Bank Market Power and the Risk Channel of Monetary Policy

Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. Bank Market Power and the Risk Channel of Monetary Policy Elena Afanasyeva and Jochen Gu¨ntner 2018-006 Please cite this paper as: Afanasyeva, Elena, and Jochen Gu¨ntner (2018). “Bank Market Power and the Risk Channel of Monetary Policy,” Finance and Economics Discussion Series 2018-006. Washington: Board of Governors of the Federal Reserve System, https://doi.org/10.17016/FEDS.2018.006. 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.

(cid:73) Bank Market Power and the Risk Channel of Monetary Policy ThisVersion: January2018 ElenaAfanasyeva∗ 20thSt.andConstitutionAvenue,NW,20551Washington,DC,USA. Emailaddress:elena.afanasyeva@frb.gov. JochenGu¨ntner∗∗ Altenbergerstrasse69,4040Linz,Austria. Emailaddress:jochen.guentner@jku.at. Abstract This paper investigates the risk channel of monetary policy through banks’ lending standards. We modify the classic costly state verification (CSV) problem by introducing a risk-neutral monopolistic bank, which maximizesprofitssubjecttoborrowerparticipation. Whilethebankcandiversifyidiosyncraticdefaultrisk, itbearstheaggregaterisk. Weshowthat, inpartialequilibrium, thebankprefersahigherleverageratioof borrowers, when the profitability of lending increases, e.g. after a monetary expansion. This risk channel persistswhenweembedourcontractinastandardNewKeynesianDSGEmodel. Usingafactor-augmented vector autoregression (FAVAR) approach, we find that the model-implied impulse responses to a monetary policyshockreplicatetheirempiricalcounterparts. Keywords: Costlystateverification,Creditsupply,Lendingstandards,Monetarypolicy,Riskchannel JELclassification: D53,E44,E52 (cid:73)WewishtothankArpadAbraham,TobiasAdrian,PooyanAmirAhmadi,MartinEichenbaum,EsterFaia,HansGersbach, MarkGertler,YuriyGorodnichenko,CharlesKahn,Jean-CharlesRochet,EmilianoSantoro,MirkoWiederholt,VolkerWieland, and Tao Zha as well as participants at the 2014 Cologne Workshop on Macroeconomics, the 3rd Macro Banking and Finance Workshop in Pavia, the XIX Vigo Workshop on Dynamic Macroeconomics, the Birkbeck Centre for Applied Macroeconomics Workshop,andseminarparticipantsatCESifo,Stanford,Northwestern,ViennaandtheFederalReserveBoardforhelpfulcomments.ElenaAfanasyevagratefullyacknowledgesfinancialsupportbytheGermanResearchFoundation(DFGgrantWI2260/1-1, 584949)andtheFP7ResearchandInnovationFundingProgram(grantFP7-SSH-2013-2). Anearlierversionofthepaperwas previouslycirculatedunderthetitle”LendingStandards,CreditBooms,andMonetaryPolicy”. ∗ElenaAfanasyevaisEconomistattheBoardofGovernorsoftheFederalReserveSystem.Thispaperreflectstheviewsofthe authorsandshouldnotbeinterpretedasreflectingtheviewsoftheBoardofGovernorsoftheFederalReserveSystemorofanyone elseassociatedwiththeFederalReserveSystem. ∗∗JochenGu¨ntnerisAssistantProfessorattheDepartmentofEconomics,JohannesKeplerUniversityLinz.

1. Introduction One of the narrative explanations of the credit boom preceding the recent financial crisis and the Great Recessionisthatfinancialintermediariestookexcessiverisksbecausemonetarypolicyrateshadbeen“too low for too long” (compare Taylor, 2007). On the one hand, loose monetary policy lowers the wholesale fundingcostsofbanksandotherfinancialintermediaries,incentivizinghigherleverageandthusriskonthe liability side of their balance sheets. On the other hand, low policy interest rates might also induce banks to lower their lending standards, i.e. to grant more and riskier loans. While risk taking on the liability side has received a lot of attention in the recent macroeconomic literature (see, e.g., Gertler and Karadi, 2011; Gertleretal.,2012),muchfewerstudieshavesofaraddressedtheaggregateimplicationsofariskchannel ofmonetarypolicyontheassetside. Thepresentpaperaimsatclosingthisgapbyfocusingontheex-ante riskattitudeofbanks. Wedevelopageneralequilibriummodel,wherethefinancialintermediarydetermines lendingstandardsbychoosinghowmuchtolendagainstagivenamountofborrowercollateral. Testingour theoreticalpredictionsempirically,wefindrobustevidenceforanasset-sideriskchannelofmonetarypolicy intheU.S.bankingsector,consistentwiththemodel. Inthispaper,weprovideamicroeconomicfoundationforbanks’decisiontolowertheir“lendingstandards”inresponsetoamonetaryexpansion. Tothisend,wereformulatethecostlystateverification(CSV) contractinTownsend(1979)andGaleandHellwig(1985)inordertoallowforanontrivialroleoffinancial intermediaries. TheCSVcontractprovidesanaturalstartingpoint,giventhatitspartiesdetermineboththe quantityofcredit(viatheamountlent)andthequalityofcredit(viatheborrower’sex-anteimplieddefault risk). However,inconventionalimplementationsofthecontractinmodelsofthefinancialaccelerator,such asBernankeetal.(1999),financialintermediariesarepassiveanddonotbearanyrisk. Wedepartfromtheseassumptionsandintroduceamonopolisticbankthatchoosesitslendingstandards. The resulting contract is incentive-compatible, robust to ex-post renegotiations, and resembles a standard debtcontract(compareGaleandHellwig,1985). Italsoimpliesauniquepartialequilibriumsolutionandthe well-knownpositiverelationshipbetweentheexpectedexternalfinancepremium(EFP)andtheborrower’s leverageratio. FollowinganexogenousincreaseintheexpectedEFP,e.g.duetoamonetaryexpansion,the monopolisticbankfindsitprofitabletolendmoreagainstagivenamountofborrowercollateral. Thereason is that it benefits from the increase in borrower leverage through a larger share in total profits, while it can price in the higher default probability of the borrower through the rate of return on non-defaulting loans, 2

thusincreasingitsnetinterestmargin. Inordertoquantifytheeffectsofourpartialequilibriummechanisminresponsetoamonetaryexpansion and over the business cycle, we embed our modified and the classic version of the optimal debt contract in an otherwise standard New Keynesian dynamic stochastic general equilibrium (DSGE) model. In contrast toBernankeetal.(1999)andmostoftheexistingliterature,ourmodelimpliesanincreaseinbanklending relativetoborrowercollateralandthusahigherleverageratioofborrowersinresponsetoanexpansionary monetarypolicyshock. Overthebusinesscycle,bothmodelscanreplicatethedynamiccross-correlationsof keyvariableswithoutputqualitativelyandquantitatively,whileourmodelalsoreplicatestheunconditional moments of bank-related balance sheet variables that are either missing or constant in standard models of thefinancialaccelerator. Prior research based on microeconomic bank-level data (Jime´nez et al., 2014; Ioannidou et al., 2015) hasshownthatlowerovernightinterestratesmightinducebankstocommitlargerloanvolumeswithfewer collateral requirement to ex-ante riskier firms. Similarly, Paligorova and Santos (2017) use bank-loan data andfindcompellingevidenceinfavoroftherisk-takingchannelofmonetarypolicyintheU.S.Formacroeconomictimeseries,theresultsintheliteratureareratherambiguous(see,e.g.,Buchetal.,2014). Theuse of aggregated data in this context is complicated by the limited availability of suitable measures of banks’ riskappetiteandacomparativelyshortsampleperiod. Ontheonehand,econometricmodelswithanexcessivenumberofparametersarethuspronetooverfitting. Ontheotherhand,small-scaleVARmodelsmight contain insufficient information to identify the structural shocks of interest (compare Forni and Gambetti, 2014). To address these issues, we adopt the factor-augmented vector autoregression (FAVAR) approach proposed by Bernanke et al. (2005), which allows us to parsimoniously extract information from a large set of macroeconomic time series, thereby mitigating both the concern of overfitting and the concern of informationalsufficiency. Tocapturethecredit-riskattitudeofbanks,weusethequantifiedqualitativemeasuresfromtheFederal Reserve’sSeniorLoanOfficerOpinionSurveyonBankLendingPractices(SLOOS)1,whichreflectchanges inlendingstandardsoflargedomesticaswellasU.S.branchesandagenciesofforeignbanksataquarterly frequency,startingin1991Q1. Incontrasttothepriorempiricalliterature,weconsider19differentmeasures of lending standards, such as the net percentage of banks increasing collateral requirements or tightening 1Thesedataarepubliclyavailableathttps://www.federalreserve.gov/data/sloos/sloos.htm. 3

loan covenants for various categories of loans, borrowers and banks, in order to capture the comovement intheunderlyingtimeseries. BasedonBernankeetal.’s(2005)one-stepBayesianestimationapproachby Gibbssamplingwithrecursiveidentificationofmonetarypolicyshocks,wefindthatall19SLOOSmeasures of lending standards decrease in response to a monetary expansion. This loosening of lending standards is accompanied by an increase in loan riskiness2, the net interest margin and bank profits from the so-called CallReportsthatisqualitativelyandquantitativelyinlinewithourtheoreticalpredictions. Our empirical findings are qualitatively robust to variations in the FAVAR specification and alternative identificationstrategies. InlightofrecentevidencethatU.S.monetarypolicybecamemoreforward-looking duringoursampleperiod,weincludevariablesfromtheFed’sGreenbookintheFAVARobservationequation. Amongfurtherrobustnesschecks,weadoptthehigh-frequencyidentificationapproachinBarakchian andCrowe(2013),whichdoesnotrelyonaVARspecification. We finally find that our results carry over to alternative measures of financial intermediaries’ risk appetite. Inparticular,weshowthatBassettetal.’s(2014)measureofthesupplycomponentofbanklending standardsdecreases,whilethenetpercentageofdomesticbankseasinglendingstandardsduetohigherrisk tolerance increases in response to a monetary expansion. Moreover, two market-based measures of lending standards – Gilchrist and Zakrajsˇek’s (2012) “excess bond premium” and the Chicago Fed’s National FinancialConditionscreditsubindex–decreasesignificantlyafteranexpansionarymonetarypolicyshock. Theremainderofourpaperisorganizedasfollows. Section2derivestheoptimalfinancialcontractand discussestheriskchannelinpartialequilibrium. InSection3,weembedthiscontractinaquantitativeNew KeynesianDSGEmodel. Section4sketchesoureconometricapproachandpresentsnewempiricalevidence ofanasset-sideriskchannelofmonetarypolicyintheU.S.bankingsector. Section5concludes. 2. TheOptimalDebtContractinPartialEquilibrium In this section, we show that it can be optimal for a lender to increase the amount of credit per unit of borrowercollateralinresponsetoexpansionarymonetarypolicy,evenifthisraisesthedefaultprobabilityof agivenborrowerandthedefaultrateacrossborrowers. Inotherwords,thelenderlowersitscreditstandards. Tothisend,wedrawonaproblemofthetypeanalyzedinTownsend(1979)andGaleandHellwig(1985), andembeddedinaNewKeynesianDSGEmodelbyBernankeetal.(1999). TheCSVcontractaccountsfor 2LoanriskinessismeasuredasanaverageriskscorefromtheTermsofBusinessLendingSurveyoftheFederalReserve. 4

bothdimensionsofacreditexpansion: (i)thequantityofcredit,i.e.theamountlent,and(ii)thequalityof credit,i.e.theexpecteddefaultthresholdoftheborrowerthatabankiswillingtotolerate. Itprovidesthusa micro-foundationforbanks’optimaldecisiononlendingstandardsduringacreditexpansion. In contrast to Bernanke et al. (1999) and most recent contributions, we formulate the optimal financial contractfromthelender’sperspective.3 Inparticular,weassumethatarisk-neutralbankdecideshowmuch tolendagainstagivenamountofborrowercollateral. Accordingly,thebankdeterminestheentrepreneur’s total capital expenditure and expected default threshold. Note that introducing an active financial intermediaryisaprerequisiteforanalyzingtheeffectofmonetarypolicyonbanklendingstandards. Inourmodel, thelatterareendogenouslydeterminedthroughthebank’sconstrainedprofit-maximizationproblem. We further assume that market power in the credit market is in the hands of the bank, which makes a “take-it-or-leave-it”loanoffertoborrowers,similartothatinValencia(2014). Inorderforafirmtoaccept thisoffer,itmustbeatleastaswelloffwithaswithouttheloan. Whilerepresentingoneofmanyconceivable profit-sharing agreements, this can be motivated by the prevalence of relationship lending between banks andsmallormedium-sizedenterprises.4 Inwhatfollows,wespecifythedetailsoftheoptimalloancontract in partial equilibrium. Assuming that each entrepreneur borrows from at most one bank, the latter can enter a contract with one entrepreneur independently of its relations with others, and we can consider a representativebank-entrepreneurpairing(compareGaleandHellwig,1985). 2.1. TheContractingProblem Suppose that, at time t, entrepreneur i purchases capital Q Ki for use at t+1, where Ki is the quantity t t t ofcapitalpurchasedandQ isthepriceofoneunitofcapitalinperiodt. Thegrossreturnperunitofcapital t expenditure by entrepreneur i, ωi Rk , depends on the ex-post aggregate return on capital, Rk , and an t+1 t+1 t+1 idiosyncraticcomponent,ωi . FollowingBernankeetal.(1999),therandomvariableωi ∈ [0,∞)isi.i.d. t+1 t+1 acrossentrepreneursiandtimet,withacontinuousanddifferentiablecumulativedistributionfunctionF(ω) andanexpectedvalueofunity. 3Recallthat,inBernankeetal.(1999),thereisnoactiverolefortheso-called“financialintermediary”,whichmerelydiversifies awaytheidiosyncraticproductivityrisksofentrepreneursandinstitutionalizestheparticipationconstraintofarisk-aversedepositor, alongwhichthefirmmoveswhenmakingitsoptimalcapitalandborrowingdecision. 4Forexample,PetersenandRajan(1995)useasimpledynamicsettingtoshowthatthevalueoflendingrelationshipsdecreases inthedegreeofcompetitionincreditmarkets. Thereasonisthatamonopolistlendercanpostponeinterestpaymentsinorderto extractfuturerentsfromtheborrowingfirm,effectively“subsidizingthefirmwhenyoungordistressedandextractingrentslater” (PetersenandRajan,1995,p.408).Asimilarargumentappliesforthemonopolistbankinourmodel,whichcanfullydiversifythe idiosyncraticproductivityrisksbylendingtotheentirecrosssectionoffirms. 5

Entrepreneurifinancescapitalpurchasesattheendofperiodtusingaccumulatednetworth,Ni,aswell t astheborrowedamount Bi,sothattheentrepreneur’sbalancesheetisgivenby t Q Ki = Ni+Bi. (1) t t t t Abstracting from alternative investment opportunities of entrepreneurs, the maximum equity participation(MEP)conditioninGaleandHellwig(1985)istriviallysatisfied.5 AsinValencia(2014),entrepreneur iborrowstheamount Bi fromamonopolisticbank,thatisendowedwithend-of-period-t networthorbank t capitalNbandraisesdepositsD fromhouseholds. DefiningaggregatelendingtoborrowersasB ≡ (cid:82)1 Bidi, t t t 0 t thebank’saggregatebalancesheetidentityinperiodtisgivenby B ≡ Nb+D. (2) t t t The need for borrower collateral arises from the presence of a state-verification cost paid by the lender in order to observe entrepreneur i’s realization of ωi , which is private information. We assume that this t+1 costcorrespondstoafixedproportionµ ∈ (0,1]oftheentrepreneur’stotalreturnoncapitalinperiodt+1, ωi Rk Q Ki,sothatinitiallyuninformedagentsmaybecomeinformedbypayingafeewhichdependson t+1 t+1 t t theinvestedamountandthestate(compareTownsend,1979). Boththeborrowerandthelenderarerisk-neutralandcareaboutexpectedreturnsonly,whereasdepositorsarerisk-averse. Accordingly,thebankpromisestopaytherisk-freegrossrateofreturnRn ondeposits t ineachaggregatestateoftheworld,ascharacterizedbytherealizationofRk . t+1 Let Zi denote the gross non-default rate of return on the period-t loan to entrepreneur i. Given Rk , t t+1 Q Ki,andNi,thefinancialcontractdefinesarelationshipbetweenZi andanex-postcutoffvalue t t t t ZiBi ω¯i ≡ t t , (3) t+1 Rk Q Ki t+1 t t (cid:16) (cid:17) suchthattheborrowerpaysthelenderthefixedamountω¯i Rk Q Kiandkeepstheresidual ωi −ω¯i · t+1 t+1 t t t+1 t+1 Rk Q Ki ifωi ≥ ω¯i . Ifωi < ω¯i ,thelendermonitorstheborrower,incurstheCSVcost,andextracts t+1 t t t+1 t+1 t+1 t+1 theremainder(1−µ)ωi Rk Q Ki,whiletheentrepreneurdefaultsandreceivesnothing. t+1 t+1 t t In contrast to Bernanke et al. (1999), we assume that the lender determines the amount of credit to entrepreneuri, Bi, foragivenamountofborrowercollateral, Ni. Yet, theentrepreneurwillonlyacceptthe t t 5Proposition2inGaleandHellwig(1985)statesthatanyoptimalcontractisweaklydominatedbyacontractwithMEP,where thefirmputsallofitsownliquidassets–hereNi–onthetable. t 6

bank’s loan offer if the corresponding expected return is at least as large as in “financial autarky”, without thebankloan: E   (cid:90) ∞ (cid:16) ω−ω¯i (cid:17) Rk Q KidF(ω)   ≥ E (cid:40)(cid:90) ∞ ωRk NidF(ω) (cid:41) = E Rk Ni, (4) t ω¯i t+1 t+1 t t  t 0 t+1 t t t+1 t t+1 where the last equality uses the assumption that (cid:82)∞ ωdF(ω) = E(ω) = 1. Hence, the bank must promise 0 the borrower an expected return no smaller than the expected return from investing her own net worth, Ni, t whichimpliesthatinvestmentopportunitiesarecontinuousanddonothaveaminimumsize. Thebank’sexpectedgrossreturnonaloantoentrepreneuricanbewrittenas   E  ω¯i (cid:104) 1−F (cid:16) ω¯i (cid:17)(cid:105) +(1−µ) (cid:90) ω¯i t+1 ωdF(ω)  Rk Q Ki. t t+1 t+1  t+1 t t 0 Giventhatthebankpaystherisk-freerateofreturn,Rn,ondeposits,whileweassumethatnocostsaccrueon t (cid:16) (cid:17) (cid:16) (cid:17) itsownnetworth,Nb,thebank’saggregatefundingcostsequalRnD = Rn B −Nb = Rn Q K −N −Nb . t t t t t t t t t t t Supposethatthebankassigns Nb,i ofitstotalnetworth, Nb,totheloantoentrepreneuri.6 Thenthebank’s t t constrainedprofitmaximizationproblemforaloantoentrepreneuriisgivenby   max E  ω¯i (cid:104) 1−F (cid:16) ω¯i (cid:17)(cid:105) +(1−µ) (cid:90) ω¯i t+1 ωdF(ω)  Rk Q Ki−Rn (cid:16) Q Ki−Ni−Nb,i (cid:17) , (5) K t i,ω¯i t+1 t t+1 t+1 0  t+1 t t t t t t t   s.t. E  (cid:90) ∞ (cid:16) ω−ω¯i (cid:17) Rk Q KidF(ω)  ≥ E Rk Ni. t ω¯i t+1 t+1 t t  t t+1 t t+1 2.2. TheContractwithoutAggregateRisk As a starting point, consider the case when the aggregate return on capital, Rk , is known in advance. t+1 As a consequence, the only risk immanent in the loan contract between the bank and entrepreneur i arises fromtheidiosyncraticproductivityrealization,ωi . t+1 Given that the non-default repayment on the loan to entrepreneur i, ZiBi, is constant across all unobt t served ω-states and the CSV cost is a fixed proportion µ of the entrepreneur’s total return, the financial contractisincentive-compatibleaccordingtoProposition1inGaleandHellwig(1985). Thecontractwithoutaggregateriskfurtherresemblesastandarddebtcontract (SDC),since(i)itinvolvesafixedrepayment to the lender as long as the borrower is solvent, (ii) the borrower’s inability to repay is a necessary and 6Weonlyconsidercaseswhereaggregateshocksaresmallenough, sothatthebankneverdefaults. Asaconsequence, the assignmentofbankcapitaltoaparticularloaniiswithoutlossofgeneralityandmainlyfornotationalconsistency. 7

sufficient condition for bankruptcy, and (iii) if the borrower defaults, the bank recovers as much as it can.7 Hence, the optimal contract between the bank and each entrepreneur is a SDC with MEP, as in Bernanke et al. (1999). Moreover, the optimal contract is robust to ex-post renegotiations, if µ represents a pure verification cost rather than a bankruptcy cost. In the latter case, it would be optimal to renegotiate the terms of the loan ex post in order to avoid default, whereas, in the former case, incentive compatibility requires monitoringtheborrowerwheneverheorshecannotrepay.8 Fornotationalconvenience,let (cid:16) (cid:17) (cid:104) (cid:16) (cid:17)(cid:105) (cid:90) ω¯i t (cid:16) (cid:17) (cid:90) ω¯i t Γ ω¯i ≡ ω¯i 1−F ω¯i + ωdF(ω) and µG ω¯i = µ ωdF(ω) t t t t 0 0 denote the expected share of total profits and the expected CSV costs accruing to the lender in period t, (cid:16) (cid:17) where0 < Γ ω¯i < 1bydefinition,andnotethat t (cid:16) (cid:17) (cid:16) (cid:17) (cid:16) (cid:17) (cid:16) (cid:17) (cid:16) (cid:17) (cid:16) (cid:17) Γ(cid:48) ω¯i = 1−F ω¯i > 0, Γ(cid:48)(cid:48) ω¯i = −f ω¯i < 0, µG(cid:48) ω¯i ≡ µω¯if ω¯i > 0. t t t t t t t Wecanthenwritetheexpectedshareoftotalprofitsnetofmonitoringcostsreceivedbythelenderandthe (cid:16) (cid:17) (cid:16) (cid:17) (cid:16) (cid:17) expectedshareoftotalprofitsgoingtotheborrowerasΓ ω¯i −µG ω¯i and1−Γ ω¯i ,respectively. t t t Defining the expected external finance premium (EFP), s ≡ Rk /Rn, the entrepreneur’s capital/net t t+1 t worthratio,ki ≡ Q Ki/Ni,aswellasni ≡ Nb,i/Niandusingtheabovenotation,thebank’sconstrainedprofit t t t t t t t maximizationproblemin(5)canequivalentlybewrittenas (cid:104) (cid:105) (cid:104) (cid:105) max Γ(ω¯i )−µG(ω¯i ) ski−(ki−1−ni) s.t. 1−Γ(ω¯i ) ski = s, (6) t+1 t+1 t t t t t+1 t t t ki,ω¯i t t+1 wherewehaveomittedtheexpectationsoperator,sinceRk andthuss areassumedtobeknowninadvance. t+1 t Thecorrespondingfirst-orderconditionswithrespecttoki,ω¯i ,andtheLagrangemultiplierλi are t t+1 t (cid:104) (cid:105) (cid:104) (cid:105) ki : Γ(ω¯i )−µG(ω¯i ) s −1+λi 1−Γ(ω¯i ) s = 0, t t+1 t+1 t t t+1 t (cid:104) (cid:105) ω¯i : Γ(cid:48)(ω¯i )−µG(cid:48)(ω¯i ) ski−λiΓ(cid:48)(ω¯i )ski = 0, t+1 t+1 t+1 t t t t+1 t t (cid:104) (cid:105) λi : 1−Γ(ω¯i ) ski−s = 0. t t+1 t t t 7Proposition3inGaleandHellwig(1985)statesthatanycontractisweaklydominatedbyaSDCwiththeabovethreefeatures. 8ThecentralassumptionisthatthebankincurstheCSVcostinordertoverifytheentrepreneur’sidiosyncraticrealizationofω beforeagreeingtorenegotiate,becausetheborrowercannottruthfullyreportdefaultwithouttheriskofbeingmonitored(compare CovasandDenHaan,2012). 8

Figure1:IllustrationoftheOptimalCSVContractwithoutAggregateRiskandtheEffectsofExpansionaryMonetaryPolicy. 5.5 5 4.5 4 3.5 3 2.5 2 1.5 1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 ω )ω(k Iso profit curves (lender) Participation constraint (borrower) 6 5.5 5 4.5 4 3.5 3 2.5 2 1.5 1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 ω )ω(k Old iso profit curves (lender) New iso profit curves (lender) Participation constraint (borrower) 2.8 2.6 2.4 2.2 2 1.8 1.6 1.4 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 ω∗ ω ω∗ old new ∗ k )ω(k ∗ k wen dlo Old tangential iso profit curve (lender) New tangential iso profit curve (lender) Participation constraint (borrower) 9

