Financial Capital and the Macroeconomy: A Quantitative Framework

Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. Financial Capital and the Macroeconomy: A Quantitative Framework Michael T. Kiley and Jae W. Sim 2011-27 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.

Financial Capital and the Macroeconomy: A Quantitative Framework (cid:3) Michael T. Kiley Jae W. Sim y z May 5, 2011 Abstract Financial intermediation transforms short-term liquid assets into longterm capital assets. As a result, risk taking, in the form of long-term commitments despite unresolved short-term funding risk, is an essential element of intermediation. If such funding risk must be addressed by costly recapitalization and/ordistressed assetsalesdue to capitalmarket frictions, an increase in uncertainty can cause a disruption in the intermediation process by forcing risk-neutral intermediaries to behave in a risk-aversemanner. Ouranalysisexaminesthisbehaviortheoreticallyand empirically. We (cid:133)rst develop a dynamic macroeconomic model in which the balance sheet/liquidity condition of (cid:133)nancial intermediaries plays an important role in the determination of asset prices and economic activity under time-varying uncertainty. Second, we present new evidence on the importance of uncertainty facing (cid:133)nancial intermediaries for credit terms and volume and for aggregate economic activity, thereby partially quantifying the signi(cid:133)cance of capital market frictions. We adopt a structural identi(cid:133)cation strategy in which the predictions of our theory, in the form of sign restrictions, play an important role. 1 Introduction The global (cid:133)nancial crisis has shown that the balance sheet/liquidity condition of (cid:133)nancial institutions can have important real e⁄ects on the macroeconomy. Indeed, a root cause of (cid:133)nancial instability appears to be the reliance on shorttermfundingof(cid:133)nancialinvestmentinpotentiallyilliquidcapitalassets. Tothe extent that the essence of (cid:133)nancial intermediation lies in the transformation of We would like to thanks seminar participants at the 2011 ASSA meetings, the Bank (cid:3) of Canada, Bank of Japan, and Federal Reserve Board for comments on an earlier draft (circulated under the title (cid:147)The Dynamic E⁄ects of Bank Capital in General Equilibrium(cid:148)). Webene(cid:133)tedgreatlyfrom theassistanceofMarkCarlson,whohelpedcreatethedataweuse on(cid:133)rm-levelvolatilitywithinthe(cid:133)nancialintermediationsector. Wewouldalsoliketothank BillBassett,Mary Beth Chosak,John Driscoll,and Egon Zakrajsek forsharing theirdata. Board ofGovernors ofthe FederalReserve System y Board ofGovernors ofthe FederalReserve System z 1

short-term liquid assets into long-term capital assets, the potential imbalance between the liquidity of intermediaries(cid:146)funding and their investment assets is an inherent feature of modern (cid:133)nance. Such an imbalance, however, could cause a signi(cid:133)cant disruption in the (cid:133)nancial intermediation process, taking a large toll on real economic activity, especially when capital markets su⁄er from information problems. For instance, if outside capital is costly to raise because of information asymmetries between insiders and outsiders, (cid:133)nancial institutions may take preemptive measures to reduce their exposure to an increase in uncertainty, thereby foregoing otherwise pro(cid:133)table investment opportunities. Likewise, if interbank transactions involving balance sheet assets is costly because of lack of transparency and growing counter-party risks, (cid:133)nancial institutions may employ caution against taking large unhedged positions because undoing such positions may involve a substantial degree of distressed sales. Such preemptive measures, though individually rational, could collectively bring about a tightening in the availability of credit and decline in economic activity, which in the extreme could manifest itself in a (cid:133)nancial crisis. The discussion above suggests an important link between economic uncertaintyandactivity,mediatedbycapitalmarketfrictionfacing(cid:133)nancialintermediaries. However,withintheworkhorseacademicframeworkformacroeconomic analysis, the links between (cid:133)nancial intermediation and macroeconomic outcomes are thin to non-existent (although the (cid:133)eld is growing, e.g., Adrian and Shin (2010), Brunnermeier and Pedersen (2009), Gertler and Kiyotaki (2010) and He and Krishnamurthy (2008)). Meanwhile, banking, (cid:133)nance, and macroeconomics are typically not integrated in the models used at policy institutions (e.g., the discussion in Boivin et al. (2010)). Our goal is to take a deeper look at how such a link operates in a modern economy, quantifying the signi(cid:133)cance of capital market frictions, and potentially identifying intervention points for future public policies. To that end, we take a dual approach. First, we develop a dynamic model in which the balance sheet/liquidity condition of (cid:133)nancial intermediaries plays an important role in the determination of asset prices and economic activity under time-varying uncertainty. Second, we present new evidence on the importance of uncertainty facing (cid:133)nancial intermediaries for credit terms and quantity and for aggregate economic activity, thus quantifying the signi(cid:133)cance of capital market frictions. We adopt a structural identi(cid:133)cation strategy in which the predictions of our theory, in the form of sign restrictions, play an important role. In our model, we provide a general-equilibrium, business-cycle framework thatgeneralizestheliquiditybasedassetpricingframework(LAPM,Holmstr(cid:246)m and Tirole (2001)) from the viewpoint of (cid:133)nancial intermediaries operating under a capital (margin) constraint. The (cid:133)nancial intermediaries in the model are required to make investment commitments before a complete resolution of idiosyncratic funding risk that can be addressed only by costly re(cid:133)nancing (of the type emphasized by, for example, Myers and Majluf (1984) and Bolton and Freixas (2000)); this environment forces intermediaries to behave in a riskaverse manner. The resulting caution against taking a large unhedged position 2

givenshort-runfundinguncertaintycreatesanintermediaryspeci(cid:133)cpricingkernel that can deviate from the stochastic discount factor of a representative householdevenwhentheintermediaryisfullyownedbythehousehold,pushing equilibrium asset returns away from their counterpart in the absence of such intermediation frictions, causing aggregate investment and output to respond to shocks to intermediaries.1 It is worthwhile to emphasize that the caution adopted by our otherwise risk-neutral intermediaries arises because of the frictions in (cid:133)nancial markets we assume; other approaches have resorted to assuming risk-aversion on the partofintermediariestogeneratesimilarbehavior(e.g.,HeandKrishnamurthy (2008)). Using this model, we show that an increase in uncertainty, in the sense of mean preserving spread, can have a powerful impact on credit market conditions and economic activity even though such an uncertainty shock does not have any direct implication for real allocations in a frictionless economy. Wethenusethetheoreticalpredictionsofourmodelregardingtheimpactof an uncertainty shock to (cid:133)nancial intermediaries to quantify the macroeconomic importance of capital market frictions facing (cid:133)nancial institutions. We start by constructing an uncertainty measure, an empirical counterpart of the timevarying idiosyncratic uncertainty in the theoretical model, using daily equity price movements at large bank-holding companies in the United States. To quantify the impact of structural shocks to the uncertainty measure, we frame ourstructuraleconometricanalysisinasetofBayesiansignrestrictionsinformed by our model(cid:146)s predictions, which identify the dynamic e⁄ects of disturbances to the intermediation sector on macroeconomic variables. Implementation of our identifying assumptions (cid:133)nds quantitatively important e⁄ects of shocks to the intermediation sector on economic activity, with increased uncertainty leading to a tightening in lending terms and declines in lendingandeconomicactivity. Theuseoftheoreticalrestrictionstoinformidenti(cid:133)cationofintermediationshocksisanotableadvanceoverpreviousmacroeconomic e⁄orts, which have used debatable assumptions, such as recursive timing assumptions, to identify such e⁄ects (e.g., Berrospide and Edge (2010), Lown and Morgan (2006) and Ciccarelli et al. (2010)).2 In particular, our approach 1While outside the main interest of our analysis, the magnitude of the return premium created by the intermediation wedge in this paper is notable (e.g., can explain almost a half of measured equity premiums under our baseline calibration), suggesting that incorporation offrictionssuchasthoseweconsiderhasimportantimplicationsbeyondourspeci(cid:133)cfocuson the links between the level of capitalization at intermediaries, lending and lending spreads, and realactivity. Theintermediary speci(cid:133)cpricing kernelin ourframework providesa structural justi(cid:133)cation of the time-varying discount factor of Jermann and Quadrini (2009), who deriveasuper(cid:133)cially-similarpricingkernelfromareduced-formquadraticadjustmentcostfor dividends. 2The literature examining the e⁄ectofconditionswithin the banking sectoron lending or other bank decisions is vast, although much of this work takes a microeconomic perspective. Forexample,BergerandUdell(1994)foundlittlelinkbetweenbankcapitalandlending,while HancockandWilcox(1993)foundmoreimportantlinks,withbanksfacingacapitalshortfall tendingtocrimp lending. Subsequentresearch hastended tosupportthedepressinge⁄ectof poor conditions in the banking sector for outcomes identi(cid:133)ed at the microeconomic level by HancockandWilcox(1993). Forexample,BIS(2010)summarizedsimilarstudies,usingdata 3

allows us to purge (cid:145)(cid:148)business cycle(cid:148)correlations between lending and activity from our estimates of the e⁄ects of shocks to intermediaries on real activity, following a strategy similar to Uhlig (2005) and Mountford and Uhlig (2009) in their analyses of monetary policy and (cid:133)scal policy, respectively. Indeed, our results reveal clearly that the (cid:133)nancial shocks we identify are di⁄erent from those in these other VAR approaches. This result is not very surprisingbecauseourfocusonuncertaintyshocksisafairlynarrowperspective, as our model framework implies that nearly any shock a⁄ecting the balance sheet/liquiditypositionof(cid:133)nancialintermediarieswillimpact(cid:133)nancialmarkets and real activity. In this sense, our new evidence helps highlight some of the possiblyimportanteconomicmechanisms,butallowsforthepossibilityofmuch richer investigations of (cid:133)nancial shocks in the future. Finally, our focus on uncertainty shocks provides novel evidence on the role of this type of factor in macroeconomic (cid:135)uctuations, evidence complementary to, for example, Bloom (2009).3 2 The Model In our model, (cid:133)nancial intermediation is central to the provision of credit and themanagementofhouseholdportfolios. Thefollowingthreeassumptionsmake intermediationimportant: (i)householdsneedliquidityservicesfromdepositsat (cid:133)nancial intermediaries, which implies that households accept returns on intermediarydepositsbelowtheriskfreerate;(ii)householdslacktheskillnecessary to invest and manage their (cid:133)nancial resources and turn to (cid:133)nancial intermediaries to manage investment decisions; and (iii) intermediaries themselves face capital market frictions, owing to the con(cid:135)icts of interests and the information asymmetry between the (cid:133)nancial intermediaries and their owners, the households, which creates a dilution cost for the intermediaries when raising equity capital. The model economy consists of a representative household, a continuum of (cid:133)nancial intermediaries, a continuum of competitive (cid:133)nal-goods producers, and a continuum of competitive investment-goods producers. We start with the (cid:133)nancial intermediaries. fromanumberofstudies,thattendedtopointinthatdirection;morerecently,RiceandRose (2011) also (cid:133)nd that banks with lowercapitallevels tend to crimp lending. 3Ourframeworkcanbeusedtoanalyzeanumberofpolicyissues(cid:150)related,forexample,to stabilizationpoliciesincreditmarketssuchasdirectgovernmentlendingorcapitalinjections into the banking system (as highlighted in Gertler and Kiyotaki (2010)) or the transition e⁄ects of capital regulation (of the sort discussed heuristically in Admati et al. (2010) and Hanson et al. (2011)). In our related research (see Kiley and Sim (2011)), we show in detail how ourmodelcan be used to analyze such issues. 4

