Financial Business Cycles

Board of Governors of the Federal Reserve System International Finance Discussion Papers Number 1116 August 2014 Financial Business Cycles Matteo Iacoviello NOTE: International Finance Discussion Papers are preliminary materials circulated to stimulate discussion and critical comment. References to International Finance Discussion Papers (other than an acknowledgment that the writer has had access to unpublished material) should be cleared with the author or authors. Recent IFDPs are available on the Web at www.federalreserve.gov/pubs/ifdp/. This paper can be downloaded without charge from the Social Science Research Network electronic library at www.ssrn.com.

(cid:3) Financial Business Cycles Matteo Iacoviello† Federal Reserve Board August 28, 2014 Abstract Using Bayesian methods, I estimate a DSGE model where a recession is initiated by losses suffered by banks and exacerbated by their inability to extend credit to the real sector. The event triggering the recession has the workings of a redistribution shock: a small sector of the economy – borrowers who use their home as collateral – defaults on their loans. When banks hold little equity in excess of regulatory requirements, the losses require them to react immediately, either by recapitalizing or by deleveraging. By deleveraging, banks transform the initial shock into a credit crunch, and, to the extent that some firms depend on bank credit, amplify and propagate the shock to the real economy. I find that redistribution and other financial shocks that affect leveraged sectors accounts for two–thirds of output collapse during the Great Recession. KEYWORDS: Banks; DSGE Models; Collateral Constraints; Housing; Bayesian Estimation. JEL CODES: E32, E44, E47. (cid:3)The views expressed in this paper are those of the author and do not necessarily reflect the views of the Board of the Governors of the Federal Reserve or the Federal Reserve System. I thank seminar participants at the RED Conference on Financial Frictions, the Riksbank, the Magyar Nemzeti Bank, the New York Fed, the SED, Birkbeck College, the HULM Conference, HEC Lausanne, the University of Georgia, the ESSIM, the University of Kentucky, theBankofEngland,GeorgetownUniversity,andtheLACEAConferenceinLimaforusefulfeedbackonthisproject. IalsothankMarcoCagetti,LucaGuerrieri,ErasmusKersting,SkanderVanDenHeuvel,TommasoMonacelli,Jaume Ventura, and Missaka Warusawitharana for many useful discussions and conversations. ymatteo.iacoviello@frb.gov. Address: Federal Reserve Board, 20th and C St. NW, Washington DC 20551. Phone: 202-452-2426. 1

1 Introduction In this paper I estimate, using Bayesian methods, a model with banks and financially constrained households and firms. I present a basic model which conveys the main ideas. I then take a richer version of this model to the data, estimate it using Bayesian methods, and use it to provide an accounting of the role played by different financial shocks and frictions during the financial crisis. The main questions that I ask are: (1) How much can redistributions of wealth – such as those that take place when borrowers default on their debts — disrupt the credit intermediation process? (2) Can changes in credit standards affect business cycles? (3) How important are shocks to asset prices for business fluctuations? To answer these questions, I add financial frictions on banks, on households, and on firms to an otherwise standard RBC model and conduct a horse race between familiar shocks (a shock to the consumption/leisure margin, shocks to technology) and not–so– familiar ones. The not–so–familiar ones are redistribution shocks1 (transfers of wealth from savers toborrowersthattakeplaceintheeventofdefault); creditsqueezes(changesinmaximumloan–to– value ratios); and asset price shocks (changes in the value of collateral). These “financial shocks” were arguably at the core of the last recession. More generally, financial factors were at the core of at least two of the last three recessions in the United States (the 1990–91 recession and the Great Recession of 2007–2009). Yet a large class of estimated dynamic equilibrium models either ignore financial frictions, or consider one set of financial frictions independently from others. While this approach might be useful for building intuition, it eludes a proper quantification of the role of financial factors in business fluctuations, especially when several sets of financial frictions reinforce and amplify each other. The estimation of the model parameters and structural shocks gives large prominence to financialbusinesscycles. Ifindthatfinancialshocksaccountfortwo–thirdsofthedeclineinprivateGDP duringthe2007–2009recession, andtheyalsoplayanimportant, althoughlesssizeable, roleduring other recessions. Although model parameters and shocks are jointly estimated, my approach has also the natural interpretation of a business cycle accounting exercise. This happens because some of the key shocks are directly used as observables at the estimation stage, so that their filtering is decoupled from the estimation of the rest of the model’s structural parameters.2 At the core of the paper is the idea that business cycles are financial rather than real. That is, 1Throughout the paper, I use the terms “redistribution shocks”, “repayment shocks” and “default shocks” interchangeably. 2Myapproachisinspiredbyalargebodyofliterature,includingtherecentworkbyJermannandQuadrini(2012) who construct time series for financial and technology shocks using a Solow-residual-style approach and show that the series constructed using this approach are highly correlated with those obtained through a Bayesian estimation exercise. 2