Proposition1. Theoptimalcontractimpliesapositiverelationship,ki = ψ(s)withψ(cid:48)(s) > 0,betweenthe t t t expectedEFP, s ≡ Rk /Rn,andtheoptimalcapital/networthratio,ki ≡ Q Ki/Ni. t t+1 t t t t t Proof. SeeAppendixA.1. Accordingly,anexogenousincreaseintheexpectedEFP,forexampleduetoareductionintherisk-free rate,Rn,inducesthebanktolendmoreagainstagivenamountofborrowernetworthandthuscollateral. t 2.3. TheRiskChannel ThemechanismdrivingourpartialequilibriumresultisillustratedinFigure1,wheretimesubscriptsand indexsuperscriptsaresuppressedfornotationalconvenience. Notethatthelender’siso-profitcurves(IPCs) andtheborrower’sparticipationconstraint(PC)canbeplottedin(k,ω¯)-spaceandthattheconstrainedprofit maximum of the bank is determined by the tangential point between the PC and the (lowest) IPC.9 The correspondingexpressionsfortheborrower’sPCandthelender’sIPCare 1 k ≥ (7) PC 1−Γ(ω¯) and πb−1−n k IPC = (cid:2)Γ(ω¯)−µG(ω¯) (cid:3) s−1 , (8) whereπb denotesanarbitrarylevelofbankprofits. From(7),thePCisnotaffectedbytheEFP, s. Intheabsenceofaggregaterisk,theborrower’sexpected shareoftotalprofits,1−Γ(ω¯),mustbenosmallerthanher“skininthegame”,1/k ≡ N/QK. Foranygiven ω¯ andthusanexpectedshareoftotalprofits,theborrower’sPCdeterminesaminimumvalueofthelender’s “skin in the game”, k, below which the entrepreneur does not accept the offered loan contract. The bank’s IPC in (8) accounts for expected monitoring and funding costs. By choosing the tangential point between theborrower’sPCanditslowestIPCin(k,ω¯)-space, thebankminimizesits“skininthegame”foragiven expected share of total profits, Γ(ω¯). Note that, for QK = N, the borrower is fully self-financed, never defaults(ω¯ = 0),andretainsalltheprofits(1−Γ(0) = 1). The first panel of Figure 1 illustrates the tangential point between the borrower’s PC and the lender’s IPC for the calibration in Bernanke et al. (1999). Now consider the effects of a monetary expansion, i.e. 9OnlineAppendixA.1provesthattheoptimalcontractyieldsauniqueinteriorsolution. 10

a decrease in Rn and thus an increase in s ≡ Rk/Rn, where Rk is known in advance. While the borrower’s PC remains unaffected, the lender’s IPCs are tilted upwards, as shown in the second panel. Although the borrower would accept any point above its PC on the new IPC, this is no longer optimal from the lender’s perspective. ThebankcanmovetoalowerIPCandthustoahigherlevelofprofits,asindicatedinthethird panel. In doing so, however, it must satisfy the borrower’s PC, as in the new optimal contract (k∗ ,ω∗ ), new new whereboththebank’sexpectedprofitshare,Γ(ω¯),andits“skininthegame”,k,haveincreased. Thepreviousdiscussionillustratesacrucialfeatureoftheoptimaldebtcontract. Foraprofit-maximizing bank,itisoptimaltorespondtoanincreaseintheEFP(e.g.duetoamonetaryexpansion)bylendingmore againstagivenamountofcollateral,thusincreasingtheentrepreneur’sleverageratio. Inpartialequilibrium, asimilarqualitativeresultarisesfromtheoptimaldebtcontractinBernankeetal.(1999),yetforadifferent reason. Inparticular,financialintermediariesmakezeroprofitsandthelender’sPCjustequatestheexpected return on the loan net of monitoring costs to the risk-free rate. A monetary expansion loosens the PC and inducestheentrepreneurtoraisemoreexternalfundsagainstagivenamountofcollateral,whiletheexpected return to the lender decreases. The expansion of credit is therefore driven by a shift in demand due to the increasedcreditworthinessofborrowers. In contrast, the increase in the borrower’s leverage ratio in Figure 1 represents the optimal response of thebank. Inourmodel,amonetaryexpansionlowerstheinterestrateondepositsandthusthefundingcost of the lender in (5), while it does not affect the borrower’s PC in (4). Ceteris paribus, the profitability of the marginal loan increases, whereas the demand for credit is unchanged. Since entrepreneurs’ net worth is predetermined, the increase in lending leads to an increase in borrower leverage. From (3), the higher leverage ratio implies a higher default threshold, ω¯, and a higher default probability of the loan. This correspondstotherisk-takingchannelofmonetarypolicydescribed,forexample,inAdrianandShin(2011) and Borio and Zhu (2012). By affecting the rates of return on both sides of the bank’s balance sheet, a monetary expansion raises the profitability of financial intermediaries, thus shifting the supply of credit. While moving along the borrower’s PC, the bank must compensate the entrepreneur for a lower share of totalprofitsbyincreasingitsown“skininthegame”. 2.4. TheContractwithAggregateRisk Inthedynamicmodel,theaggregatereturnoncapitalisexanteuncertain. Asaconsequence,thedefault threshold characterizing a loan contract between the bank and entrepreneur i, ω¯i , generally depends on t+1 11

the ex-post realization of Rk . Bernanke et al. (1999) circumvent this complication by presuming that, t+1 given the risk aversion of depositors, the lender’s participation constraint must be satisfied ex post and the entrepreneurbearsanyaggregaterisk. Similarly,weassumethattheborrower’sPCmustbesatisfiedexpost andthatthebankabsorbsanyaggregaterisk. Thisassumptionisonlyviable,ifthebank’scapitalbuffer,Nb, t issufficienttoshielddepositorsfromanyfluctuationsinRk ,sothatthebankneverdefaults.10 t+1 Inordertounderstandtheimplicationsofourassumption,recallthePCinequation(7). Giventhatthe borrower’scapitalexpenditure,Q Ki,andnetworth,Ni,arepredeterminedinperiodt+1,theex-postshare t t t (cid:16) (cid:17) of total profits, 1−Γ ω¯i , and the corresponding default threshold, ω¯i , can not be made contingent on t+1 t+1 the aggregate state of the economy. From the definition of the cutoff in (3), the non-default rate of return, Zi,mustthenbestate-contingentinordertooffsetunexpectedrealizationsofRk . t t+1 IncontrasttoBernankeetal.(1999),wherebothω¯i andZiarestate-contingentandcountercyclical(in t+1 t thesensethatahigherthanexpectedrealizationofRk lowersthedefaultthresholdandthenon-defaultrate t+1 of return required by the lender), here ω¯i is predetermined and acyclical, while Zi is procyclical. Higher t+1 t than expected realizations of Rk raise Zi, whereas the borrower’s and the lender’s expected profit shares t+1 t aredeterminedbytheir“skininthegame”,i.e.bytherelativesharesofNi andBi inQ Ki. Althoughneither t t t t oftheex-postversionsseemsfullyconsistentwiththecommonperceptionthatthenon-defaultrateofreturn onbankcreditispredeterminedandthusacyclical,theprocyclicalityofZi inourcontractcanbeinterpreted t asthebankhavingastakeinthefirmintermsofeitherequityoralong-termlendingrelationship. Hence,it isinthebank’sinterestthatborrowersdefaultonlyduetoidiosyncraticrisk,whichcanbediversifiedaway, ratherthanduetoaggregaterisk. Whileaformalproofisbeyondthescopeofthecurrentpaper,Appendix A.3providesasimpleheuristicalargumentfortheoptimalityofthisrisk-sharingagreement. The ex-post version of our financial contract is incentive-compatible and resembles a standard debt contract,ifandonlyifRk isobservedbybothpartieswithoutincurringacost(compareGaleandHellwig, t+1 1985).11 Otherwise, the non-default rate of return on the loan, Zi, can not be made contingent on the state t oftheeconomy,whereasentrepreneursgenerallyhavenoincentivetomisreportatrueobservedstate. 10Inotherwords,weassumethatthefluctuationsinthebank’snetreturnonlending, (cid:82)1 (cid:104) Γ (cid:16) ω¯i (cid:17) −µG (cid:16) ω¯i (cid:17)(cid:105) Rk QKidi,are 0 t+1 t+1 t+1 t t smallenoughtobeabsorbedwithoutthebankdefaulting. 11Onecouldarguethat,byholdingaperfectlydiversifiedloanportfolio,thebankcandeducetheex-postrealizationofRk , t+1 unlessentrepreneursmisreporttheirreturnsinanunobservedstateinasystematicwayacrossi. However,wealreadyknowthat entrepreneurshavenoincentivetolie,ifZiisindependentofωi . NotethatasimilarargumentmustimplicitlyholdinBernanke t t+1 etal.(1999)foroptimality. 12

Proposition2. Eveninthecasewithaggregaterisk,theoptimalcontractbetweenthebankandentrepreneur (cid:110) (cid:111) i implies a positive relationship, ki = ψ(s) with ψ(cid:48)(s) > 0, between the expected EFP, s ≡ E Rk /Rn, t t t t t t+1 t andtheoptimalcapital/networthratio,ki ≡ Q Ki/Ni. t t t t Proof. SeeAppendixA.2. 3. TheGeneralEquilibriumModel Whiletheprevioussectionillustratesthatamonetaryexpansionmightinduceaprofit-maximizingbank to lower its lending standards, the partial equilibrium analysis is confined to variables specified in the contract. In what follows, we embed both our optimal debt contract and the contract in Bernanke et al. (1999) inanotherwisestandardNewKeynesianDSGEmodelinordertobeabletoquantifytheirimplicationsfor avarietyofmacroeconomicvariables,inresponsetoamonetarypolicyshockandoverthebusinesscycle. Thegeneralequilibriummodelcompriseseighttypesofeconomicagents: Arepresentativehousehold, perfectly competitive capital goods and intermediate goods producers, a continuum of monopolistically competitivelaborunionsandretailers,respectively,amonetaryauthority,acontinuumofentrepreneurs,and a monopolistic bank. Since we borrow the former six from the existing literature, only entrepreneurs and thebankarediscussedhereindetail. 3.1. TheModelEnvironment Therepresentativehouseholdsupplieshomogeneouslabortomonopolisticallycompetitivelaborunions, consumes,andsavesintermsofrisk-freebankdeposits. Therepresentativecapitalgoodsproducerbuysthe non-depreciatedcapitalstockfromentrepreneurs,makesaninvestmentdecisionsubjecttoadjustmentcosts, and sells the new capital stock to entrepreneurs within the same period without incurring any capital gains orlosses. Therepresentativeintermediategoodsproducerrentscapitalfromentrepreneurs,hireslaborfrom laborunions,andsellsintermediateoutputtoretailersinacompetitivewholesalemarket. Retailers(unions) diversify the homogeneous intermediate good (labor input of households) without incurring any costs and arethusabletosetthepriceonfinaloutput(wage)abovetheirmarginalcost,i.e.thepriceoftheintermediate good.12 Monetary policy follows a standard Taylor (1993) rule. Since the optimization problems of these 12Monopolisticallycompetitivelaborunionsandretailersareintroducedinordertoallowfornominalwageandpricerigidities withoutunnecessarilycomplicatingtheproductionandinvestmentdecisionsoffirms(compareBernankeetal.,1999). 13

agents are standard in the literature, we defer a detailed discussion to Appendix B, focusing instead on the optimalbehaviorofcompetitiveentrepreneursandthemonopolisticbankingeneralequilibrium. 3.1.1. Entrepreneurs Attheendofperiodt,entrepreneursusetheiraccumulatednetworth,N,topurchaseproductivecapital, t K,fromcapitalgoodsproducersataprice Q intermsofthenumeraire. Tofinancethedifferencebetween t t theirnetworthandtheirtotalcapitalexpenditures,entrepreneursmustborrowanamount B = Q K −N in t t t t realtermsfrombanks,wherevariableswithoutanindexsuperscriptdenoteeconomy-wideaggregates. Theaggregaterealrateofreturnperunitofcapitalinperiodtdependsontherealrentalrateonutilized capital,rku,thecapitalgainonthenon-depreciatedcapitalstock,(1−δ)K ,betweent−1andt,andthe t t t−1 capitalutilizationcosta(u): t rku +(1−δ)Q −a(u) Rk = t t t t . (9) t Q t−1 A continuum of risk-neutral entrepreneurs, indexed i ∈ [0,1], is hit by an idiosyncratic disturbance ωi t inperiodt. Asaresult,theex-postrateofreturnofentrepreneuriperunitofcapitalequalsωiRk. Following t t Bernankeetal.(1999),weassumethatωi isi.i.d.acrosstimetandacrossentrepreneursi,withacontinuous t (cid:110) (cid:111) and differentiable cumulative distribution function F(ω) over a non-negative support, where E ωi = 1 ∀t t andthecorrespondinghazardrateh(ω) ≡ f (ω)/[1−F(ω)]satisfies∂ωh(ω)/∂ω > 0. IncontrasttoBernankeetal.(1999)andvariationsthereof,entrepreneurscanoperateeveninfinancial autarky by purchasing Q K = N in period t. In order for an entrepreneur to accept a loan offer, its terms, t t t i.e.theamount B andthenominalnon-defaultrateofreturn,Z,mustbesuchthattheentrepreneurexpects t t tobenoworseoffthaninfinancialautarky. Assumingconstantreturnstoscale(CRS),thedistributionofnet worth, Ni, across entrepreneurs is irrelevant. As a consequence, the aggregate version of the participation t constraintinequation(4)canbewrittenas (cid:40)(cid:90) ∞ Z (cid:41) (cid:110) (cid:111) E ωRk Q K − t dF(ω) ≥ E Rk N, (10) t ω¯t+1 t+1 t t π t+1 t t+1 t where (cid:110) theexpe (cid:111) ctationisoverRk t+1 ,andω¯ t+1 denotestheexpected defaultthresholdinperiodt+1,defined byE t ω¯ t+1 Rk t+1 Q t K t ≡ E t {Z t /π t+1 }B t . Using the definition of ω¯ t+1 to substitute out E t {Z t /π t+1 } and expressing the aggregate profit share of entrepreneursinperiodtas1−Γ(ω¯ ),equation(B.4)canequivalentlybewrittenas t 14

(cid:110) (cid:111) (cid:110) (cid:111) E t [1−Γ(ω¯ t+1 )]Rk t+1 Q t K t ≥ E t Rk t+1 N t . (11) Note that the ex-post realized value of Γ(ω¯ t+1 ) generally depends on the realization of Rk t+1 through ω¯ t+1 . Similar to Bernanke et al. (1999), we assume that this constraint must be satisfied ex post. Implicit in this is the assumption that Rk is observed by both parties without incurring a cost, and that the non-default t+1 repayment,Z,canthusbemadecontingentontheaggregatestateoftheeconomy. t In order to avoid that entrepreneurial net worth grows without bound, we assume that an exogenous fraction(1−γe)oftheentrepreneurs’shareoftotalrealizedprofitsisconsumedeachperiod.13 Asaresult, entrepreneurialnetworthattheendofperiodtevolvesaccordingto N = γe[1−Γ(ω¯ )]RkQ K . (12) t t t t−1 t−1 Tosumup,theentrepreneurs’equilibriumconditionscomprisetherealrateofreturnperunitofcapital in (B.3), the ex-post participation constraint in (B.5), the evolution of entrepreneurial net worth in (B.6), and the real amount borrowed, B = Q K −N. Moreover, the definition of the expected default threshold, t t t t E t ω¯ t+1 ,determinestheexpectednon-defaultrepaymentperunitborrowedbytheentrepreneurs,E t {Z t /π t+1 }. 3.1.2. TheBank For tractability, we assume a single monopolistic financial intermediary, which collects deposits from households and provides loans to entrepreneurs. In period t, this bank is endowed with net worth or bank capital Nb. Abstracting from bank reserves or other types of bank assets, its balance sheet identity in real t termsisgivenbyequation(2). TheCSVprobleminTownsend(1979)impliesthat,ifentrepreneuridefaults (cid:16) (cid:17) due to ωiRkQ Ki < Zi /π Bi , the bank incurs a proportional cost µωiRkQ Ki and recovers the t t t−1 t−1 t−1 t t−1 t t t−1 t−1 remainingreturnoncapital,(1−µ)ωiRkQ Ki . t t t−1 t−1 In period t, the risk-neutral bank observes entrepreneurs’ net worth, Ni, and makes a take-it-or-leave-it t offertoeachentrepreneuri. Asaconsequence,itholdsaperfectlydiversifiedloanportfoliobetweenperiod tandperiodt+1. Althoughthebankcanthusdiversifyawayanyidiosyncraticriskarisingfromthepossible default of entrepreneur i, it is subject to aggregate risk through fluctuations in the ex-post rate of return on capital, Rk t+1 , and the aggregate default threshold, ω¯ t+1 . In order to be able to pay the risk-free nominal 13Intheliterature,itiscommontoassumethatanexogenousfractionofentrepreneurs“dies”eachperiodandconsumesitsnet worthuponexit.Thedynamicimplicationsofeitherassumptionareidentical. 15

rate of return Rn on deposits in each state of the world, the bank must have sufficient net worth to protect t depositorsfromunexpectedfluctuationsinRk . t+1 Now consider the bank’s problem of making a take-it-or-leave-it offer to entrepreneur i with net worth Ni in period t. The contract offered by the bank specifies the real amount of the loan, Bi, and the nominal t t grossrateofreturnincaseofrepayment,Zi. GiventhatNiispredeterminedattheendofperiodt,thebank’s t t choice of Bi also determines the entrepreneur’s total capital expenditure, Q Ki = Bi +Ni. Given Q Ki and t t t t t t t N t i,thebank’schoiceofZ t i furtherimpliesanexpecteddefaultthreshold,E t ω¯ t+1 ,fromequation(3). Wecan thusrewritethebank’sconstrainedprofit-maximizationproblemforaloantoentrepreneurias (cid:40) (cid:41) (cid:104) (cid:16) (cid:17) (cid:16) (cid:17)(cid:105) Rn (cid:16) (cid:17) max E Γ ω¯i −µG ω¯i Rk Q Ki− t Q Ki−Ni−Nb,i , (13) K t i,ω¯i t+1 t t+1 t+1 t+1 t t π t+1 t t t t whereΓ (cid:16) ω¯i (cid:17) ≡ (cid:82)ω¯i tωdF(ω)+ω¯i (cid:104) 1−F (cid:16) ω¯i (cid:17)(cid:105) ,µG (cid:16) ω¯i (cid:17) ≡ µ (cid:82)ω¯i tωdF(ω),and Nb,i denotestheshareoftotal t 0 t t t 0 t banknetworthassignedtotheloantoentrepreneuri,subjecttotheparticipationconstraintin(4). (cid:110) (cid:111) Thecorrespondingfirst-orderconditionswithrespectto Ki,E ω¯i ,λb,i ,whereλb,idenotestheex-post t t t+1 t t valueoftheLagrangemultiplierontheparticipationconstraint,aregivenby (cid:40) (cid:41) (cid:110)(cid:104) (cid:16) (cid:17)(cid:105) (cid:111) Rn Ki : E Γ(ω¯i )−µG(ω¯i )+λb,i 1−Γ(ω¯i ) Rk = E t , (14) t t t+1 t+1 t t+1 t+1 t π t+1 (cid:110)(cid:104) (cid:105) (cid:111) (cid:110) (cid:111) E ω¯i : E Γ(cid:48)(ω¯i )−µG(cid:48)(ω¯i ) Rk = E λb,iΓ(cid:48)(ω¯i )Rk , (15) t t+1 t t+1 t+1 t+1 t t t+1 t+1 (cid:104) (cid:105) λb,i : 1−Γ(ω¯i ) Rk Q Ki = Rk Ni. (16) t t+1 t+1 t t t+1 t In Proposition 2, we show that the optimal debt contract between entrepreneur i and the bank implies (cid:110) (cid:111) a positive relationship between the expected EFP, s t ≡ E t Rk t+1 π t+1 /Rn t , and the optimal capital/net worth ratio,ki ≡ Q Ki/Ni. Notethat(B.9)equatestheexpectedmarginalreturnofanadditionalunitofcapitalto t t t t the bank and the entrepreneur to the expected marginal cost of an additional unit of bank deposits in real terms. Assuming that the participation constraint is satisfied ex post, this implies a positive relationship (cid:110) (cid:111) (cid:110) (cid:111) between E t Rk t+1 π t+1 /Rn t and E t ω¯i t+1 . Moreover, (B.11) equatesthe entrepreneur’sexpected payoffwith (cid:110) (cid:111) and without the bank loan and implies a positive relationship between E ω¯i and Q Ki/Ni.14 Together, t t+1 t t t 14Thisbecomesevident,whenweusetheex-postassumptionthatRk t+1 andω¯ t+1 areuncorrelatedandrewrite(B.11)as (cid:104) (cid:105) Ni 1 1−Γ(ω¯i ) ≥ t ≡ , t+1 QKi ki t t t 16

these two conditions determine the positive ex-ante relationship between the expected EFP in period t+1 (cid:110) (cid:111) andtheleverageratiochosenbythebankinperiodt,whilethefirst-orderconditionwithrespecttoE ω¯i t t+1 pinsdowntheex-postvalueoftheLagrangemultiplier,λb,i. t (cid:110) (cid:111) (cid:110) (cid:111) Given Ni, Q Ki, and E Rk , the definition of the expected default threshold, E ω¯i , implies an t t t t t+1 t t+1 (cid:110) (cid:111) expectednon-defaultrealrateofreturnontheloantoentrepreneuri, E t Z t i/π t+1 , whilethesameequation (cid:110) (cid:111) evaluated ex post determines the actual non-default repayment conditional on Ni, Q Ki, E ω¯i , and the t t t t t+1 (cid:16) (cid:17) (cid:16) (cid:17) realization of Rk . By the law of large numbers, Γ ω¯i − µG ω¯i denotes the bank’s expected share of t+1 t t total period-t profits (net of monitoring costs) from a loan to entrepreneur i as well as the bank’s realized profit share from its diversified loan portfolio of all entrepreneurs. Accordingly, we can rewrite the bank’s aggregateexpectedprofitsinperiodt+1as (cid:40) (cid:41) E t V t b +1 = E t (cid:2)Γ(ω¯ t+1 )−µG(ω¯ t+1 ) (cid:3) Rk t+1 Q t K t − π R t+ n t 1 (cid:16) Q t K t −N t −N t b (cid:17) , (17) where the expectation is over all possible realizations of Rk t+1 and π t+1 , while V t b +1 is free of idiosyncratic risk. The entrepreneurs’ participation constraint in (B.5) implies that ω¯ t+1 and thus (cid:2)Γ(ω¯ t+1 )−µG(ω¯ t+1 ) (cid:3) are predetermined in period t + 1. To keep the problem tractable, we assume that aggregate risk is small relativetothebank’snetworth,Nb,sothatbankdefaultneveroccursinequilibrium. t Inordertoavoidthatitsnetworthgrowswithoutbound,weassumethatanexogenousfraction(1−γb) ofthebank’sshareoftotalrealizedprofitsisconsumedeachperiod.15 Asaresult,banknetworthattheend ofperiodtevolvesaccordingto Nb = γbVb. (18) t t 3.2. CalibrationandSteadyState Our New Keynesian DSGE model is parsimoniously parameterized and standard in many dimensions. For this reason, we follow the existing literature in calibrating most of the parameter values. We set the coefficientofconstantrelativeriskaversion,σ,equalto2andtheFrischelasticityoflaborsupplytoη = 3. Weassumehabitformationinconsumptionwithacoefficienthof0.65. Therelativeweightoflaborinthe i.e.,entrepreneuri’sexpectedreturnoncapitalwiththeloanrelativetofinancialautarkymustbenosmallerthantheentrepreneur’s (cid:104) (cid:105) (cid:110) (cid:111) “skininthegame”.Since 1−Γ(ω¯i ) isstrictlydecreasinginE ω¯i ,theparticipationconstraintimpliesapositiverelationship (cid:110) (cid:111) t+1 t t+1 betweenE ω¯i andki. t t+1 t 15Alternatively,onecouldthinkofthis“consumption”asadistributionofdividendstoshareholdersorbonuspaymentstobank managers,whichareinstantaneouslyconsumed. 17

utility function, χ, is determined by a target value of 1/3 for steady-state employment. The representative household discounts future utility with a subjective discount factor of β = 0.995, implying a steady-state real interest rate of 2% per annum. Following Basu (1996) and Chari et al. (2000), we set the elasticity of substitution between different consumption and investment varieties, (cid:15) , equal to 10 and the elasticity of p substitutionbetweendifferentlaborvarietiesto(cid:15) =10. w The productive capital stock depreciates at a quarterly rate of δ = 2.5%. We set the investment adjustmentcostcoefficienttoitsestimatebasedonamodelwiththesamerealandnominalrigiditiesinChristiano etal.(2005),i.e.φ = 2.5. AsinBernankeetal.(1999),theelasticityofoutputwithrespecttotheprevious periodcapitalstock,α,issetto0.35. TheCalvoprobabilitythatamonopolisticallycompetitiveretailerand union can adjust its price and wage, respectively, in any given period is assumed to be θ = θ = 0.75 – a p w valueinthemiddleoftherangeofestimatesinChristianoetal.(2005). In line with the estimate in Christensen and Dib (2008), we assume a moderate amount of interest rate inertia in monetary policy, i.e. ρ = 0.7418, while the central bank’s responsiveness to contemporaneous deviations of inflation and output from their steady state is set to φ = 1.5 and φ = 0.5, respectively. We π y areprimarily interestin theeffectsof anunexpected monetaryexpansion. The shockto theTaylorrule, ν, t is assumed to follow a mean-zero i.i.d. process with an unconditional standard deviation of σ = 0.0058, ν theestimateinChristensenandDib(2008). The remaining parameters relate to the optimal debt contract between the bank and the continuum of entrepreneurs. To avoid that either the bank or an entrepreneur grows indefinitely, we assume that 5% and 1.5%oftheirnetworthisconsumedeachquarter,implyinganaveragesurvivalrateof5yearsand16years, respectively.16 The relative monitoring cost in case of default, µ, is set to 20%, a value at the lower end of the range reported in Carlstrom and Fuerst (1997) and in the middle of the range of estimates reported in Levinetal.(2004). Moreover,weassumethatidiosyncraticproductivitydrawsarelog-normallydistributed withunitmeanandavarianceof0.18andthatthedefaultthreshold,ω¯,is0.35inthesteadystate. Together, theseparametervaluesimplyanannualdefaultrateofentrepreneurscloseto4.75%,anannualnon-default interestrateonbankloansof4.8%,andaleverageratioofentrepreneursequalto1.537,whichcorresponds to the median value of leverage ratios for U.S. non-financial firms in Levin et al. (2004). Their sample of quotedfirmsrangesfrom1997Q1to2003Q3. Table1summarizesourbenchmarkcalibration. 16Notethat,inadditiontothisexogenousconsumption,anendogenousfractionofentrepreneursdefaultsineachperioddueto aninsufficientidiosyncraticrealizationofωi. Totalexitoffirmsisthusgivenbythesumoftheexogenousconsumptionandthe 18

Table1:BenchmarkCalibrationofParameterValues. Householdandproductionsector Parameter Value coefficientofrelativeriskaversion σ 2 Frischelasticityoflaborsupply η 3 habitformationinhouseholdconsumption h 0.65 relativeweightoflaborinutilityfunction χ 5.19 quarterlydiscountfactorofhouseholds β 0.995 elasticityofoutputwithrespecttocapital α 0.35 quarterlydepreciationrateofphysicalcapital δ 0.025 coefficientofquadraticinvestmentadjustmentcosts φ 2.5 elasticityofcapitalutilizationadjustmentcosts σ 0.4 u elasticityofsubstitutionbetweenretailervarieties (cid:15) 10 p Calvoprobabilityofquarterlypriceadjustments θ 0.75 p elasticityofsubstitutionbetweenlaborvarieties (cid:15) 10 w Calvoprobabilityofquarterlywageadjustments θ 0.75 w Optimalfinancialcontract Parameter Value exogenousconsumptionrateofentrepreneurialnetworth 1−γe 0.015 exogenousconsumptionrateofbanknetworth 1−γb 0.05 monitoringcostsasafractionoftotalreturnoncapital µ 0.20 varianceofidiosyncraticproductivitydraws σ2 0.18 ω steady-statedefaultthresholdofentrepreneurs ω¯ 0.35 Monetarypolicy Parameter Value interest-ratepersistenceinmonetarypolicyrule ρ 0.7418 responsivenessofmonetarypolicytoinflationdeviations φ 1.5 π responsivenessofmonetarypolicytooutputdeviations φ 0.5 y standarddeviationofunsystematicmonetarypolicyshocks σ 0.0058 ν This calibration implies an annual capital-output ratio of 1.945, a consumption share of households, entrepreneurs, and bankers of 0.696, 0.078, and 0.025, respectively, and an investment share in output of 0.195 in the steady state. The share of net worth and loans in total capital purchases amounts to 0.651 and 0.350, respectively, and implies an equivalent distribution of gross profits between entrepreneurs and thebank. Monitoringcostsamounttolessthan0.6%ofsteady-stateoutput. Bankloansarefundedthrough depositsandbankcapitalwithrelativesharesof0.824and0.176. Theimpliedleverageratioofentrepreneurs of1.537wasexplicitlytargetedinthecalibration. We assume zero trend inflation in the steady state. Accordingly, all interest rates can be interpreted in realterms. Fromthebenchmarkcalibration,weobtainanannualizedrisk-freerateofreturnondepositsof 2%,anannualizedaggregaterateofreturnoncapitalof6.2%,anon-defaultrateofreturnonbankloansof 6.8%,andanannualizedEFPof4.2%. Thesteady-statedefaultrateofentrepreneursincreaseswiththedefaultthreshold,ω¯,andtheexogenous endogenousdefaultrate. 19

variance of idiosyncratic productivity realizations, σ2. For our baseline calibration, the annualized default ω rateequals4.7%. Notethatthisdefaultaccountsforpartoftheoverallturnoverofentrepreneursinthesteady stateonly. Eachperiod,1.5%ofentrepreneurialand5%ofbanknetwortharealsoconsumedexogenously. Thesteady-statevaluesofselectedvariablesandratiosaresummarizedinTable2. 3.3. DynamicSimulationResults 3.3.1. TheRiskChannelofMonetaryPolicy Figure2plotsselectedimpulseresponsestoanexpansionarymonetarypolicyshock,i.e.anexogenous reductionintheunsystematiccomponentoftheTaylorrule,for“Ourcontract”againstthe“BGGcontract” in Bernanke et al. (1999). The formulation of the optimal debt contract is the only dimension along which thetwomodelsdiffer.17 Allimpulseresponsefunctionsareexpressedintermofpercentagedeviationsfrom thesteadystate,exceptforthepolicyrate,theloanrate,thenetinterestmargin,andtheexpectedEFP,which areexpressedintermsofpercentagepoints. Considerfirstourcontract. In response to a monetary expansion, the policy rate, Rn, decreases on impact, albeit not by the full t amountoftheshock,sincetheinterestrateruleimpliesacontemporaneousreactiontoinflationandoutput, whicharebothabovetheirsteady-statevalues. Thereductioninthepolicyrateispassedthroughtothenon- 17Itisimportanttonotethat,apartfromNb =Vb =0,reformulatingthedebtcontracthaslittleeffectonthesteady-statevalues. ss ss Table2:SelectedSteady-StateValuesforBenchmarkParameterCalibration. Steady-StateVariableorRatio Computation Value capital-outputratio K/(4·Y) 1.9451 householdconsumptionrelativetooutput C/Y 0.6963 entrepreneurconsumptionrelativetooutput Ce/Y 0.0784 bankconsumptionrelativetooutput Cb/Y 0.0251 capitalinvestmentrelativetooutput I/Y 0.1945 employmentasashareoftimeendowment∗ H 1/3 (cid:16) (cid:17) grosspricemarkupofretailers∗ (cid:15) / (cid:15) −1 1.1111 p p grosswagemarkupoflaborunions (cid:15) /((cid:15) −1) 1.1111 w w leverageratioofentrepreneurs∗ QK/N 1.5372 defaultmonitoringcostsrelativetooutput µG(ω¯)RkQK/Y 0.0057 annualizeddefaultrateofentrepreneurs∗ 4·F(ω¯) 4.735% annualizedrisk-freepolicyinterestrate∗ 4·(Rn−1) 2.010% annualizedinterestrateonbankloans∗ 4·(Z−1) 6.816% (cid:16) (cid:17) annualizedrateofreturnoncapital 4· Rk−1 6.195% (cid:16) (cid:17) annualizedexternalfinancepremium 4· Rk/Rn−1 4.164% Note:Superscript∗indicatessteady-statevaluestargetedinthebenchmarkcalibration. 20