2.1 Financial Intermediaries 2.1.1 Return Structure Financialintermediariesuseamixofdebt(deposits)andequityfromhouseholds to invest in capital assets. A (cid:133)nancial intermediary i purchases capital asset K (i) at a market price Q and rents out this capital to (cid:133)nal-goods (cid:133)rms for t+1 t net rental income de(cid:133)ned as RK =R~K U (cid:24)(U )P t+1 t+1 t+1 (cid:0) t+1 t+1 where R~K is the nominal rental rate per utilization unit of capital asset t+1 (K (i)U (i)), U (i) is the utilization rate, (cid:24)(U ) is the real cost of t+1 t+1 t+1 t+1 utilization and P is the price level of the (cid:133)nal-goods. Equivalently, the t+1 rental income can be thought of as dividends from the (cid:133)nal goods (cid:133)rms, in which case K (i) should be interpreted as the number of shares. The total t+1 return from the investment is composed of rents/dividends (RK K (i)) and t+1 t+1 thecapitalgainsassociatedwiththechangesinthepriceofcapitalassets/shares ((1 (cid:14))Q K (i)=Q ), where (cid:14) denotes the depreciation rate.4 t+1 t+1 t (cid:0) To model the balance sheet/liquidity risk that (cid:133)nancial intermediaries face, weassumethattherateofreturnfrominvestmentissubjecttoamultiplicative idiosyncratic shock such that the total rate of return can be decomposed into two components, idiosyncratic and aggregate, RF (i) = (cid:15) (i)RF (1) t+1 t+1 t+1 RK +(1 (cid:14))Q = (cid:15) (i) t+1 (cid:0) t+1 t+1 Q (cid:20) t (cid:21) where (cid:15) (i) is the idiosyncratic component of the return and RF is the t+1 t+1 aggregatecomponent. Theidiosyncraticshockfollowsatime-varyinglognormal distribution, log(cid:15) (i) N( 0:5(cid:27)2;(cid:27)2) (2) t (cid:24) (cid:0) t t wheretheidiosyncraticreturnvolatilityevolvesovertimeaccordingtoaMarkov process, log(cid:27) =(1 (cid:26) )log(cid:27)(cid:22)+(cid:26) log(cid:27) +u , u iid N(0;(cid:6)2): (3) t (cid:0) (cid:27) (cid:27) t (cid:0) 1 t t (cid:24) Note that an increase in uncertainty is a mean preserving spread: while the second moment of the distribution (2) is time-varying, the (cid:133)rst moment of the distributionistime-invariant, i.e., E[(cid:15) t (i)(cid:27) t ]=E[(cid:15) t (i)]=1owingtothecorrecj tion to the Jensen(cid:146)s inequality in (2). Given the linear investment technology, such a mean preserving spread has no direct implications for real allocations in an economy without capital market frictions; however, capital market frictions will imply important e⁄ects from such disturbances on real allocations. 4Inbroadterms,thereturnstructureofourintermediariesshareaspectsofthoseanalyzed by Gertlerand Kiyotaki(2010). 5

2.1.2 Capital Constraint We assume that (cid:133)nancial intermediaries are subject to a minimum capital ratio (or margin requirement) that may vary over time. Denoting this minimum capital ratio by m , the capital constraint is given by t B (i) 1 t+1 m : (4) t (cid:0) Q K (i) (cid:21) t t+1 The equation states that the ratio of debts to assets must be less than 1 m . t (cid:0) Our analysis does not take a stand on the speci(cid:133)c mechanism that generates the capital constraint. In reality, such constraints re(cid:135)ect both market forces (e.g., market discipline on leverage due to contract enforceability problem) and regulatoryrestrictions. Forexample,theValue-at-Risk(VaR)frameworkwidely adopted by both real (cid:133)nancial institutions and regulatory authorities implicitly implies a capital constraint of the form in (4).5 5To see this point more formally, consider an (cid:11) VaR constraint, which requires that the (cid:0) defaultprobabilityofany(cid:133)nancialinstitutionshouldbelowerthan(cid:11)%. Formallythismeans that Pr (cid:15)t+1(i)Et(R t F +1 )QtKt+1(i) (cid:0) R t B +1 Bt+1(i) (cid:20)(cid:0) N(cid:22) t (cid:20) (cid:11) where N(cid:22) t is the lo(cid:16)wer bound of the net-worth. For tractability, such(cid:17)an approach typically (cid:0) assumeshomogeneityoftheproblem byrestrictingthelowerboundtobeproportionaltothe future value ofthe current investment scale,i.e., (cid:0) N(cid:22) t= (cid:0) ntR t B +1 QtKt+1(i) where the proportionality factor nt is exogenously time-varying. One interpretation of such homogeneitycouldbethattheshareholdersalsobearsomeburdenofbankruptcycost,where the bankruptcy cost itself is proportional to the scale of the balance sheet (see for instance, Bernanke et al.(1999)). Using this parameterization,the VaR constraint can be stated as F Et R (R t B + t F + 1 1 ) (cid:18) Q B tK t+ t+ 1( 1 i ( ) i) (cid:0) nt (cid:19)!(cid:20) (cid:11) whereF()isthecdfof(cid:15). Assumingaconstantvolatility,wecantheninverttherelationship (cid:1) to derive Et R (R t B + t F + 1 1 ) (cid:18) Q B tK t+ t+ 1( 1 i ( ) i) (cid:0) nt (cid:19) (cid:20) F(cid:0) 1((cid:11)) orequivalently 1 (cid:0) Q B tK t+ t+ 1( 1 i ( ) i) (cid:21) 1 (cid:0) F(cid:0) 1((cid:11)) Et R (R t B + t F + 1 1 ) (cid:0) nt (cid:17) mt. (5) One could call the right hand side of the inequality a minimum capital ratio (or margin requirement)anddenoteitbymt. UndertheVaRapproach,theminimumcapitalratio/margin requirement depends on the expected return negatively when default is allowed (i.e., when (cid:11)>0 ), as higher expected returns allow for greater leverage while satisfying the VaR constraint. Our constraint (4) is consistent with this approach only when (cid:11)=0(under typical assumptionsforF()),i.e.,when(cid:133)nancialintermediariesareneverallowedtodefaultandare (cid:1) requiredtoraiseenoughcapitaltostaya(cid:135)oat. Wetakethisapproachfortworeasons: First, themainconclusionofouranalysisdoesnotdependonalinkbetweenleverageandexpected asset returns, though such a link will probably strengthen the conclusion; Second, we can substantiallysimplifytheanalysisbyfocusingonequitymarketfriction and sidesteppingthe problem of pricing debt securities, making our approach closer to Adrian and Shin (2010) than to Brunnermeierand Pedersen (2009). 6

Inequilibrium,thecapitalconstraintisalwaysbindingfortworeasons: First, as discussed further below, the household is willing to pay a liquidity premium foritsdepositssincetheintermediarydepositscreatenon-pecuniaryreturnsfor the household. Second, even without the liquidity premium, (cid:133)nancial intermediaries prefer to issue debt rather than to issue equity owing to the dilution cost associated with equity issuance, which will be explained shortly. As a consequence, the (cid:133)nancial intermediaries follow a (cid:147)pecking order(cid:148)in their capital structure choice. We will prove that the capital constraint binds in the steady state. 2.1.3 Timing of Events As highlighted in the introduction, a key aspect of our analysis involves the disconnect between intermediaries(cid:146)lending commitments and their short-run funds. To model this disconnect in a tractable manner, we adopt the following timing convention: (1) At the beginning of each period, the aggregate componentofreturns(RF)becomesknown. (2)Afterobservingtheaggregateshocks, t the intermediary makes investment (Q K (i)) and borrowing (BB (i)) decit t+1 t+1 sions. (3) After the investment/borrowing decisions, the level of the idiosyncratic shock ((cid:15) (i)) becomes known to the intermediary and dividend payout t /equity issuance decisions (D t (i)T0) are made. Thetimingconventionimpliesthatthe(cid:133)nancialintermediarieshavetomake investment commitments before they know their (random) realization of internal funds. It also implies that the revenue shock becomes known only after the borrowing markets for intermediaries are closed. While this precise timing is somewhat arbitrary, it captures important features of reality. In particular, the timing convention represents parsimoniously the short-run funding risks that (cid:133)nancial intermediaries face. For example, (cid:133)nancial intermediaries always face uncertainty about the balance between their short-run loanable funds and/or the cost of such funds in retail/wholesale borrowing markets and the use of outstanding loan commitments; alternatively, realized income can fall short of the funding needs associated with their precommitments due to credit losses or (cid:135)uctuations in asset values. Under such conditions and when outside equity is more expensive than borrowing, funding uncertainty can make the intermediariesadoptaprecautionary stanceinmakinginvestment/depositdecisionseven when all intermediaries are risk-neutral.6 6A similar timing convention has been used by Wen (2009) in the context of bu⁄er stock savingofrisk-aversehouseholdsandbyGertlerandKiyotaki(2010)inthecontextofinterbank marketborrowingdecisionofriskneutralbanks. Atthispoint,aquestionregardingtheroleof interbanktransactionsshouldbecomeapparent. Inourenvironment,thepresenceorabsence ofinterbank borrowing market afterthe realization ofidiosyncratic shock does not a⁄ect the main conclusion of the analysis. This is because the (cid:133)nancial intermediaries are assumed to commit to the capital structure chosen before the realization of the shock. Borrowing more through the interbank market to cope with cash (cid:135)ow shortfalls simply worsens the problem because it increases leverage. Whatcanhelpthesituation,ifexists,isane¢ cientsecondarymarketinwhichcapitalassets onintermediarybalancesheetscanbetradedsuchthatacashstrappedintermediarycansell some portion of its assets to a cash rich intermediary and use the proceeds to buy back a 7

2.1.4 Evolution of Capital Tocapturetheroleof(cid:133)nancialmarketfrictionsfortheintermediaries,weadopt a costly equity (cid:133)nance framework. Owing to the information asymmetry between the intermediaries and the potential owners, equity issuance involves a dilution e⁄ect, a phenomenon that a dollar amount of equity issuance reduces the value of existing shares more than a dollar. We operationalize this e⁄ect by assuming that the actual cash (cid:135)ow related with equity is given by a function ’(D (i)) de(cid:133)ned as, t D (i) if D (i) 0 ’(D t (i)) = (1 ’(cid:22) t )D (i) if D t (i) (cid:21) <0 t t (cid:26) (cid:0) = D (i) ’(cid:22) min D (i);0 : t t (cid:0) (cid:1) f g In words, when the intermediary pays out a positive amount of dividends, the cash out(cid:135)ow associated with equity is simply given by the dividends payout, D (i). Howeverwhentheintermediaryissuesnewequities(D (i)<0),thecash t t in(cid:135)ow associated with the notional value D (i) is reduced to (1 ’(cid:22))D (i). t t (cid:0) (cid:0) (cid:0) Following Bolton and Freixas (2000), we call the foregone cash (cid:135)ow ’(cid:22)D (i) a t (cid:0) dilution cost.7 In each period, (cid:133)nancial intermediaries face the following (cid:135)ow of funds constraint, 0 = (cid:15) (i)RFQ K (i)+B (i) (6) t t t 1 t t+1 (cid:0) Cash In(cid:135)ow [RBB (i)+Q K (i)+’(D (i))]: (cid:0) | t t {zt t+1 } t Cash Out(cid:135)ow The cash in(cid:135)ow is compos|ed of revenue fr{ozm last period(cid:146)s}investment (lending) (cid:15) (i)RFQ K (i) and new borrowing from the household B (i). The t t t 1 t t+1 (cid:0) portionofitsdebt,therebysatisfyingthecapitalconstraintwithoutissuingnewshares,which isassumed to be costly in thisresearch aswillbe explained below. However,itisnaturalto assume that the same information problem that makes the equity (cid:133)nance costly also makes interbank transfer of balance sheet assets di¢ cult (as was apparent in the (cid:133)nancial crisis of 2008, where secondary markets for bank loans became severely distressed). Given that such frictionsinahypotheticalsecondarymarketforbankassetshavesimilarimplicationsascostly equity (cid:133)nancing, we simplify the analysis by assuming either the absence of such secondary market or at least that the marginal cost of interbank transfer of assets are greater than the marginalcost ofequity issuance. 7Inreality,thecostofissuingequitycouldstemfrommanysources. Forexample,outsiders whoinvestinnewsharesoftheintermediarymaynotbeabletodistinguishanegativeincome shock from diversion or ine¢ ciency of management. In such an environment, outsiders need to investigate the balance sheet of the intermediary before they invest to verify that the intermediary complies with the rule of truthful reporting. Furthermore, as shown by Ross (1977)andMyersandMajluf(1984),outsiders,notknowingthetrueinvestmentopportunities of the intermediary, require initialdiscounts to protect themselves from (cid:147)lemons(cid:148). This type of friction is evident in market data, where, for example, equity issuance costs take the form of underwriting fees for investment banks and initial discounts of seasoned equity o⁄erings (SEOs). 8