rather than originated and propagated by changes in technology, business cycles are mostly caused by disruptions in the flow of resources between different groups of agents. In the model economy of thispaper, thesedisruptionstakeplacewhenagroupofagentsdefaultsonitsobligations, therefore paying back less than contractually agreed. Or when credit limits are relaxed or tightened either in response to changes in asset prices or for some other exogenous reason. Of course, many of the stories told here resemble familiar accounts of the Great Recession: the bursting of the housing bubble merely changed the value of houses in units of consumption, yet it lead to a wave of defaults and to a severe crisis in the financial sector. The ensuing problems of the financial institutions that owned mortgages lead to a reduction in the supply of credit to all sectors of the economy. Many of these ideas are all familiar. The novel elements are the financial shocks, and the estimation.3 Several of the ideas and modeling devices in this paper build on an important tradition in macroeconomicmodelingthattreatsbanksasintermediariesbetweensaversandborrowers. Recent contributions include Brunnermeier and Sannikov (2014), Angeloni and Faia (2013), Gerali, Neri, Sessa, and Signoretti (2010), Kiley and Sim (2011), Kollmann, Enders, and Muller (2011), Meh and Moran (2010), Williamson (2012), and Van den Heuvel (2008). The reason why banks exist in my model is purely technological: without banks, the world would be autarchic and agents would be unable to transfer resources across each other and over time. As in the recent work by Gertler and Karadi (2011) and Gertler and Kiyotaki (2010), I give a prominent role to banks by assuming that intermediaries face a balance sheet constraint when obtaining deposits. In these papers however, the shock that causes a financial business cycle is a shock to the quality of bank capital that is, by design, calibrated to produce a downturn as big as in the data. Instead, I either calibrate – in the basic model – the size of the shock by using information on losses suffered by financial intermediaries during the Great Recession, or estimate – in the extended model – all the shocks using Bayesian techniques. The advantage of the estimation strategy is obvious, and opens the avenue for a richer treatment of many of the questions that are left unanswered in the paper. Another important difference is that I combine in the model two sets of financial frictions: on the one hand, banks face frictions in obtaining funds from households; on the other, entrepreneurs face frictions in obtaining funds from banks. Section 2 describes the basic model and considers how a financial shock that hits the balance sheet of the bank can lead to a decline in output and credit and to a rise in interest rate spreads. Section3presentstheextendedmodelthatistakentothedataanddescribestheestimationresults. Section4illustratesthetransmissionmechanismoffinancialshocksintheestimatedmodel. Section 3Regarding the focus on estimation, closely related to my work are the papers of Jermann and Quadrini (2012) and Christiano, Motto, and Rostagno (2014), but these models do not have an explicit modeling of the banking sector. 3

5 concludes. The Appendix contains additional details on the models and on the data. 2 The Basic Model and the Impact of a Financial Shock 2.1 Overview of the Model I consider a discrete–time economy. The economy features three agents: households, bankers, and entrepreneurs. Each agent has a unit mass.4 Households work, consume and buy real estate, and make one–period deposits into a bank. The household sector in the aggregate is net saver. Entrepreneurs accumulate real estate, hire households, and borrow from banks. In between the households and the entrepreneurs, bankers intermediate funds. The nature of the banking activity implies that bankers are borrowers when it comes to their relationship with households, and are lenders when it comes to their relationship with the credit–dependent sector – the entrepreneurs. I design preferences in a way that two frictions coexist and interact in the model’s equilibrium: first, bankers are credit constrained in how much they can borrow from the patient savers; second, entrepreneurs are credit constrained in how much they can borrow from bankers. 2.2 Main Model Features. Below, I describe the main features of the model. The complete set of model equations can be found in Appendix A. Households. The representative household chooses consumption C , housing H , and time H,t H,t spent working N to solve the following intertemporal problem: H,t ∑∞ maxE βt (logC +jlogH +τ log(1(cid:0)N )), 0 H H,t H,t H,t t=0 where β is the discount factor, subject to the following flow–of–funds constraint: H C H,t +D t +q t (H H,t (cid:0)H H,t−1 ) = R H,t−1 D t−1 +W H,t N H,t +ε t , (1) where D denotes bank deposits (earning a predetermined, gross return R ), q is the price of t H,t t housinginunitsofconsumption, andW isthewagerate. Housingdoesnotdepreciate. Theterm H,t ε denotes a redistribution shock that transfers wealth from the bank to the household (the same t 4Except for the introduction of the banking sector, the model structure closely follows a flexible price version of the basic model in Iacoviello (2005), where credit-constrained entrepreneurs borrow from households directly. Here, banks intermediate between households and entrepreneurs. 4