Figure2:SelectedImpulseResponseFunctionstoanExpansionaryMonetaryPolicyShockforDifferentOptimalDebtContracts. Policy Rate Loan Rate Net Interest Margin Expected EFP 0 0 0.04 0.05 0.02 −0.2 −0.2 0 0 −0.4 Our contract −0.4 −0.02 −0.05 BGG contract −0.04 −0.1 5 10 15 20 5 10 15 20 5 10 15 20 5 10 15 20 Default Threshold Default Rate Leverage Ratio Bank Profit Share 1 5 0.5 1 0 0 0 0 −5 −1 −0.5 −1 −10 −2 −15 −1 −2 5 10 15 20 5 10 15 20 5 10 15 20 5 10 15 20 Bank Lending Bank Deposits Net Worth Bank Net Worth 1.5 8 0.2 1 0 2 6 0.5 −0.2 1 4 0 −0.4 2 −0.6 0 0 5 10 15 20 5 10 15 20 5 10 15 20 5 10 15 20 Output Consumption Investment Return on Capital 0.6 1.5 1 0.4 2 1 0.5 0.2 1 0.5 0 0 0 −0.5 0 5 10 15 20 5 10 15 20 5 10 15 20 5 10 15 20 Quarters Quarters Quarters Quarters Notes:Allimpulseresponsefunctionsareexpressedintermsofpercentagedeviationsfromsteadystate,exceptforthepolicyrate, theloanrate,thenetinterestmargin,andtheexpectedEFP,whichareexpressedintermsofpercentagepoints. default rate of return on loans, Z, which also decreases on impact and follows virtually the same pattern. t Themonetaryexpansionfurtherimpliesanunexpectedincreaseintherealrateofreturnoncapital,Rk,and t thusintheex-postrealizedEFP,asconjecturedinourpartialequilibriumanalysis.18 Assuming that the entrepreneurs’ participation constraint must be satisfied ex post, their share in gross profits,1−Γ(ω¯ ),ispredeterminedintheperiodoftheshock. Accordingly,neitherthedefaultthreshold,ω¯ , t t northedefaultrate, F(ω¯ ), ofentrepreneursrespondsonimpact. Thefactthatprofitsaresplitaccordingto t thepredeterminedleverageratio,Q K /N ,impliesthatbothentrepreneursandthebankbenefitfroma t−1 t−1 t−1 monetaryexpansion. Asaresult,banknetworth,Nb,andentrepreneurialnetworth,N,increaseonimpact. t t 18TheimpulseresponsefunctioninFigure2showstheex-anteexpectedratherthantheex-postrealizedEFPanddoestherefore notreflecttheunexpectedincreaseintheperiodofthemonetarypolicyshock. 21

From t +1 on, the price of capital declines (not shown), implying capital losses to the entrepreneurs, which are correctly anticipated by all economic agents under rational expectations (RE) in the absence of furthershocks. Nevertheless, theexpectedEFPforperiodt+1isaboveitssteady-statevaluebyabout0.7 basispoints,whichinducesthebanktograntmoreloansbothinabsolutetermsandrelativetoentrepreneurs’ networth. Asaconsequence,theleverageratioofentrepreneursincreasesfromtheendofperiodtonwards andpeaksafterfivequartersat0.21%aboveitssteady-statevalueof1.537. This increase in borrower leverage allows the bank to demand a larger share of gross expected profits realizedinperiodt+1byraisingthenon-defaultrateofreturnonbankloansrelativetothepolicyrateand thus its net interest margin. Together with the implied default threshold, ω¯ t+1 , the expected default rate of entrepreneurs,F(ω¯ t+1 ),risesaboveitssteady-statevalue. Themaximumeffectisreachedaftersixquarters, whenthedefaultthresholdis0.4%aboveitssteady-statevalueof0.35,andthedefaultrateofentrepreneurs isabout3basispointsaboveitssteady-statevalueof1.18%. Now recall that the classic formulation of the CSV contract implies that entrepreneur i determines the optimalamountoflending,Bi,andthustheleverageratioforapredeterminedamountofnetworth,Ni,while t t the“financialintermediary”onlycorrespondstoaparticipationconstraint. Assumingperfectdiversification acrossborrowersandtherisk-sharingagreementinBernankeetal.(1999),thepassivefinancialintermediary mustbreakevenineachrealizedstateoftheeconomy. Hence, thereisnoroleforbankcapital, Nb = 0∀t, t andtheentirewindfallgainfromthemonetaryexpansionaccruestotheentrepreneurs. Figure2showsthat,fortheBGGcontract,theentrepreneurs’defaultthreshold,defaultrate,andleverage ratioaswellastheexpectedEFPandnetinterestmarginalldecreaseinresponsetoamonetaryexpansion. Asaresult,thepartialequilibriummechanismworksintheoppositedirection. Incontrastwithourcontract andthepopularnotionofabanklendingchannelofmonetarypolicy,theBGGcontractfurthermoreimplies aninitialcontractionratherthananexpansionofbanklending. ThesecrucialdifferencesarisefromtheassumptioninBernankeetal.(1999)thatacompetitivefinancial intermediarymerelytransformshouseholddepositsintoloanstoentrepreneursoneforone. Incontrast,the monopolisticbankinourmodelretainsashareoftotalprofits,accumulatesownnetworth,andisthusable toexpandlendingdespiteanevenmorepronouncedandpersistentreductionindeposits. Thebank’smarket powerandourassumptionaboutaggregaterisksharingmanifestthemselvesinaweakerpass-throughfrom monetarypolicytotheloanrate,relativetotheBGGcontract,andanincreaseratherthanadecreaseinthe netinterestmargin,whichmeasurestheexpectedprofitabilityofbankloans. 22

The more pronounced increase in borrower net worth, N, as well as the contraction of aggregate bank t lending, B,implythewell-knowndecreaseintheleverageratioofentrepreneurs, Q K/N = (N +B)/N, t t t t t t t in Bernanke et al. (1999), whereas the introduction of a risk channel in this paper facilitates a reduction in depositsandanexpansionofbanklendingatthesametime. 3.3.2. RiskTakingovertheBusinessCycle Arelatedquestioniswhetherournewmechanismmattersforreplicatingtheunconditionalmomentsof certainkeyvariablesoverthebusinesscycle. Forthispurpose,weaugmentourbenchmarkNewKeynesian DSGEmodelwithfouradditionalshockprocessestototalfactorproductivity,consumerpreferences,andthe marginalefficiencyofinvestment,aswellasso-called“riskshocks”tothestandarddeviationofidiosyncratic productivity draws, σ . While our calibration of the former three is based on the Maximum Likelihood ω,t estimationresultsinChristensenandDib(2008),unanticipatedandanticipatedriskshocksarecalibratedin linewiththeBayesianestimationresultsinChristianoetal.(2014). TableC.1intheAppendixsummarizes thecalibrationofadditionalshockprocesses. Figure 3 plots the dynamic cross-correlations of selected variables and ratios with output based on the theoreticalmodelwithourdebtcontractandtheoptimaldebtcontractinBernankeetal.(1999),respectively, against their empirical counterparts. To capture the variability at business cycle frequencies, both the data andthesimulatedtimeseriesareHP-filteredwithλ = 1,600beforecomputingtheunconditionalmoments. Figure3illustratesthatbothmodelsreplicatetheempiricalcross-correlationsofoutputand,especially, investment reasonably well. Moreover, the simulated default rate of entrepreneurs tracks the correlation of delinquencyratesonbusinessloanswithoutputinthedatasurprisinglywell. Theimportanceofintroducing ariskchannelbecomesevidentwhenconsideringbank-relatedvariables. Themodelwithourcontractdoes substantiallybetterinreplicatingtheempiricalcross-correlationsofbanks’SLOOScollateralrequirements andthenetinterestmarginfromCallReports,inparticularcontemporaneously. Theunconditionalmoments ofbanks’loan-to-depositratioandreturnoncapitalcanonlybeassessedinourmodelinameaningfulway, whereas,inBernankeetal.(1999),theformerisconstantatunity,whilethelatterisnotdefinedatall. 3.3.3. SensitivityAnalysis An important question is whether the results in Figure 2 are sensitive to our choice of parameters. For thisreason,weperformanumberofrobustnesscheckswithintherangeofcommonlyusedparametervalues. First,ourresultsarequalitativelyandquantitativelyrobusttotheabsenceofhabitformationinconsumption 23

Figure3:Cross-CorrelationofSelectedVariablesatPeriodtwithOutputatperiodt+τ,DSGEModelandData. Output Investment Loans/Deposits Net Income/Bank Equity 1 0.6 0.6 0.5 0.5 0.4 0.4 0.2 0.2 0 0 0 0 −0.2 −0.2 −0.5 −0.5 −0.4 −0.4 −10 0 10 −10 0 10 −10 0 10 −10 0 10 τ τ τ τ Collateral Requirements Delinquency Rate Net Interest Margin 0.5 0.5 0.5 Data Our contract 0 0 0 BGG contract −0.5 −0.5 −0.5 −10 0 10 −10 0 10 −10 0 10 τ τ τ Notes: SimulatedtimeseriesanddataareHP-filtered(λ=1,600). Inthedata,outputcorrespondstolog(realGDPpercapita), investmenttolog(realinvestmentexpenditurepercapita),loans/depositstolog(loansandleasesinbankcredit/demanddeposits) atcommercialbanks,netincome/bankequitytoCallReportslog(netinterestincome/totalequitycapital)forcommercialbanksin theU.S.,collateralrequirementstothenetpercentageofdomesticbanksincreasingcollateralrequirementsforlargeandmiddlemarketfirms,delinquencyratetodelinquencyrateonbusinessloans;allcommercialbanks,andnetinterestmargintoCallReports netinterestmarginforallU.S.banks. (h = 0)aswellastothepresenceofpriceandwageindexationtopastinflationbyretailersandlaborunions, respectively. Second,theresultsarequalitativelyrobusttotheintroductionofnonzerotrendinflation. Forexample,an annualizedsteady-stateinflationrateof1%marginallylowersthepeakresponseoftheborrowers’leverage ratio,defaultrate,andothercontractvariableswhileincreasingtheirpersistencesomewhat. Third,theabsenceofinvestmentadjustmentcosts(φ = 0)substantiallymagnifiestheimpulseresponses ofcontractvariables,suchastheexpectedEFP,andincreasesthereforetheriskchannelofmonetarypolicy. With zero adjustment costs, however, the response of investment becomes unreasonably large. In contrast, higher investment adjustment costs, the absence of variable capital utilization (σ → ∞), and the absence u ofwagestickiness(ξ = 0)attenuatetheriskchannelquantitatively,albeitnotqualitatively. w Fourth,ourresultsarequalitativelyrobusttoalternativespecificationsofaTaylor-typeinterest-raterule, suchasaresponsetopastorexpectedfutureratherthancurrentinflation(compareBernankeetal.,1999),a responsetopastorexpectedfutureratherthancurrentoutput,orastrongerresponsetodeviationsofinflation 24

fromsteadystate.19 Theonlyparameterthatmattersisthedegreeofinterest-rateinertiaintheTaylorrule. Following a monetary expansion, higher inertia implies that the policy rate remains “too low for too long” andmagnifiesthustheeffectoftheriskchannel(seealsoFigureC.2intheAppendix). 4. TheEmpiricalEvidence Intheexistingliterature,evidenceforarisk-takingchannelofmonetarypolicyontheassetsideismostly confinedtomicroeconomicloan-leveldata(see,e.g.,Jime´nezetal.,2014;Ioannidouetal.,2015;Paligorova andSantos,2017). Whenmacroeconomictimeseriesareused,theresultsareoftenambiguous. Maddaloni and Peydro´ (2011) exploit the cross-sectional variation in economic conditions across euro-area countries to show that corporate banks soften their lending standards in response to low short-term interest rates and thattheimpactonlendingstandardsisamplifiedbythedurationofrelativelylowinterestrates. Sincetheir identification strategy rests on a common monetary policy stance in the euro area, it is not suitable for the U.S., where they find little evidence for a risk channel of monetary policy. Using a rich panel of banking data with 140 time series in a FAVAR model, Buch et al. (2014) find evidence in favor of asset-side risk takingforsmallU.S.banksonly. Importantly,Buchetal.(2014)useadifferentmeasureofassetrisk–the riskiness of new loans from the Survey of Terms of Business Lending of the U.S. Federal Reserve, which restrictstheirsampleperiodto1997Q2-2008Q2. Instead, we use the quantified qualitative survey measures of bank lending standards from the Federal Reserve’s SLOOS, which are available from 1991Q1 onwards. Similar to Buch et al. (2014), we employ a FAVARmodel,whichallowsustoparsimoniouslyusetheinformationinalargenumberofmacroeconomic timeseries,therebyreducingtheriskofomitted-variablebias(seealsoBernankeetal.,2005).20 Weextract the so-called factors from a comprehensive set of real economic activity measures including indicators of production, investment, and employment. In order to be able to detect a risk channel of monetary policy, we augment the macroeconomic and financial time series commonly used in the FAVAR literature by 19 measures of lending standards, such as the net percentage of banks increasing collateral requirements or tighteningloancovenants,forseveralcategoriesofloans,borrowers,andbanks. Figure4plotstheselending 19Notethatourresultsarenotaffectedbyaresponseofmonetarypolicytotheso-called“outputgap”,i.e.thedeviationofactual frompotentialoutput,underflexibleprices. Duetotheneutralityofmoney,potentialoutputisidenticaltosteady-stateoutputin theabsenceofnominalrigidities. 20In Appendix F.1, we illustrate that the response of SLOOS lending standards to a monetary policy shock is not robust to differentchoicesforthemeasureofrealeconomicactivityinasmall-scaleVARmodel. 25

Figure4:SLOOSLendingStandardsandtheEffectiveFederalFundsRate,1991Q1-2015Q4. 100 50 0 −50 −100 1991Q1 1995Q1 1999Q1 2003Q1 2007Q1 2011Q1 2015Q1 gninethgit sknab fo egatnecrep ten :sdradnats gnidneL 8 6 4 2 0 1991Q1 1995Q1 1999Q1 2003Q1 2007Q1 2011Q1 2015Q1 munna rep tnecrep :RFF Notes:SeeAppendixDforadetaileddescriptionoflendingstandardmeasures. standardsagainsttheeffectivefederalfundsrate. Notethatthesubstantialcomovementinlendingstandards overthesampleperiodmightbecapturedwellevenbyarelativelysmallnumberofcommonfactors. 4.1. TheEconometricSpecification Suppose that the observation equation relating the N ×1 vector of informational time series, X, to the t K×1vectorofunobservablefactors,F ,andtheM×1vectorofobservablevariables,Y,withK+M << N, t t isgivenby X = ΛfF +ΛyY +e, (19) t t t t where Λf is an N ×K matrix of factor loadings of the unobservable factors, Λy is an N × M matrix of factorloadingsoftheobservablevariables,ande isan N ×1vectoroferrortermsfollowingamultivariate t normaldistributionwithmeanzeroandcovariancematrix,R. Suppose further that the joint dynamics of the unobserved factors in F and the observable variables in t Y canbecapturedbythetransitionequation t      F Y t  = Φ(L)  F Y t−1  +ν t , (20) t t−1 where Φ(L) is a lag polynomial of order d and ν is a (K + M) × 1 vector of error terms following a t multivariate normal distribution with mean zero and covariance matrix, Q. The error terms in e and ν are t t assumedtobecontemporaneouslyuncorrelated. 26

Estimating the FAVAR model in (19) and (20) requires transforming the data to induce stationarity of thevariables.21 Ourbaselinesamplecontainsquarterlyobservationsfor1991Q1-2008Q2. Whilethestartis determinedbytheavailabilityoftheSLOOSmeasuresofbanklendingstandards,weexcludetheperiodafter 2008,whenU.S.monetarypolicywaseffectivelyoperatingthroughthebalancesheetoftheFederalReserve ratherthanthroughtheFederalFundsrate(compareFigure4). Thepredominanceofunconventionalpolicy measureswouldrequireadifferentstrategyforidentifyingmonetarypolicyshocksduringthisperiod. FollowingBernankeetal.(2005),weidentifymonetarypolicyshocksrecursively,orderingtheFederal Fundsratelastinequation(20). Inourcase,thisimpliesthattheunobservedfactorsdonotrespondtomonetary policy innovations within the same quarter, while the idiosyncratic components of the informational timeseriesinX arefreetorespondonimpact.22 Onecouldarguethatseniorloanofficerstakeintoaccount t thecurrentmonetarystancewhendecidingontheirlendingstandards. Hence,itisimportanttonotethatthe SLOOS is conducted by the Federal Reserve, so that results are available before the quarterly meetings of theFederalOpenMarketCommittee(FOMC),inlinewithouridentificationscheme. WeestimatetheFAVARmodelin(19)and(20)byaone-stepBayesianapproach,applyingmulti-move Gibbs sampling to sample jointly from the latent factors and the model parameters. Appendix E provides details on the prior distributions, the Gibbs sampler, and how we monitor the convergence of the latter. In our baseline specification, we set the lag order of the transition equation to two quarters and consider the FederalFundsrateastheonlyobservablevariablein(20),i.e. M = 1.23 TodeterminetheappropriatenumberofunobservablefactorsinourFAVARspecification,weconsulta number of selection criteria, monitor the joint explanatory power of F and Y for bank lending standards, t t andchecktherobustnessofourresultsbyaddingmorefactors. ThetestsofOnatski(2009)andAlessietal. (2010)pointtothreeandfivefactors,respectively. Tryingspecificationswithuptosevenfactors,wefound thatourresultswerenotaffectedqualitatively.24 Inwhatfollows,wethereforerefertothespecificationwith threeunobservablefactorsasthebaselineFAVARmodel. 21ThetransformationofvariablesisdetailedinAppendixD.NotethatthemeasuresofbanklendingstandardsentertheFAVAR modelin(standardized)levels,i.e.withoutfirst-differencingordetrending,giventhattheyarestationarybyconstruction. 22Bernankeetal.(2005)applythesamerecursiveorderingtoaFAVARmodelinmonthlydata. 23Resultsforlagordersoneandthreeareverysimilar.AddingCPIasanobservablevariable(M=2)doesnotaffectourresults. 24Table F.1 in the Appendix reports the adjusted R2 for each of the 19 SLOOS measures with one, three, five, and seven unobservablefactors,illustratingthatasmallnumberfactorsissufficienttocapturethecommoncomovementinlendingstandards. Ourresultsarealsoconsistentwiththeso-called“screeplot”, whichplotstheeigenvaluesof X indescendingorderagainstthe t numberofprincipalcomponents. Inourcase,thescreeplotdisplaysasteepnegativeslopeandakinkaroundthefifthprincipal component,supportingtheresultsbasedontheselectioncriteriaandtherobustnesschecks. 27

4.2. ResultsfromtheStructuralFAVARModel 4.2.1. ImpulseResponseFunctions Figure5plotstheresponsesofselectedvariablesfromthetheoreticalDSGEmodeltoanexpansionary monetarypolicyshockagainsttheirempiricalcounterpartsfromthebenchmarkFAVARmodelwith K = 3 latentfactors. Inordertofacilitateacomparisonofthetheoreticalandempiricalimpulseresponsefunctions, thebank’scollateralrequirements,bankprofits,andinvestmentareexpressedintermsoftheirunconditional standarddeviations,whilethepolicyrateandthebank’snetinterestmarginareconvertedtoannualizedbasis points,bothintheDSGEandtheFAVARmodel. Oneperiodonthe x-axiscorrespondstoonequarter. Inthetheoreticalmodel,thepolicyrateconvergessmoothlytoitssteady-statevalue,whiletheempirical effectivefederalfundsratedisplayssubstantialovershootingabouttwoyearsafterthemonetaryexpansion. Hence,theinitialincreaseintheempiricalnetinterestmarginisquicklyreversed,turningintoamarginally significant decrease, while the response of the theoretical net interest margin remains positive throughout. Despitethisdiscrepancyinthetransmissionoftheshockthroughinterestratesandspreads,ourtheoretical modelisabletoreplicatetheempiricalimpulseresponsesofbanklendingstandards,profits,andinvestment. IntheDSGEandtheFAVARmodel,bankssignificantlylowertheircollateralrequirementsinresponse to an expansionary monetary policy shock, thus raising the demand for productive capital and investment. Figure5: ImpulseResponsesofSelectedVariablestoanExpansionaryMonetaryPolicyShock,DSGEModelandFAVARModel withThreeUnobservedFactors. Policy Rate 250 200 150 100 50 0 −50 −100 −150 −200 0 20 stniop sisab dezilaunnA Net Interest Margin 40 30 20 10 0 −10 −20 0 20 Quarters stniop sisab dezilaunnA Collateral Requirements 0.3 0.2 0.1 0 −0.1 −0.2 −0.3 −0.4 0 20 Quarters snoitaived dradnatS Bank Profit 0.8 0.6 0.4 0.2 0 −0.2 −0.4 −0.6 0 20 Quarters snoitaived dradnatS Investment 0.3 0.2 0.1 0 −0.1 −0.2 −0.3 −0.4 0 20 Quarters snoitaived dradnatS DSGE FAVAR Quarters Notes: IntheFAVARmodel,theeffectivefederalfundsrateisusedasameasureofthemonetarypolicyrate,theCallReportsnet interestmarginforallU.S.banksasaproxyforthetheoreticalinterestratespread,thenetpercentageofdomesticbanksincreasing collateralrequirementsforlargeandmiddle-marketfirmsasameasureofbanklendingstandards,theCallReportsnetincomefor commercialbanksintheU.S.tomeasurebankprofit,andtheISMManufacturing: NewOrdersIndexasaproxyforinvestment. SeeAppendixDforadetaileddescriptionofthedata.FortheFAVARmodel,medianresponsesareplottedwithpointwise16th/84th and5th/95thpercentiles. 28

Figure6:ImpulseResponsesofLoanRiskinesstoanExpansionaryMonetaryPolicyShock,DSGEModelandFAVARModelwith ThreeUnobservedFactors. STBL Riskiness 0.25 0.2 0.15 0.1 0.05 0 −0.05 −0.1 −0.15 −0.2 0 20 snoitaived dradnatS DSGE FAVAR Quarters Notes:ThemeasureofloanriskinessisobtainedfromtheTermsofBusinessLendingSurveyoftheFederalReserve.Inparticular, wecomputeweightedaverageriskscoreacrossallparticipatingbanksforthesample1997Q2-2008Q2. FortheFAVARmodel, medianresponsesareplottedwithpointwise16th/84thand5th/95thpercentiles. Importantly,thebank’sbehaviorisdrivenbyanincreaseinprofits,whichwealsofindintheFAVARmodel, albeitnotstatisticallysignificant. Inthemodelandthedata,looseningoflendingstandardsisaccompanied byanincreaseinloanriskiness(seeFigure6). Theempiricalmeasureofloanriskinessiscomputedbasedon theTermsofBusinessLendingSurveyoftheFederalReserve. FigureF.3intheAppendixshowsthatall19 measuresoflendingstandardsdecreaseinresponsetoanexpansionarymonetarypolicyshock,whileFigures G.1,G.2,andG.3illustratetherobustnessofthisfindingfor1,5,and7unobservedfactors,respectively. 4.2.2. AlternativeMeasuresofLendingStandards Toaddressconcernsthatourresultmightbedrivenbyloandemandratherthanloansupply,wereplace the“raw”lendingstandardsinX bythealternativemeasureproposedbyBassettetal.(2014),whichadjusts t changesinlendingstandardsformacroeconomicandbank-specificfactorsthatmightsimultaneouslyaffect thedemandforbankcredit. Panel(a)ofFigureG.7illustratesthat,despiteaquantitativelysmallerdecrease, thisalternativeindicatorrespondstoanexogenousmonetaryexpansioninexactlythesameway.25 25Recallthat,inouroriginalFAVARmodel,thefirstfactorprimarilycapturesthecommoncomovementinlendingstandards. WhilereplacingthelatterinX mightthereforeaffecttheimpulseresponsefunctionsevenqualitatively,thisdoesnotseemtobethe t case.Moreover,Bassettetal.(2014)showthatanexogenousdisruptioninthesupplyofbankcreditleadstoasignificanteasingof monetarypolicy.Inthislight,thepositiveconditionalcomovementthatwefindbetweenlendingstandardsandtheeffectiveFederal 29

Figure7:ImpulseResponsesofAlternativeMeasuresofLendingStandardstoanExpansionaryMonetaryPolicyShock. (a) Adjusted Lending Standards 0.4 0.3 0.2 0.1 0 −0.1 −0.2 −0.3 −0.4 0 20 Quarters snoitaived dradnatS (b) SLOOS Risk Tolerance 0.4 0.3 0.2 0.1 0 −0.1 −0.2 −0.3 −0.4 0 20 Quarters snoitaived dradnatS (c) Excess Bond Premium 0.4 0.3 0.2 0.1 0 −0.1 −0.2 −0.3 −0.4 0 20 Quarters snoitaived dradnatS (d) NFCI Credit Subindex 0.4 0.3 0.2 0.1 0 −0.1 −0.2 −0.3 −0.4 0 20 Quarters snoitaived dradnatS Notes: Median responses with pointwise 16th/84th and 5th/95th percentiles, based on the FAVAR model with three unobserved factors,wherethe19SLOOSlendingstandardmeasureshavebeenreplacedby(a)thecreditsupplyindicatorproposedbyBassett et al. (2014); (b) the net percentage of domestic banks easing lending standards due to increased risk tolerance; (c) the excess bondpremiumproposedbyGilchristandZakrajsˇek(2012);(d)theNFCIcreditsubindexpublishedbytheFederalReserveBank ofChicago.SeeAppendixDforadetaileddescriptionofthedata. TheSLOOSalsoasksseniorloanofficersforthereasonsthatinducedthemtoadjustlendingstandards. Among the latter, the category “risk tolerance” allows us to explicitly address the question whether banks’ riskappetiteplayedanyrolewheneasinglendingstandardsinresponsetoamonetaryexpansion. Panel(b) ofFigureG.7plotsthe(negative)impulseresponsefunctionofthenetpercentageofdomesticbankseasing lendingstandardsduetoincreasedrisktolerance. Thefindingofastatisticallysignificantincreasesupports ourinterpretationofbanks’easingoflendingstandardsasariskchannelofmonetarypolicy. Whilethefocusofourpaperisonlendingstandardsandcollateralrequirements,inparticular,qualitative surveysliketheSLOOScanbecriticizedforbeingmorepronetosubjectivenessorintentionalmisreporting. Hence,wealsoinvestigatetheimpulseresponsesoftwomarket-basedmeasuresofthefinancialsector’srisk attitude: the“excessbondpremium”proposedbyGilchristandZakrajsˇek(2012)–acomponentofthe“GZ spread” that captures cyclical changes in the relationship between objective default risk and credit spreads – and the credit subindex of the Chicago Fed’s National Financial Conditions Index (NFCI) – a composite measureofcreditconditions. Panels(c)and(d)ofFigureG.7illustratethatboththeexcessbondpremium and the NFCI credit component decrease significantly in response to an exogenous monetary expansion, indicatinganincreasein“theeffectiverisk-bearingcapacityofthefinancialsector”(compareGilchristand Zakrajsˇek, 2012) and thus an expansion in the supply of credit, consistent with the risk-taking channel of Fundsrateisunlikelytobecontaminatedbyreversecausalityfrombankbehaviortomonetarypolicy. 30

monetarypolicy. 4.2.3. RobustnessofIdentifyingStrategy BarakchianandCrowe(2013)provideempiricalevidencethatU.S.monetarypolicypost1988became more forward-looking, implying that a credible identification of exogenous monetary shocks must account forpolicymakers’expectationsaboutfutureeconomicactivityandpricedynamicsduringoursampleperiod. WhileourbenchmarkspecificationofX alreadycontainsforward-lookingvariables,suchastheS&P500or t businessandconsumersurveydata,onecouldarguethattheBoardofGovernorsusesadditionalinformation when forming its monetary policy decisions. For this reason, we include 13 quarterly time series from the PhiladelphiaFed’sGreenbookdataset,expressedintermsofone-year-aheadexpectationsofaveragegrowth rates, directly in the vector X and find that the impulse responses of lending standards to an expansionary t monetary policy shock are quantitatively very similar to those presented above and statistically significant atthe10%levelfor1,3,and5factors. For7factors,ourestimatesbecomelessprecise,whiletheeasingof lendingstandardsremainssignificantaccordingtotheerrorbandscontaining68%oftheprobabilitymass.26 Moreover,weabandontheFAVARmodelaltogetherinfavorofahigh-frequencyidentificationapproach. Following Barakchian and Crowe (2013), we extract an alternative time series of monetary policy shocks from daily changes in federal funds futures yields for different maturities around FOMC meeting dates.27 We then regress each variable of interest on P = 4 own lags as well as the contemporaneous and Q = 12 lagged observations of the quarterly aggregate of this monthly shock series in a distributed lag regression model. Figure G.5 in the Appendix plots the impulse responses of selected variables from the theoretical DSGEmodeltoanexpansionarymonetarypolicyshockagainsttheirempiricalcounterpartsandillustrates that our findings in Figure 5 are qualitatively robust to the identifying strategy in Barakchian and Crowe (2013). Notealsothat,basedonthehigh-frequencyidentificationofmonetarypolicyshocks,theincreasein bankprofitsisstatisticallysignificant. AsintheFAVAR,thelooseningoflendingstandardsisaccompanied by an increase in loan riskiness (see Figure G.6). The qualitative robustness carries over to all 19 SLOOS lendingstandardsmeasuresandthealternativemeasuresofthefinancialsector’sriskappetiteinFigureG.7. 26TheprojectionsfromtheFed’sGreenbookarereleasedtothepublicwithalagoffiveyearsandarecurrentlyavailableupto 2010Q4.Formoredetails,seeTableD.2intheAppendix.Allresultsareavailablefromtheauthorsuponrequest. 27The median correlation of the resulting shock series with the shock series based on the last 10,000 draws from the Gibbs samplerforourbaselineFAVARmodelis0.273andhighlystatisticallysignificant(seealsoFigureG.4intheAppendix). 31