cash out(cid:135)ow consists of repayment to the household for last period(cid:146)s borrowing RBB (i), where RB is the borrowing rate of the intermediary, and new t t t investment Q K (i). The last item in (6) can be cash in(cid:135)ow or cash out(cid:135)ow t t+1 depending on the sign of D (i). When it is negative, the actual cash in(cid:135)ow t is reduced by a constant factor, ’(cid:22).8 By rearranging the terms and using the de(cid:133)nition of capital, the (cid:135)ow of funds constraint can be interpreted as the law of motion for equity capital, i.e., E (i)= N (i) + ’(D (i)) t t t (cid:0) Net-Worth Cash Flow for Equity where the net-worth of the int|erm{zed}iary is g|iven{zby } N (i) = (cid:15) (i)RFQ K (i) RBB (i) t t t t (cid:0) 1 t (cid:0) t t = E (i)+[(cid:15) (i)RF 1]Q K (i) (RB 1)B (i): t (cid:0) 1 t t (cid:0) t (cid:0) 1 t (cid:0) t (cid:0) t 2.1.5 Value Maximization Problem To de(cid:133)ne the optimization problem of an intermediary, it is useful to introduce an expectation operator that accounts for idiosyncratic uncertainty, E i t ( (cid:1) ). The conditioningsetoftheoperatorincludesallinformationuptotimetexceptthe current realization of the idiosyncratic shock (cid:15) (i). We can then formally state t the value maximization problem of the intermediary as follows. The intermediary optimizes over Q K (i) , B (i) and D (i) to maximize s s+1 s+1 s V t B(i)=max 1 (cid:12)s (cid:0) t Et (cid:3) P s E i t [D s (i)] (7) s=t (cid:20) s (cid:21) X + 1 (cid:12)s (cid:0) t Et (cid:3) P s(cid:22) s (i) (1 (cid:0) m s )Q s K s+1 (i) (cid:0) B s+1 (i) s=t (cid:26) s (cid:20) (cid:21)(cid:27) X + s 1 =t (cid:12)s (cid:0) t Et (cid:26) (cid:3) P s s E i t (cid:20) (cid:21) s (i)[(cid:15) s (i)R s FQ s (cid:0) 1 K s (i)+B s+1 (i) X RBB (i) Q K (i) ’(D (i))] (cid:0) s s (cid:0) s s+1 (cid:0) s (cid:21)(cid:27) where(cid:3) isthemarginalutilityoftherepresentativehousehold,(cid:22) (i)and(cid:21) (i) s s s are the Lagrangian multipliers associated with the capital constraint and the (cid:135)ow of funds constraint, respectively. 8Gomes (2001) points out that the per unit cost of equity issuance is either constant or declining, exhibiting an increasing returns to scale. An alternative approach considered in JermannandQuadrini(2009)assumesaquadraticadjustmentcostindividendpayouts/equity issuance. Such an assumption is motivated by empirical evidence that dividend payouts are smooth. In contrast to dividend payouts, equity (cid:133)nancing and/or share repurchases are better described as lumpy, discrete event. In reality, modeling the mix of smooth dividend streamsandlumpyequityissuance/sharerepurchasesjointlywouldrequireconsideringavery complicatedcorporate(cid:133)nancingproblem,whichlieswelloutsideourinterestinthekeyfactors driving the links between bank capitalization and realeconomic activity. 9

Notethattheintermediaryisrisk-neutralanddiscountsthefuturedividends bythemarginalutilityofrepresentativehousehold,theowneroftheinstitution. Alsonotethatthe(cid:135)owoffundsconstraintanditsshadowvalue(cid:21) (i)arewithin s the expectation operator E i t ( (cid:1) )(cid:150)under our timing assumption, the intermediary hastodecidehowmuchtoborrowandinvestbeforeitcomestoknowthevalue of idiosyncratic shock (cid:15) (i). This implies that the intermediary does not know s its own shadow value of internal funds until the idiosyncratic cash (cid:135)ow shock becomes known and the intermediary needs to form an expectation based on aggregateconditions. Wecansummarizethee¢ ciencyconditionsoftheproblem as follows, FOC for Q K (i): t t+1 (cid:15) E i t [(cid:21) t (i)] = (cid:22) t (i)(1 (cid:0) m t ) (8) (cid:3) RF + (cid:12)Et (cid:3) t+1 E i t+1 [(cid:21) t+1 (i)(cid:15) t+1 (i)] (cid:5) t+1 (cid:20) t t+1(cid:21) FOC for B (i): t+1 (cid:15) (cid:3) RB E i t [(cid:21) t (i)]=(cid:22) t (i)+(cid:12)Et (cid:3) t+1 E i t+1 [(cid:21) t+1 (i)] (cid:5) t+1 (9) (cid:20) t t+1(cid:21) FOC for D (i): t (cid:15) 1=(cid:21) (i)’(D (i)) (10) t 0 t where (cid:5) P =P . On the right side of the FOCs for investment and bort+1 t+1 t (cid:17) rowing, all macroeconomic variables at t+1 are taken out of the expectation operator E i t+1 ( (cid:1) ), since the conditioning set of E i t+1 ( (cid:1) ) includes those variables attimet+1. Incontrast,theFOCfordividendsisnotintegratedovertheidiosyncratic uncertainty. This is because the dividends/equity (cid:133)nancing decisions are made after the realization of the shock. To see that the capital constraint binds in the steady state, consider the version of (9) that arises in the absence of aggregate uncertainty, i.e., when (cid:3) t =(cid:3) t+1 , E i t [(cid:21) t (i)]=E i t+1 [(cid:21) t+1 (i)], and (cid:5) t+1 =1, (cid:22) 1 =(cid:12)RB: (cid:0) Ei[(cid:21)(i)] Since the idiosyncratic uncertainty does not disappear in the steady state, the shadowvalueofthe(cid:135)owoffundsconstraintisstillintegratedoveridiosyncratic uncertainty. Binding capital constraint, and hence (cid:22)>0 requires (cid:12)RB <1. As shown below, this is indeed the case owing to the liquidity premium households place on deposits.9 Note that by multiplying 1 m to both sides of (9) and t (cid:0) 9There can be other ways to ensure the binding capital constraint. For example, one can assume that the intermediary is impatient or subject to a constant death probability. Alternatively,one can introduce a tax shield fordebt. 10

subtracting the resulting expression from (8), we can merge the two FOCs into (cid:3) RF m tE i t [(cid:21) t (i)]=(cid:12)Et (cid:3) t+1 E i t+1 [(cid:21) t+1 (i)(cid:15) t+1 (i)] (cid:5) t+1 (11) (cid:20) t t+1(cid:21) (cid:3) RB (cid:0) (cid:12)Et (cid:3) t+1(1 (cid:0) m t )E i t+1 [(cid:21) t+1 (i)] (cid:5) t+1 (cid:20) t t+1(cid:21) This is the version of the e¢ ciency condition that will be used extensively in our analysis that follows. To operationalize (11) for a sharper characterization of the equilibrium, we need to show how the intermediaries in the model form expectations regarding their liquidity condition, which is summarized by two measures, E i t [(cid:21) t (i)] and E i t [(cid:21) t (i)(cid:15) t (i)]. 2.1.6 Intermediary Asset Pricing Our model has a symmetric equilibrium for three reasons: (cid:133)nancial intermediaries are risk-neutral; the (cid:133)rst moment of the idiosyncratic shock is timeinvariant; and (cid:133)nally, the intermediaries decide how much to invest and to borrow before the realization of their idiosyncratic shocks. In this symmetric equilibrium: all(cid:133)nancialintermediarieschoosethesamelevelofinvestmentand borrowing,i.e.,K (i)=K (j)andB (i)=B (j)foralliandj [0;1]. t+1 t+1 t+1 t+1 2 This greatly facilitates aggregation. However, dividends/equity issuance decisions are conditioned upon the realization of the idiosyncratic shock. The same thing can be said about the shadow value of the (cid:135)ow of funds constraint, which is the summary measure of the liquidity condition of a particular intermediary. Afterimposingthebindingcapitalconstraintandthesymmetricequilibrium condition, we can express the (cid:135)ow of funds constraint as D (i) ’(cid:22) min D (i);0 =(cid:15) (i)RFQ K t (cid:0) (cid:1) f t g t t t (cid:0) 1 t RB(1 m )Q K m Q K : (cid:0) t (cid:0) t (cid:0) 1 t (cid:0) 1 t (cid:0) t t t+1 At the time of dividend payout/equity issuance decision, all other quantities of the above expression are predetermined. Since the LHS is strictly increasing in D (i) everywhere, we can (cid:133)nd a unique level of the revenue shock that satis(cid:133)es t the (cid:135)ow of funds constraint with D (i)=0. If we let D (i)=0 and solve for (cid:15) , t t t we obtain an equity (cid:133)nancing threshold, RB 1 Q K (cid:15) =(1 m ) t +m t t+1: (cid:3)t (cid:0) t (cid:0) 1 R t F t R t F Q t 1 K t (cid:0) If (cid:15) (i) (cid:15) , paying out a strictly positive amount of dividends is optimal while t (cid:21) (cid:3)t it is optimal to issue equities (D (i) < 0), incurring the dilution cost of ’(cid:22) if t (cid:15) (i) < (cid:15) . This and (10) imply that the shadow value of internal funds of t (cid:3)t the intermediaries depends on the realization of the idiosyncratic shock in the following way: 1 if (cid:15) (i) (cid:15) (cid:21) t (i)=1=’ 0 (D t (i))= 1=(1 ’(cid:22))>1 if (cid:15) t (i) (cid:21) <(cid:15) (cid:3)t : (12) (cid:26) (cid:0) t (cid:3)t 11

The discussion above regarding the equity (cid:133)nance threshold can be used to transformthee¢ ciencycondition(11)intoaformthatismoreconvenientfora quantitative analysis of the model, which requires us to evaluate two measures of liquidity condition: E i t [(cid:21) t (i)] and E i t [(cid:21) t (i)(cid:15) t (i)]. To that end, let s t (i) be a standardization of (cid:15) (i) de(cid:133)ned as t s (i)=(cid:27) 1(log(cid:15) (i)+0:5(cid:27)2): (13) t (cid:0)t t t Sinces (i)isamonotonictransformationof(cid:15) (i)andfollowsastandardnormal t t distribution, we can integrate the shadow value over the idiosyncratic uncertainty as follows 1 E i t [(cid:21) t (i)] = 1 (cid:1) dF((cid:15))+ 1 ’(cid:22) (cid:1) dF((cid:15)) (14) Z(cid:15)t(cid:21) (cid:15)(cid:3)t Z(cid:15)t(cid:20) (cid:15)(cid:3)t (cid:0) (cid:8)(s ) ’(cid:22) = 1 (cid:8)(s )+ (cid:3)t =1+ (cid:8)(s )>1: (cid:0) (cid:3)t 1 ’(cid:22) 1 ’(cid:22) (cid:3)t (cid:0) (cid:0) (14) implies that the intermediary(cid:146)s ex ante valuation of a sure dollar is always greater than a dollar as long as the probability of costly recapitalization is strictly positive. What is uncertain here is not the dollar, but its valuation. While the realized shadow value takes only two values: it is either 1 or 1=(1 ’(cid:22)), the expected shadow value is time varying as aggregate conditions (cid:0) change. It is this expected value that matters for the commitment decisions for investment/borrowing. The more likely is costly equity (cid:133)nancing, the higher the expected shadow value of internal funds. Usingpropertiesofthelognormaldistributionandnotingthat 0 1(cid:15)f((cid:15) j (cid:27) t )d(cid:15)= 1 for all bounded positive parameter (cid:27) , one can easily see that t R (cid:15) E i t [(cid:21) t (i)(cid:15) t (i)]= (cid:15) t dF((cid:15))+ 1 t ’(cid:22) dF((cid:15)) (15) Z(cid:15)t(cid:21) (cid:15)(cid:3)t Z(cid:15)t(cid:20) (cid:15)(cid:3)t (cid:0) (cid:8)(s (cid:27) ) ’(cid:22) =1 (cid:0) (cid:8)(s (cid:3)t (cid:0) (cid:27) t )+ 1 (cid:3)t (cid:0) ’(cid:22) t =1+ 1 ’(cid:22) (cid:8)(s (cid:3)t (cid:0) (cid:27) t )>1: (cid:0) (cid:0) where (cid:8)(s (cid:27) ) comes from the truncated lognormal distribution.10 (15) im- (cid:3)t (cid:0) t pliesthattheintermediary(cid:146)sexantevaluationofarandomvariable,whosemean is equal to a dollar, is always greater than a dollar. In contrast to the case of E i t [(cid:21) t (i)],whatisuncertainisboththecash-(cid:135)owanditsvaluation,whichmakes ’(cid:22) E i t [(cid:21) t (i)(cid:15) t (i)] = 1+ 1 ’(cid:22) (cid:8)(s (cid:3)t (cid:0) (cid:27) t ) (cid:0) ’(cid:22) < 1+ 1 ’(cid:22) (cid:8)(s (cid:3)t ) = E i t [(cid:21) t (i)] (cid:0) 10The following property of lognormal distribution is used to derive the expression in the main text (see Johnson et al.(1994) ): Z(cid:15) (cid:21) (cid:15)(cid:3)t (cid:15)f((cid:15) j (cid:27)t)d(cid:15)=[1 (cid:0) (cid:8)(s(cid:3)t (cid:0) (cid:27)t)] Z0 1(cid:15)f((cid:15) j (cid:27)t)d(cid:15); wheref( (cid:27)t)isthepdfofthelognormaldistributionconditionedupontheparameter(cid:27)t and (cid:1)j s is de(cid:133)ned as (13). (cid:3)t 12

