is zero) 1.0 0 2 4 6 8 10 12 14 16 Quarter Figure A.8: Inputs and output IRFs to the consumption block following Ben Zeev and Khan(2015)investmentspecificnewsshock. Source: Author’s calculations and data compiled from Federal Reserve Economic Data (FRED), Federal Reserve Bank of St. Louis; replication files for Ramey (2016), and the SurveyofProfessionalForecasters,FederalReserveBankofPhiladelphia. 54

Real Fed Funds Income Stock Market Real Estate 0.3 4 2.5 0.2 0.4 3 2.0 0.1 2 0.2 1.5 0.0 1 0.1 0.0 0 1.0 0.2 1 0.5 0.2 0.3 2 0.0 0 10 0 10 0 10 0 10 Quarter Quarter Quarter Quarter Consumption 0.5 Empirical IRF 0.4 Estimated IRF 0.3 90 percent CI 0.2 0.1 0.0 Estimated IRF Contributions Income 0.1 Stocks Real Estate 0.2 Intertemporal substitution with rational expectations (Actual estimated int. subs. contribution is zero) 0 2 4 6 8 10 12 14 16 Quarter Figure A.9: Inputs and output IRFs to the consumption block following Fernald (2014) utilization-adjustedTFPshock. Source: Author’s calculations and data compiled from Federal Reserve Economic Data (FRED), Federal Reserve Bank of St. Louis; replication files for Ramey (2016), and the SurveyofProfessionalForecasters,FederalReserveBankofPhiladelphia. 55

Real Fed Funds Income Stock Market Real Estate 0.2 4 0.5 0.3 3 0.0 0.2 0.0 2 0.5 0.1 0.2 1 1.0 0.0 0 1.5 0.1 0.4 1 2.0 0.2 2 0.6 2.5 0.3 3 0 10 0 10 0 10 0 10 Quarter Quarter Quarter Quarter Consumption 0.2 Empirical IRF Estimated IRF 90 percent CI 0.0 0.2 Estimated IRF Contributions Income 0.4 Stocks Real Estate Intertemporal substitution with rational expectations 0.6 (Actual estimated int. subs. contribution is zero) 0 2 4 6 8 10 12 14 16 Quarter Figure A.10: Inputs and output IRFs to the consumption block following Francis et al. (2014)unanticipatedTFPshock. Source: Author’s calculations and data compiled from Federal Reserve Economic Data (FRED), Federal Reserve Bank of St. Louis; replication files for Ramey (2016), and the SurveyofProfessionalForecasters,FederalReserveBankofPhiladelphia. 56