4.2.4. ExtendedSamplePeriod Despite concerns that the effective Federal Funds rate represents an incomplete measure of monetary policyatthezerolowerbound(ZLB),weextendoursampleperiodto2015Q4asafinalrobustnesscheck. InAppendixG.3,wereproduceFigures5,G.7,andF.3fortheextendedsamplebasedontheFAVARmodel with three unobserved factors and the high-frequency identification approach. When including the ZLB period, our theoretical model continues to replicate the empirical impulse responses of the effective Federal Funds rate, banks’ collateral requirements from SLOOS, and investment to a monetary policy shock. For the FAVAR model, the responses of banks’ net interest margin and profits are imprecisely estimated and tend toward the opposite direction, whereas the net interest margin’s response remains significantly positive for the identifying strategy in Barakchian and Crowe (2013). At the same time, Figures G.10 and G.11showthatall19SLOOSlendingstandardsdecreasesignificantlyinresponsetoamonetaryexpansion, while Figures G.12 and G.13 indicate a significant easing of alternative measures of the financial sectors’ lending standards, regardless of the chosen identification.28 It is beyond the scope of this paper to identify monetary policy shocks attributable to the unconventional monetary policy during the zero lower bound period. Kurtzman et al. (2017) study the effect of large-scale asset purchase programs of the Federal Reserveandfindlooseningoflendingstandardsandhigherbankrisk-takingmeasuredbyloanriskiness, thus corroboratingourbaselinefindings. 5. ConcludingRemarks Inthispaper,wereformulatethewell-knownapplicationofTownsend’s(1979)CSVcontractinBernanke etal.(1999)fromtheperspectiveofamonopolisticbank,whichchoosestheamountofriskylendingagainst borrowercollateralsubjecttotheparticipationconstraintofacontinuumofentrepreneurs. Weassumethat boththebankandentrepreneursarerisk-neutral. Whilethebankcandiversifyanyidiosyncraticdefaultrisk of borrowers, it bears the aggregate risk. In partial equilibrium, the optimal debt contract yields a positive relationship between the expected EFP and the borrower’s leverage ratio chosen by the bank. As a result, an exogenous increase in the expected EFP induces the bank to lend more against a given amount of borrower collateral in order to gain a larger “share of the pie”. At the same time, entrepreneurs become more 28ThecreditsupplyindicatorproposedbyBassettetal.(2014)isonlyavailableuntil2008Q2.Forthisreason,weomititinour robustnesschecksfortheextendedsample. 32

leveragedandthusmorelikelytodefaultexpost. WethenembedourversionoftheCSVcontractinanotherwisestandardNewKeynesianDSGEmodel. Incontrasttothepriorliterature,anexpansionarymonetarypolicyshockleadstoahump-shapedincreasein theexpectedEFPandthebank’snetinterestmargin,whichmeasurestheprofitabilityofloans. Asaresult, our model predicts an increase in bank lending relative to borrower collateral, a higher leverage ratio, and thus a higher expected default rate of entrepreneurs, in line with the risk channel of monetary policy (see, e.g.,AdrianandShin,2011;BorioandZhu,2012). Using a FAVAR model and including measures of bank lending standards from the Federal Reserve’s SeniorLoanOfficerOpinionSurvey(SLOOS),weshowthatourtheoreticalmodelreplicatestheempirical impulse responses of banks’ self-reported collateral requirements, their net interest margin and profits as wellasinvestmenttoamonetarypolicyshockbothqualitativelyandquantitatively. U.S.bankssignificantly lower all 19 lending standards in response to an unexpected reduction in the effective Federal Funds rate. Thisfindingcarriesovertoalternativemeasuresoffinancialintermediaries’riskappetiteandisrobusttothe high-frequencyidentificationofmonetarypolicyshocksinBarakchianandCrowe(2013). While our results can be interpreted as robust evidence for an ex-ante risk channel of monetary policy (i.e.lowerlendingstandards),wedonotshowempiricalevidenceofex-post risktaking(i.e.higherdefault rates). Thereasonisthataggregatecharge-offanddelinquencyratesarereportedforthestock ofloansand leasesatcommercialbanks. Itisthereforeunclearwhetheradefaultingloanwasoriginatedbeforeofafter the monetary policy shock occurred. By tracking each loan in the Bolivian credit register from origination to maturity, Ioannidou et al. (2015) show that lower overnight interest rates induce banks to commit larger loan volumes with fewer collateral requirements to ex-ante riskier firms that are more likely to default ex post. Asimilaranalysisbasedonloan-leveldataisbeyondthescopeofthispaperandleftforfuturework. 33

6. References Adrian,TobiasandHyunSongShin(2011).“FinancialIntermediariesandMonetaryEconomics,”in: Friedman,B.,Woodford,M.(Eds.),HandbookofMonetaryEconomics,Volume3A. Alessi, Lucia, Matteo Barogozzi, and Marco Capasso (2010). “Improved Penalization for Determining the NumberofFactorsinApproximateFactorModels”,Statistics&ProbabilityLetters80: 1806-1813. Barakchian,S.MahdiandChristopherCrowe(2013).“Monetarypolicymatters: Evidencefromnewshocks data,”JournalofMonetaryEconomics60(8): 950-966. Bassett, William F., Mary Beth Chosak, John C. Driscoll, and Egon Zakrajsˇek (2014). “Changes in bank lendingstandardsandthemacroeconomy,”JournalofMonetaryEconomics62(1): 23-40. Basu, Susanto (1996). “Procyclical Productivity: Increasing Returns or Cyclical Utilization?” Quarterly JournalofEconomics111(3): 719-751. Bernanke, Ben S., Mark Gertler, and Simon Gilchrist (1999). “The Financial Accelerator in a Quantitative BusinessCycleFramework,”in: Taylor,J.,Woodford,M.(Eds.),HandbookofMacroeconomics. Bernanke, Ben S., Jean Boivin, and Piotr Eliasz (2005). “Measuring the Effects of Monetary Policy: A FAVARApproach,”QuarterlyJournalofEconomics120(1): 387-422. Board of Governors of the Federal Reserve System (U.S.), Senior Loan Officer Opinion Survey on Bank LendingPractices,http://www.federalreserve.gov/boarddocs/SnLoansurvey/. Board of Governors of the Federal Reserve System (U.S.), Survey of Terms of Business Lending, https://www.federalreserve.gov/releases/e2/current/. Borio,ClaudioandHaibinZhu(2012).“Capitalregulation,risk-takingandmonetarypolicy: Amissinglink inthetransmissionmechanism?”JournalofFinancialStability8(4): 236-251. Buch, Claudia, Sandra Eickmeier, and Esteban Prieto (2014). “In search for yield? Survey-based evidence onbankrisktaking,”JournalofEconomicDynamicsandControl43: 12-30. Carlstrom, C. and Timothy Fuerst (1997). “Agency Costs, Net Worth, and Business Fluctuations: A ComputableGeneralEquilibriumAnalysis,”AmericanEconomicReview87(5): 893-910. Chari,V.V.,PatrickJ.Kehoe,andEllenR.McGrattan(2000).“StickyPriceModelsoftheBusinessCycle: CantheContractMultiplierSolvethePersistenceProblem?”Econometrica68(5): 1151-1179. Christensen, Ian and Ali Dib (2008). “The Financial Accelerator in an Estimated New Keynesian Model,” ReviewofEconomicDynamics11(1): 155–178. Christiano, Lawrence J., Martin Eichenbaum, and Charles L. Evans (2005). “Nominal Rigidities and the DynamicEffectsofaShocktoMonetaryPolicy,”JournalofPoliticalEconomy113(1): 1-45. Christiano, Lawrence J., Roberto Motto, and Massimo Rostagno (2014). “Risk Shocks,” American EconomicReview104(1): 27-65. 34

Covas,FranciscoandWouterJ.DenHaan(2012).“TheRoleofDebtandEquityFinanceOvertheBusiness Cycle,”EconomicJournal122(565): 1262-1286. FederalReserveBankofPhiladelphia,GreenbookDataSets,https://www.philadelphiafed.org/research-anddata/real-time-center/greenbook-data. FederalReserveBankofSt.Louis,FRED,https://fred.stlouisfed.org. Forni, Mario and Luca Gambetti (2014), “Sufficient information in structural VARs,” Journal of Monetary Economics66(1): 124-136. Gale, Douglas and Martin Hellwig (1985). “Incentive-Compatible Debt Contracts: The One-Period Problem,”ReviewofEconomicStudies52(4): 647-663. Gertler,MarkandPeterKaradi(2011).“Amodelofunconventionalmonetarypolicy,”JournalofMonetary Economics58(1): 17-34. Gertler, Mark, Nobuhiro Kiyotaki, and Albert Queralto (2012). “Financial crises, bank risk exposure and governmentfinancialpolicy,”JournalofMonetaryEconomics59(S):S17-S34. Gilchrist,SimonandEgonZakrajsˇek(2012).“CreditSpreadsandBusinessCycleFluctuations,”American EconomicReview102(4): 1692-1720. Ioannidou,Vasso,StevenOngena,andJose´-LuisPeydro´ (2015).“MonetaryPolicy,Risk-TakingandPricing: EvidencefromaQuasi-NaturalExperiment,”ReviewofFinance19(1): 95-144. Jime´nez,Gabriel,StevenOngena,Jose´-LuisPeydro´,andJesusSaurina(2014).“HazardousTimesforMonetary Policy: What Do Twenty-Three Million Bank Loans Say about the Effects of Monetary Policy on CreditRisk-Taking?” Econometrica82(2): 463-505. Kurtzman, Robert. J., Stephan Luck, and Tom Zimmermann (2017). “Did QE Lead Banks to Relax Their LendingStandards? EvidencefromtheFederalReserve’sLSAPs?,” FinanceandEconomicsDiscussion Series2017-093.BoardofGovernorsoftheFederalReserveSystem(U.S.). Levin,AndrewT.,FabioM.Natalucci,andEgonZakrajsˇek(2004).“TheMagnitudeandCyclicalBehavior ofFinancialMarketFrictions,”FederalReserveBoardFinanceandEconomicsDiscussionSeries04-70. Maddaloni,AngelaandJose´-LuisPeydro´ (2011).“BankRisk-taking,Securitization,Supervision,andLow InterestRates: EvidencefromtheEuro-areaandtheU.S.LendingStandards,”ReviewofFinancialStudies 24(6): 2121-2165. Onatski,Alexei(2009).“TestingHypothesesabouttheNumberofFactorsinLargeFactorModels,”Econometrica77(5): 1447-1479. Paligorova,TeodoraandJoa˜oA.C.Santos(2017).“MonetaryPolicyandBankRisk-Taking: Evidencefrom theCorporateLoanMarket,”JournalofFinancialIntermediation30: 35-49. Petersen,MitchellA.andRaghuramG.Rajan(1995).“TheEffectofCreditMarketCompetitiononLending Relatioships,”QuarterlyJournalofEconomics110(2): 407-443. 35

Taylor,JohnB.(1993).“DiscretionversusPolicyRulesinPractice,”Carnegie-RochesterConferenceSeries onPublicPolicy39: 195-214. Taylor, John B. (2007). “Housing and Monetary Policy,” Proceedings – Economic Policy Symposium – JacksonHole: 463-476. Townsend,RobertM.(1979).“OptimalContractsandCompetitiveMarketswithCostlyStateVerification,” JournalofEconomicTheory21(2): 265-293. Valencia, Fabia´n (2014). “Monetary policy, bank leverage, and financial stability,” Journal of Economic DynamicsandControl47: 20-38. 36

AppendixA. TheOptimalLoanContract This appendix provides details on the optimal financial contract, following the logic in Bernanke et al. (1999). Giventhedifferentassumptionsabouttherolesofborrowersandlenders,however,wedeviatefrom thelatter,wherethisisnecessary. AppendixA.1. WithoutAggregateRisk Intheabsenceofaggregaterisk,theloancontractbetweenthebankandentrepreneuriisonlyaffectedby theentrepreneur’sidiosyncraticriskωi. Consequently,thebank’sconstrainedprofitmaximizationproblem canbeformulatedasinequation(6),wherealltermsaredefinedinthemaintext. Giventheborrower’snetworth,thebankchoosesthevolumeoftheloanandthusk. Foranyvalueofk, theentrepreneur’sparticipationconstraint(PC)pinsdownthedefaultthresholdω¯i,whichsplitstheexpected totalprofitsfromtheinvestmentprojectbetweentheborrowerandthelender. Givenω¯i,thenon-defaultrate ofreturnontheloantoentrepreneuri,Zi ,willthenbedeterminedby(3). t+1 For notational convenience, we suppress any time subscripts and index superscripts throughout the appendix, while our aim remains to derive the properties of the optimal contract between the bank and entrepreneuri. AppendixA.1.1. TheEFPandLoanSupply Inwhatfollows,weestablishapositiverelationship,k = ψ(s),ψ(cid:48)(s) > 0,betweentheexternalfinance premium (EFP) s ≡ Rk/R and the bank’s optimal choice of the capital/net worth ratio k ≡ QK/N. The Lagrangiancorrespondingtotheconstrainedprofit-maximizationproblemin(6)isgivenby L = (cid:2)Γ(ω¯)−µG(ω¯) (cid:3) sk−(k−1−n)+λ{[1−Γ(ω¯)]sk−s}, where n ≡ Nb/N and λ is the Lagrangian multiplier on the borrower’s PC. The corresponding first-order conditions(FOCs)are k : (cid:2)Γ(ω¯)−µG(ω¯) (cid:3) s−1+λ[1−Γ(ω¯)]s = 0, ω¯ : (cid:2)Γ(cid:48)(ω¯)−µG(cid:48)(ω¯) (cid:3) sk−λΓ(cid:48)(ω¯)sk = 0, λ : [1−Γ(ω¯)]sk−s = 0. NotethattheassumptionsmadeaboutΓ(ω¯)andµG(ω¯)implythatthebank’sexpectedprofitsharenet ofexpecteddefaultcostssatisfies Γ(ω¯)−µG(ω¯) > 0 for ω¯ ∈ (0,∞) (A.1) and lim Γ(ω¯)−µG(ω¯) = 0, lim Γ(ω¯)−µG(ω¯) = 1−µ. ω¯→0 ω¯→∞ In order for the bank’s profits to be bounded in the case where the borrower defaults with probability one, wethereforeassumethat s < 1/(1−µ)(compareBernankeetal.,1999). 37

Wefurtherassumethatω¯h(ω¯)isincreasinginω¯,whereh(ω¯)denotesthehazardrate f (ω¯)/[1−F(ω¯)].29 Hence,thereexistsanω¯∗ suchthat Γ(cid:48)(ω¯)−µG(cid:48)(ω¯) = [1−F(ω¯)] (cid:2) 1−µω¯h(ω¯) (cid:3) (cid:84) 0 for ω¯ (cid:83) ω¯∗, i.e.,thebank’sexpectednetprofitsharereachesaglobalmaximumatω¯∗. Moreover,theaboveassumption impliesthat ∂[ω¯h(ω¯)] Γ(cid:48)(ω¯)G(cid:48)(cid:48)(ω¯)−Γ(cid:48)(cid:48)(ω¯)G(cid:48)(ω¯) = [1−F(ω¯)]2 > 0 forallω¯. (A.2) ∂ω¯ ConsiderfirsttheFOCw.r.t.ω¯,whichimpliesthat Γ(cid:48)(ω¯)−µG(cid:48)(ω¯) λ(ω¯) = . Γ(cid:48)(ω¯) Takingthepartialderivativew.r.t.ω¯,weobtain Γ(cid:48)(ω¯) (cid:2)Γ(cid:48)(cid:48)(ω¯)−µG(cid:48)(cid:48)(ω¯) (cid:3) −Γ(cid:48)(cid:48)(ω¯) (cid:2)Γ(cid:48)(ω¯)−µG(cid:48)(ω¯) (cid:3) λ(cid:48)(ω¯)= . [Γ(cid:48)(ω¯)]2 µ[Γ(cid:48)(cid:48)(ω¯)G(cid:48)(ω¯)−Γ(cid:48)(ω¯)G(cid:48)(cid:48)(ω¯)] = < 0, (A.3) [Γ(cid:48)(ω¯)]2 becauseΓ(cid:48)(ω¯) = 1−F(ω¯) > 0andΓ(cid:48)(cid:48)(ω¯)G(cid:48)(ω¯)−Γ(cid:48)(ω¯)G(cid:48)(cid:48)(ω¯) < 0from(A.2)forallω¯. Takinglimits, lim λ(ω¯) = 1, lim λ(ω¯) = 0. ω¯→0 ω¯→ω¯∗ IncontrasttoBernankeetal.(1999),λ(ω¯)isthereforeadecreasingfunctionofthecutoff. Thisisduetothe fact that, while the bank’s expected share of total profits is increasing in ω¯, a higher default threshold also implies a higher expected verification cost. At ω¯∗, the increase in the expected verification cost, µG(cid:48)(ω¯), exactlyoffsetstheincreaseinthebank’sexpectedgrossprofitshare,Γ(cid:48)(ω¯). Asaconsequence,theshadow valueoflooseningtheborrower’sPCconvergestozeroasω¯ → ω¯∗. FromtheFOCw.r.t.k,wecanfurthermoredefineafunction 1 ρ(ω¯) ≡ = s. Γ(ω¯)−µG(ω¯)+λ[1−Γ(ω¯)] Takingthepartialderivativew.r.t.ω¯,weobtain ρ(cid:48)(ω¯)= −ρ(ω¯)2(cid:8)Γ(cid:48)(ω¯)−µG(cid:48)(ω¯)+λ(cid:48)(ω¯)[1−Γ(ω¯)]−λ(ω¯)Γ(cid:48)(ω¯) (cid:9) = −ρ(ω¯)2(cid:8) λ(ω¯)Γ(cid:48)(ω¯)+λ(cid:48)(ω¯)[1−Γ(ω¯)]−λ(ω¯)Γ(cid:48)(ω¯) (cid:9) = −ρ(ω¯)2λ(cid:48)(ω¯)[1−Γ(ω¯)] > 0, (A.4) (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)(cid:32)(cid:32)(cid:32)(cid:32) (cid:124) (cid:123)(cid:122) (cid:125)(cid:124)(cid:123)(cid:122)(cid:125)(cid:124) (cid:123)(cid:122) (cid:125) <0 <0 >0 29GiventhatweborrowthedefinitionsofΓ(ω¯)andΓ(ω¯)−µG(ω¯)fromBernankeetal.(1999),ourassumptionaboutthehazard rateanditsimplicationsareidenticaltothoseintheirAppendixA. 38

wherethesecondequalityusestheFOCw.r.t.ω¯. Inthelimit,asω¯ goesto0andω¯∗,respectively, lim ρ(ω¯) =1 (dueto lim λ(ω¯) = 1and limG(ω¯) = 0), ω¯→0 ω¯→0 ω¯→0 1 lim ρ(ω¯) = ≡ s∗ (dueto lim λ(ω¯) = 0). ω¯→ω¯∗ Γ(ω¯∗)−µG(ω¯∗) ω¯→ω¯∗ Accordingly, there is a one-to-one mapping between the optimal cutoff, ω¯, and the premium on external funds, s, as in Bernanke et al. (1999). Inverting the function s = ρ(ω¯), we can therefore express the cutoff asω¯ = ω¯ (s),whereω¯(cid:48)(s) > 0for s ∈ (1,s∗). FromtheFOCw.r.t.λ,i.e.theborrower’sPC,wefinallydefine 1 Ψ(ω¯) = = k. 1−Γ(ω¯) Takingthepartialderivativew.r.t.ω¯,weobtain Ψ(cid:48)(ω¯) = −Ψ(ω¯)2(cid:2) −Γ(cid:48)(ω¯) (cid:3) = Ψ(ω¯)2[1−F(ω¯)] > 0. (A.5) (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)(cid:32)(cid:32) (cid:124)(cid:123)(cid:122)(cid:125)(cid:124) (cid:123)(cid:122) (cid:125) >0 >0 Hence,thequalitativeimplicationsarethesameasinBernankeetal.(1999). Takinglimits, 1 lim Ψ(ω¯) = 1, lim Ψ(ω¯) = < ∞. ω¯→0 ω¯→ω¯∗ 1−Γ(ω¯∗) Combiningk = Ψ(ω¯)andω¯ = ω¯ (s),whereΨ(cid:48)(ω¯) > 0andω¯(cid:48)(s) > 0,wecanexpressthecapital/networth ratio,k = QK/N,asafunctionk = ψ(s),whereψ(cid:48)(s) > 0for s ∈ (1,s∗). AppendixA.1.2. ProofofInteriorSolution Bernanke et al. (1999) use a general equilibrium argument to justify their assumption of an interior solution, i.e. an optimal contract with ω¯ < ω¯∗ and s < s∗. In particular, they argue that “as s approaches s∗ from below, the capital stock becomes unbounded. In equilibrium this will lower the excess return s.” (compareBernankeetal.,1999,p.1384). Here,weemployananalyticalargumentinstead. Recallthatthelender’siso-profitcurves(IPC)andthe borrower’sparticipationconstraint(PC)in(k,ω¯)-spacecanbewrittenas πb−1−n k IPC = (cid:2)Γ(ω¯)−µG(ω¯) (cid:3) s−1 , (A.6) 1 k ≥ , (A.7) PC 1−Γ(ω¯) whereπb denotesanarbitrarylevelofbankprofits. Recall further that, in (k,ω¯)-space, the optimal contract is determined by the tangential point of the borrower’sPCwiththelowestIPCofthelender. Considerfirsttheborrower’sPCin(A.7). SinceΓ(cid:48)(ω¯) > 0, k is a strictly increasing function for any ω¯ ∈ [0,∞), so that the borrower’s PC has a positive slope PC everywherein(k,ω¯)-space. Considernextthelender’sIPCin(A.6). Takingthepartialderivativeofk w.r.t.ω¯, IPC 39

 ∂ ∂ ω k ¯ (cid:12) (cid:12) (cid:12) (cid:12) (cid:12) IPC = (cid:16) 1−πb+n (cid:17) (cid:8)(cid:2)Γ (cid:2)Γ (ω¯ (cid:48)( ) ω¯ − ) µ − G µ ( G ω¯ (cid:48) ) ( (cid:3) ω¯ s ) − (cid:3) s 1 (cid:9)2   > = < 0 0 0 f f f o o o r r r ω ω ω ¯ ¯ ¯ ∈ = ∈ [ ( ω¯ 0 ω¯ ∗ , ∗ ω , ¯ ∞ ∗) ) . Accordingly,thelender’sIPChasapositiveslopein(k,ω¯)-spaceleftof ω¯∗ andanegativesloperightof ω¯∗. Sincetheoptimalcontractrequiresthat (cid:12) (cid:12) ∂k(cid:12) ∂k(cid:12) (cid:12) (cid:12) = (cid:12) (cid:12) , ∂ω¯ (cid:12) ∂ω¯ (cid:12) IPC PC atthetangentialpoint,andwealreadyknowthat ∂k (cid:12) (cid:12) Γ(cid:48)(ω¯) (cid:12) (cid:12) = > 0 for ω¯ ∈ [0,∞) ∂ω¯ (cid:12) PC [1−Γ(ω¯)]2 theoptimaldefaultthresholdcanonlylieinω¯ ∈ [0,ω¯∗),whichguaranteesaninteriorsolutiontothebank’s constrainedprofitmaximizationproblem.30 Thiscompletestheproof. AppendixA.1.3. ProofofUniqueness As shown above, the tangential point of the borrower’s participation constraint (PC) and the lender’s iso-profit curve (IPC) is located on the interval [0,ω¯∗). Uniqueness requires that there is exactly one such point,i.e.,weneedtoshowthatthereexistsonlyoneω¯ thatsatisfiesboth 1 πb−1−n k PC = 1−Γ(ω¯) = (cid:2)Γ(ω¯)−µG(ω¯) (cid:3) s−1 = k IPC (A.8) and ∂k (cid:12) (cid:12) Γ(cid:48)(ω¯) (cid:16) 1−πb+n (cid:17) s (cid:2)Γ(cid:48)(ω¯)−µG(cid:48)(ω¯) (cid:3) ∂k (cid:12) (cid:12) ∂ω¯ (cid:12) (cid:12) (cid:12) PC ≡ [1−Γ(ω¯)]2 = (cid:8)(cid:2)Γ(ω¯)−µG(ω¯) (cid:3) s−1 (cid:9)2 ≡ ∂ω¯ (cid:12) (cid:12) (cid:12) IPC , (A.9) asthelevelsofkaswellastheslopesimpliedbythePCandtheIPCareidenticalatthepointoftangency. Inwhatfollows,wesuppressthedependenceofΓ(ω¯)andG(ω¯)ontheirargumentω¯ fornotationalease. Notethat(A.8)and(A.9)canbemergedintoasingleconditionthatmustholdatthetangentialpoint: Γ(cid:48)−µG(cid:48) 1−πb+n = . (A.10) Γ(cid:48) s GiventhatΓ(cid:48) = 1−F (cid:44) 0on[0,ω¯∗),wecanrewrite(A.10)as (cid:32) (cid:33) µG(cid:48) 1−πb+n G(cid:48) 1 1−πb+n 1− = ⇔ = 1− , Γ(cid:48) s Γ(cid:48) µ s theright-handsideofwhichisconstantandthusahorizontallinein(k,ω¯)-space. Partiallydifferentiatingtheleft-handsidewithrespecttoω¯ yields 30NotethatourlineofargumentequallyappliestotheformulationofthefinancialcontractinBernankeetal.(1999),likewise guaranteeinganinteriorsolution. 40

∂(G(cid:48)/Γ(cid:48)) G(cid:48)(cid:48)Γ(cid:48)−Γ(cid:48)(cid:48)G(cid:48) = > 0 forallω¯ from(A.2). ∂ω¯ (Γ(cid:48))2 Given that the left-hand side is monotonically increasing in ω¯, it can cross the horizontal line defined by the right-hand side at no more than one point on [0,ω¯∗), yielding a unique point of tangency between the borrower’sPCandthelender’sIPC.31 Thiscompletestheproof. AppendixA.2. WithAggregateRisk In the presence of aggregate risk, the loan contract between the bank and entrepreneur i is affected by theentrepreneur’sidiosyncraticrisk,ωi ,aswellasbytheex-postrealizationofRk . Inthisappendix,we t+1 t+1 establish a positive relationship between the entrepreneur’s capital/net worth ratio, ki ≡ Q Ki/Ni, and the t t t t ex-anteexpected externalfinancepremium(EFP), s ≡ E Rk /Rn. Again,wesuppresstimesubscriptsand t t t+1 t indexsuperscriptsfornotationalconvenience. Following Bernanke et al. (1999), it is convenient to write total profits per unit of capital expenditures as u˜ωRk, where u˜ denotes an aggregate shock to the gross real rate of return on capital, while ω continues to denote the entrepreneur’s idiosyncratic productivity shock, where E(u˜) = E(ω) = 1. Using definitions fromthemaintextandAppendixAppendixA.1,wecanrewritethebank’sconstrainedprofitmaximization probleminequation(6)as max E (cid:8)(cid:2)Γ(ω¯)−µG(ω¯) (cid:3) u˜sk−(k−1−n) (cid:9) s.t. E{[1−Γ(ω¯)]u˜sk−u˜s} ≥ 0. k,ω¯ ThecorrespondingLagrangian, L = E (cid:8)(cid:2)Γ(ω¯)−µG(ω¯) (cid:3) u˜sk−(k−1−n)+λ([1−Γ(ω¯)]u˜sk−u˜s) (cid:9) , yieldsthefollowingfirst-orderconditions(FOCs): k : E (cid:8)(cid:2)Γ(ω¯)−µG(ω¯) (cid:3) u˜s−1+λ[1−Γ(ω¯)]u˜s (cid:9) = 0, ω¯ : E (cid:8)(cid:2)Γ(cid:48)(ω¯)−µG(cid:48)(ω¯) (cid:3) u˜sk−λΓ(cid:48)(ω¯)u˜sk (cid:9) = 0, λ : E{[1−Γ(ω¯)]u˜sk−u˜s} = 0. Asdiscussedinthemaintext,weassumethattheborrower’sparticipationconstraint(PC)issatisfiedex post, i.e.foreachrealizationofu˜. Asaconsequence,ω¯ andanyfunctionthereof, suchasΓ(ω¯)andΓ(cid:48)(ω¯), forexample,isindependentoftherealizationofu˜. Usingthisassumption,theaboveFOCssimplifyto k : E (cid:8)(cid:2)Γ(ω¯)−µG(ω¯) (cid:3) u˜s+λ[1−Γ(ω¯)]u˜s (cid:9) = 1, ω¯ : (cid:2)Γ(cid:48)(ω¯)−µG(cid:48)(ω¯) (cid:3) = λΓ(cid:48)(ω¯), λ : [1−Γ(ω¯)]k = 1. 31Note thatG(cid:48)/Γ(cid:48) is defined on ω¯ ∈ [0,∞) and takes values on [0,∞). For this reason, the intersection betweenG(cid:48)/Γ(cid:48) and (cid:104) (cid:16) (cid:17) (cid:105) 1− 1−πb+n /s /µexistsforπb(cid:62)1+n−s. 41