aslongas(cid:27) >0,re(cid:135)ectinganegativecovariancebetweentheshadowvalueand t the idiosyncratic shock in (12). This negative covariance is intuitive (cid:150)(cid:133)rms with a large positive idiosyncratic shock do not need costly equity (cid:133)nancing, and hence have a lower shadow value of internal funds, than do (cid:133)rms with a large negative idiosyncratic shock. In summary, the caution created by the commitment structure imposed on the investmenttechnologyamid unresolved idiosyncratic fundingriskmanifests itselfintheconservativeexantevaluationofrandomandnon-randomcash(cid:135)ow. This sets a higher bar for the required return on investment as will be shown below. Using (14) and (15), we can eliminate all expressions involving the expectationoperatorE i t ( (cid:1) )in(11)andtransformthee¢ ciencyconditionforinvestment into an asset pricing formula. To that end, it is convenient to rewrite the FOC as m t =(cid:12)Et (cid:26) (cid:3) (cid:3) t+ t 1E i t+ E 1 i t [ [ (cid:21) (cid:21) t t + (i 1 ) ( ] i)] (cid:20) E i t+ E 1 [ i t (cid:21) + t 1 + [(cid:21) 1 ( t+ i) 1 (cid:15) ( t+ i) 1 ] (i)]R (cid:5) t t F + + 1 1 (cid:0) (1 (cid:0) m t ) R (cid:5) t t B + + 1 1 (cid:21)(cid:27) : Let(cid:17) ’(cid:22)=(1 ’(cid:22)). Afterdividingtheexpressionthroughbym andsubstituting t (cid:17) (cid:0) (14)and(15)intheabove,wecanderivetheintermediaryassetpricingformula, 1 R~F RB 1=Et ( M t B ;t+1 " m t (cid:5) t t + + 1 1 (cid:0) (1 (cid:0) m t ) (cid:5) t t + + 1 1 !#) (16) where the intermediary(cid:146)s pricing kernel is given by 1+(cid:17)(cid:8)(s ) (cid:3) 1+(cid:17)(cid:8)(s ) MB =MH (cid:3)t+1 =(cid:12) t+1 (cid:3)t+1 t;t+1 t;t+1 1+(cid:17)(cid:8)(s ) (cid:3) 1+(cid:17)(cid:8)(s ) (cid:20) (cid:3)t (cid:21) t (cid:20) (cid:3)t (cid:21) and the risk adjusted return is given as 1+(cid:17)(cid:8)(s (cid:27) ) R~F =RF (cid:3)t+1(cid:0) t+1 <RF : t+1 t+1 1+(cid:17)(cid:8)(s ) t+1 (cid:20) (cid:3)t+1 (cid:21) The above asset pricing formula looks di⁄erent from a textbook version mainly for two reasons. First, the formula is a levered asset pricing formula. Unlike in the textbook version which assumes away leverage choice, the returns are levered up to the inverse of capital ratio. To see this point, assume m =1. t One can then see the second term vanish and the formula looks closer to the conventional one, i.e., 1=Et [M t B ;t+1(cid:1) R~ t F +1 =(cid:5) t+1 ]: Second, the intermediary speci(cid:133)c pricing kernel is a (cid:133)ltered version of the representative household(cid:146)s pricing kernel, where the (cid:133)lter is the ratio of the shadow value of internal funds today vs. tomorrow. The (cid:133)lter could potentially weaken the role of the representative household as a marginal investor even though all (cid:133)nancial intermediaries are owned by the households. Suppose that in the beginning of current period, a bad news about aggregate returns arrives. This, holding other things constant, increases the probability of costly 13

recapitalization(cid:8)(s )sinceevenanormalrangeofidiosyncraticreturnmaynot (cid:3)t beenoughtomeetthefundingneedsassociatedwithtoday(cid:146)sinvestment. Ifthe aggregate shock is strong enough, the ratio of shadow values tomorrow vs. today substantially declines, making overall required return on capital (1=MB ) t;t+1 rise, which suppresses today(cid:146)s investment. The intermediary asset pricing formula can be applied to price any asset with arbitrary random/non-random return structure. To (cid:133)x the idea, suppose anassetX whosepricemustbedeterminedingeneralequilibrium. Forinstance, one can think of an arbitrary lending opportunity with no default risk. If the representative household can directly purchase such an asset, the asset will be priced according to 1=Et [M t H ;t+1(cid:1) R X H ;t+1 =(cid:5) t+1 ] where RH is the asset return under the direct investment of representative X;t+1 household. However, if the representative household does not have the skills necessary to invest in such assets and a (cid:133)nancial intermediary has to invest on behalf of the household, the asset will have to be priced according to 1=Et [M t B ;t+1(cid:1) R X F ;t+1 =(cid:5) t+1 ] where RF is the asset return when the marginal investors are the (cid:133)nancial X;t+1 intermediaries. In general the two rates of returns are not equalized except in a non-stochastic steady state. We call the di⁄erence RF RH spreads. X;t+1(cid:0) X;t+1 We will show shortly, by numerical analysis, that any real or (cid:133)nancial disturbancethattightenstheliquidityconditionoftheintermediarytendstoincrease spreads, even when the disturbance has no direct implication for a frictionless economy. Note that the economic content of the spreads are neither related to default risks nor with the covariance structure of the underlying asset returns with the representative household(cid:146)s consumption growth rate.11 Our discussion of the intermediary asset pricing can also shed light on the nature of the (cid:135)uctuations in lending standards. A well known empirical fact is that the lending standards, measured by Senior Loan O¢ cer Opinion Survey, which reports the proportion of senior loan o¢ cers who have tightened their lending standards recently, is highly correlated with a popular measure of credit spreads such as the di⁄erence between BBB-rated bond and 10 year Treasury yields, with their correlation coe¢ cient being close to 0.8. The survey on lending standards may be revealing that the lending institutions tighten standards and increase spreads when the shadow value of their internal funds increases; in principle, such tighter lending standards can occur without any changes in borrowers(cid:146)fundamentals if the balance sheet condition of lending institutions is impaired. In our framework, such an attitude (or willingness to lend) toward new lending opportunity is summarized by MB . Of course, t;t+1 another natural interpretation of such survey results is that they re(cid:135)ect the time-varying quality of borrowers, e.g., the creditworthiness of potential bank 11In the above discussion, we use an unlevered version of the intermediary asset pricing formula forsimplicity. However,the argument goes through forthe generalformula. 14

borrowers. While we do not object such conventional interpretation, our discussion of the intermediary asset pricing formula points to another possibility, and research has demonstrated that (cid:135)uctuations in default risk and recovery rates of non-(cid:133)nancial borrowers may be insu¢ cient to understand movements in borrowing spreads and lending standards (see Huang and Huang (2003) and Chen et al. (2009)). The form of the intermediary asset pricing formula is super(cid:133)cially similar to Jermann and Quadrini (2009), who derive a similar pricing kernel from a reduced-formconvexadjustmentcostofdividend;however,ourapproachderives from a speci(cid:133)c set of structural frictions. It is also super(cid:133)cially similar to the intermediary asset pricing formula of He and Krishnamurthy (2008); however, theyderivetheirintermediary-speci(cid:133)cpricingkernelfromtheassumptionofrisk averse intermediaries. The link to the LAPM (Liquidity-Based Asset Pricing Model)ofHolmstr(cid:246)mandTirole(2001)ismoredirect: Inourcase,theliquidity premium arises from costly recapitalization of (cid:133)nancial intermediaries, while the premium exists for non-(cid:133)nancial corporations with potential investment opportunity or working capital needs in Holmstr(cid:246)m and Tirole (2001). Finally, we note that, when ’(cid:22) =0, the asset pricing formula collapses to 1 RF RB 1=Et M t H ;t+1 m (cid:5) t+1 (cid:0) (1 (cid:0) m t ) (cid:5) t+1 (cid:26) (cid:20) t (cid:18) t+1 t+1(cid:19)(cid:21)(cid:27) and idiosyncratic uncertainty plays no role in the determination of asset price. Anyarbitrarilylargeamountofuncertaintysimplydoesnotmatterforrealallocations. Inthissense, costlyequity(cid:133)nanceisthekeyfrictioninourframework. 2.1.7 Illiquidity of Balance Sheet Assets and Adjustment Costs In our timing convention, we assume that there exist factors that make the intraperiodadjustmentofbalancesheetassetsdi¢ cult,requiringthecommitment of participants. In reality, there are also reasons why interperiod as well as intraperiod adjustments of loan portfolio can be costly. As pointed out by many, for instance, Diamond and Rajan (2000), (cid:133)nancial assets of intermediaries are inherently illiquid: First, a substantial knowledge about the characteristics of borrowers is an indispensable prerequisite for successful selections of new borrowers and churning out ine¢ cient existing borrowers. Second, a substantial partofbalancesheetassetsiscomposedofitemsthatarenoteasilymarketable since the intermediaries cannot commit themselves to work for the second buyers after the sale of such (cid:133)nancial assets. Such an illiquidity of balance sheet assets may be the fundamental force behind the slow dynamics often found in balance sheet data. To capture this aspect in a parsimonious way, we assume that there exists a constant return-to-scale convex adjustment cost associated with changing the nominal stock of (cid:133)nancial assets of the intermediaries: (cid:13)(cid:22) Q K 2 (cid:13)(Q K ;Q K )= t t+1 1 Q K , (cid:13)(cid:22) 0 t (cid:0) 1 t t t+1 2 (cid:18) Q t (cid:0) 1 K t (cid:0) (cid:19) t (cid:0) 1 t (cid:21) 15

Withtheadjustmentfrictioninbalancesheet,itisstraightforwardtoshowthat the intermediary asset pricing formula is modi(cid:133)ed into 1 R~F RB 1=Et ( M t B ;t+1 " m t (cid:5) t t + + 1 1 (cid:0) (1 (cid:0) m t ) (cid:5) t t + + 1 1 !#) (17) (cid:13)(cid:22) Q K (cid:13)(cid:22) Q K 2 (cid:0) m t (cid:18) Q t t (cid:0) 1 t K +1 t (cid:0) 1 (cid:19) (cid:0) Et ( M t B ;t+12m t "(cid:18) Q t+ t K 1 t+ t+ 1 2 (cid:19) (cid:0) 1 #) : Though not explicit in (17), the (cid:135)ow of funds constraint and the equity (cid:133)nance threshold need to be modi(cid:133)ed accordingly as well. Thesedynamiccostsofadjustingthebalancesheetof(cid:133)nancialintermediaries are not important for the qualitative predictions of the model, but will help match the dynamics of adjustment apparent in the data. 2.1.8 Cost of Capital From a theoretical perspective, the relevant cost facing intermediaries is a marginal cost of funds (or a weighted average of marginal costs), as can be seen directly by rewriting (11) as Et f M t H ;t+1E i t+1 [(cid:21) t+1 (i)(cid:15) t+1 (i)]R t F +1g MB of Investment RB = m| tE i t [(cid:21) t (i)]+(1 (cid:0) {zm t )Et M t H ;t+1E }i t+1 [(cid:21) t+1 (i)] (cid:5) t+1 : (cid:26) t+1(cid:27) MC of Investment The above equa|tes the marginal bene(cid:133)t{(zLHS) and the marginal c}ost (RHS) of investment. Evidently it is an weighted average of two components, the one associated with the marginal cost of raising capital and the one associated with marginal borrowing cost. However, policy debates often center around a slightly di⁄erent concept, so called weighted average cost of capital (WACC). Given the importance of the concept in policy discussion, we show how such a measure can be constructed in our environment. To that end, we need show how the return on equity, i.e., the stock market return on (cid:133)nancial shares vB(i) VB(i)=(cid:3) evolves over t (cid:17) t t time. Exploiting the recursive structure in (7), we can express the value of intermediary as v t B(i)=d t (i)+Et M t H ;t+1(cid:1) E i t+1 [v t B +1 (i)] where d (i) = D (i)=P . The Bellman(cid:2) equation can then b(cid:3)e thought of as the t t t stochasticlawofmotionofthemarketvalueoftheintermediary. Thetotalstock market value of all intermediaries can be constructed by a direct integration of individual values, i.e., v t B (cid:17) E i t [v t B(i)]= v t B(i)di= v t B(s)d(cid:8)(s): Z Z 16