shock, with opposite sign, appears in the banker’s budget constraint too). Here, it captures losses on banks which are gains from the households and, absent equilibrium effects, should wash out in the aggregate (they do not in this model). The optimality conditions yield standard first–order conditions for consumption/deposits, housing demand, and labor supply: ( ) 1 1 = β E R , (2) C H t C H,t H,t H,t+1( ) q j q t t+1 = +β E , (3) C H H t C H,t H,t H,t+1 W τ H,t = . (4) C 1(cid:0)N H,t H,t Entrepreneurs. The representative entrepreneur solves the following problem: ∑∞ maxE βt logC , 0 E E,t t=0 subject to: C E,t +q t (H E,t (cid:0)H E,t−1 )+R E,t L E,t−1 +W H,t N H,t +ac EE,t = Y t +L E,t , (5) Y = Hν N1−ν, (6) ( t E,t−1 )H,t q L (cid:20) m E t+1 H (cid:0)m W N . (7) E,t H t E,t N H,t H,t R E,t+1 where equations (5), (6) and (7) denote the budget constraint, the production function and the borrowing constraint respectively. Inequation(5), entrepreneursconsumeC ,accumulatehousing(commercialrealestate)H , E,t E,t produce Y and pay wages to households. The term L denotes the loans that banks extend to t E,t entrepreneurs, yielding a gross return R . The term ac = ϕ EE (LE;t −LE;t(cid:0)1 )2 (where L E,t EE,t 2 LE E denotes the steady-state value of L ) is a quadratic loan portfolio adjustment cost, assumed to E,t be external to the entrepreneur. This cost penalizes entrepreneurs for changing their loan balances too quickly between one period and the next, and captures the idea that the volume of lending changes slowly over time.5 Equation (6) states that real estate, combined with household labor, produces the final output Y . t Equation(7)istheborrowingconstraint. Entrepreneurscannotborrowmorethanafractionm H 5Aliaga-Daz and Olivero (2010) present a DSGE model of hold-up effects where switching banks is costly for entrepreneurs. Curdia and Woodford (2010) and Goodfriend and McCallum (2007) develop models of financial intermediation with convex portfolio adjustment costs which mimic the functional form adopted here. 5

oftheexpectedvalueoftheirrealestatestock. Inaddition,theborrowingconstraintstipulatesthat a fraction m of the wage bill must be paid in advance, as in Neumeyer and Perri (2005). I assume N that entrepreneurs discount the future more heavily than households and bankers. Formally, their discount factor satisfies the restriction that β < 1 . This assumption guarantees E γ 1 +(1−γ ) 1 E(cid:12)H E (cid:12)B that the borrowing constraint will bind in a neighborhood of the steady state. Denote with λ the multiplier associated with the borrowing constraint normalized by the E,t marginal utility of consumption. The optimization conditions for loans, real estate and labor are respectively: ( ) ( ) ∂ac 1 1 1(cid:0)λ (cid:0) LE,t = β E R , (8) E,t ∂L c E t E,t+1 c ( ( E),t) E,t (( E,t+1) ) q 1 νY 1 q (cid:0)λ m E t+1 = β E q + t+1 , (9) t E,t H t R c E t t+1 H c E,t+1 E,t E,t E,t+1 (1(cid:0)ν)Y t = W N . (10) H,t H,t 1+m λ N E,t As the first–order conditions show, credit constraints – as measured by the multiplier on the borrowing constraint λ – introduce a wedge between the cost of factors and their marginal E,t product,thusactingasataxonthedemandforcreditandthedemandforthefactorsofproduction. The wedge is intertemporal in the consumption Euler equation (8) and in the real estate demand equation (9); it is intratemporal in the case of the labor demand equation (10). Bankers. The representative banker solves the following problem: ∑∞ maxE βt logC 0 B B,t t=0 where β < β , subject to: B H C B,t +R H,t−1 D t−1 +L E,t +ac EB,t = D t +R E,t L E,t−1 (cid:0)ε t , (11) where D denotes household deposits, L are loans to entrepreneurs, and C is banker’s private t E,t B,t consumption. Note that this formulation is equivalent to a formulation where bankers maximize a convex function of dividends (discounted at rate β ), once C is reinterpreted as the residual B B,t income of the banker after depositors have been repaid and loans have been issued. As for the entrepreneurial problem, the term ac = ϕ EB (LE;t −LE;t(cid:0)1 )2 is a quadratic portfolio loan adjust- EB,t 2 LE ment cost, assumed to be external to the banker. The term ε is the redistribution shock that, t when positive, transfers resources from the bank to the household. 6