Partiallydifferentiatingtheborrower’sex-postPCw.r.t.kandω¯,respectively,weobtain ∂ ∂ω¯ ∂ω¯ 1−Γ(ω¯) = 1−Γ(ω¯)−Γ(cid:48)(ω¯)k = 0 ⇒ = > 0 ∂k ∂k ∂k Γ(cid:48)(ω¯)k and ∂ ∂ω¯ ∂ω¯ = −Γ(cid:48)(ω¯)k = 0 ⇒ = 0. ∂s ∂s ∂s FurthermoredefiningΥ(ω¯) ≡ Γ(ω¯)−µG(ω¯)+λ[1−Γ(ω¯)],totaldifferentiationoftheFOCw.r.t.kyields (cid:40) (cid:32) (cid:33)(cid:41) ∂ω¯ ∂ω¯ E u˜Υ(ω¯)+u˜sΥ(cid:48)(ω¯) ds+ dk = 0 ∂s ∂k (cid:40) (cid:41) (cid:40) (cid:41) ∂ω¯ ∂ω¯ ⇔ E u˜sΥ(cid:48)(ω¯) dk = −E u˜Υ(ω¯)+u˜sΥ(cid:48)(ω¯) ds ∂k ∂s (cid:110) (cid:111) dk E u˜Υ(ω¯)+u˜sΥ(cid:48)(ω¯) ∂ω¯ E{u˜Υ(ω¯)} ⇒ = − (cid:110) (cid:111) ∂s = − (cid:110) (cid:111) > 0, ds E u˜sΥ(cid:48)(ω¯) ∂ω¯ E u˜sΥ(cid:48)(ω¯) ∂ω¯ ∂k ∂k wherethefinalequalitymakesuseofourpreviousresultsthat∂ω¯/∂k > 0,∂ω¯/∂s = 0,and Υ(cid:48)(ω¯)= Γ(cid:48)(ω¯)−µG(cid:48)(ω¯)−λ(ω¯)Γ(cid:48)(ω¯)+λ(cid:48)(ω¯)[1−Γ(ω)] = λ(cid:48)(ω¯)k−1 < 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)(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)(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)(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)(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:124) (cid:123)(cid:122) (cid:125) =0fromtheFOCw.r.t.ω¯ SimilartoBernankeetal.(1999),theoptimalloancontractthereforeimpliesapositiverelationshipbetween theborrower’scapital/networthratioandtheex-anteexpectedEFPeveninthepresenceofaggregaterisk. Thiscompletestheproof. AppendixA.3. HeuristicArgumentforourRisk-SharingAgreement Suppose that Zi was predetermined and thus acyclical in period t+1. Given that Bi and Q Ki are also t t t t predetermined in t +1, the definition of the default threshold in (3) implies that ω¯i is a strictly convex, t+1 decreasing function in Rk ∀Zi,Rk > 0.32 Accordingly, an unexpected decrease in Rk raises ω¯i by t+1 t t+1 t+1 t+1 morethananequivalentunexpectedincreaseinRk lowersω¯i ,i.e.,symmetricfluctuationsinRk imply t+1 t+1 t+1 asymmetric fluctuations in the default threshold and thus in the default rate of entrepreneurs, even if the idiosyncratic productivity shocks were uniformly distributed. This asymmetry is amplified if ωi follows t+1 a log-normal distribution with ω¯i in the left tail of the distribution, as we assume below. Since default t+1 imposesaresourcecostontheeconomyinthismodel,any(unexpected)cyclicalityofω¯i overthebusiness t+1 cycleisundesirable. Ourrisk-sharingagreement,wherethebankbearstheaggregateriskandhenceω¯i is t+1 acyclicalonimpact,eliminatestheshareofthemonitoringcostthatisduetotheasymmetricfluctuationsin entrepreneurdefault. 32RecallthatZiandRk arethegrossnon-defaultratesofreturnonaloantoentrepreneuriandperunitofcapital,respectively. t t+1 42

AppendixB. TheGeneralEquilibriumModel Thegeneralequilibriummodelcompriseseighttypesofeconomicagents: Arepresentativehousehold, a representative capital goods producer, a representative intermediate goods producer, a continuum of monopolisticallycompetitiveretailers,acontinuumofmonopolisticallycompetitivelaborunions,acontinuum ofperfectlycompetitiveentrepreneurs,amonopolisticbank,andamonetaryauthority. AppendixB.1. Entrepreneurs Attheendofperiodt,entrepreneursusetheiraccumulatednetworth,N,topurchaseproductivecapital, t K,fromcapitalgoodsproducersataprice Q intermsofthenumeraire. Tofinancethedifferencebetween t t their net worth and total capital expenditures, Q K, entrepreneurs must borrow an amount B = Q K −N t t t t t t inrealtermsfrombanks,wherevariableswithoutanindexsuperscriptdenoteeconomy-wideaggregates. Theentrepreneurdecidesonthedegreeofcapitalutilizationu andrentspartofcapitalservicesu K t t t−1 to the intermediate goods producers (introduced below). The revenue from selling the capital services is rku K and the cost (in real terms) of adjusting the capital utilization rate is a(u)K , where we assume t t t−1 t t−1 a(cid:48) > 0anda(cid:48)(cid:48) > 0. Theoptimizationproblemoftheentrepreneurisgivenby: (cid:104) (cid:105) max rku −a(u) ωK t t t t−1 ut Intheaggregateoptimum,i.e.averagedoverallentrepreneurs,itmustholdthat rk = a(cid:48)(u). (B.1) t t AsinChristianoetal.(2014),weemploythefollowingfunctionalformfortheadjustmentcostfunctionof thecapitalutilizationrate: a(u) = rk ss (cid:2) exp{σ (u −1)}−1 (cid:3) , (B.2) t u t σ u whererk referstothesteady-staterentalrateofcapitalservices. ss Theaggregaterealrateofreturnperunitofcapitalinperiodt dependsontherealrentalrateofcapital services, rku, and the capital gain of the non-depreciated capital stock, (1−δ)K , between t−1 and t in t t t−1 realterms,netofcapitalutilizationadjustmentcostsa(u): t rku +(1−δ)Q −a(u) Rk = t t t t . (B.3) t Q t−1 A continuum of risk-neutral entrepreneurs, indexed i ∈ [0,1], is hit by an idiosyncratic disturbance ωi in t period t. As a result, the ex-post rate of return of entrepreneur i per unit of capital equals ωiRk. Following t t Bernankeetal.(1999),weassumethatωi isi.i.d.acrosstimetandacrossentrepreneursi,withacontinuous t (cid:110) (cid:111) and differentiable cumulative distribution function F(ω) over a non-negative support, where E ωi = 1 ∀t t andthecorrespondinghazardrateh(ω) ≡ f (ω)/[1−F(ω)]satisfies∂ωh(ω)/∂ω > 0. In contrast to Bernanke et al. (1999) and variations thereof, we assume that entrepreneurs can operate eveninfinancialautarkybypurchasing Q K = N inperiodt. Inorderforanentrepreneurtoacceptaloan t t t 43

offer, the terms of the loan, i.e. the amount B and the nominal non-default rate of return, Z, must be such t t thattheentrepreneurexpectstobenoworseoffthaninfinancialautarky. Assumingconstantreturnstoscale (CRS),thedistributionofnetworth,Ni,acrossentrepreneursisirrelevant. Asaconsequence,theaggregate t versionoftheparticipationconstraintinequation(4)canbewrittenas (cid:40)(cid:90) ∞ Z (cid:41) (cid:110) (cid:111) E ωRk Q K − t dF(ω) ≥ E Rk N, (B.4) t ω¯t+1 t+1 t t π t+1 t t+1 t where (cid:110) theexpec (cid:111) tationisoverRk t+1 , andω¯ t+1 denotestheexpected defaultthresholdinperiodt+1, defined byE t ω¯ t+1 Rk t+1 Q t K t ≡ E t {Z t /π t+1 }B t . Using the definition of ω¯ t+1 to substitute out E t {Z t /π t+1 } and expressing the aggregate profit share of entrepreneursinperiodtas1−Γ(ω¯ ),equation(B.4)canequivalentlybewrittenas t (cid:110) (cid:111) (cid:110) (cid:111) E t [1−Γ(ω¯ t+1 )]Rk t+1 Q t K t ≥ E t Rk t+1 N t . (B.5) Note that the ex-post realized value of Γ(ω¯ t+1 ) generally depends on the realization of Rk t+1 through ω¯ t+1 . Similar to Bernanke et al. (1999), we assume that this constraint must be satisfied ex post. Implicit in this is the assumption that Rk is observed by both parties without incurring a cost, and that the non-default t+1 repayment,Z,canthusbemadecontingentontheaggregatestateoftheeconomy. t In order to avoid that entrepreneurial net worth grows without bound, we assume that an exogenous fraction (1 − γe) of the entrepreneurs’ share of total realized profits is consumed in each period.33 As a result,entrepreneurialnetworthattheendofperiodtevolvesaccordingto N = γe[1−Γ(ω¯ )]RkQ K . (B.6) t t t t−1 t−1 Tosumup,theentrepreneurs’equilibriumconditionscomprisetherealrateofreturnperunitofcapital in (B.3), the ex-post participation constraint in (B.5), the evolution of entrepreneurial net worth in (B.6), and the real amount borrowed, B = Q K −N. Moreover, the definition of the expected default threshold, t t t t E t ω¯ t+1 ,determinestheexpectednon-defaultrepaymentperunitborrowedbytheentrepreneurs,E t {Z t /π t+1 }. AppendixB.1.1. RiskShocks WefollowChristianoetal.(2014)tointroducerisksshock,σ ,intothemodel,whichcapturetheextent ω,t ofcross-sectionaldispersioninω. RiskshocksfollowanAR(1)-processwithautocorrelationcoefficientρ σ and mean-zero normally distributed disturbances, uσ. To incorporate both unanticipated and anticipated t componentsofriskshocks,weadoptthefollowingrepresentationfromChristianoetal.(2014): loguσ = ξ +ξ +···+ξ , t 0,t 1,t−1 p,t−p 33Intheliterature,itiscommontoassumethatanexogenousfractionofentrepreneurs“dies”eachperiodandconsumesitsnet worthuponexit.Thedynamicimplicationsofeitherassumptionareidentical. 44

where p = 8,ξ denotestheunanticipatedcomponent,whileξ , j > 0,areso-called“news”components. 0,t j,t Weassumethefollowingcorrelationstructure: Eξ ξ ρ [ ξ i,j] = (cid:113)(cid:16) i, (cid:17) t (cid:16) i,t (cid:17) , i, j = 0,...,p, (B.7) Eξ2 Eξ2 i,t i,t where ρ [i,j] ∈ [−1,1]. For parsimony, the standard deviation of the anticipated component is equal to σ , ξ σ whilethestandarddeviationsofallnewscomponentsareassumedtobeidenticalandequaltoσ . ξ AppendixB.2. TheBank For tractability, we assume a single monopolistic financial intermediary, which collects deposits from households and provides loans to entrepreneurs. In period t, this bank is endowed with net worth or bank capital Nb. Abstracting from bank reserves or other types of bank assets, the balance sheet identity in real t termsisgivenbyequation(1). TheCSVprobleminTownsend(1979)impliesthat,ifentrepreneuridefaults due to ωiRkQ Ki < (Zi /π)Bi , the bank incurs a proportional cost µωiRkQ Ki and recovers the t t t−1 t−1 t−1 t t−1 t t t−1 t−1 remainingreturnoncapital,(1−µ)ωiRkQ Ki . t t t−1 t−1 In period t, the risk-neutral bank observes entrepreneurs’ net worth, Ni, and makes a take-it-or-leave-it t offertoeachentrepreneuri. Asaconsequence,itholdsaperfectlydiversifiedloanportfoliobetweenperiod tandperiodt+1. Althoughthebankcanthusdiversifyawayanyidiosyncraticriskarisingfromthepossible default of entrepreneur i, it is subject to aggregate risk through fluctuations in the ex-post rate of return on capital, Rk t+1 , and the aggregate default threshold, ω¯ t+1 . In order to be able to pay the risk-free nominal rate of return Rn on deposits in each state of the world, the bank must have sufficient net worth to protect t depositorsfromunexpectedfluctuationsinRk . t+1 Nowconsiderthebank’sproblemofmakingatake-it-or-leave-itoffertoentrepreneuriwithnetworthNi t inperiodt. Thecontractofferedbythebankspecifiestherealamountoftheloan, Bi,andthenominalgross t rateofreturnincaseofrepayment,Zi. GiventhatNiispredeterminedattheendofperiodt,thebank’schoice t t of Bi also determines the entrepreneur’s total capital expenditure, Q Ki = Bi + Ni. Moreover, given Q Ki t t t t t t t (cid:110) (cid:111) and N t i, the bank’s choice of Z t i implies an expected default threshold E t ω¯ t+1 through E t ω¯ t+1 Rk t+1 Q t K t ≡ E t {Z t /π t+1 }B t . Hence,wecanequivalentlyrewritethebank’sconstrainedprofit-maximizationproblemfor aloantoentrepreneurias (cid:40) (cid:41) (cid:104) (cid:16) (cid:17) (cid:16) (cid:17)(cid:105) Rn (cid:16) (cid:17) max E Γ ω¯i −µG ω¯i Rk Q Ki− t Q Ki−Ni−Nb,i , (B.8) K t i,ω¯i t+1 t t+1 t+1 t+1 t t π t+1 t t t t whereΓ (cid:16) ω¯i (cid:17) ≡ (cid:82)ω¯i tωdF(ω)+ω¯i (cid:104) 1−F (cid:16) ω¯i (cid:17)(cid:105) ,µG (cid:16) ω¯i (cid:17) ≡ µ (cid:82)ω¯i tωdF(ω),and Nb,i denotestheshareoftotal t 0 t t t 0 t banknetworthassignedtotheloantoentrepreneuri,subjecttotheparticipationconstraintin(4). (cid:110) (cid:111) Thecorrespondingfirst-orderconditionswithrespectto Ki,E ω¯i ,λb,i ,whereλb,idenotestheex-post t t t+1 t t 45

valueoftheLagrangemultiplierontheparticipationconstraint,aregivenby (cid:40) (cid:41) (cid:110)(cid:104) (cid:16) (cid:17)(cid:105) (cid:111) Rn Ki : E Γ(ω¯i )−µG(ω¯i )+λb,i 1−Γ(ω¯i ) Rk = E t , (B.9) t t t+1 t+1 t t+1 t+1 t π t+1 (cid:110)(cid:104) (cid:105) (cid:111) (cid:110) (cid:111) E ω¯i : E Γ(cid:48)(ω¯i )−µG(cid:48)(ω¯i ) Rk = E λb,iΓ(cid:48)(ω¯i )Rk , (B.10) t t+1 t t+1 t+1 t+1 t t t+1 t+1 (cid:104) (cid:105) λb,i : 1−Γ(ω¯i ) Rk Q Ki = Rk Ni. (B.11) t t+1 t+1 t t t+1 t Following Bernanke et al. (1999), we show in Appendix Appendix A.2 that the optimal debt contract between entrepreneur i and the bank implies a positive relationship between the expected EFP, s ≡ t (cid:110) (cid:111) E t Rk t+1 π t+1 /Rn t ,andtheoptimalcapital/networthratio,k t i ≡ Q t K t i/N t i. Here, instead, we go beyond this “reduced-form” result and utilize the entire structure inherent in the first-order conditions. Note that (B.9) equates the expected marginal return of an additional unit of capital tothebankandtheentrepreneurtotheexpectedmarginalcostofanadditionalunitofbankdepositsinreal terms. Assuming that the participation constraint is satisfied ex post, this implies a positive relationship (cid:110) (cid:111) (cid:110) (cid:111) between E t Rk t+1 π t+1 /Rn t and E t ω¯i t+1 . Moreover, (B.11) equatesthe ent (cid:110) repren (cid:111) eur’sexpected payoffwith and without the bank loan and implies a positive relationship between E ω¯i and Q Ki/Ni.34 Together, t t+1 t t t these two conditions determine the positive ex-ante relationship between the expected EFP in period t+1 (cid:110) (cid:111) andtheleverageratiochosenbythebankinperiodt,whilethefirst-orderconditionwithrespecttoE ω¯i t t+1 pinsdowntheex-postvalueoftheLagrangemultiplier,λb,i. t (cid:110) (cid:111) (cid:110) (cid:111) Given Ni, Q Ki, and E Rk , the definition of the expected default threshold, E ω¯i , implies an t t t t t+1 (cid:110) (cid:111) t t+1 expectednon-defaultrealrateofreturnontheloantoentrepreneuri, E t Z t i/π t+1 , whilethesameequation (cid:110) (cid:111) evaluated ex post determines the actual non-default repayment conditional on Ni, Q Ki, E ω¯i , and the t t t t t+1 realizationofRk . t+1 (cid:16) (cid:17) (cid:16) (cid:17) Bythelawoflargenumbers,Γ ω¯i −µG ω¯i denotesthebank’sexpectedshareoftotalperiod-tprofits t t (net of monitoring costs) from a loan to entrepreneur i as well as the bank’s realized profit share from its diversified loan portfolio of all entrepreneurs. Accordingly, we can rewrite the bank’s aggregate expected profitsinperiodt+1as (cid:40) (cid:41) E t V t b +1 = E t (cid:2)Γ(ω¯ t+1 )−µG(ω¯ t+1 ) (cid:3) Rk t+1 Q t K t − π R t+ n t 1 (cid:16) Q t K t −N t −N t b (cid:17) , (B.12) wheretheexpectationisoverpossiblerealizationsofRk t+1 andπ t+1 , whileV t b +1 isfreeofidiosyncraticrisk. The entrepreneurs’ participation constraint in (B.5) implies that ω¯ t+1 and thus (cid:2)Γ(ω¯ t+1 )−µG(ω¯ t+1 ) (cid:3) are predeterminedinperiodt+1. Inordertokeeptheproblemtractable,weassumethataggregateriskissmall 34Thisbecomesevident,whenweusetheex-postassumptionthatRk t+1 andω¯ t+1 areuncorrelatedandrewrite(B.11)as (cid:104) (cid:105) Ni 1 1−Γ(ω¯i ) ≥ t ≡ , t+1 QKi ki t t t i.e.,entrepreneuri’sexpectedreturnoncapitalwiththeloanrelativetofinancialautarkymustbenosmallerthantheentrepreneur’s (cid:104) (cid:105) (cid:110) (cid:111) “skininthegame”.Since 1−Γ(ω¯i ) isstrictlydecreasinginE ω¯i ,theparticipationconstraintimpliesapositiverelationship (cid:110) (cid:111) t+1 t t+1 betweenE ω¯i andki. t t+1 t 46

relativetothebank’snetworth,Nb,sothatbankdefaultneveroccursinequilibrium. t Inordertoavoidthatitsnetworthgrowswithoutbound,weassumethatanexogenousfraction(1−γb) ofthebank’sshareoftotalrealizedprofitsisconsumedeachperiod.35 Asaresult,banknetworthattheend ofperiodtevolvesaccordingto Nb = γbVb. (B.13) t t AppendixB.3. Households Therepresentativehouseholdisrisk-averseandderivesutilityfromaDixit-Stiglitzaggregateofimperfectlysubstitutableconsumptiongoods, (cid:34)(cid:90) 1 (cid:15)p−1 (cid:35) (cid:15)p (cid:15)p −1 C t = C t (j) (cid:15)p dj . (B.14) 0 Households have an infinite planning horizon and discount their future expected utility with the subjective discountfactorβ < 1. Theycantransferwealthintertemporallybysavingintermsofbankdeposits,which pay the risk-free nominal return Rn between t and t +1.36 We allow for habit formation in consumption. t Householdssupplyhomogenouslabortothemonopolisticallycompetitivelaborunions,whichdifferentiate laboratnocostandsetnominalwages. Thehousehold’sconstrainedoptimizationproblemcanbesummarizedas max E (cid:88)∞ βte   (cid:16) C t /C t h −1 (cid:17)1−σ −χ h t 1+1 η   , Ct,ht,Dt 0 t=0 t 1−σ 1+ 1 η  a˜ Rn (cid:90) 1 (cid:32) wm (cid:33)−(cid:15)w C +D +ra˜ = t−1 + t D +hd wm t dm+Π˜ , (B.15) t t t t π π t−1 t t w t t t 0 t whereD arerealdeposits,a˜ istherealpayoffofnominalstate-contingentassets,r isthestochasticdiscount t t t factorbetweenperiodtandt+1,π t = P t /P t−1 isthegrossinflationrate,andP t ≡ (cid:20) (cid:82) 0 1 P t (j)1−(cid:15)pdj (cid:21) 1− 1 (cid:15)p isthe corresponding aggregate price index. Π˜ denotes net lump-sum transfers of profits to the household from t theretailersandlaborunions,whereashd (cid:82)1 wm (cid:16) wm t (cid:17)−(cid:15)w dmistherealwageincomeofthehousehold. The t 0 t wt parameterhdeterminesthestrengthofhabitformation,whilethepreferenceshockse evolvesaccordingto t loge = ρ loge +(cid:15)e, (cid:15)e ∼ N(0,σ2). t e t−1 t t e Thefirst-orderconditionswithrespectto{C ,D},whereλ denotestheLagrangemultiplierofthebudget t t t 35Alternatively,onecouldthinkofthis“consumption”asadistributionofdividendstoshareholdersorbonuspaymentstobank managers,whichareinstantaneouslyconsumed. 36Notethatdepositsarerisk-free,aslongasthebankcarriessufficientnetworthtoshielditsdepositorsfromfluctuationsinthe aggregatereturnoncapital.Assumingthatthereturnondepositsisrisk-freeinrealterms,i.e.thatthebankcompensatesdepositors alsoforunexpectedfluctuationsintherateofinflation,doesnotaffectourresultqualitatively. 47

constraint,are  1−σ  (cid:32) (cid:33)1−σ  C t : e t  C C h t  C t −1−βhE t  e t+1 C C t+ h 1 C t −1  = λ t , t−1 t (cid:40) (cid:41) Rn D t : λ t = βE t λ t+1 t . π t+1 WediscussthechoiceoftheoptimallaborsupplybelowinSubsectionAppendixB.7,jointlywiththelabor unions’choiceoftheoptimalwagerate. AppendixB.4. CapitalGoodsProducers After production in period t has taken place, capital producers purchase the non-depreciated capital stockfromentrepreneurs,investinaDixit-Stiglitzaggregateofimperfectlysubstitutableinvestmentgoods, (cid:34) (cid:35) (cid:15)p (cid:82)1 (cid:15)p−1 (cid:15)p−1 I t ≡ 0 I t (j) (cid:15)p dj ,andsellthenewstockofcapitaltoentrepreneursattherelativepriceQ t . Weassume thatturningfinaloutputintoproductivecapital,i.e.grossinvestment,iscostlyduetopossibledisruptionsof the production process, replacement of installed capital, or learning. The accumulation of physical capital canthenbewrittenas (cid:34) (cid:32) (cid:33)(cid:35) I K = (1−δ)K +x 1−S t I, (B.16) t t−1 t t I t−1 where S (cid:16) It (cid:17) = φ (cid:16) It −1 (cid:17)2 , S(1) = S(cid:48)(1) = 0, and S(cid:48)(cid:48)(1) = φ (compare, e.g., Christiano et al., 2005). It−1 2 It−1 Weassumethataninvestment-specificshock, x,affectstheproductionofcapitalgoodsandthatthisshock t followsanAR(1)-process: logx = ρ logx +(cid:15)x, (cid:15)x ∼ N(0,σ2). t x t−1 t t x The profit-maximization problem of the representative capital goods producer, subject to the capital accumulationequationin(B.16),isgivenby (cid:88)∞ max βs{Q t+s [K t+s −(1−δ)K t+s−1 ]−I t+s }, It s=0 whilethecorrespondingFOCwithrespecttoinvestmentinperiodtisgivenby  (cid:32) (cid:33)2 (cid:32) (cid:33)   (cid:32) (cid:33)(cid:32) (cid:33)2  Q t x t  1− φ 2 I I t −1 −φ I I t −1 I I t  +βφE t  Q t+1 x t+1 I t I +1 −1 I t I +1  = 1. (B.17) t−1 t−1 t−1 t t AppendixB.5. IntermediateGoodsProducers Intermediate goods producers rent the productive capital stock from entrepreneurs and hire labor from households,payingacompetitiverentalrateoncapitalservicesandawageratedeterminedinthelabormarket, respectively. Toconvertcapitalandlaborintointermediateorwholesalegoods, theyusethefollowing Cobb-Douglasproductionfunction: Y = A K˜αh1−α, t t t t 48

where A denotesastationaryshocktototalfactorproductivity(TFP)thatfollowstheAR(1)-process t logA = ρ logA +(cid:15)a, (cid:15)a ∼ N(0,σ2). t a t−1 t t a Notethatthefirstinputargumentoftheproductionfunction,K˜ ,standsforcapitalservices,definedas t K˜ = u K , (B.18) t t t−1 whereu istheutilizationrateofcapitalinperiodtchosenbyentrepreneurs. t Supposethatthepriceofthehomogeneouswholesalegoodintermsofthenumeraireis1/X,sothatthe t gross flexible-price markup of retail goods over the wholesale good is X. The static optimization problem t oftheintermediategoodsproducercanthenbesummarizedas 1 max A K˜αh1−α−rkK˜ −wh, K˜ t,ht X t t t t t t t t whichyieldsthefollowingFOCs: Y K˜ : Xrk = α t , t t t K˜ t Y h : Xw = (1−α) t . t t t h t AppendixB.6. Retailers Monopolisticallycompetitiveretailerspurchasehomogeneousintermediateoutput,diversifyatnocost, andreselltohouseholdsandcapitalgoodsproducerforconsumptionandinvestmentpurposes,respectively. We assume staggered price setting a` la Calvo (1983), where θ denotes the exogenous probability of not p beingabletoreadjusttheprice. A retailer allowed to reset its price in period t chooses the optimal price, P∗, in order to maximize the t presentvalueofcurrentandexpectedfutureprofits,subjecttothedemandfunctionfortherespectiveproduct varietyinperiodt+s, s = 0,...,∞,Y t+s (j) = (cid:0) P t,s /P t+s (cid:1)−(cid:15)pY t+s ,where P t,s isthepriceofaretailerthatwas lastallowedtobesetinperiodt.37 Hence,theprofitmaximizationproblemofaretailerinperiodtis   m P a ∗ x E t   (cid:88)∞ θs p Λ t,t+s Π t,s   , t s=0 whereΛ t,t+s ≡ βsE t [U(cid:48)(C t+s )/U(cid:48)(C t )·P t /P t+s ]denotesthestochasticdiscountfactorand (cid:34) P∗ (cid:35)−(cid:15)p Π t,s ≡ (P∗ t −MC t,s ) P t+ t s Y t+s , 37Theisoelasticdemandschedulefortheproductofretailer jcanbederivedfromthedefinitionsofaggregatedemandY = t (cid:34) (cid:82) 0 1 Y t (j) (cid:15)p (cid:15)p −1 dj (cid:35) (cid:15)p (cid:15)p −1 andtheaggregatepriceindexP t = (cid:20)(cid:82) 0 1 P t (j)1−(cid:15)pdj (cid:21) 1− 1 (cid:15)p. 49

where MC istheretailer’snominalmarginalcostinperiodt+ s. Thecorrespondingoptimalitycondition t,s isgivenby (cid:88)∞ (cid:34) (cid:15) (cid:35) E t θs p Λ t,t+s Y t+s P (cid:15) t+ p s P∗ t − (cid:15) − p 1 MC t,s = 0. s=0 p InordertoarriveattheNewKeynesianPhillipscurve,wecombinetheaboveFOCwiththedefinitionofthe aggregatepriceindex, P = (cid:26) θ P 1−(cid:15)p +(1−θ ) (cid:0) P∗(cid:1)1−(cid:15)p (cid:27)1/(1−(cid:15)p ) . t p t−1 p t AppendixB.7. WageSetting WefollowSchmitt-Grohe´ andUribe(2006)tointroducenominalwagestickiness. Firmshirelaborfrom acontinuumoflabormarketsofmeasure1indexedbym ∈ [0,1]. Ineachlabormarketm,wagesaresetby amonopolisticallycompetitivelaborunion. Theunionfaceslabordemand (cid:0) Wm/W (cid:1)−(cid:15)whd,whereWm isthe t t t t nominal wage charged by the union in market m at time t, W ≡ (cid:20) (cid:82)1(cid:0) Wm (cid:1)1−(cid:15)wdm (cid:21)1/(1−(cid:15)w) is an economyt 0 t widewageindexandhd isaggregatelabordemandbyfirms. Ineachlabormarket,theuniontakesW andhd t t t asexogenous. Thelaborsupplybytheunionsatisfieshm = (cid:16) wm t (cid:17)−(cid:15)w hd,wherewm ≡ Wm/P andw ≡ W/P. Theresourceconstraintimpliesh = hd (cid:82)1 hmdm,whic t hyield w s t t t t t t t t t t 0 t (cid:90) 1 (cid:32) wm (cid:33)−(cid:15)w h = hd t dm. (B.19) t t w 0 t We assume that households have access to a complete set of nominal state-contingent assets A˜ . Each t period,consumerscanpurchase A˜ t+1 atthenominalcost E t r t A˜ t+1 ,wherer t isthestochasticdiscountfactor betweentandt+1. Thevariablea˜ ≡ A˜ /P denotestherealpayoffinperiodtofnominalstate-contingent t t t−1 assetspurchasedint−1. Nominalwagestickinessisintroducedbytheassumptionthat,eachperiod,afractionθ ∈ [0,1)oflabor w unionscannotreoptimizethenominalwage. Intheselabormarkets,wagesareindexedtopastinflation,π . t−1 Letβtw/µ˜ betheLagrangemultiplieron(B.19)andβtλ theLagrangemultiplieronthehouseholdbudget t t t constraint. ThentheLagrangianassociatedwiththehouseholdoptimizationproblemisgivenby (cid:88)∞ (cid:40) (cid:34) (cid:90) 1 (cid:32) wm (cid:33)−(cid:15)w a˜ Rn (cid:35) L =E βt U(C ,C ,h)+λ hd t dm−C −D −ra˜ + t−1 + t D 0 t t−1 t t t w t t t t π π t−1 t=0 0 t t t λw (cid:34) (cid:90) 1 (cid:32) wm (cid:33)−(cid:15)w (cid:35)(cid:41) + t t h −hd t dm . µ˜ t t w t 0 t TheFOCswithrespecttoh andwm areasfollows: t t λw −U (C ,C ,h) = t t (B.20) h t t−1 t µ˜ t and  wm =  w˜ t ifwm t issetoptimally,and t wm π /π otherwise. t−1 t−1 t 50