The total value of the (cid:133)rm is identical to the expected value of an individual intermediary before the realization of the idiosyncratic shock. By integrating the individual Bellman equation over heterogeneous units, we obtain v t B =d+ t (cid:0) d (cid:0)t +Et M t H ;t+1(cid:1) v t B +1 (18) where d+ and d represent the value of po (cid:2) sitive dividen (cid:3) d payments and equity t (cid:0)t issuance, aggregated across intermediaries. Formally they are de(cid:133)ned as d+ d (s)d(cid:8)(s) and d d (s)d(cid:8)(s): t (cid:17) t (cid:0)t (cid:17)(cid:0) t Zst(cid:21) s(cid:3)t Zst(cid:20) s(cid:3)t The textbook version of weighted average cost of capital is de(cid:133)ned as Et R t W +1 =m tEt R t S +1 +(1 (cid:0) m t )R t B +1 (19) where RS is the return on equity. The return on equity is measured by the t+1 stock market return on (cid:133)nancial shares, which can be de(cid:133)ned as vB RS (cid:5) t+1 t+1 (cid:17) t+1 "Et [M t H ;t+1(cid:1) v t B +1 ] # where Et [mH t;t+1(cid:1) v t B +1 ] is the ex dividend price at time t and v t B +1 is the cumdividendpriceattimet+1. Weclaimthatsuchformulaisnotdirectlyapplicable if the capital market deviates from the Miller-Modigliani (MM) theorem as herein. To correct the e⁄ect of the deviation from MM theorem, the formula should be modi(cid:133)ed to include a correction term, vB ’(cid:22)dB RS (cid:5) t+1 + t+(cid:0)1 : (20) t+1 (cid:17) t+1 "Et [M t H ;t+1(cid:1) v t B +1 ] Et [M t H ;t+1(cid:1) v t B +1 ] # Thereturnonequityhastwocomponents: theconventionalstockmarketreturn and the average cost of new equity issuance per unit of total market value. At thispoint, theformulamaylooksarbitrarytosomereaders, butweshowbelow that (20) is consistent with the household optimization condition. 3 Rest of the Economy 3.1 Household Therepresentativehouseholdconsumesthe(cid:133)nal-goodsandearnsmarketwages bysupplyinglaborinputsfortheproductionof(cid:133)nalgoods. Weassumethatthe householdlacksnecessaryskillstodirectlymanageinvestmentprojects. Forthis reason, the household invests its saving through (cid:133)nancial intermediaries. The household can either invest in the shares of the intermediaries or make deposits to the intermediaries. 17

3.1.1 Budget Constraint Undertheassumptionsmadeabove,thebudgetconstraintoftherepresentative household can be expressed as 1 0 = W H +RBB P C PS(i)S (i)di (21) t t t t (cid:0) t t (cid:0) t t+1 Z0 1 B + [max D (i);0 +PS (i)]S (i)di (cid:0) t+1 Z0 f t g t (cid:0) 1;t t where B = B (i)di, W is a nominal wage rate, H is labor hours, and S (i) t t t t t is the number of shares outstanding at time t. PS (i) is the time t value of shares outsta R nding at time t 1. PS(i) is the ex t (cid:0) -d 1 i ; v t idend value of equity at (cid:0) t time t. The two values are related by the following accounting identity, PS(i)=PS (i)+X (i) (22) t t 1;t t (cid:0) whereX (i)isthevalueofnewsharesissuedattimet. Thecostlyequity(cid:133)nance t assumption adopted for the (cid:133)nancial intermediary implies that X (i)= (1 ’(cid:22))min D (i);0 : (23) t t (cid:0) (cid:0) f g Substituting(22)and(23)inthebudgetconstraintoftherepresentativehousehold, one can see that the budget constraint is equivalent to 1 0 = W H +RBB B P C PS(i)S (i)di (24) t t t t (cid:0) t+1 (cid:0) t t (cid:0) t t+1 Z0 1 + [max D (i);0 +(1 ’(cid:22))min D (i);0 +PS(i)]S (i)di: f t g (cid:0) f t g t t Z0 3.1.2 Preferences Forthepreferencesoftherepresentativehousehold,weadoptthemoststandard speci(cid:133)cations for quantitative analyses in the literature. One such speci(cid:133)cation canbefoundinSmetsandWouters(2007). Morespeci(cid:133)cally,weadoptinternal habitformationinconsumptionandalabordisutilityseparablefromtheutility of consumption. To model the value households place on their deposits, we adopt the deposit in the utility speci(cid:133)cation originating from Sidrauski (1967), which captures the non-pecuniary bene(cid:133)ts provided by (cid:133)nancial institutions.12 Formally, the preferences are given by u(C ;C ;B =P ;H ) = log(C aC ) (25) t t 1 t+1 t t t t 1 (cid:0) (cid:0) (cid:0) (cid:16) B (i) (H )1+ + (cid:18)log t+1 di : t (cid:0) 1+ P (cid:18)Z t (cid:19) 12Recent application also can be found in Van den Heuvel(2008). 18

The household problem is straightforward: the household chooses C , H , t t f B (i), S (i) to maximize its value, t+1 t g V t H =max 1 (cid:12)s (cid:0) t Et u(C s ;C s 1 ;B s+1 =P s ;H s ) (cid:0) s=t X subject to the budget constraint (24). Let (cid:3) denote the Lagrangian multiplier t associated with the budget constraint (24). 3.1.3 Pricing Financial Intermediaries We now show how the representative household prices the debts and equities of the (cid:133)nancial intermediaries. The FOCs for consumption, deposits and shares are given by FOC for C : t (cid:15) 1 a (cid:3) t = (cid:12)Et (26) C aC (cid:0) C aC t (cid:0) t (cid:0) 1 (cid:20) t+1 (cid:0) t(cid:21) FOC for B (i): t+1 (cid:15) (cid:18)=(cid:3) (cid:3) RB 1= t +(cid:12)Et t+1 t+1 (27) B (i)=P (cid:3) (cid:5) t+1 t (cid:20) t t+1(cid:21) FOC for S (i): t (cid:15) (cid:3) P t S(i) = (cid:12)Et (cid:3) t+1 E i t+1 [max f D t+1 (i);0 g (28) (cid:26) t +(1 ’(cid:22))min D (i);0 +PS (i)] (cid:0) f t+1 g t+1 (cid:27) The FOC for consumption is standard. The FOC for intermediary debt is di⁄erent from a standard asset pricing formula because of the non-pecuniary bene(cid:133)tofdeposit. Thiscreatesaliquiditypremiumthatthehouseholdiswilling to fore-go in making deposits at a rate lower than risk-free rate. Formally, the liquidity premium can be de(cid:133)ned as (cid:3) R RB (cid:18)=(cid:3) (cid:12)Et t+1 t+1 t+1 = t 0 (cid:3) (cid:5) (cid:0) (cid:5) B (i)=P (cid:21) (cid:20) t (cid:18) t+1 t+1(cid:19)(cid:21) t+1 t where R is a risk-free rate that satis(cid:133)es the (cid:133)ctitious asset pricing equation, t+1 1 = (cid:12)Et [((cid:3) t+1 =(cid:3) t )(R t+1 =(cid:5) t+1 )]. In the non-stochastic steady state, we have 1=(cid:12)R and (cid:18)=(cid:3) =1 (cid:12)RB; B=P (cid:0) which implies that (cid:12)RB 1 with the inequality strict if (cid:18) >0. This proves the (cid:20) statement that the capital constraint binds for the intermediaries in the steady state. 19

We now turn to the issue of how to price the shares of the (cid:133)nancial intermediaries. In discussing the cost of capital for intermediaries, we made a claim that the asset pricing formula for the intermediary shares must have a correction term to the conventional one, re(cid:135)ecting the costly equity (cid:133)nancing friction. To show this, (cid:133)rst note that since there is no persistence in the (cid:133)rst moment of the idiosyncratic shock and the second moment shock is shared by all intermediaries, the ex-dividend price of all shares are the same regardless of realization of idiosyncratic shock today. Hence, PS(i) = PS for all i, and trivt t ially, E i t+1 [P t S +1 (i)] = P t S +1 . Next, noting that E i t+1 [max f D t+1 (i);0 g ] = D t + +1 , E i t+1 [min f D t+1 (i);0 g ] = (cid:0) D t(cid:0)+1 and D t+1 = D t + +1(cid:0) D t(cid:0)+1 , we can rewrite the asset pricing formula (28) as 1=(cid:12)Et (cid:3) (cid:3) t+1 D t+1 P + S P t S +1 +(cid:12)Et (cid:3) (cid:3) t+1 ’(cid:22)D P t(cid:0) S +1 (cid:20) t (cid:18) t (cid:19)(cid:21) " t t # Since tomorrow(cid:146)s cum-dividend (real) price (D +PS )=P =v and tot+1 t+1 t+1 t+1 day(cid:146)sex-dividend(real)priceP t S=P t =Et (M t H ;t+1 v t+1 ),thisprovestheexistence of the correction term created by the costly equity (cid:133)nance. In equilibrium, S (i) = S (i) = 1 for all i. We can then see that (24) is t t+1 equivalent to P C =W H +RBB B +D +’(cid:22)D : (29) t t t t t t (cid:0) t+1 t t(cid:0) where D D (s )d(cid:8)(s ) and D D (s )d(cid:8)(s ). Hence, a direct conseque t nc (cid:17) eofth t ec t ostlye t quity(cid:133)na t(cid:0) nc (cid:17) ea (cid:0) ssu s m t(cid:20)p s t (cid:3)t ion t for t theho t useholdproblemis R R thatthecostofequity(cid:133)nanceistransferredbacktotherepresentativehousehold in a lump sum fashion. 3.2 Technology Tosavespace,ourdescriptionoftherestofthemodeleconomywillbebrief. Our goal in this analysis is to investigate the role of funding-market frictions facing (cid:133)nancialintermediaries. Giventhatthesefrictionsariseindependentlyofothers suchasnominalfrictions,wetakethemodelascloseaspossibletoarealbusiness cyclebenchmarkforthevirtueofsimplicity. Whilewekeepdistinctionsbetween nominal and real variables in our notation (thereby allowing easy integration of monetary policy questions at a later stage), price adjustment is frictionless in this analysis. 3.2.1 Final Goods A continuum of competitive (cid:133)rms produce (cid:133)nal goods using capital and labor in a constant return-to-scale (CRS) Cobb-Douglas technology. They solve the following static pro(cid:133)t maximization problem, max P Z (K (j)U (j))1 (cid:11)HH(j)(cid:11) W H (j) RK(K (j)U (j)) Kt(j)Ut(j);Ht(j) t t t t (cid:0) t (cid:0) t t (cid:0) t t t where Z is an aggregate technology shock. Since the scale of the problem is t indeterminate, one could assume a representative (cid:133)rm instead of a continuum. 20

3.2.2 Investment A continuum of competitive (cid:133)rms produce investment goods by combining an input of (cid:133)nal goods and a CRS adjustment technology. Following Christiano et al. (2003) and Smets and Wouters (2007), we specify a convex investment adjustment cost and model the investment problem as follows, V t I =maxEt X s 1 =t (cid:12)t (cid:0) s (cid:3) P s s ( Q s I s (k) (cid:0) P s " I s (k)+ (cid:31)(cid:22) 2 (cid:18) I s I (cid:0) s ( 1 k (k ) ) (cid:0) 1 (cid:19) 2 I s (cid:0) 1 (k) #) : Again, the problem is scale-free and can be thought of as the one of a representative (cid:133)rm instead of a continuum. 3.3 Market Clearing Condition Goods market clearing requires that aggregate production equal the sum of consumption, investment, and the various resource costs (adjustment costs) assumed in our quantitative framework (cid:31)(cid:22) i i 2 (cid:28)(cid:22) q k 2 q k y t =c t +i t + 2 (cid:18) t (cid:0) i t (cid:0) 1 t (cid:0) 1 (cid:19) i t (cid:0) 1 + 2 (cid:18) q t t (cid:0) t 1 + k 1 t (cid:5) t (cid:0) 1 (cid:19) t (cid:0) (cid:5) 1 t t: 4 Predictions and Model-Based Identi(cid:133)cation Insight into the quantitative predictions of our model for the e⁄ects of shocks to the intermediation sector for economic activity and credit spreads requires a calibration closely tied to the data. To develop such an anchoring, we examine the predictions of our model for a range of variables following an increase in idiosyncratic uncertainty, create a new data series on idiosyncratic uncertainty within the intermediation sector based on the cross-sectional variance of daily equity returns for large (cid:133)nancial institutions, and then use the predictions of our model for the sign of the response of (cid:133)nancial institutions(cid:146)value of internal funds and lending following an increase in uncertainty to identify the impact of shocks to the intermediation sector on real activity while ensuring that such identi(cid:133)eddisturbancesarepurgedoftypical(cid:147)business-cycle(cid:148)(cid:135)uctuations. After these discussions, we then return to our model and illustrate how a broader array of (cid:133)nancial developments (cid:150)indeed, any that a⁄ect the balance sheet of intermediaries(cid:150)canhaveimportantmacroeconomicconsequencesinourmodel. 4.1 Uncertainty Shock: Model(cid:146)s Prediction Aswehighlightedearlier,developmentswithintheintermediationsector,suchas an increase in the idiosyncratic uncertainty regarding returns facing intermediaries,areimportantformacroeconomic(cid:135)uctuationsgiventhe(cid:133)nancialfrictions in our model (and would be neutral with respect to macroeconomic outcomes 21

in the absence of such frictions). While this qualitative point is clear from the (complex) system of equations governing the economy(cid:146)s equilibrium, the quantitative nature of these e⁄ects is less clear, and we illustrate the qualitative predictions of our model along this dimension via a simulation exercise. To perform these simulations, we (cid:133)rst assign parameter values. There are three parameters that govern key aspects of the model(cid:146)s predictions for the macroeconomic e⁄ects of intermediation shocks: the cost of equity issuance ’(cid:22), the long run standard deviation of return on asset (cid:27)(cid:22), and the weight on the deposit in the utility (cid:18). We try to adopt reasonable values for the (cid:133)rst two parameters by tying these values to data from (cid:133)nancial markets. The estimates/calibrations for the equity issuance cost varies a lot in the literature ranging from 0:08 in Gomes (2001) to 0:30 in Cooley and Quadrini (2001). We chose ’(cid:22) = 0:30, following Cooley and Quadrini (2001). While this choice is on the high side of the range, we made this choice to replicate the harsh (cid:133)nancing environment seen during the recent (cid:133)nancial turmoil. Regarding the volatility, we set (cid:27)(cid:22) =0:05, implying an annual volatility level of 0:10, to match the standard deviation of return on asset (pro(cid:133)ts/total asset) of U.S. banking sector reported in Demirguc et al. (2003). With regard to the weight of deposits in the utility function ((cid:18)), we choose its value to match (roughly) the net interest margin of (cid:133)nancial intermediaries, RE RB. Saunders and Schu- (cid:0) macher (2000) and Demirguc et al. (2003) provide an international comparison of such margins, which range from a low of 160 bps (Swiss) to a high of 500 bps (Spain and U.S.) on average during the period of 1988-1995. Conditioned upon ’(cid:22) = 0:30 and (cid:27)(cid:22) = 0:05, setting (cid:18) = 0:07 roughly matches the interest rate margin in the data. Note that the interest rate margin is a sum of two components, RE RB =RE R+R RB. With (cid:18) =0:07, about half of the (cid:0) (cid:0) (cid:0) marginisexplainedbyareturnpremiumoverriskfreerateRE Randtherest (cid:0) of the margin is explained by the liquidity premium R RB in our framework. (cid:0) With regard to other parameters, we choose the investment and balance sheet adjustment cost parameters and the parameter governing habit persistencesoastodeliverhump-shapedimpulsesresponsefunctiontotypicalshocks. To deliver the slow dynamics for intermediaries(cid:146)balance sheet observed in the data, we specify a small loan adjustment cost by setting (cid:13)(cid:22) equal to 1. This choice,togetherwiththechoiceofinvestmentadjustmentcostparameter,helps us match the persistent response of lending. For the investment adjustment cost parameter, we set (cid:31)(cid:22) = 0:5, a moderate value similar to those reported in macroeconomic analyses (of other issues). We calibrate the habit persistence parameter as a=0:75, a value in the typical range. For the parameters that can be considered traditional, we make standard choices whenever possible. The risk free rate in the steady state is set at R = 1=(cid:12) = 1:01 in quarterly frequency. The depreciation rate (cid:14) is set equal to 0:025. We assume a relatively elastic labor supply by setting the inverse of Frischelasticityparameter equalto0:1andwechoosetheweightofthelabor disutility as (cid:16) =1. We set (cid:11)=0:60, a fairly standard setting. Wecannowillustratethee⁄ectsofanuncertaintyshock. Figure1showsthe impact of an increase in (idiosyncratic) uncertainty within the (cid:133)nancial sector. 22

In this experiment, we consider a fairly persistent shock process. We set (cid:26) = (cid:27) 0:85,nearthevalueinBloom(2009)andachoicethatwillbebroadlyconsistent with ourempiricalevidence below. We considerashock thatincreases the level of uncertainty 10 percent immediately. The frictionless economy (black circles) exhibits a complete dichotomy between (cid:133)nancial (cid:135)ows and real variables: the changes in uncertainty create large adjustment in dividends and equity (cid:133)nance, with no (cid:133)rst order consequences for real allocations. Tounderstandtheeconomicimpactofuncertaintyshockunderthe(cid:133)nancial friction, it is useful to remember that the uncertainty shock becomes known at the beginning of the period, before the realization of idiosyncratic returns. While such a second moment shock is a mean preserving spread as emphasized earlier, implying both greater upside and downside potential to investment, the increase in downside risk (the left tail) is especially important in our environment, a phenomenon known as (cid:147)the bad news principle(cid:148)(Bernanke (1983)). Because of the greater dispersion in idiosyncratic returns, some intermediaries (cid:133)nd themselves with unusually large amount of cash in(cid:135)ow. However, at the time of investment/borrowing decisions, the increased probability of costly equity (cid:133)nancing aggravates intermediaries(cid:146)concern for liquidity and increases the internal valuation of internal funds, as displayed in panel (e). The cost of intermediary capital increases relative to the risk-free rate, which is transmitted to other credit markets as shown by the increase in the spreads in panel (g). The funding pressure facing the (cid:133)nancial intermediaries should be met by raising internal funds (e.g., cutting back in dividends), by outside equity, or by downsizing the balance sheet (e.g., cutting back in lending or sales of assets). Each of these options is costly to the intermediaries as the outside capital requires dilution costs and deleveraging of the balance sheet implies the loss of the intermediation margin. As a consequence, the intermediaries in the model economy respond by trying to strike a balance between their options for balance sheet adjustment. In panel (c), we can see that the dividends payouts, while increasing, are substantially lower relative to the frictionless case. Panel (d) shows that equity issuance in the presence of the (cid:133)nancial friction responds to the shock more strongly than in the frictionless case. Panel (h) shows that the intermediaries deleverage their balance sheet substantially by cutting back on lending. Panel (i) (l) display the consequence of such deleveraging on real (cid:24) allocations: aggregate hours, investment and output contract persistently. With regard to model predictions, we note three aspects that we will emphasize in our empirical analysis below. In particular, (cid:133)gure 1 shows that an increase in uncertainty within the intermediation sector leads to an increase in the value of funds within the sector, a widening in the borrowing spread, and a decline in lending. We take these predictions to the data after discussing our empirical measure of uncertainty within the intermediation sector. 4.2 Some Data on Uncertainty In order to examine the magnitude of the quantitative e⁄ects of developments withintheintermediationsector,weneedtobringsomedataondevelopmentsat 23

intermediariesandexaminetheirinteractionwithmacroeconomicdevelopments. Giventheearlierdiscussion, wefocusonthedegreeofidiosyncraticuncertainty within the intermediation sector. Several approaches to gauging such uncertainty within the intermediation sectorarepossible. Forexample,apossiblyfruitfulapproachcouldexaminethe indicators of ((cid:133)rm-speci(cid:133)c) uncertainty derived from (cid:133)nancial market prices, e.g. options on intermediaries. However, we are interested in constructing a long time series on uncertainty that is representative of the majority of the intermediation sector within the United States, and construction of an optionsimplied volatility measure for a broad set of (cid:133)nancial (cid:133)rms over the past forty years was not feasible for this study. Our measure of uncertainty with the intermediation sector is based in realized volatility. Speci(cid:133)cally, we analyze the period from the (cid:133)rst quarter of 1973 until the third quarter of 2010 and gather daily equity prices for the top-25 banking organizations (as measured by total assets) within the United States each quarter (e.g., the composition of the top- 25 is allowed to change each quarter). We then construct the cross-sectional standard deviation of the daily percent change in equity prices across these (cid:133)nancialintermediaries; ourfocusoncross-sectionalvariationisconsistentwith our emphasis on idiosyncratic uncertainty. We take the average of this crosssectional standard deviation within a quarter as our measure of idiosyncratic uncertainty. Figure 2 shows the variation in this measure (indexed to equal 1 in 1974Q1) over the 1974-2010 period. Several points are apparent. First, this measure of uncertainty, while varying signi(cid:133)cantly over time, is not especially strongly correlatedwithrecessionsasde(cid:133)nedbytheNationalBureauofEconomicResearch (the shaded regions); this may help our empirical identi(cid:133)cation strategy below, as we want to illustrate the independent e⁄ect of (cid:133)nancial-sector developments onmacroeconomicoutcomes,ratherthandevelopments(cid:147)intheotherdirection(cid:148) (i.e., the impact of macroeconomic developments on the (cid:133)nancial sector). Second, this measure exploded to unprecedented levels during the (cid:133)nancial crisis that (according to this data) began in the third quarter of 2008 and remained high through the third quarter of 2009. Other notable periods include the elevated level of uncertainty regarding (cid:133)nancial intermediaries from late 1990 to early 1993 (which corresponded to a portion of the period covering the U.S. Savings and Loan crisis and the (cid:133)nancial headwinds of the early 1990s) and the quite low level of uncertainty during the 2003-2006 period (a time at which excesses in leverage were building according to many analysts, ex post). 4.3 A Bayesian Approach to Identi(cid:133)cation With the model predictions and data discussed in the previous two sections in hand, we now turn to an exploration of the data to see whether the role of uncertaintywithintheintermediationsector,andhencetheroleofbalance-sheet considerations at (cid:133)nancial intermediaries more generally, for macroeconomic (cid:135)uctuations are borne out empirically. Ashighlightedabove,weviewthreepredictionsofourtheoreticalframework 24

as informative with regard to developments at intermediaries following an increase in uncertainty within the intermediation sector. Speci(cid:133)cally, in response to an increase in uncertainty, our model predicts An increase in the value of internal funds at intermediaries that reduces (cid:15) the willingness to lend; A widening in the borrowing spread; and (cid:15) A decline in lending. (cid:15) It is straightforward to use these theoretical restrictions to identify the effects of shocks to the (cid:133)nancial intermediation sector on macroeconomic outcomes. Speci(cid:133)cally, we apply the Bayesian approach of Uhlig (2005), which considers the set of impulse responses in a vector autoregression (VAR) consistent with these identifying restrictions.13 This approach (cid:133)nds all responses consistent with the identifying restrictions and develops the set of responses for all variables embedded in the VAR. As a result, the (cid:133)ndings regarding macroeconomicresponsescanbeconsideredreasonablyrobust,especiallyascompared to relatively atheoretical identifying restrictions within a VAR approach (such as recursive orderings, which assume delayed responses for certain variables as in the analysis of banking shocks in Lown and Morgan (2006) and Berrospide and Edge (2010)).14 Withthatsaid,itisalsoimportant,especiallywithinalargeVAR,toinclude restrictionsoutsidethoseofspeci(cid:133)cinterest,astheBayesianapproachde(cid:133)nesa setofresponsessatisfyingtheimposedrestrictionsusingorthogonalrotationsof theshockstothesystem;inclusionofrestrictionsonresponsestoshocksoutside those of interest help insure robustness, as such additional restrictions help to more sharply delineate the di⁄erences across orthogonal innovations within the system. This is potentially valuable in our analysis, as it is possible that a (negative,recessionary)generalbusinesscycleshockwouldresultinadeclinein lending and willingness to lend along with a decline in real GDP. We purge our system of these types of shocks, to focus especially on a causal e⁄ect associated with intermediation shocks. Therefore, our analysis identi(cid:133)es two orthogonal shocks(cid:150)an(uncertainty)intermediationshockandabusinesscycleshock. The restrictions imposed on these shocks are A (cid:133)nancial (uncertainty) intermediation shock increases our mea- (cid:15) sureofidiosyncraticuncertaintyandtheborrowingspread,decreaseswillingnesstolendandlending,andisorthogonaltothebusiness-cycleshock; A Business cycle (recession) shock lowers real GDP and real invest- (cid:15) ment, increases the unemployment rate, and is orthogonal to the other identi(cid:133)ed shocks. 13Ourimplementation uses the algorithm ofRubio-Ramirez et al.(2010). 14Withregardtorobustness,seethediscussionsinFaust(1998),CanovaandNicolo(2002), and Uhlig (2005) 25