Iflabordemandcurvesandcostsofsupplyinglaborareidenticalacrosslabormarkets,theoptimallyset wagewillbethesameacrossmarkets,aswell. Todeterminew˜ ,wewritethepartoftheLagrangianrelevant t fortheoptimalwagesetting, Lw = E t (cid:88) s ∞ =0 (θ w β)s   (cid:81) k s = w 1 (cid:16) t+ π s π t+ t+ k− k 1 (cid:17)  −(cid:15)w hd t+s   w˜1 t −(cid:15)w (cid:89) k= s 1 (cid:32) π π t+ t+ k− k 1 (cid:33) −w˜ − t (cid:15)w w µ˜ t t + + s s   . ThentheFOCwithrespecttow˜ isgivenby t E t (cid:88) s ∞ =0 (θ w β)s   w˜ t (cid:81) k s w =1 t+ (cid:16) s π π t+ t+ k− k 1 (cid:17)  −(cid:15)w hd t+s   (cid:15) w (cid:15) − w 1 w˜ t (cid:89) k= s 1 (cid:32) π π t+ t+ k− k 1 (cid:33) − −U λ h ( t+ t s +s)   = 0. (B.21) Equation (B.21) implies that, when allowed to reoptimize in period t, each union sets the real wage so that its future expected marginal revenues are equal to the average marginal cost of supplying labor. The marginalrevenuesperiodsafterthemostrecentreoptimizationequals (cid:15)w −1w˜ (cid:81)s (cid:16) πt+k−1 (cid:17) ,where (cid:15)w isthe (cid:15)w t k=1 πt+k (cid:15)w −1 markupofwagesoverthemarginalcostsoflaborthatwouldprevailwithoutwagestickiness. Themarginal cost of supplying labor equals the marginal rate of substitution between consumption and leisure, −Uh(t+s). λt+s Hence, µ˜ denotes the wedge between the disutility of labor and the average real wage in the economy and t canbeinterpretedastheaveragemarkupoflaborunions. Inordertostate(B.21)recursively,define f t 1 = (cid:32) (cid:15) w (cid:15) − w 1 (cid:33) w˜ t E t (cid:88) s ∞ =0 (βθ w )sλ t+s (cid:32) w w˜ t+ t s (cid:33)(cid:15)w hd t+s (cid:89) k= s 1 (cid:32) π π t+ t+ k− k 1 (cid:33)(cid:15)w −1 and f t 2 = −w˜ − t (cid:15)wE t (cid:88) s ∞ =0 (βθ w )sw(cid:15) t+ w s hd t+s U h (C t+s ,C t+s−1 ,h t+s ) (cid:89) k= s 1 (cid:32) π π t+ t+ k− k 1 (cid:33)(cid:15)w . Then f1 and f2 canbewrittenrecursivelyasfollows: t t f1 = (cid:32) (cid:15) w −1 (cid:33) w˜ λ (cid:32) w t (cid:33)(cid:15)w hd +θ βE (cid:32) π t+1 (cid:33)(cid:15)w −1(cid:32) w˜ t+1 (cid:33)(cid:15)w −1 f1 ; (B.22) t (cid:15) t t w˜ t w t π w˜ t+1 w t t t and f2 = −U (C ,C ,h) (cid:32) w˜ t (cid:33)−(cid:15)w hd +θ βE (cid:32) w˜ t+1 π t+1 (cid:33)(cid:15)w f2 . (B.23) t h t t−1 t w t w t w˜ π t+1 t t t TheFOCwithrespecttow˜ canthenbewrittenas t f1 = f2. (B.24) t t Aggregationacrosslabormarketsimplies h t = (1−θ w )hd t (cid:88)∞ θ w s   W˜ t−s (cid:81) k s W =1 (cid:16) π π t+ t+ k− k− s− s 1 (cid:17)  −(cid:15)w . (B.25) s=0 t 51

Definingthemeasureofwagedispersionas s˜ t ≡ (1−θ w ) (cid:88)∞ θ w s   W˜ t−s (cid:81) k s W =1 (cid:16) π π t+ t+ k− k− s− s 1 (cid:17)  −(cid:15)w , s=0 t wecanrewriteequation(B.25)as h = s˜hd, (B.26) t t t wheretheevolutionofwagedispersionovertimeisgivenby (cid:32) w˜ (cid:33)−(cid:15)w (cid:32) w (cid:33)−(cid:15)w (cid:32) π (cid:33)(cid:15)w s˜ = (1−θ ) t +θ t−1 t s˜ . (B.27) t w w t−1 w w π t t t−1 Fromthedefinitionofthewageindex, W t ≡ (cid:20) (cid:82) 0 1 (W t m)1−(cid:15)wdm (cid:21)1/(1−(cid:15)w) , itfollowsthattherealwagerate, w,canbeexpressedas t (cid:32) π (cid:33)1−(cid:15)w w1−(cid:15)w = (1−θ )w˜1−(cid:15)w +θ w1−(cid:15)w t−1 . (B.28) t w t w t−1 π t Equations(B.22)-(B.28)describetheequilibriuminthelabormarket. AppendixB.8. MonetaryPolicyandMarketClearing We assume that the central bank sets the nominal interest rate, Rn, according to the following standard t Taylorrule: R R n n t = (cid:32) R R n t n −1 (cid:33)ρ  (cid:32) π π t (cid:33)φπ (cid:32) Y Y t (cid:33)φy   1−ρ eνt. (B.29) ss ss ss ss Hence,thecentralbankreactstodeviationsofinflationandoutputfromtheirrespectivesteady-statevalues andmightsmoothinterestratesovertimewithaweightρ. UnsystematicdeviationsfromtheTaylorrulein (B.29)arecapturedbyamean-zeroi.i.d.randomvariable,ν. t Themodelisclosedbytheeconomy-wideresourceconstraint, Y =C +Ce+Cb+I +a(u)K +µG(ω¯ )RkQ K , (B.30) t t t t t t t−1 t t t−1 t−1 whereCe andCb denotetherealconsumptionofentrepreneurialandbanknetworth,respectively,a(u)K t t t t−1 denotestherealadjustmentcostsduetocapitalutilization,andµG(ω¯ )RkQ K theaggregatemonitoring t t t−1 t−1 costsinperiodt. 52

AppendixC. AdditionalSimulationResults AppendixC.1. Calibration TableC.1summarizesthecalibrationofexogenousshockprocessesotherthanmonetarypolicyshocks usedforthesimulationandcomputationoftheoreticalunconditionalautocorrelationsandcross-correlation with output in Figure C.1 and Figure 3 in the main text. The calibration of productivity, preference, and investment-specificshocksisbasedontheMaximumLikelihoodestimationresultsinChristensenandDib (2008), while unanticipated and anticipated risk shocks are calibrated in line with the Bayesian estimation resultsinChristianoetal.(2014). TableC.1:CalibrationofAdditionalShockProcesses. Shockprocess Parameter Value autocorrelationcoefficientoftotalfactorproductivity ρ 0.7625 a standarddeviationoftotalfactorproductivityshocks σ 0.0096 a autocorrelationcoefficientofconsumerpreferences ρ 0.6165 e standarddeviationofconsumerpreferenceshocks σ 0.0073 e autocorrelationcoefficientofinvestmentefficiency ρ 0.6562 x standarddeviationofinvestmentefficiencyshocks σ 0.0097 x autocorrelationcoefficientofexogenousprocessforσ ρ 0.97 ω σ standarddeviationofunanticipatedriskshocks σ 0.07 σ correlationcoefficientofanticipatedriskshocks ρ 0.39 ξ standarddeviationofanticipatedriskshocks σ 0.028 ξ AppendixC.2. UnconditionalAutocorrelations Figure C.1 plots the unconditional autocorrelation coefficients of selected variables and ratios from the benchmark New-Keynesian DSGE model with our optimal debt contract and the optimal debt contract in Bernankeetal.(1999)(BGG)againsttheirempiricalcounterparts,wherebothsimulatedtimeseriesanddata are HP-filtered before computing second moments. Figure C.1 illustrates that the autocorrelation patterns impliedbyeitheroftheDSGEmodelsisqualitativelyandquantitativelyinlinewiththoseinthedata. AppendixC.3. “TooLowforTooLong” Inspired by the motivation in Taylor (2007), we conduct an informal test of the “too-low-for-too-long” hypothesis. According to this hypothesis, a prolonged deviation of monetary policy from what is justified byeconomicconditionsmightleadtoexcessiverisktakinginthefinancialsector. Notethat, inourmodel, a transitory deviation from the Taylor rule becomes more persistent, the higher the degree of interest-rate inertia. Inthissubsection,wethereforecomparetheeffectsofatypicalexpansionarymonetarypolicyshock for two different values of the Taylor-rule coefficient on the lagged policy rate, ρ, without modifying the otherparametersofthemodel. Figure C.2 illustrates that higher interest-rate inertia and thus a more persistent reduction in the policy rate, Rn, implies an increase in both the peak effect and the persistence of the impulse response functions t of the entrepreneurial leverage ratio and default threshold to a monetary easing. Accordingly, the optimal looseningofbanklendingstandards,measuredbytheincreaseinbanklendingrelativetoborrowercollateral 53

FigureC.1:SerialCorrelationofSelectedVariablesandRatiosbetweenPeriodtandPeriodt−τ,DSGEModelandData. Output Investment Loans/Deposits Net Income/Bank Equity 1 1 1 1 0.5 0.5 0.5 0.5 0 0 0 0 −0.5 −0.5 −0.5 0 5 10 0 5 10 0 5 10 0 5 10 τ τ τ τ Collateral Requirements Delinquency Rate Net Interest Margin 1 1 1 0.5 0.5 0.5 Data Our contract 0 BGG contract 0 0 −0.5 −0.5 −0.5 0 5 10 0 5 10 0 5 10 τ τ τ Notes: SimulatedtimeseriesanddataareHP-filtered(λ=1,600). Inthedata,outputcorrespondstolog(realGDPpercapita), investmenttolog(realinvestmentexpenditurepercapita),loans/depositstolog(loansandleasesinbankcredit/demanddeposits) atcommercialbanks,netincome/bankequitytoCallReportslog(netinterestincome/totalequitycapital)forcommercialbanksin theU.S.,collateralrequirementstothenetpercentageofdomesticbanksincreasingcollateralrequirementsforlargeandmiddlemarketfirms,delinquencyratetodelinquencyrateonbusinessloans;allcommercialbanks,andnetinterestmargintoCallReports netinterestmarginforallU.S.banks. inourmodel,andthesubsequentincreaseinthedefaultrateofborrowersbecomesmorepronounced,when thenominalpolicyrateismoreinertial. Inthecurrentexample,anincreaseintheTaylor-rulecoefficient,ρ, from 0.90 to 0.95 almost doubles the maximum response of the leverage ratio from 3.9 to 7.4 basis points above its steady-state value of 1.537 and postpones the turning point in the leverage ratio (from above to belowitssteadystate)by1quarter. Theeffectsontheimpulseresponsefunctionsofoutput, consumption, andinvestmentarequalitativelythesameandofasimilarorderofmagnitude. 54

FigureC.2:SelectedImpulseResponseFunctionstoanExpansionaryMonetaryPolicyShockof25BasisPointsforρ=0.90and ρ=0.95. Policy Rate Loan Rate Net Interest Margin Expected EFP 0 0 0.06 0.06 0.04 0.04 −0.2 −0.2 ρ=0.90 0.02 0.02 −0.4 ρ=0.95 −0.4 0 0 5 10 15 20 5 10 15 20 5 10 15 20 5 10 15 20 Default Threshold Default Rate Leverage Ratio Bank Profit Share 1 1 4 0.4 0.5 0.5 2 0.2 0 0 0 0 5 10 15 20 5 10 15 20 5 10 15 20 5 10 15 20 Bank Lending Bank Deposits Net Worth Bank Net Worth 0 2 2 −0.2 10 −0.4 1 1 −0.6 5 −0.8 0 0 0 5 10 15 20 5 10 15 20 5 10 15 20 5 10 15 20 Output Consumption Investment Return on Capital 1 2 2 2 1 1 0.5 1 0 0 0 0 5 10 15 20 5 10 15 20 5 10 15 20 5 10 15 20 Quarters Quarters Quarters Quarters Notes:Allimpulseresponsefunctionsareexpressedintermsofpercentagedeviationsfromsteadystate,exceptforthepolicyrate, theloanrate,thenetinterestmargin,andtheexpectedEFP,whichareexpressedintermsofpercentagepoints. 55

AppendixD. Data TableD.1:DataandTransformationsUsedintheBaselineFAVARModel. Overall No. in SeriesIDa Slowb Transformationc Description No. Block 1 1 INDPRO yes 5 Industrial Production Index: Total (2012=100,SA) 2 2 IPBUSEQ yes 5 Industrial Production: Business Equipment(2012=100,SA) 3 3 IPCONGD yes 5 Industrial Production: Consumer Goods(2012=100,SA) 4 4 IPDCONGD yes 5 Industrial Production: Durable ConsumerGoods(2012=100,SA) 5 5 IPDMAN yes 5 Industrial Production: Durable Manufacturing (NAICS) (2012=100,SA) 6 6 IPDMAT yes 5 IndustrialProduction: DurableMaterials(2012=100,SA) 7 7 IPFINAL yes 5 Industrial Production: Final Products (Market Group) (2012=100, SA) 8 8 IPMAN yes 5 Industrial Production: Manufacturing(NAICS)(2012=100,SA) 9 9 IPMAT yes 5 Industrial Production: Materials (2012=100,SA) 10 10 IPMINE yes 5 Industrial Production: Mining (2012=100,SA) 11 11 IPNCONGD yes 5 Industrial Production: Nondurable ConsumerGoods(2012=100,SA) 12 12 IPNMAN yes 5 Industrial Production: Nondurable Manufacturing (NAICS) (2012=100,SA) 13 13 IPNMAT yes 5 Industrial Production: nondurable Materials(2012=100,SA) 14 14 IPUTIL yes 5 Industrial Production: Electric and GasUtilities(2012=100,SA) 15 15 BSCURT02USM160S38 yes 1 Business Tendency Surveys for Manufacturing: Rate of Capacity Utilization(%ofCapacity),SA 16 16 RPI yes 5 Real personal income, Billions of 2009chainedUSD,SAAR Continuedonnextpage 38Serieswasdiscontinuedin2015Q3. 56

TableD.1–Continuedfrompreviouspage Overall No. in SeriesIDa Slowb Transformationc Description No. Block 17 17 W875RX1 yes 5 Real personal income excluding currenttransferreceipts,Billionsof 2009chainedUSD,SAAR 18 18 GDPC1 yes 5 Real Gross Domestic Product, Billionsof2009USDchained,SAAR 19 1 CE16OV yes 5 CivilianEmployment(thous.,SA) 20 2 DMANEMP yes 5 All Employees: Durable Goods (thous.,SA) 21 3 EMRATIO yes 4 Employment-PopulationRatio(Percent,SA) 22 4 MANEMP yes 5 All Employees: Manufacturing (thous.,SA) 23 5 PAYEMS yes 5 All Employees: Total Nonfarm (thous.,SA) 24 6 SRVPRD yes 5 All Employees: Service-Providing Industries(thous.,SA) 25 7 USCONS yes 5 All Employees: Construction (thous.,SA) 26 8 USGOVT yes 5 All Employees: Government (thous.,SA) 27 9 USINFO yes 5 All Employees: Information Services(thous.,SA) 28 10 USMINE yes 5 All Employees: Mining and Logging(thous.,SA) 29 11 USPRIV yes 5 AllEmployees: TotalPrivateIndustries(thous.,SA) 30 12 AWHNONAG yes 1 Average Weekly Hours of Production and Nonsupervisory Employees: TotalPrivate(SA) 31 13 CES1000000007 yes 1 Average Weekly Hours of Production and Nonsupervisory Employees: MiningandLogging(SA) 32 14 CES0800000007 yes 1 Average Weekly Hours of Production and Nonsupervisory Employees:PrivateServiceProviding,(SA) 33 15 CES3100000007 yes 1 Average Weekly Hours of Production and Nonsupervisory Employees: Durables(SA) 34 16 CES2000000007 yes 1 Average Weekly Hours of Production and Nonsupervisory Employees: Construction(SA) Continuedonnextpage 57

TableD.1–Continuedfrompreviouspage Overall No. in SeriesIDa Slowb Transformationc Description No. Block 35 17 CES5000000007 yes 1 Average Weekly Hours of Production and Nonsupervisory Employees: Information(SA) 36 18 CES4000000007 yes 1 Average Weekly Hours of Production and Nonsupervisory Employees: Trade,Transportation,Utilities (SA) 37 19 CES6000000007 yes 1 Average Weekly Hours of Production and Nonsupervisory Employees: ProfessionalandBusinessServices(SA) 38 1 PCECC96 yes 5 Real Personal consumption expenditure, SAAR, chained 2009 BIL USD 39 1 HOUST no 4 Housing Starts: Total: New Privately Owned Housing Units Started(thsd. ofunits)SAAR 40 2 HOUSTMW no 4 Housing Starts: Midwest: New Privately Owned Housing Units Started(thsd. ofunits)SAAR 41 3 HOUSTNE no 4 Housing Starts: Northeast: New Privately Owned Housing Units Started(thsd. ofunits)SAAR 42 4 HOUSTS no 4 Housing Starts: South: New Privately Owned Housing Units Started(thsd. ofunits)SAAR 43 5 HOUSTW no 4 Housing Starts: West: New Privately Owned Housing Units Started(thsd. ofunits)SAAR 44 6 PERMIT no 4 New Private Housing Units AuthorizedbyBuildingPermits,(thsd. of units)SAAR 45 1 S&P500 no 5 S&P 500 Stock Price Index, NSA, endofperiod 46 1 EXCAUS no 5 Canadian Dollars to One U.S. Dollar,NSA 47 2 EXJPUS no 5 Japanese Yen to One U.S. Dollar, NSA 48 3 EXSZUS no 5 Swiss Francs to One U.S. Dollar, NSA Continuedonnextpage 58

TableD.1–Continuedfrompreviouspage Overall No. in SeriesIDa Slowb Transformationc Description No. Block 49 4 EXUSUK no 5 U.S. Dollars to One British Pound, NSA 50 1 AAA no 1 Moody’s Seasoned Aaa Corporate BondYield,Percent,NSA 51 2 BAA no 1 Moody’s Seasoned Baa Corporate BondYield,Percent,NSA 52 3 FEDFUNDS no 1 EffectiveFFR,Percent,NSA 53 4 GS1 no 1 1-Year Treasury Constant Maturity Rate,Percent,NSA 54 5 GS10 no 1 10-YearTreasuryConstantMaturity Rate,Percent,NSA 55 6 GS3 no 1 3-Year Treasury Constant Maturity Rate,Percent,NSA 56 7 GS3M no 1 3-Month Treasury Constant MaturityRate,Percent,NSA 57 8 GS5 no 1 5-Year Treasury Constant Maturity Rate,Percent,NSA 58 9 AAA FFR no 1 Spread: AAA-FFR 59 10 BAA FFR no 1 Spread: BAA-FFR 60 11 GS1 FFR no 1 Spread: GS1-FFR 61 12 GS10 FFR no 1 Spread: GS10-FFR 62 13 GS3 FFR no 1 Spread: GS3-FFR 63 14 GS3M FFR no 1 Spread: GS3M-FFR 64 15 GS5 FFR no 1 Spread:GS5-FFR 65 1 BOGNONBR39 no 5 Non-BorrowedReservesofDepositoryInstitutions,MillUSD,SA 66 2 AMBSL no 5 MonetaryBase,BillUSD,SA 67 3 M1 no 5 M1,BillUSD,SA 68 4 M2 no 5 M2,BillUSD,SA 69 5 MZM no 5 MZM,BillUSD,SA 70 6 TOTLL no 5 Total Loans and Leases, Bill USD, SA 71 7 REALLN no 5 Realestateloans,BillUSD,SA 72 8 BUSLOANS no 5 C&Iloans,BillUSD;SA 73 9 CONSUMER no 5 Consumerloans,BillUSD,SA 74 1 CPIAUCSL yes 5 Consumer Price Index for All Urban Consumers: All Items, 1982- 84=100,SA Continuedonnextpage 39SerieswasdiscontinuedinMay2013. 59

TableD.1–Continuedfrompreviouspage Overall No. in SeriesIDa Slowb Transformationc Description No. Block 75 2 CPIFABSL yes 5 Consumer Price Index for All Urban Consumers: Food and Beverages,1982-84=100,SA 76 3 CPILFESL yes 5 ConsumerPriceIndexforAllUrban Consumers: AllItemsLessFood& Energy,1982-84=100,SA 77 4 CPIMEDSL yes 5 ConsumerPriceIndexforAllUrban Consumers: Medical Care, 1982- 84=100,SA 78 5 DNRGRG3M086SBEA yes 5 Personalconsumptionexpenditures: Energy goods and services, chaintypeindex,2009=100 79 6 DPCXRG3M086SBEA yes 5 Personal consumption expenditures: Market-basedPCEexcluding food and energy, chain-type index, 2009=100 80 7 PPICRM no 5 Producer Price Index: Crude Materials for Further Processing, 1982=100,SA 81 8 PPIFCG yes 5 Producer Price Index: Finished ConsumerGoods,1982=100,SA 82 9 PPIFGS yes 5 Producer Price Index: Finished Goods,1982=100,SA 83 10 PPIIEG yes 5 Producer Price Index: Intermediate EnergyGoods,1982=100,SA 84 11 PPIITM yes 5 Producer Price Index: Intermediate Materials: Supplies&Components, 1982=100,SA 85 1 CSCICP02USM661S40 no 1 ConsumerOpinionSurveys: Confidence Indicators: Composite Indicator,2005=1.00,SA,endofperiod 86 1 SUBLPDCILS N.Q no 1 Net percentage of domestic banks tightening standards for C&I loans to large and middle-market firms, Percentage Continuedonnextpage 40Serieswasdiscontinuedin2013Q2. 60

TableD.1–Continuedfrompreviouspage Overall No. in SeriesIDa Slowb Transformationc Description No. Block 87 2 SUBLPDCILTC N.Q no 1 Net percentage of domestic banks increasingthecostofcreditlinesto largeandmiddle-marketfirms,Percentage 88 3 SUBLPDCILTL N.Q no 1 Net percentage of domestic banks tightening loan covenants for large and middle-market firms, Percentage 89 4 SUBLPDCILTM N.Q no 1 Net percentage of domestic banks reducing the maximum size of credit lines for large and middlemarketfirms,Percentage 90 5 SUBLPDCILTQ N.Q no 1 Net percentage of domestic banks increasing collateral requirements for large and middle-market firms, Percentage 91 6 SUBLPDCILTS N.Q no 1 Net percentage of domestic banks increasingspreadsofloanratesover banks’ cost of funds to large and middle-marketfirms,Percentage 92 7 SUBLPDCISS N.Q no 1 Net percentage of domestic banks tightening standards for C&I loans tosmallfirms,Percentage 93 8 SUBLPDCISTC N.Q no 1 Net percentage of domestic banks increasingthecostofcreditlinesto smallfirms,Percentage 94 9 SUBLPDCISTL N.Q no 1 Net percentage of domestic banks tightening loan covenants for small firms,Percentage 95 10 SUBLPDCISTM N.Q no 1 Net percentage of domestic banks reducing the maximum size credit linesforsmallfirms,Percentage 96 11 SUBLPDCISTQ N.Q no 1 Net percentage of domestic banks increasing collateral requirements forsmallfirms,Percentage 97 12 SUBLPDCISTS N.Q no 1 Net percentage of domestic banks increasingspreadsofloanratesover banks’costoffundstosmallfirms, Percentage Continuedonnextpage 61

TableD.1–Continuedfrompreviouspage Overall No. in SeriesIDa Slowb Transformationc Description No. Block 98 13 SUBLPDRCS N.Q no 1 Net percentage of domestic banks tighteningstandardsforcommercial realestateloans,Percentage 99 14 SUBLPFCIS N.Q no 1 Net percentage of foreign banks tightening standards for approving C&Iloans,Percentage 100 15 SUBLPFCITC N.Q no 1 Netpercentageofforeignbanksincreasing costs of credit lines, Percentage 101 16 SUBLPFCITL N.Q no 1 Net percentage of foreign banks tightening loan covenants, Percentage 102 17 SUBLPFCITM N.Q no 1 Netpercentageofforeignbanksreducing the maximum size of credit lines,Percentage 103 18 SUBLPFCITQ N.Q no 1 Net percentage of foreign banks increasing collateralization requirements,Percentage 104 19 SUBLPFRCS N.Q no 1 Net percentage of foreign banks tighteningstandardsforcommercial realestateloans,Percentage 105 1 AHETPI yes 5 Average Hourly Earnings of Production and Nonsupervisory Employees: Total Private, USD per Hour,SA 106 2 CES0600000008 yes 5 Average Hourly Earnings of Production and Nonsupervisory Employees: Goods producing, USD perhour,SA 107 3 CES0800000008 yes 5 Average Hourly Earnings of Production and Nonsupervisory Employees: PrivateServiceProducing, USDperHour,SA 108 4 CES1000000008 yes 5 Average Hourly Earnings of Production and Nonsupervisory Employees: MiningandLogging,USD perHour,SA 109 5 CES2000000008 yes 5 Average Hourly Earnings of Production and Nonsupervisory Employees: Construction, USD per Hour,SA Continuedonnextpage 62

TableD.1–Continuedfrompreviouspage Overall No. in SeriesIDa Slowb Transformationc Description No. Block 110 6 CES3000000008 yes 5 Average Hourly Earnings of Production and Nonsupervisory Employees: Manufacturing, USD per Hour,SA 111 1 A015RX1Q020SBEA no 1 Change in real private inventories: Nonfarm, Billions of 2009 chained USD,SAAR 112 2 B018RX1Q020SBEA no 1 Change in real private inventories: Farm, Billions of 2009 chained USD,SAAR 113 3 NAPMNOI no 1 ISM Manufacturing: New Orders Index,SA 114 4 PRFI d no 5 Real Gross Private Domestic ResidentialInvestment,BillionsofReal Dollars, SA (deflated with the respectiveimplicitdeflator) 115 5 PNFI d no 5 Real Gross Private Domestic Nonresidential Investment, Billions of Real Dollars, SA (deflated with the respectiveimplicitdeflator) 116 1 TFBAIL MA NQ no 1 Charge-off rate on loans; All commercialbanks,SA 117 2 STTFBAILB MA NQ no 1 Charge-off rate on business loans; Allcommercialbanks,SA 118 3 STTFBAILC MA NQ no 1 Charge-off rate on consumer loans; Allcommercialbanks,SA 119 4 STTFBAILCC MA NQ no 1 Charge-offrateoncreditcardloans; Allcommercialbanks,SA 120 5 STTFBAILCO MA NQ no 1 Charge-off rate on other consumer loans;Allcommercialbanks,SA 121 6 STTFBAILF MA NQ no 1 Charge-off rate on loans to finance agricultural production; All commercialbanks,SA 122 7 STTFBAILR MA NQ no 1 Charge-off rate on lease financing receivables; All commercial banks, SA 123 8 STTFBAILS MA NQ no 1 Charge-offrateonloanssecuredby real estate; All commercial banks, SA Continuedonnextpage 63

TableD.1–Continuedfrompreviouspage Overall No. in SeriesIDa Slowb Transformationc Description No. Block 124 9 STTFBAILSF XDO MA NQ no 1 Charge-off rate on farmland loans, booked in domestic offices; All commercialbanks,SA 125 10 STTFBAILSS XDO MA NQ no 1 Charge-off rate on single family residential mortgages, booked in domestics offices; All commercial banks,SA 126 11 STTFBAILSX XDO MA NQ no 1 Charge-off rate on commercial real estate loans (excluding farmland), booked in domestic offfices; All commercialbanks,SA 127 12 STTFBAIL XEOP MA NQ no 1 Delinquencyrateonloans;Allcommercialbanks,SA 128 13 STTFBAILB XEOP MA NQ no 1 Delinquencyrateonbusinessloans; Allcommercialbanks,SA 129 14 STTFBAILC XEOP MA NQ no 1 Delinquency rate on consumer loans;Allcommercialbanks,SA 130 15 STTFBAILCC XEOP MA NQ no 1 Delinquency rate on credit card loans;Allcommercialbanks,SA 131 16 STTFBAILCO XEOP MA NQ no 1 Delinquencyrateonotherconsumer loans;Allcommercialbanks,SA 132 17 STTFBAILF XEOP MA NQ no 1 Delinquencyrateonloanstofinance agricultural production; All commercialbanks,SA 133 18 STTFBAILR XEOP MA NQ no 1 Delinquencyrateonleasefinancing receivables; All commercial banks, SA 134 19 STTFBAILS XEOP MA NQ no 1 Delinquency rate on loans secured by real estate; All commercial banks,SA 135 20 STTFBAILSF XEOP XDO MA NQ no 1 Delinquencyrateonfarmlandloans, booked in domestic offices; All commercialbanks,SA 136 21 STTFBAILSS XEOP XDO MA NQ no 1 Delinquency rate on single-family residential mortgages, booked in domestic offices; All commercial banks,SA Continuedonnextpage 64

TableD.1–Continuedfrompreviouspage Overall No. in SeriesIDa Slowb Transformationc Description No. Block 137 22 STTFBAILSX XEOP XDO MA NQ no 1 Delinquency rate on commercial real estate loans (excluding farmland), booked in domestic offices; Allcommercialbanks,SA 138 1 BANKPROFIT no 5 BEA Profits of Other Financial Institutions,BillionsofUSD,SAAR 139 2 FEDPROFIT no 5 BEA Profits of Federal Reserve Banks,BillionsofUSD,SAAR 140 3 CALLNETINCOME no 5 NetIncomeforCommercialBanks, Thous. USD,NSA,adjustedforcumulativeaccounting 141 4 CALLNETINTINCOME no 5 NetInterestIncomeforCommercial Banks,Thous. USD,NSA,adjusted forcumulativeaccounting 142 5 CALLNETMARGIN no 1 Net Interest Margin for US Banks, Percent,EndofPeriod,NSA a Macroeconomic time series are taken from the FRED database, lending standards measures are taken from the SeniorLoanOfficerOpinionSurvey(SLOOS)oftheFederalReserve. b Ifyes,avariableisassumedtobeslow-movingwhenestimatedwithaprincipalcomponentapproach. c Variabletransformationscodesareasfollows:1-notransformation,2-difference,4-logarithm,5-log-difference. 65

TableD.2:DataandTransformationsUsedintheRobustnessChecks. SeriesID Transformationa Description GB RGDPdot 1 Greenbookprojectionsforquarter-on-quartergrowthinrealGDP,chain weighted(annualizedpercentagepoints) GB PGDPdot 1 Greenbookprojectionsforquarter-on-quartergrowthinpriceindexfor GDP,chainweighted(annualizedpercentagepoints) GB UNEMP 1 Greenbookprojectionsfortheunemploymentrate,(percentagepoints) GB CPIdot 1 Greenbook projections for quarter-on-quarter headline CPI inflation, (annualizedpercentagepoints) GB CORECPIdot 1 Greenbookprojectionsforquarter-on-quartercoreCPIinflation,(annualizedpercentagepoints) GB RCONSUMdot 1 Greenbook projections for quarter-on-quarter growth in real personalconsumptionexpenditure,chainweighted(annualizedpercentage points) GB RNRESINVdot 1 Greenbook projections for quarter-on-quarter growth in real business fixedinvestment,chainweighted(annualizedpercentagepoints) GB RRESINVdot 1 Greenbookprojectionsforquarter-on-quartergrowthinrealresidential investment,chainweighted(annualizedpercentagepoints) GB RFEDGOVdot 1 Greenbook projections for quarter-on-quarter growth in real federal governmentconsumptionandgrossinvestment,chainweighted(annualizedpercentagepoints) GB RSLGOVdot 1 Greenbookprojectionsforquarter-on-quartergrowthinrealestateand local government consumption and gross investment, chain weighted (annualizedpercentagepoints) GB NGDPdot 1 Greenbook projections for quarter-on-quarter growth in nominal GDP (annualizedpercentagepoints) GB HOUSING 4 Greenbookprojectionsforhousingstarts(millionsofunits) GB INDPRODdot 1 Greenbook projections for quarter-on-quarter growth in the industrial productionindex(annualizedpercentagepoints) ADJLS 1 SupplycomponentofSLOOSlendingstandardsinBassettetal.(2014) (Net percentage of banks tightening lending standards, adjusted for macroeconomicandbank-specificfactorsthatalsoaffectloandemand) EBP 1 Excess Bond Premium of Gilchrist and Zakrajsˇek (2012) (annualized percentagepoints) NFCICREDIT 1 ChicagoFedNationalFinancialConditionsCreditSubindex(index) SLOOSRISKTOL 1 Netpercentageofbankslooseninglendingstandardsduetoanincrease inrisktolerance a Variabletransformationscodesareasfollows:1-notransformation,2-difference,4-logarithm,5-log-difference. 66

AppendixE. BayesianEstimationoftheFAVARModel In order to jointly estimate equations (19) and (20) using Bayesian methods it is convenient to rewrite themodelinstate-spaceform:         X t  =  Λf Λy  F t  +  e t  (E.1) Y 0 I Y 0 t t      F t  = Φ(L)  F t−1  +ν t , (E.2) Y Y t t−1 where Y is the M ×1 vector of observables, F is the K ×1 vector of unobservable factors, and X is the t t t N × 1 vector of informational time series. We restrict the loading coefficient matrices Λf of dimension N ×K and Λy of dimension N × M in order to identify the factors uniquely. The vector error terms e and t ν areassumedtobenormallydistributedanduncorrelated,i.e.e ∼ N(0,R)andν ∼ N(0,Q),whereRisa t t t diagonalmatrix. In one-step Bayesian estimation, all parameters are treated as random variables. The parameter vector θ contains the factor loadings and the variance-covariance matrix of the observation equation in (19) as wellastheVARcoefficientsandthevariance-covariancematrixofthetransitionequationin(20),i.e.,θ = (cid:16) (cid:17) Λf,Λy,R,vec(Φ),Q . In addition, the unobservable factors are treated as random variables and sampled. Theobservationandtransitionequationscanberewrittenas X =ΛF +e (E.3) t t t F =Φ(L)F +ν, (E.4) t t−1 t whereΛistheloadingmatrix, X = (cid:0) X(cid:48),Y(cid:48)(cid:1) ,e = (cid:0) e(cid:48),0 (cid:1) ,and F = (cid:0) F(cid:48),Y(cid:48)(cid:1) . Let X˜ = (X ,X ,...,X )and t t t t t t t t t 1 2 T F˜ = (F ,F ,...,F ) denote the respective histories from time 1 to T. Our goal is to obtain the marginal t 1 2 T (cid:16) (cid:17) densitiesoftheparametersandfactors, whichcanbeintegratedoutofthejointposteriordensity p θ,F˜ . T Hence,weareinterestedinthefollowingobjects: (cid:90) (cid:16) (cid:17) (cid:16) (cid:17) p F˜ = p θ,F˜ dθ, (E.5) T T (cid:90) (cid:16) (cid:17) p(θ) = p θ,F˜ dF˜ . (E.6) T T AppendixE.1. TheGibbsSampler Weusethemulti-moveGibbssamplingapproachofCarterandKohn(1994),whichalternatelysamples fromtheparametersandthefactorsasfollows: 1. Chooseastartingvaluefortheparametervectorθ . 0 (cid:16) (cid:17) 2. Draw F˜(1) fromtheconditionaldensity p F˜ |X˜ ,θ . T T T 0 (cid:18) (cid:19) 3. Drawθ(1) fromtheconditionaldensity p θ|X˜ ,F˜(1) . T T Repeatsteps2and3untilconvergence. 67

AppendixE.2. ChoiceofStartingValues Anobviouschoiceforθ isthesolutionimpliedbyprincipalcomponentanalysis(compareBernankeet 0 al.,2005),whichweuseasabaselineinmostruns. However,startingthechains(evenverylongones)from thesamepointmaynotbesufficienttoachievethetargetdistribution,inpractice,evenifthechainappears to have converged. Therefore, we experimented with “agnostic” starting values, e.g. vec(Φ) = 0, Q = I, Λf = 0, Λy = OLS of the regression of X on Y and R = fitted residual covariance matrix from the OLS regression of X on Y, without substantial effects on our results. We furthermore ran multiple consecutive chainsof1milliondrawseach,settingthestartingvaluesofthesubsequenttothevaluesobtainedinthelast iterationofthepreviouschain. Giventhatthechainswerehighlyautocorrelatedforsomeoftheparameters, weappliedthinningandkeptonlyeveryfifthdraw. AppendixE.3. ConditionalDensitiesandPriors (cid:16) (cid:17) Inordertodrawfrom p F˜ |X˜ ,θ ,weapplyKalmanfilteringtechniques(seeKimandNelson,1999). T T Due to the memoryless Markov property of F, the conditional distribution of the history of factors can be t expressedasaproductoftheconditionaldistributionsoffactorsatdatet: (cid:16) (cid:17) (cid:16) (cid:17)(cid:89)T−1 (cid:16) (cid:17) p F˜ T |X˜ T ,θ = p F T |X˜ T ,θ p F t |F t+1 ,X˜ t ,θ . (E.7) t−1 Theoriginalmodelislinear-Gaussian,whichimplies F |X˜ ,θ ∼ N (cid:0) F ,P (cid:1) (E.8) T T T|T T|T F t |F t+1 ,X˜ t ,θ ∼ N (cid:0) F t|t,Ft+1 ,P t|t,Ft−1 (cid:1) , (E.9) where (cid:16) (cid:17) F = E F |X˜ ,θ , (E.10) T|T T T (cid:16) (cid:17) P =Cov F |X˜ ,θ , (E.11) T|T T T F t|t,Ft+1 = E (cid:16) F t |F t+1 X˜ t ,θ (cid:17) = E (cid:0) F t |F t+1 ,F t|t ,θ (cid:1) , (E.12) P t|t,Ft−1 =Cov (cid:16) F t |F t+1 X˜ t ,θ (cid:17) =Cov (cid:0) F t |F t+1 ,F t|t ,θ (cid:1) . (E.13) F and P are calculated by the Kalman filter for t = 1,...,T, conditional on θ and the respective data t|t t|t historyX˜ . TheKalmanfilterstartingvaluesarezeroforthefactorsandtheidentitymatrixforthecovariance t matrix. Further,aKalmansmootherisappliedtoobtaintheupdatedvaluesof F and P . T−1|T−1,FT T−1|T−1,FT The priors on the parameters in Λ and the variance-covariance matrix of the observation equation, R, areasfollows. SinceRisassumedtobediagonal,estimatesofΛandthediagonalelementsR ofRcanbe ii obtainedfromOLSequationbyequation. Conjugatepriorsareassumedtohavetheform R ∼ iG(δ /2,η /2) (E.14) ii 0 0 (cid:16) (cid:17) Λ|R ∼ N 0,R M−1 , (E.15) i ii ii 0 68

where,followingBernankeetal.(2005),wesetδ = 6,η = 2·10−3 and M = I. Giventheabovepriors,it 0 0 0 canbeshownthatthecorrespondingposteriordistributionshavetheform R |X˜ ,F˜ ∼iG(δ/2,η/2) (E.16) ii T T i (cid:16) (cid:17) Λ|R ,X˜ ,F˜ ∼ N Λ¯ ,R M¯−1 , (E.17) i ii T T i ii i where (cid:34) (cid:18) (cid:19)−1 (cid:35)−1 δ =δ /2+eˆ(cid:48)eˆ +Λˆ(cid:48) M−1+ F˜(cid:48)i F˜i Λˆ , (E.18) i 0 i i i 0 T T i η =η /2+T, (E.19) 0 (cid:18) (cid:19) Λ¯ = M¯−1 F˜(cid:48)i F˜i Λˆ , (E.20) i i T T i M¯ = M +F˜(cid:48)i F˜i , (E.21) i 0 T T and F˜i aretheregressorsoftheithequation. T The priors on the transition (state) equation are as follows. As the transition equation corresponds to (cid:16) (cid:17) a standard VAR, it can be estimated by OLS equation by equation to obtain vec Φˆ and Qˆ. We impose a conjugateNormal-Inverse-Wishartprior, Q ∼iW(Q ,K +M+2) (E.22) 0 vec(Φ)|Q ∼ N(0,Q⊗Ω ), (E.23) 0 where the diagonal elements of Q are set to the residual variances of the corresponding univariate regres- 0 sions, σˆ2, as in Kadiyala and Karlsson (1997). The diagonal elements of Ω are set in the spirit of the i 0 Minnesotaprior,i.e.thepriorvarianceofthecoefficientonvariable jatlagk inequationiisσ2/kσ2. This i j prioryieldsthefollowingconjugateposterior: (cid:16) (cid:17) Q|X˜ ,F˜ ∼iW Q¯,T +K +M+2 (E.24) T T (cid:16) (cid:16) (cid:17) (cid:17) vec(Φ)|Q,X˜ ,F˜ ∼ N vec Φ¯ ,Q⊗Ω¯ , (E.25) T T where Q¯ = Q +Vˆ(cid:48)Vˆ +Φˆ(cid:48) (cid:20) Ω + (cid:16) F˜(cid:48) F˜ (cid:17)−1 (cid:21)−1 Φˆ (E.26) 0 0 T−1 T−1 Φ¯ =Ω¯ (cid:16) F˜(cid:48) F˜ (cid:17) Φˆ (E.27) T−1 T−1 Ω¯ = (cid:16) Ω−1+F˜(cid:48) F˜ (cid:17)−1 (E.28) 0 T−1 T−1 andVˆ isthematrixofOLSresiduals. FollowingBernankeetal.(2005)andAmirAhmadiandUhlig(2009), weenforcestationaritybytruncatingdrawsofΦwherethelargesteigenvalueexceeds1inabsolutevalue. 69

AppendixE.4. MonitoringConvergence Geman and Geman (1984) show that both joint and marginal distributions will converge to their target distributions at an exponential rate as the number of replications approaches infinity. In practice, however, the Gibbs sampler may converge slowly and requires careful monitoring. We monitor convergence by (i) plotting the coefficients against the number of replications (level shifts and trends should not occur); (ii) comparingthemediansandmeansofthecoefficientsatdifferentpartsofthechain(largedifferencesshould notoccur);(iii)plottingandcomparingthemediansofthefactorsobtainedfromfirstandsecondhalfofthe chain (large and frequent deviations should not occur). The corresponding figures for our baseline model with 3 factors are reported below. It turns out that convergence is quite slow and becomes increasingly difficulttoachieve,ifweincreasethenumberofunobservedfactors. AppendixE.5. NormalizationofUnobservedFactors Due to the fundamental indeterminacy of factor models, the unobserved factors can only be estimated uptoarotation. Forthisreason,wemustimposeasetofstandardrestrictionsontheobservationequationin ordertoidentifythefactorsuniquely. FollowingBernankeetal.(2005),weeliminaterotationsoftheform F∗ = AF +BY. SolvingthisexpressionforF andpluggingtheresultintotheobservationequationin(19) t t t t yields X = ΛfA−1F∗+(Λy+ΛfA−1B)Y. (E.29) t t t Hence,theuniqueidentificationoffactorsrequiresthatA−1F∗ = F andΛfA−1B= 0. Bernankeetal.(2005) t t suggest imposing sufficient (overidentifying) restrictions by setting A = I and B = 0. Moreover, the onestepestimationapproachrequiresthatthefirstK variablesinthevectorX belongtothesetofslow-moving t variables(compareTableD.1). 70

FigureE.1:MonitoringofFactorConvergenceandFactorUncertaintyfortheBaselineFAVARModel. 2 2 Median First Half 5%−Percentile Median Second Half Median 1.5 1.5 95%−Percentile 1 1 0.5 0.5 0 0 −0.5 −0.5 −1 −1 −1.5 −1.5 −2 −2 1991Q1 1994Q1 1997Q1 2000Q1 2003Q1 2006Q1 1991Q1 1994Q1 1997Q1 2000Q1 2003Q1 2006Q1 (a)Factor1:Medianoffirst&secondhalfofdrawspostburn-in. (b)Factor1:Medianofalldrawsafterburn-in&90%coverage. 1.5 1.5 Median First Half 5%−Percentile Median Second Half Median 1 1 95%−Percentile 0.5 0.5 0 0 −0.5 −0.5 −1 −1 −1.5 −1.5 −2 −2 −2.5 −2.5 1991Q1 1994Q1 1997Q1 2000Q1 2003Q1 2006Q1 1991Q1 1994Q1 1997Q1 2000Q1 2003Q1 2006Q1 (c)Factor2:Medianoffirst&secondhalfofdrawspostburn-in. (d)Factor2:Medianofalldrawsafterburn-in&90%coverage. 1 1 Median First Half 5%−Percentile Median Second Half Median 0.8 0.8 95%−Percentile 0.6 0.6 0.4 0.4 0.2 0.2 0 0 −0.2 −0.2 −0.4 −0.4 −0.6 −0.6 −0.8 −0.8 1991Q1 1994Q1 1997Q1 2000Q1 2003Q1 2006Q1 1991Q1 1994Q1 1997Q1 2000Q1 2003Q1 2006Q1 (e)Factor3:Medianoffirst&secondhalfofdrawspostburn-in. (f)Factor3:Medianofalldrawsafterburn-in&90%coverage. 71

AppendixF. EmpiricalEvidence AppendixF.1. Small-ScaleVARModel In order to corroborate our argument in the main text, consider the following example of a small-scale VAR model of the U.S. economy including four observable variables: real activity (either non-farm employment or real GDP), prices (CPI), banks’ risk attitude in lending (the net percentage of domestic banks tightening standards for C&I loans), and a monetary policy instrument (the Federal Funds rate). The VAR model is estimated on quarterly data for 1991Q2-2008Q2 and two lags. As in Angeloni et al. (2013), we detrend the non-stationary variables in logarithms and the stationary variables in levels using the HP-filter (Hodrick and Prescott, 1997) with λ = 1,600. Monetary policy shocks are identified recursively, ordering the Federal Funds rate last in the VAR. A similar identifying assumption will later be made in the FAVAR analysis. FigureF.1plotstheimpulseresponsefunctionstoamonetaryeasingof25basispointsfortwodifferent specifications of the VAR model. In the upper panel, we include non-farm employment as a proxy for real economic activity, whereas we include real GDP in the lower panel. Note that all other variables as well as the identifying assumptions are identical across the two specifications. In the upper panel, bank lending standardsdonotseemtorespondsignificantly,accordingtothetwostandarderrorconfidencebands,while thecorrespondingpointestimatesuggestsatighteningofstandardswithapeakaroundtenquartersafterthe expansionarymonetarypolicyshock. Inthelowerpanel,however,whererealeconomicactivityismeasured byrealGDPratherthanemployment,theimpulseresponsefunctionssuggestastatisticallysignificanteasing ofbanklendingstandardsinresponsetothesamemonetarypolicyshock. FigureF.1:ImpulseResponsestoanExpansionaryMonetaryPolicyShockinaSmallVAR. x 10−3 Employment x 10−4 CPI x 10−4 Real GDP x 10−4 CPI 4 5 15 2 2 0 10 0 1 −5 5 −2 0 0 −4 −10 −6 −5 −1 −15 −8 0 10 20 0 10 20 0 10 20 0 10 20 Lending Standards FFR Lending Standards FFR 0.2 2 4 0.2 2 0 0 0 0 −0.2 −2 −0.2 −2 0 10 20 0 10 20 0 10 20 0 10 20 Quarters Quarters Quarters Quarters (a)Usingemploymentasthemeasureofrealeconomicactivity. (b)UsingrealGDPasthemeasureofrealeconomicactivity. Notes:Pointestimateswithtwostandarderrorconfidencebands. 72

AppendixF.2. ExplanatoryPowerofLatentFactors Given thatour maininterest isin explainingthe fluctuationsin lendingstandards, Table F.1reports the median adjusted R2 for each of the 19 SLOOS measures based on the FAVAR model with one, three, five, andsevenunobservablefactors. Wefindthatthefirstfactorexhibitsahighcorrelationwithmostmeasuresof banklendingstandards. TherespectiveadjustedR2 rangesfrom.148forforeignbankstighteningstandards for commercial real estate loans to .882 for domestic banks increasing the cost of credit lines to large and middlefirms. Withveryfewexceptions,addingfurtherfactorsimprovesthistightfitonlymarginally. TableF.1:AdjustedR2forSLOOSMeasuresofLendingStandards,1991Q1-2008Q2. No. LendingStandardDescription 1factor 3factors 5factors 7factors 1 domesticbankstighteningstandardsonC&Iloans 0.880 0.890 0.905 0.907 tolargeandmiddlefirms 2 domesticbanksincreasingthecostsofcreditlines 0.882 0.867 0.862 0.857 tolargeandmiddlefirms 3 domestic banks tightening loan covenants for 0.877 0.909 0.914 0.922 largeandmiddlefirms 4 domestic banks reducing the maximum size of 0.870 0.879 0.885 0.885 creditlinestolargeandmiddlefirms 5 domesticbanksincreasingcollateralrequirements 0.523 0.603 0.613 0.614 forlargeandmiddlefirms 6 domestic banks increasing spreads of loan rates 0.875 0.849 0.848 0.830 overbanks’costoffundstolargeandmiddlefirms 7 domestic banks tightening standards for C&I 0.774 0.804 0.839 0.843 loanstosmallfirms 8 domesticbanksincreasingthecostofcreditlines 0.800 0.800 0.843 0.842 tosmallfirms 9 domestic banks tightening loan covenants for 0.811 0.826 0.840 0.840 smallfirms 10 domestic banks reducing the maximum size of 0.734 0.713 0.747 0.732 creditlinestosmallfirms 11 domesticbanksincreasingcollateralrequirements 0.270 0.362 0.420 0.397 forsmallfirms 12 domestic banks increasing spreads of loan rates 0.830 0.844 0.875 0.867 overbanks’costoffundstosmallfirms 13 domesticbankstighteningstandardsforcommer- 0.467 0.597 0.718 0.725 cialrealestateloans 14 foreign banks tightening standards for approving 0.728 0.784 0.789 0.803 C&Iloans 15 foreignbanksincreasingcostsofcreditlines 0.719 0.730 0.759 0.780 16 foreignbankstighteningloancovenants 0.759 0.784 0.785 0.798 17 foreign banks reducing the maximum size of 0.584 0.638 0.633 0.682 creditlines 18 foreignbanksincreasingcollateralrequirements 0.430 0.511 0.493 0.503 19 foreignbankstighteningstandardsforcommercial 0.148 0.204 0.190 0.230 realestateloans Notes:MedianadjustedR2basedonlast10,000drawsfromtheGibbssamplerforthebaselineFAVARmodelwithone,three,five, andsevenunobservedfactors. 73

AppendixF.3. HistoricalVarianceDecomposition Weareprimarilyinterestedintheresponseofthe19measuresofbanklendingstandardstoexpansionary monetarypolicyshocks,onaverageoverthesampleperiod. InordertoassesstheplausibilityofourFAVAR specification and the resulting monetary shock series, we consider the historical variance decomposition (HVD) of the standardized changes in lending standards. Figure F.2 plots the cumulative contributions of monetarypolicyshockstofluctuationsintheFederalFundsrateandlendingstandardsforasinglecandidate drawfromtheGibbssampler,afterdiscardingasufficientlylongburn-inphase.41 Over the second half of the sample, we find that unexpected monetary policy shocks contribute to the reduction in the Federal Funds rate after the dot-com bubble and, to a lesser extent, to the gradual change in the monetary policy stance during the boom preceding the Great Recession.42 Moreover, the FAVAR modelattributesasizeableshareoftheinitialtighteningandsubsequentlooseningofbanklendingstandards between 1998 and 2005 to monetary shocks. Note that this HVD pattern is shared by all 19 measures. In line with conventional wisdom, the abrupt tightening of lending standards in 2008 is not associated with unexpectedmonetarypolicyshocks. AppendixF.4. ImpulseResponseFunctionsofSLOOSLendingStandards AppendixG. RobustnessofEmpiricalEvidence AppendixG.1. NumberofLatentFactors 41ThereasonforplottingtheHVDbasedonasinglemodelisthatpointwisemediancontributionsbasedonalldrawsimply jumpingbetweendifferentcandidatesandarethusnotinterpretableinasensibleway.Nevertheless,thelatterresultsarequalitatively andquantitativelyverysimilartothoseinFigureF.2,whichcanthereforebeconsideredasrepresentative. 42Itiswell-knownthatHVDcontributionsgothroughatransitionphasethatcanbeprotractedifthetimeseriesinquestionare seriallycorrelated.Here,thetransitionphaselastsuntilroughly1998andourdiscussionthereforefocusesontheresultsthereafter. 74

rofsrotcaFdevresbonUeerhThtiwledoMRAVAFehtnisdradnatSgnidneLdnaRFFfonoitisopmoceDecnairaVlacirotsiHotskcohSyciloPyratenoMfonoitubirtnoC :2.FerugiF .2Q8002-1Q1991 4 dradnatS gnidneL 3 dradnatS gnidneL 2 dradnatS gnidneL 1 dradnatS gnidneL etaR sdnuF laredeF 04 06 04 2 04 04 02 02 02 02 0 0 0 0 0 ataD 02− 02− DVH 2− 02− 04− 02− 5002 0002 5991 5002 0002 5991 5002 0002 5991 5002 0002 5991 5002 0002 5991 9 dradnatS gnidneL 8 dradnatS gnidneL 7 dradnatS gnidneL 6 dradnatS gnidneL 5 dradnatS gnidneL 04 04 04 05 02 02 02 02 0 0 0 0 0 02− 02− 02− 05− 02− 5002 0002 5991 5002 0002 5991 5002 0002 5991 5002 0002 5991 5002 0002 5991 41 dradnatS gnidneL 31 dradnatS gnidneL 21 dradnatS gnidneL 11 dradnatS gnidneL 01 dradnatS gnidneL 05 06 06 03 02 04 04 02 01 0 02 0 02 01 0 0 0 02− 02− 01− 05− 04− 01− 5002 0002 5991 5002 0002 5991 5002 0002 5991 5002 0002 5991 5002 0002 5991 91 dradnatS gnidneL 81 dradnatS gnidneL 71 dradnatS gnidneL 61 dradnatS gnidneL 51 dradnatS gnidneL 04 05 05 05 02 02 0 0 0 0 0 02− 02− 05− 05− 05− 5002 0002 5991 5002 0002 5991 5002 0002 5991 5002 0002 5991 5002 0002 5991 .serusaemdradnatsgnidnelfonoitpircseddeliatedarofDxidneppAeeS.relpmassbbiGehtmorfwardetadidnacelgnisarofsetamitsetnioP:setoN 75

rofsrotcaFdevresbonUeerhThtiwledoMRAVAFenilesaBehtnikcohSyciloPyratenoMyranoisnapxEspb52aotserusaeMdradnatSgnidneLfosesnopseReslupmI :3.FerugiF .2Q8002-1Q1991 4 dradnatS gnidneL 3 dradnatS gnidneL 2 dradnatS gnidneL 1 dradnatS gnidneL etaR sdnuF laredeF 5.0 5.0 5.0 5.0 5.0 0 0 0 0 0 5.0− 5.0− 5.0− 5.0− 5.0− 02 0 02 0 02 0 02 0 02 0 9 dradnatS gnidneL 8 dradnatS gnidneL 7 dradnatS gnidneL 6 dradnatS gnidneL 5 dradnatS gnidneL 5.0 5.0 5.0 5.0 5.0 0 0 0 0 0 5.0− 5.0− 5.0− 5.0− 5.0− 02 0 02 0 02 0 02 0 02 0 41 dradnatS gnidneL 31 dradnatS gnidneL 21 dradnatS gnidneL 11 dradnatS gnidneL 01 dradnatS gnidneL 5.0 5.0 5.0 5.0 5.0 0 0 0 0 0 5.0− 5.0− 5.0− 5.0− 5.0− 02 0 02 0 02 0 02 0 02 0 91 dradnatS gnidneL 81 dradnatS gnidneL 71 dradnatS gnidneL 61 dradnatS gnidneL 51 dradnatS gnidneL 5.0 5.0 5.0 5.0 5.0 0 0 0 0 0 5.0− 5.0− 5.0− 5.0− 5.0− 02 0 02 0 02 0 02 0 02 0 sretrauQ sretrauQ sretrauQ sretrauQ sretrauQ .serusaemdradnatsgnidnelfonoitpircseddeliatedarofDxidneppAeeS.selitnecrepht59/ht5dnaht48/ht61esiwtniophtiwsesnopsernaideM:setoN 76