For each shock, we impose these restrictions over the (cid:133)rst four periods of the impulse. Note especially that by including a business cycle shock we attempttopurgetheresponse to(cid:133)nancialintermediationshocks oftheendogenous(cid:135)uctuationsinlendingassociatedwithtypical(cid:135)uctuationsinaggregatedemand/supply. Otherusesofsignrestrictions(e.g.,MountfordandUhlig(2009)) adopt a similar business-cycle shock. Our VAR includes eight variables: (the log of) real GDP; (the log of) real (cid:133)xed investment; the unemployment rate; the real federal funds rate (de(cid:133)ned as the nominal federal funds rate minus the change in the core Personal Consumption Expenditures (PCE) price index over the previous four quarters); the spread between the BBB corporate bond rate and the 10-yr Treasury rate; the share of banks more willing to lend to consumers from the Senior Loan O¢ cer Opinion Survey; (the log of) bank lending; and (the log of) our measure of idiosyncratic uncertainty within the intermediation sector. The intermediation (uncertainty) shock restrictions are applied to the last four variables, with a decline in willingness to lend and lending accompanying an increase in uncertainty. The estimation sample is 1974:Q1 to 2010:Q3 and the VAR includes two lags; (By using willingness to lend to consumers, our sample period is considerably longer than that of other VAR analyses using other questions from the Senior Loan O¢ cer(cid:146)s Opinion Survey(e.g., Lown and Morgan (2006) andBerrospideandEdge(2010); wediscusstherobustnessofourresultslater). The impulse responses to an intermediation (uncertainty) shock identi(cid:133)ed via this procedure are reported in (cid:133)gure 3; the lines represent the 68-percent con(cid:133)dence intervals and the dots represent the model predictions that were presented in the previous section.15 Panel (a) shows that the structural shock immediatelyincreasestheuncertaintymeasureby10percent. Asshowninpanel (b),willingnesstolendfalls(asindicatedbythejumpinthelines,aswillingness to lend is reported on an inverted scale); this jump is reminiscent of the jump in the internal value of funds (shown in the dots, but not comparable empirically; the presentation is meant to illustrate the correspondence).16 Lending (panel (d)) also jumps down. This shock has important macroeconomic e⁄ects: The BBB-bond spread rises notably (e.g., by about 20 basis points), indicating spillovers to (cid:133)nancial conditions more generally (panel (c)); moreover, hours, real investment, and real GDP decline notably (by about 1/3 percent, 1 1/4 percent,and1/3percent,respectively).17 Overall,bothlendingandrealinvestment decline substantially more sharply than real GDP, with peak responses just below a decline of 1 percent. The more pronounced e⁄ect on investment and lending is similar, qualitatively, to the predictions of our model. 15As in our discussion, other researchers employing the same Bayesian approach have emphasizedtheoverallshapeofresponsesand68-percentcon(cid:133)denceintervals(e.g.,Faust(1998), Uhlig (2005),Mountford and Uhlig (2009)). 16Indeed, we have plotted willingness to lend and divided this series by 10, to put it in units comparable to the jump in the shadow value of funds; these values should be taken as qualitative indications ofthe direction ofe⁄ect 17The hours response in the data is the negative of the change in the unemployment rate multiplied by the inverse of the average ratio of employment to the labor force over the estimation period. 26

With regard to robustness, we considered two alternatives to the identi(cid:133)cation scheme we highlight as our main analysis. First, we relaxed the restriction that lending must fall following an uncertainty shock (on the view that some readers may view a restriction on lending as too close to a direct restriction on thereale⁄ectsofuncertaintyshocks). Relaxingthisrestriction,asshownin(cid:133)gure 4, had essentially no e⁄ect on the impact of uncertainty shocks for (cid:133)nancial and real outcomes within our VAR. Second, we ended the estimation sample in 2007Q4,beforethejumpinouruncertaintymeasurerecordedin2008;thisshift allowsustoconsidertherobustnessoftheempiricallinksweidentifytoepisodes prior to the recent (cid:133)nancial crisis. As shown in (cid:133)gure 5, the shift in sample period increased the standard errors associated with the impact of uncertainty shockson (cid:133)nancialand realvariables(and nowonlywith 68-percentcon(cid:133)dence set for the impact on the BBB spread continues to exclude zero, while other con(cid:133)dence intervals are wide). However, the nature of the impulse responses at the median are very similar to those for the entire sample period for lending, real GDP, the unemployment rate, and the BBB spread. These two exercises suggestthatthebroadimplicationsofourframeworkcaptureimportantempirical regularities, although the importance of these regularities is more apparent using developments during the 2008 (cid:133)nancial crisis. 4.4 Comparison to Other VAR approaches Another dimension of robustness regards the correspondence between the intermediation (uncertainty) shocks estimated by our approach and those found usingotherapproaches. Asmentionedpreviously,onepopularapproachinvolves arecursiveorderingscheme,aspursuedinLownandMorgan(2006),Berrospide andEdge(2010), andCiccarellietal.(2010). Inthisapproach, researcherstypically include a measure from surveys of (cid:133)nancial institution of willingness to lend or net tightening in lending standards, and identify shocks to intermediationbyassumingthatsuchshocksimmediatelyimpactstandardsbutonlya⁄ect spending with a lag (e.g., a standard Cholesky ordering for identi(cid:133)cation in a VAR). In a more recent approach, Bassett III et al. (2010) use micro-level information on banks responding to the Senior Loan O¢ cer(cid:146)s Opinion Survey in the UnitedStatestoidentifychangesinstandardsthatareorthogonaltoalonglist of conditions at the bank level; these authors suggest this approach may better identify the change in loan supply than the macroeconomic VAR approach. Interestingly, these authors show that their identi(cid:133)ed loan supply shocks are very similar to those using the recursive ordering in a VAR. We compare our uncertainty shocks to the loan supply shocks from Bassett III et al. (2010) (both those from their micro-level and recursive VAR approaches) in (cid:133)gure 6. As shown in the upper panel, our uncertainty shocks are not very correlated with either the VAR recursive shocks (upper panel) or the micro-based shocks (the lower panel), with simple correlations near 0 (as opposed to a correlation near 3=4 for the two alternatives). In this sense, our uncertaintyshocksarecapturingadi⁄erentfactorfromthosefoundusingthese 27

measures of loan supply shocks. We view this result as unsurprising, as our model implies that loan supply should be a⁄ected by uncertainty and by a wide range of other factors as well. 4.5 Balance Sheet Shock Indeed, wewouldliketoemphasizethatwehavetakenaveryfocusedapproach inourempiricalexerciseandexaminedtheimpactofashiftinidiosyncraticuncertainty within our model and empirically. Our model implies a much broader set of implications. Speci(cid:133)cally, any disturbance that alters the balance-sheet (orliquidity)positionofintermediarieshasimportantmacroeconomice⁄ectsin our model. In this sense, our empirical analysis con(cid:133)rms the important role of intermediation,butprobablyunderplaystheoverallmacroeconomicsigni(cid:133)cance of shocks to the intermediation sector by not considering a comprehensive set of developments impacting intermediaries(cid:146)balance sheet positions. We illustrate this basic point in (cid:133)gure 7, in which we consider a hypothetical aggregate shock to the balance sheets of (cid:133)nancial intermediaries. For this experiment, we modify the (cid:135)ow of funds constraint as 0 = (cid:15) (i)RFQ K (i)+F +B (i) RBB (i) t t t (cid:0) 1 t t t+1 (cid:0) t t (cid:13)(cid:22) Q K (i) 2 Q K (i) t t+1 1 Q K (i) ’(D (i)): (cid:0) t t+1 (cid:0) 2 (cid:18) Q t (cid:0) 1 K t (i) (cid:0) (cid:19) t (cid:0) 1 t (cid:0) t where F denotes the shock to the balance sheet. We assume that the shock t follows an AR(1) process, F =(cid:26) F +(cid:15)F: t F t 1 t (cid:0) We consider a relatively transient shock setting (cid:26) =0:6 such that the half life F of the shock is no greater than 3 quarters. The size of (cid:15)F is roughly 20% of the t normal level of intermediary equity capital, as shown in panel (a). For general equilibrium consistency, we assume that the shock is a balance sheet transfer from the households to the intermediaries in a lump sum fashion. Notethattheshockisadditivetothepro(cid:133)t: assuch,theshockdoesnothave direct implication for the marginal pro(cid:133)tability of intermediary investment. As aresult, theshockwouldnothavesubstantialreale⁄ectsonafrictionlesseconomy(i.e., aneconomywith’(cid:22) =0). However, underthefundingmarketfriction that we consider, the shock is relevant information for the risk management of the intermediaries. The shock a⁄ects the liquidity condition of the intermediaries, which in(cid:135)uences the marginal valuation of investment opportunity. For a straightforward comparison, (cid:133)gure 7 also displays the case of the frictionless economy(denotedbyblackcircles)togetherwiththecaseofthemodeleconomy (blue solid lines). Consider the frictionless case (cid:133)rst. The windfall cash in(cid:135)ow improves the internal funds substantially, hence less need for outside equity, re(cid:135)ected in the largedropintheequityissuancecuto⁄showninpanel(b). Sincetheshockdoes nothaveimplicationforthemarginalpro(cid:133)tabilityof(cid:133)nancialinvestment,alarge numberofintermediariessimplydisbursetheextracash(cid:135)owasdividends(panel 28

(c)). Equity issuance, shown in panel (d) also substantially decreases as there is less need for outside funds. Such (cid:133)nancial (cid:135)ows, however, do not have any consequences for real allocations. Since the (cid:133)nancial markets are frictionless, the shadow value of extra cash is always equal to one, not responding to the liquidity condition as shown in panel (e). As a result, weighted average cost of capitalofintermediaries(panel(f))andspreads(panel(g))showzeroresponses. Withnochangesinthecostsofcapitalatvariouslevelsoftheeconomy,thelevel of lending is also unresponsive to the shock (panel (h)), implying no changes in employment, real investment, and output (panel (i), (k) and (l)). Finally, it is notable that the consumption also exhibits zero response. While the balance sheetshockisatransferfromthehouseholdstotheintermediaries,suchtransfer is exactly o⁄set by the reverse transfer, increase in dividends and decrease in equity issuance, resulting in zero response in consumption. We now turn to the case with the (cid:133)nancial friction. As in the frictionless case, the liquidity condition of the (cid:133)nancial intermediaries is dramatically improved by the shock and the probability of having to tap the equity market for additional funding declines substantially, indicated by the plunge in the equity issuance threshold (cid:15) . The responses of dividends and equity issuance are more (cid:3)t or less the same as in the frictionless case. What is di⁄erent is the massive drop in the expected shadow value of internal funds shown in panel (e). As a consequence, the cost of intermediary capital declines about 50 basis points in panel (f) and a strong positive spill over e⁄ect for general lending terms ensues asthecreditspreadsdeclineasmuchas300basispointsinpanel(g). Whilethe shockdoesnota⁄ectthefundamentalsofinvestment, themuchlowervaluation of internal funds allow the intermediaries to substantially expand their balance sheet as seen in the expansion of lending in panel (h). This would not be the case if the intermediaries were not constrained by the (cid:133)nancial friction before the shock. Panel (i) (l) exhibit the responses of variables related with economic ac- (cid:24) tivity. In panel (i), one can see that hours increase substantially. While consumption initially declines to allow a greater investment in intermediary debts, the response of consumption shown in panel (j) is very much muted relative to other endogenous variables. Aggregate investment and output all show strong positive response to the balance sheet shock. In particular, aggregate investment leads the upside business cycle, responding to the large increase in the price of capital. One can easily see a meaningful interaction between the (cid:133)nancial and the real sectors: the initial increase in the price of capital is caused by the decisions of the intermediaries to expand their (cid:133)nancial investment. Such investmentleadstothehigherassetpricesoftheeconomy,initiatingstrongreal investmentcycle. Theresultingupturninbusinesscycleimprovesthereturnon intermediary (cid:133)nancial investment, further strengthening the liquidity condition oftheintermediaries,supportinganevenstrongergaininrealeconomicactivity. Overall, these simulations emphasize how a broad range of shocks that impact the position of (cid:133)nancial intermediaries have macroeconomic consequences in our model. In turn, this consideration implies that various policies vis-a-vis the (cid:133)nancial sector can prove important for macroeconomic outcomes. 29