-1Q1991rofrotcaFdevresbonUenOhtiwledoMRAVAFehtnikcohSyciloPyratenoMyranoisnapxEspb52aotserusaeMdradnatSgnidneLfosesnopseReslupmI :1.GerugiF .2Q8002 4 dradnatS gnidneL 3 dradnatS gnidneL 2 dradnatS gnidneL 1 dradnatS gnidneL etaR sdnuF laredeF 5.0 5.0 5.0 5.0 5.0 0 0 0 0 0 5.0− 5.0− 5.0− 5.0− 5.0− 02 0 02 0 02 0 02 0 02 0 9 dradnatS gnidneL 8 dradnatS gnidneL 7 dradnatS gnidneL 6 dradnatS gnidneL 5 dradnatS gnidneL 5.0 5.0 5.0 5.0 5.0 0 0 0 0 0 5.0− 5.0− 5.0− 5.0− 5.0− 02 0 02 0 02 0 02 0 02 0 41 dradnatS gnidneL 31 dradnatS gnidneL 21 dradnatS gnidneL 11 dradnatS gnidneL 01 dradnatS gnidneL 5.0 5.0 5.0 5.0 5.0 0 0 0 0 0 5.0− 5.0− 5.0− 5.0− 5.0− 02 0 02 0 02 0 02 0 02 0 91 dradnatS gnidneL 81 dradnatS gnidneL 71 dradnatS gnidneL 61 dradnatS gnidneL 51 dradnatS gnidneL 5.0 5.0 5.0 5.0 5.0 0 0 0 0 0 5.0− 5.0− 5.0− 5.0− 5.0− 02 0 02 0 02 0 02 0 02 0 sretrauQ sretrauQ sretrauQ sretrauQ sretrauQ .serusaemdradnatsgnidnelfonoitpircseddeliatedarofDxidneppAeeS.selitnecrepht59/ht5dnaht48/ht61esiwtniophtiwsesnopsernaideM:setoN 77

-1Q1991rofsrotcaFdevresbonUeviFhtiwledoMRAVAFehtnikcohSyciloPyratenoMyranoisnapxEspb52aotserusaeMdradnatSgnidneLfosesnopseReslupmI :2.GerugiF .2Q8002 4 dradnatS gnidneL 3 dradnatS gnidneL 2 dradnatS gnidneL 1 dradnatS gnidneL etaR sdnuF laredeF 5.0 5.0 5.0 5.0 5.0 0 0 0 0 0 5.0− 5.0− 5.0− 5.0− 5.0− 02 0 02 0 02 0 02 0 02 0 9 dradnatS gnidneL 8 dradnatS gnidneL 7 dradnatS gnidneL 6 dradnatS gnidneL 5 dradnatS gnidneL 5.0 5.0 5.0 5.0 5.0 0 0 0 0 0 5.0− 5.0− 5.0− 5.0− 5.0− 02 0 02 0 02 0 02 0 02 0 41 dradnatS gnidneL 31 dradnatS gnidneL 21 dradnatS gnidneL 11 dradnatS gnidneL 01 dradnatS gnidneL 5.0 5.0 5.0 5.0 5.0 0 0 0 0 0 5.0− 5.0− 5.0− 5.0− 5.0− 02 0 02 0 02 0 02 0 02 0 91 dradnatS gnidneL 81 dradnatS gnidneL 71 dradnatS gnidneL 61 dradnatS gnidneL 51 dradnatS gnidneL 5.0 5.0 5.0 5.0 5.0 0 0 0 0 0 5.0− 5.0− 5.0− 5.0− 5.0− 02 0 02 0 02 0 02 0 02 0 sretrauQ sretrauQ sretrauQ sretrauQ sretrauQ .sdradnatsgnidnelfonoitpircseddeliatedarofDxidneppAeeS.selitnecrepht59/ht5dnaht48/ht61esiwtniophtiwsesnopsernaideM:setoN 78

-1Q1991rofsrotcaFdevresbonUneveShtiwledoMRAVAFehtnikcohSyciloPyratenoMyranoisnapxEspb52aotserusaeMdradnatSgnidneLfosesnopseReslupmI :3.GerugiF .2Q8002 4 dradnatS gnidneL 3 dradnatS gnidneL 2 dradnatS gnidneL 1 dradnatS gnidneL etaR sdnuF laredeF 5.0 5.0 5.0 5.0 5.0 0 0 0 0 0 5.0− 5.0− 5.0− 5.0− 5.0− 02 0 02 0 02 0 02 0 02 0 9 dradnatS gnidneL 8 dradnatS gnidneL 7 dradnatS gnidneL 6 dradnatS gnidneL 5 dradnatS gnidneL 5.0 5.0 5.0 5.0 5.0 0 0 0 0 0 5.0− 5.0− 5.0− 5.0− 5.0− 02 0 02 0 02 0 02 0 02 0 41 dradnatS gnidneL 31 dradnatS gnidneL 21 dradnatS gnidneL 11 dradnatS gnidneL 01 dradnatS gnidneL 5.0 5.0 5.0 5.0 5.0 0 0 0 0 0 5.0− 5.0− 5.0− 5.0− 5.0− 02 0 02 0 02 0 02 0 02 0 91 dradnatS gnidneL 81 dradnatS gnidneL 71 dradnatS gnidneL 61 dradnatS gnidneL 51 dradnatS gnidneL 5.0 5.0 5.0 5.0 5.0 0 0 0 0 0 5.0− 5.0− 5.0− 5.0− 5.0− 02 0 02 0 02 0 02 0 02 0 sretrauQ sretrauQ sretrauQ sretrauQ sretrauQ .sdradnatsgnidnelfonoitpircseddeliatedarofDxidneppAeeS.selitnecrepht59/ht5dnaht48/ht61esiwtniophtiwsesnopsernaideM:setoN 79

AppendixG.2. High-FrequencyIdentification FollowingBarakchianandCrowe(2013),weextractanalternativetimeseriesofmonetarypolicyshocks fromdailychangesinfederalfundsfuturesyieldsfordifferentmaturitiesaroundFOMCmeetingdates. We thenregresseachvariableofinterestonP = 4ownlagsaswellasthecontemporaneousandQ = 12lagged observationsofthisexogenousmonetaryshockseriesusingadistributedlagregressionmodel. FigureG.4comparestheexogenousshockseriesbasedonhigh-frequencyidentificationandourbaseline FAVAR model with three unobserved components. The scatter plot in panel (a) illustrates that the highfrequency monetary policy shocks correlate positively with a representative draw from the Gibbs sampler with median correlation coefficient. The histogram of all correlation coefficients for the last 10,000 draws fromtheGibbssamplerinpanel(b)showsthatthecorrelationbetweenthetwoshockseriesissignificantly positiveforthevastmajorityofdraws. FigureG.5plotstheresponsesofselectedvariablesfromthetheoreticalDSGEmodeltoanexpansionary monetary policy shock against their empirical counterparts based on high-frequency identification (B&C). AsinFigure5inthemaintext,thebank’scollateralrequirements,bankprofits,andinvestmentareexpressed intermsoftheirunconditionalstandarddeviations, whilethepolicyrateandthebank’snetinterestmargin are converted to annualized basis points, both in the DSGE model and in B&C. One period on the x-axis correspondstoonequarter. FigureG.5documentsthatthefindingsdescribedinthemaintextarerobustto discardingtheFAVARmodelandusinganentirelydifferentapproachtoidentifyingmonetarypolicyshocks. FigureG.7plotstheimpulseresponsefunctionsofalternativemeasuresoflendingstandardstoanexpansionarymonetarypolicyshockbasedonthehigh-frequencyidentificationinBarakchianandCrowe(2013) anddocumentsthatthefindingsdescribedinthemaintextarequalitativelyrobusttodiscardingtheFAVAR modelinfavorofadifferentapproachtoidentifyingmonetarypolicyshocks. Finally,FigureG.8illustratesthatall19SLOOSmeasuresoflendingstandardsdecreaseinresponseto anexpansionarymonetaryshock,whetheritisidentifiedusingtheFAVARorthehigh-frequencyapproach. FigureG.4: CorrelationofMonetaryPolicyShocksBasedonHigh-FrequencyIdentificationinBarakchianandCrowe(2013)and theBaselineFAVARModelwithThreeUnobservedFactorsfor1991Q1-2008Q2. 3 2 1 0 −1 −2 −3 −4 −5 −5 −4 −3 −2 −1 0 1 2 Barakchian and Crowe (2013) srotcaf tnetal 3 htiw ledom RAVAF 450 400 350 300 250 200 150 100 50 0 −0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 Correlation coefficient (a)Medianscatterplotofstandardizedmonetarypolicyshocks ycneuqerf etulosbA (b)Histogramofcorrelationcoefficients(last10,000draws) 80

Figure G.5: Impulse Responses of Selected Variables to an Expansionary Monetary Policy Shock, DSGE Model and High- FrequencyIdentificationinBarakchianandCrowe(2013)for1991Q1-2008Q2. Policy Rate 300 200 100 0 −100 −200 −300 0 20 stniop sisab dezilaunnA Net Interest Margin 50 40 30 20 10 0 −10 −20 0 20 Quarters stniop sisab dezilaunnA Collateral Requirements 0.2 0.1 0 −0.1 −0.2 −0.3 −0.4 −0.5 −0.6 0 20 Quarters snoitaived dradnatS Bank Profit 1 0.8 0.6 0.4 0.2 0 −0.2 −0.4 0 20 Quarters snoitaived dradnatS Investment 0.6 0.4 0.2 0 −0.2 −0.4 0 20 Quarters snoitaived dradnatS DSGE B&C Quarters Notes: Intheregressions, theeffectivefederalfundsrateisusedasameasureofthemonetarypolicyrate, theCallReportsnet interestmarginforallU.S.banksasaproxyforthetheoreticalinterestratespread,thenetpercentageofdomesticbanksincreasing collateralrequirementsforlargeandmiddle-marketfirmsasameasureofbanklendingstandards,theCallReportsnetincomefor commercialbanksintheU.S.tomeasurebankprofit,andtheISMManufacturing: NewOrdersIndexasaproxyforinvestment. SeeAppendixDforadetaileddescriptionofthedata. Fortheregressionmodel,pointestimatesareplottedwithpointwiseoneandtwo-standard-errorHAC-robustbootstrapconfidenceintervals. FigureG.6:ImpulseResponsesofLoanRiskinesstoanExpansionaryMonetaryPolicyShock,DSGEModelandHigh-Frequency IdentificationinBarakchianandCrowe(2013). STBL Riskiness 0.6 0.5 0.4 0.3 0.2 0.1 0 −0.1 −0.2 0 20 snoitaived dradnatS DSGE B&C Quarters Notes:ThemeasureofloanriskinessisobtainedfromtheTermsofBusinessLendingSurveyoftheFederalReserve.Inparticular, wecomputeweightedaverageriskscoreacrossallparticipatingbanksforthesample1997Q2-2008Q2. Fortheregressionmodel, pointestimatesareplottedwithpointwiseone-andtwo-standard-errorHAC-robustbootstrapconfidenceintervals. 81

FigureG.7: ImpulseResponsesofAlternativeMeasuresofLendingStandardstoanExpansionaryMonetaryPolicyShock,High- FrequencyIdentificationinBarakchianandCrowe(2013)for1991Q1-2008Q2. (a) Adjusted Lending Standards 0.8 0.6 0.4 0.2 0 −0.2 −0.4 −0.6 −0.8 0 20 Quarters snoitaived dradnatS (b) SLOOS Risk Tolerance 0.8 0.6 0.4 0.2 0 −0.2 −0.4 −0.6 −0.8 0 20 Quarters snoitaived dradnatS (c) Excess Bond Premium 0.8 0.6 0.4 0.2 0 −0.2 −0.4 −0.6 −0.8 0 20 Quarters snoitaived dradnatS (d) NFCI Credit Subindex 0.8 0.6 0.4 0.2 0 −0.2 −0.4 −0.6 −0.8 0 20 Quarters snoitaived dradnatS Notes:Pointestimateswithpointwiseone-andtwo-standard-errorHAC-robustbootstrapconfidenceintervalsbasedondistributed lagregressionsof(a)thecreditsupplyindicatorproposedbyBassettetal.(2014);(b)thenetpercentageofdomesticbankseasing lendingstandardsduetoincreasedrisktolerance;(c)theexcessbondpremiumproposedbyGilchristandZakrajsˇek(2012);(d)the NFCIcreditsubindexpublishedbytheFederalReserveBankofChicago.SeeAppendixDforadetaileddescriptionofthedata. 82

rof )3102( eworC dna naihckaraB ni noitacfiitnedI ycneuqerF-hgiH ,kcohS yciloP yratenoM yranoisnapxE na ot serusaeM dradnatS gnidneL fo sesnopseR eslupmI :8.G erugiF .2Q8002-1Q1991 4 dradnatS gnidneL 3 dradnatS gnidneL 2 dradnatS gnidneL 1 dradnatS gnidneL etaR sdnuF laredeF 5.0 5.0 5.0 5.0 1 0 0 0 0 0 5.0− 5.0− 5.0− 5.0− 1− 1− 1− 1− 1− 02 0 02 0 02 0 02 0 02 0 9 dradnatS gnidneL 8 dradnatS gnidneL 7 dradnatS gnidneL 6 dradnatS gnidneL 5 dradnatS gnidneL 5.0 5.0 1 5.0 5.0 0 0 0 0 0 5.0− 5.0− 1− 5.0− 5.0− 1− 1− 2− 1− 1− 02 0 02 0 02 0 02 0 02 0 41 dradnatS gnidneL 31 dradnatS gnidneL 21 dradnatS gnidneL 11 dradnatS gnidneL 01 dradnatS gnidneL 5.0 5 5.0 5.0 5.0 0 0 0 0 0 5.0− 5.0− 5.0− 5.0− 1− 5− 1− 1− 1− 02 0 02 0 02 0 02 0 02 0 91 dradnatS gnidneL 81 dradnatS gnidneL 71 dradnatS gnidneL 61 dradnatS gnidneL 51 dradnatS gnidneL 5.0 5.0 5.0 5.0 5.0 0 0 0 0 0 5.0− 5.0− 5.0− 5.0− 5.0− 1− 1− 1− 1− 02 0 02 0 02 0 02 0 02 0 sretrauQ sretrauQ sretrauQ sretrauQ sretrauQ sgalnwo4=Pnoelbairavhcaefosnoissergergaldetubirtsidnodesabslavretniecnedfinocpartstoobtsubor-CAHrorre-dradnats-owtdna-enoesiwtniophtiwsetamitsetnioP:setoN .sdradnatsgnidnelfonoitpircseddeliatedarofDxidneppAeeS.)3102(eworCdnanaihckaraBniseireskcohsehtfosnoitavresbodeggal21=Qdnasuoenaropmetnocsallewsa 83

AppendixG.3. ExtendedSamplePeriod FigureG.9:ImpulseResponsesofSelectedVariablestoanExpansionaryMonetaryPolicyShock,DSGEModelandFAVARModel withThreeUnobservedFactorsfor1991Q1-2015Q4. Policy Rate 200 150 100 50 0 −50 −100 −150 −200 −250 0 20 stniop sisab dezilaunnA Net Interest Margin 15 10 5 0 −5 −10 −15 −20 0 20 Quarters stniop sisab dezilaunnA Collateral Requirements 0.15 0.1 0.05 0 −0.05 −0.1 −0.15 −0.2 −0.25 −0.3 0 20 Quarters snoitaived dradnatS Bank Profit 0.8 0.6 0.4 0.2 0 −0.2 −0.4 −0.6 0 20 Quarters snoitaived dradnatS Investment 0.3 0.25 0.2 0.15 0.1 0.05 0 −0.05 −0.1 −0.15 0 20 Quarters snoitaived dradnatS DSGE FAVAR Quarters Notes: IntheFAVARmodel,theeffectivefederalfundsrateisusedasameasureofthemonetarypolicyrate,theCallReportsnet interestmarginforallU.S.banksasaproxyforthetheoreticalinterestratespread,thenetpercentageofdomesticbanksincreasing collateralrequirementsforlargeandmiddle-marketfirmsasameasureofbanklendingstandards,theCallReportsnetincomefor commercialbanksintheU.S.tomeasurebankprofit,andtheISMManufacturing: NewOrdersIndexasaproxyforinvestment. SeeAppendixDforadetaileddescriptionofthedata.FortheFAVARmodel,medianresponsesareplottedwithpointwise16th/84th and5th/95thpercentiles. Figure G.10: Impulse Responses of Selected Variables to an Expansionary Monetary Policy Shock, DSGE Model and High- FrequencyIdentificationinBarakchianandCrowe(2013)for1991Q1-2015Q4. Policy Rate 400 300 200 100 0 −100 −200 0 20 stniop sisab dezilaunnA Net Interest Margin 50 40 30 20 10 0 −10 0 20 Quarters stniop sisab dezilaunnA Collateral Requirements 0.3 0.2 0.1 0 −0.1 −0.2 −0.3 −0.4 0 20 Quarters snoitaived dradnatS Bank Profit 4 3 2 1 0 −1 −2 −3 −4 −5 0 20 Quarters snoitaived dradnatS Investment 0.4 0.3 0.2 0.1 0 −0.1 −0.2 −0.3 −0.4 0 20 Quarters snoitaived dradnatS DSGE B&C Quarters Notes: Intheregressions, theeffectivefederalfundsrateisusedasameasureofthemonetarypolicyrate, theCallReportsnet interestmarginforallU.S.banksasaproxyforthetheoreticalinterestratespread,thenetpercentageofdomesticbanksincreasing collateralrequirementsforlargeandmiddle-marketfirmsasameasureofbanklendingstandards,theCallReportsnetincomefor commercialbanksintheU.S.tomeasurebankprofit,andtheISMManufacturing: NewOrdersIndexasaproxyforinvestment. SeeAppendixDforadetaileddescriptionofthedata. Fortheregressionmodel,pointestimatesareplottedwithpointwiseoneandtwo-standard-errorHAC-robustbootstrapconfidenceintervals. 84

rofsrotcaFdevresbonUeerhThtiwledoMRAVAFenilesaBehtnikcohSyciloPyratenoMyranoisnapxEspb52aotserusaeMdradnatSgnidneLfosesnopseReslupmI:11.GerugiF .4Q5102-1Q1991 4 dradnatS gnidneL 3 dradnatS gnidneL 2 dradnatS gnidneL 1 dradnatS gnidneL etaR sdnuF laredeF 5.0 5.0 5.0 5.0 5.0 0 0 0 0 0 5.0− 5.0− 5.0− 5.0− 5.0− 02 0 02 0 02 0 02 0 02 0 9 dradnatS gnidneL 8 dradnatS gnidneL 7 dradnatS gnidneL 6 dradnatS gnidneL 5 dradnatS gnidneL 5.0 5.0 5.0 5.0 5.0 0 0 0 0 0 5.0− 5.0− 5.0− 5.0− 5.0− 02 0 02 0 02 0 02 0 02 0 41 dradnatS gnidneL 31 dradnatS gnidneL 21 dradnatS gnidneL 11 dradnatS gnidneL 01 dradnatS gnidneL 5.0 5.0 5.0 5.0 5.0 0 0 0 0 0 5.0− 5.0− 5.0− 5.0− 5.0− 02 0 02 0 02 0 02 0 02 0 91 dradnatS gnidneL 81 dradnatS gnidneL 71 dradnatS gnidneL 61 dradnatS gnidneL 51 dradnatS gnidneL 5.0 5.0 5.0 5.0 5.0 0 0 0 0 0 5.0− 5.0− 5.0− 5.0− 5.0− 02 0 02 0 02 0 02 0 02 0 sretrauQ sretrauQ sretrauQ sretrauQ sretrauQ .serusaemdradnatsgnidnelfonoitpircseddeliatedarofDxidneppAeeS.selitnecrepht59/ht5dnaht48/ht61esiwtniophtiwsesnopsernaideM:setoN 85

rof)3102(eworCdnanaihckaraBninoitacfiitnedIycneuqerF-hgiH ,kcohSyciloPyratenoMyranoisnapxEnaotserusaeMdradnatSgnidneLfosesnopseReslupmI :21.GerugiF .4Q5102-1Q1991 4 dradnatS gnidneL 3 dradnatS gnidneL 2 dradnatS gnidneL 1 dradnatS gnidneL etaR sdnuF laredeF 5.0 5.0 5.0 5.0 5.0 0 0 0 0 0 5.0− 5.0− 5.0− 5.0− 5.0− 02 0 02 0 02 0 02 0 02 0 9 dradnatS gnidneL 8 dradnatS gnidneL 7 dradnatS gnidneL 6 dradnatS gnidneL 5 dradnatS gnidneL 5.0 5.0 5.0 5.0 5.0 0 0 0 0 0 5.0− 5.0− 5.0− 5.0− 5.0− 02 0 02 0 02 0 02 0 02 0 41 dradnatS gnidneL 31 dradnatS gnidneL 21 dradnatS gnidneL 11 dradnatS gnidneL 01 dradnatS gnidneL 5.0 5.0 5.0 5.0 5.0 0 0 0 0 0 5.0− 5.0− 5.0− 5.0− 5.0− 02 0 02 0 02 0 02 0 02 0 91 dradnatS gnidneL 81 dradnatS gnidneL 71 dradnatS gnidneL 61 dradnatS gnidneL 51 dradnatS gnidneL 5.0 5.0 5.0 5.0 5.0 0 0 0 0 0 5.0− 5.0− 5.0− 5.0− 5.0− 02 0 02 0 02 0 02 0 02 0 sretrauQ sretrauQ sretrauQ sretrauQ sretrauQ nwo4 = Pnoelbairavhcaefosnoissergergaldetubirtsidnodesabslavretniecnedfinocpartstoobtsubor-CAHrorre-dradnats-owtdna-enoesiwtniophtiwsetamitsetnioP :setoN .serusaemdradnatsgnidnelfonoitpircseddeliatedarofDxidneppAeeS.seireskcohsdednetxeehtfosnoitavresbodeggal21=Qdnasuoenaropmetnocsallewsasgal 86

FigureG.13:ImpulseResponsesofAlternativeMeasuresofLendingStandardstoanExpansionaryMonetaryPolicyShockinthe FAVARModelwithThreeUnobservedFactorsfor1991Q1-2015Q4. (a) SLOOS Risk Tolerance 0.15 0.1 0.05 0 −0.05 −0.1 0 20 Quarters snoitaived dradnatS (b) Excess Bond Premium 0.1 0.05 0 −0.05 −0.1 −0.15 0 20 Quarters snoitaived dradnatS (c) NFCI Credit Subindex 0.05 0 −0.05 −0.1 −0.15 −0.2 0 20 Quarters snoitaived dradnatS Notes: Median responses with pointwise 16th/84th and 5th/95th percentiles, based on the FAVAR model with three unobserved factors,wherethe19SLOOSlendingstandardmeasureshavebeenreplacedby(a)thenetpercentageofdomesticbankseasing lendingstandardsduetoincreasedrisktolerance;(b)theexcessbondpremiumproposedbyGilchristandZakrajsˇek(2012);(c)the NFCIcreditsubindexpublishedbytheFederalReserveBankofChicago.SeeAppendixDforadetaileddescriptionofthedata. FigureG.14:ImpulseResponsesofAlternativeMeasuresofLendingStandardstoanExpansionaryMonetaryPolicyShock,High- FrequencyIdentificationinBarakchianandCrowe(2013)for1991Q1-2015Q4. (a) SLOOS Risk Tolerance 0.8 0.6 0.4 0.2 0 −0.2 −0.4 −0.6 −0.8 0 20 Quarters snoitaived dradnatS (b) Excess Bond Premium 0.8 0.6 0.4 0.2 0 −0.2 −0.4 −0.6 −0.8 0 20 Quarters snoitaived dradnatS (c) NFCI Credit Subindex 0.8 0.6 0.4 0.2 0 −0.2 −0.4 −0.6 −0.8 0 20 Quarters snoitaived dradnatS Notes:Pointestimateswithpointwiseone-andtwo-standard-errorHAC-robustbootstrapconfidenceintervalsbasedondistributed lagregressionsof(a)thenetpercentageofdomesticbankseasinglendingstandardsduetoincreasedrisktolerance;(b)theexcess bondpremiumproposedbyGilchristandZakrajsˇek(2012);(c)theNFCIcreditsubindexpublishedbytheFederalReserveBankof Chicago.SeeAppendixDforadetaileddescriptionofthedata. 87

AppendicesReferences Angeloni, Ignazio, Ester Faia, and Marco Lo Duca (2013). “Monetary Policy and Risk Taking,” SAFE WorkingPaperSeriesNo.8. AmirAhmadi,PooyanandHaraldUhlig(2009).“MeasuringtheEffectsofaShocktoMonetaryPolicy: A BayesianFAVARApproachwithSignRestrictions.”Mimeo,GoetheUniversityFrankfurt. Barakchian,S.MahdiandChristopherCrowe(2013).“Monetarypolicymatters: Evidencefromnewshocks data,”JournalofMonetaryEconomics60(8): 950-966. Bassett, William F., Mary Beth Chosak, John C. Driscoll, and Egon Zakrajsˇek (2014). “Changes in bank lendingstandardsandthemacroeconomy,”JournalofMonetaryEconomics62(1): 23-40. Bernanke, Ben S., Mark Gertler, and Simon Gilchrist (1999). “The Financial Accelerator in a Quantitative BusinessCycleFramework,”in: Taylor,J.,Woodford,M.(Eds.),HandbookofMacroeconomics. Bernanke, Ben S., Jean Boivin, and Piotr Eliasz (2005). “Measuring the Effects of Monetary Policy: A FAVARApproach,”QuarterlyJournalofEconomics120(1): 387-422. Carter, Chris and Robert Kohn (1994). “On Gibbs Sampling for State Space Models,” Biometrika 81(3): 541-553. Christensen, Ian and Ali Dib (2008). “The Financial Accelerator in an Estimated New Keynesian Model,” ReviewofEconomicDynamics11(1): 155–178. Christiano, Lawrence J., Roberto Motto, and Massimo Rostagno (2014). “Risk Shocks,” American EconomicReview104(1): 27-65. Geman, Stuart and Donald Geman (1984). “Stochastic Relaxation, Gibbs Distributions, and the Bayesian RestorationofImages,”IEEETransactionsonPatternAnalysisandMachineIntelligence6(6): 721-741. Gilchrist,SimonandEgonZakrajsˇek(2012).“CreditSpreadsandBusinessCycleFluctuations,”American EconomicReview102(4): 1692-1720. Hodrick,RobertJ.andEdwardC.Prescott(1997).“PostwarU.S.BusinessCycles: AnEmpiricalInvestigation,”JournalofMoney,CreditandBanking29(1): 1-16. Kim,Chang-JinandCharlesR.Nelson(1999).“State-SpaceModelswithRegimeSwitching: Classicaland Gibbs-SamplingApproacheswithApplications,”MITPressBooks,TheMITPress,edition1,volume1, December1999. Kadiyala, Rao and Sune Karlsson (1997). “Numerical Methods for Estimation and Inference in Bayesian VAR-Models,”JournalofAppliedEconometrics12(2): 99-132. Schmitt-Grohe´,StephanieandMart´ınUribe(2006).“ComparingTwoVariantsofCalvo-TypeWageStickiness,”NBERWorkingPaper12740,December2006. Taylor, John B. (2007). “Housing and Monetary Policy,” Proceedings – Economic Policy Symposium – JacksonHole: 463-476. Townsend,RobertM.(1979).“OptimalContractsandCompetitiveMarketswithCostlyStateVerification,” JournalofEconomicTheory21(2): 265-293. 88