5 Conclusion In our analysis, we consider a tractable macroeconomic model in which real investment is intermediated through institutions that commit (cid:133)nancial resources in the face of idiosyncratic funding risk and a binding capital constraint. We show that the liquidity/balance sheet condition of intermediaries can be an importantdriverofassetpricesandaggregateactivity. Thispredictioniscon(cid:133)rmed by empirical evidence from our structural econometric analysis framed in a set signrestrictionsimpliedbyourmodel. Indeed,weexamineonlyasmallportion ofthepotentialempiricalimportanceofintermediationformacroeconomicoutcomesbyfocusingexclusivelyonashiftinuncertaintywithintheintermediation sector. Tothatend, wedevelopanewmeasureofsuchuncertaintyandidentify importante⁄ectsonrealGDPandunemploymentfromsuchdisturbances. Our model implies a much broader range of shocks to (cid:133)nancial intermediaries may be important, a subject for further research. Our framework allows consideration of several short term credit policies designed to address a liquidity/balance sheet crisis as well as long-term policies suchascapitalrequirements. Giventheempiricalvalidationofourmodelherein, we pursue analysis of policy implications in companion research (see Kiley and Sim (2011)). References Admati, A. R., P. M. DeMarzo, M. F. Hellwig, and P. P(cid:135)eiderer (2010, September). Fallacies, irrelevant facts, and myths in the discussion of capital regulation: Why bank equity is not expensive. Research Papers 2065, Stanford University, Graduate School of Business. Adrian, T. and H. S. Shin (2010). Financial intermediaries and monetary economics. Volume 3 of Handbook of Monetary Economics, pp. 601 (cid:150)650. Elsevier. Bassett III, W. F., M. B. Chosak, J. C. Driscoll, and E. Zakrajsek (2010). IdentifyingtheMacroeconomicE⁄ectsofBankLendingSupplyShocks.SSRN eLibrary. Berger,A.N.andG.F.Udell(1994). Didrisk-basedcapitalallocatebankcredit and cause a "credit crunch" in the united states? Journal of Money, Credit and Banking 26(3), pp. 585(cid:150)628. Bernanke,B.S.(1983). Irreversibility,uncertainty,andcyclicalinvestment. The Quarterly Journal of Economics 98(1), pp. 85(cid:150)106. Bernanke, B. S., M. Gertler, and S. Gilchrist (1999). Chapter 21 the (cid:133)nancial accelerator in a quantitative business cycle framework. Volume 1, Part 3 of Handbook of Macroeconomics, pp. 1341 (cid:150)1393. Elsevier. 30

Berrospide,J.M.andR.M.Edge(2010,December). Thee⁄ectsofbankcapital onlending: Whatdoweknow,andwhatdoesitmean? InternationalJournal of Central Banking 6(34), 1(cid:150)50. BIS (2010). Assessing the macroeconomic impact of the transition to stronger capital and liquidity requirements. Interim report of the macroeconomic assessment group, Basel Committee on Banking Supervision, Basel, Switzerland. Bloom, N. (2009). The impact of uncertainty shocks. Econometrica 77(3), pp. 623(cid:150)685. Boivin,J.,M.T.Kiley,andF.S.Mishkin(2010). Howhasthemonetarytransmission mechanism evolved over time? Volume 3 of Handbook of Monetary Economics, pp. 369 (cid:150)422. Elsevier. Bolton, P. and X. Freixas (2000). Equity, bonds, and bank debt: Capital structure and (cid:133)nancial market equilibrium under assymetric information. The Journal of Political Economy 108(2), pp. 324(cid:150)351. Brunnermeier,M.K.andL.H.Pedersen(2009). MarketLiquidityandFunding Liquidity. Review of Financial Studies 22(6), 2201(cid:150)2238. Canova,F.andG.D.Nicolo(2002,September). Monetarydisturbancesmatter for business (cid:135)uctuations in the g-7. Journal of Monetary Economics 49(6), 1131(cid:150)1159. Chen, L., P. Collin-Dufresne, and R. S. Goldstein (2009). On the relation between the credit spread puzzle and the equity premium puzzle. Review of Financial Studies 22(9), 3367(cid:150)3409. Christiano,L.,R.Motto,andM.Rostagno(2003). Thegreatdepressionandthe friedman-schwartz hypothesis. Journal of Money, Credit and Banking 35(6), 1119(cid:150)1197. Ciccarelli, M., A. Maddaloni, and J.-L. PeydrˆC(cid:181)´‚s (2010, July). Trusting the bankers: anewlookatthecreditchannelofmonetarypolicy. WorkingPaper Series 1228, European Central Bank. Cooley, T. F. and V. Quadrini (2001). Financial markets and (cid:133)rm dynamics. The American Economic Review 91(5), pp. 1286(cid:150)1310. Demirguc, A., L. Laeven, and R. Levine (2003, April). The impact of bank regulations,concentration,andinstitutionsonbankmargins. PolicyResearch Working Paper Series 3030, The World Bank. Diamond,D.W.andR.G.Rajan(2000). Atheoryofbankcapital. TheJournal of Finance 55(6), pp. 2431(cid:150)2465. Faust, J. (1998). The robustness of identi(cid:133)ed var conclusions about money. Carnegie-Rochester Conference Series on Public Policy 49, 207 (cid:150)244. 31

Gertler, M. and N. Kiyotaki (2010). Financial intermediation and credit policy in business cycle analysis. Volume 3 of Handbook of Monetary Economics, pp. 547 (cid:150)599. Elsevier. Gomes, J. F. (2001). Financing investment. The American Economic Review 91(5), pp. 1263(cid:150)1285. Hancock, D. and J. A. Wilcox (1993). Has there been a "capital crunch" in banking? the e⁄ects on bank lending of real estate market conditions and bank capital shortfalls. Journal of Housing Economics 3(1), 31 (cid:150)50. Hanson, S. G., A. K. Kashyap, and J. C. Stein (2011). A macroprudential approach to (cid:133)nancial regulation. Journal of Economic Perspectives 25(1), 3(cid:150)28. He, Z. and A. Krishnamurthy (2008, December). Intermediary asset pricing. NBER Working Papers 14517, National Bureau of Economic Research, Inc. Holmstr(cid:246)m, B. and J. Tirole (2001). Lapm: A liquidity-based asset pricing model. The Journal of Finance 56(5), pp. 1837(cid:150)1867. Huang, J.-Z. J. and M. Huang (2003). How Much of Corporate-Treasury Yield SpreadIsDuetoCreditRisk?: ANewCalibrationApproach.SSRNeLibrary. Jermann, U. and V. Quadrini (2009, September). Macroeconomic e⁄ects of (cid:133)nancialshocks. NBERWorkingPapers15338,NationalBureauofEconomic Research, Inc. Johnson, N. L., S. Kotz, and N. Balakrishnan (1994). Continuous Univariate Distributions (2nd ed.), Volume 1. Wiley. Kiley, M. T. and J. W. Sim (2011). Financial capital and the macroeconomy: Policy considerations. Finance and Economics Discussion Series 2011- 28, Board of Governors of the Federal Reserve System (U.S.). Lown,C.andD.P.Morgan(2006,September).Thecreditcycleandthebusiness cycle: New (cid:133)ndings using the loan o¢ cer opinion survey. Journal of Money, Credit and Banking 38(6), 1575(cid:150)1597. Mountford,A.andH.Uhlig(2009). Whatarethee⁄ectsof(cid:133)scalpolicyshocks? Journal of Applied Econometrics 24(6), 960(cid:150)992. Myers, S. C. and N. S. Majluf (1984). Corporate (cid:133)nancing and investment decisions when (cid:133)rms have information that investors do not have. Journal of Financial Economics 13(2), 187 (cid:150)221. Rice, T. and J. Rose (2011). When good investments go bad: The contraction in community bank lending after the 2008 gse takeover. mimeo, Board of Governors of the Federal Reserve System. 32

Ross, S. A. (1977). The determination of (cid:133)nancial structure: The incentivesignalling approach. The Bell Journal of Economics 8(1), pp. 23(cid:150)40. Rubio-Ramirez, J., D. F. Waggoner, and T. Zha (2010, 04). Structural vector autoregressions: Theoryofidenti(cid:133)cationandalgorithmsforinference. Review of Economic Studies 77(2), 665(cid:150)696. Saunders, A. and L. Schumacher (2000). The determinants of bank interest rate margins: an international study. Journal of International Money and Finance 19(6), 813 (cid:150)832. Sidrauski, M. (1967). In(cid:135)ation and economic growth. The Journal of Political Economy 75(6), 796(cid:150)810. Smets, F. and R. Wouters (2007). Shocks and frictions in us business cycles: A bayesian dsge approach. The American Economic Review 97(3), 586(cid:150)606. Uhlig, H. (2005). What are the e⁄ects of monetary policy on output? results from an agnostic identi(cid:133)cation procedure. Journal of Monetary Economics 52(2), 381 (cid:150)419. Van den Heuvel, S. J. (2008). The welfare cost of bank capital requirements. Journal of Monetary Economics 55(2), 298 (cid:150)320. Wen,Y.(2009).Ananalyticalapproachtobu⁄er-stocksaving.Technicalreport. 33

(a) uncertainty shock, % (b) equity cutoff, % (c) dividends payouts, % 15 0.2 15 10 10 0.1 5 5 0 0 0 5 0.1 5 0 10 20 30 0 10 20 30 0 10 20 30 (d) equity issuance, % (e) shadow value, pp (f) cost of capital, bps 20 15 0.8 15 10 0.6 10 0.4 5 5 0.2 0 0 0 0.2 5 5 0 10 20 30 0 10 20 30 0 10 20 30 (g) spreads, bps (h) lending, % change at an annual rate (i) hours, % 30 0.2 0.2 0 20 0 0.2 10 0.2 0.4 0 0.4 0.6 10 0.6 0.8 0 10 20 30 0 10 20 30 0 10 20 30 (j) consumption, % (k) investment, % (l) output, % 0.1 1 0.2 0.05 0 0 0 1 0.2 0.05 2 0.4 0.1 3 0.6 0 10 20 30 0 10 20 30 0 10 20 30 Figure 1: E⁄ects of Uncertainty Shock: Friction (blue solid) vs Frictionless (black circle) Economy. 34

Index,1974Q1=1 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 1975 1980 1985 1990 1995 2000 2005 2010 Figure 2: An Index of Idiosyncratic Uncertainty in the Financial Sector 35

(a) uncertainty shock, % (b) shadow value and willingness to lend (inverted), pp 1 15 10 0.5 5 0 0 5 0.5 0 5 10 15 0 5 10 15 (c) spreads, bps (d) lending, % change at an annual rate 0.5 30 0 20 0.5 10 1 0 1.5 10 2 0 5 10 15 0 5 10 15 (e) hours, % (f) investment, % 0.2 0 0 0.2 1 0.4 2 0.6 0.8 3 0 5 10 15 0 5 10 15 (g) output, % 0.2 0 0.2 0.4 0.6 0 5 10 15 Figure3: ImpactofIntermediationShock: BayesianSignRestrictions,Baseline Case. 36

(a) uncertainty shock, % (b) shadow value and willingness to lend (inverted), pp 1 15 10 0.5 5 0 0 5 0.5 0 5 10 15 0 5 10 15 (c) spreads, bps (d) lending, % change at an annual rate 0.5 30 0 20 0.5 10 1 0 1.5 10 2 0 5 10 15 0 5 10 15 (e) hours, % (f) investment, % 0.2 0 0 0.2 1 0.4 2 0.6 0.8 3 0 5 10 15 0 5 10 15 (g) output, % 0.2 0 0.2 0.4 0.6 0 5 10 15 Figure 4: Impact of Intermediation Shock: Bayesian Sign Restrictions, Alternative 1 (No restriction on lending) 37

(a) uncertainty shock, % (b) shadow value and willingness to lend (inverted), pp 1 15 10 0.5 5 0 0 5 0.5 0 5 10 15 0 5 10 15 (c) spreads, bps (d) lending, % change at an annual rate 1 30 20 0 10 1 0 10 2 0 5 10 15 0 5 10 15 (e) hours, % (f) investment, % 0.2 1 0 0 0.2 1 0.4 0.6 2 0.8 3 0 5 10 15 0 5 10 15 (g) output, % 0.2 0 0.2 0.4 0.6 0 5 10 15 Figure 5: Impact of Intermediation Shock: Bayesian Sign Restrictions, Alternative 2 (1974Q1(cid:150)2007Q4 Sample). 38

4 3 2 1 0 1 2 3 4 90 92 94 96 98 00 02 04 06 08 RECURSIVE_VAR STRUCTURAL_VAR 4 3 2 1 0 1 2 3 90 92 94 96 98 00 02 04 06 08 STRUCTURAL_VAR WEIGHTED_MICRO_DATA Figure 6: Estimates of Financial Shocks: Financial Uncertainty Shock (blue solid)vsBassettetal(2010)estimates(blackcircle: Upperpanel(cid:150)VARCholesky Ordering; Lower Panel(cid:150)Micro-based Loan Supply Shock). 39

(a) balance sheet shock, % of capital (b) equity cutoff, % (c) dividends payouts, % 25 1 60 20 0 40 15 10 1 20 5 2 0 0 5 3 20 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 (d) equity issuance, % (e) shadow value, pp (f) cost of capital, bps 20 20 0 0 0 20 20 5 40 40 60 10 60 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 (g) spreads, bps (h) lending (financial investment), % (i) hours, % 100 0.4 0 0.3 0.4 0.3 100 0.2 0.2 200 0.1 0.1 300 0 0 400 0.1 0.1 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 (j) consumption, % (k) investment, % (l) output, % 0.04 1.5 0.4 0.3 0.02 1 0.2 0 0.5 0.1 0.02 0 0 0.04 0.5 0.1 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 Figure 7: E⁄ects of Balance Sheet Transfer Shock: Friction (blue solid) vs Frictionless (black circle) Economy. 40