Adjustmentcostaside,theflowoffundsconstraintofthebankerimplicitlyassumesthatdeposits can be freely converted into loans. To make matters more interesting and more realistic, I assume that the bank is constrained in its ability to issue liabilities by the amount of equity capital (assets less liabilities) in its portfolio. This constraint can be motivated by standard limited commitment problems or by regulatory concerns. For instance, typical regulatory requirements – such as those agreed by the Basel Committee on Banking Supervision – posit that banks hold a capital to assets ratio greater than or equal to some predetermined ratio. Denoting with K = L (cid:0)D (cid:0)E ε B,t E,t t t t+1 the bank capital at the beginning of the period (before loan losses caused by redistribution shocks have been realized), a capital adequacy constraint can be reinterpreted as a standard borrowing constraint, that is:6 D (cid:20) γ (L (cid:0)E ε ). (12) t E E,t t t+1 In equation (12), the left–hand side denotes banks liabilities D , while the right–hand side t denotes the fraction of bank assets that can be used as collateral, once expected losses are taken into account. Letm (cid:17) β E (C /C )denotethebanker’sstochasticdiscountfactor. Denotewithλ B,t B t B,t B,t+1 B,t themultiplieronthecapitaladequacyconstraintnormalizedbythemarginalutilityofconsumption. The optimality conditions for deposits and loans are respectively: 1(cid:0)λ = E (m R ), (13) B,t t B,t H,t ∂ac 1(cid:0)γ λ + EB,t = E (m R ). (14) E B,t ∂L t B,t E,t+1 E,t The interpretation of the two first–order condition is straightforward. It also illustrates why deposits D and loans L pay different returns in equilibrium. Consider the ways a bank can t E,t increase its consumption by one extra unit today. 1. The banker can consume more today by borrowing from the household, increasing deposits D by one unit. By doing so, the bank reduces its equity by one unit, thus tightening its t borrowing constraint one–for–one and reducing the utility value of an extra deposit by λ . B,t Overall, today’s payoff from the deposit is 1(cid:0)λ . The next–period expected cost is given B,t by the stochastic discount factor times the interest rate R . H,t 2. Thebankercanconsumemoretodaybyreducingloansbyoneunit. Bylendingless, thebank tightens its borrowing constraint, since it reduces its equity. The utility cost of tightening 6For the extended model, Appendix B derives the borrowing constraint starting from the capital adequacy constraint. 7

the borrowing constraint through lower loans is equal to γ λ . Intuitively, the more loans E B,t are useful as collateral for the bank activity (the higher γ is), the larger is the utility cost E of reducing loans. Forthebanktobeindifferentbetweencollectingdepositsandmakingloans,theadjustedreturns across loans and deposits must be equalized. Given that R is determined from the household H,t problem, the banker will be borrowing constrained, and λ will be positive, if m is sufficiently B,t B,t lower than the inverse of R . In turn, if λ is positive, the required returns on loans R will H,t B,t E,t be higher, the lower γ is. Intuitively, when γ is low, the liquidity value of loans is lower, and E E the compensation required by the bank to be indifferent between lending and borrowing becomes higher. Moreover, loans will pay a return that is (near the steady state) higher than the cost of deposits, since, so long as γ is lower than one, they are less liquid than deposits. E Market Clearing. I normalize the total supply of housing to unity. The market clearing conditions for goods and housing are respectively: Y = C +C +C , (15) t H,t B,t E,t H +H = 1. (16) E,t H,t Steady State Properties. In the non–stochastic steady state of the model, the interest rate on deposits equals the inverse of the household discount factor. This can be seen immediately from equation (2) evaluated at steady state. That is: 1 R = . (17) H β H In addition, when evaluated at their non–stochastic steady state, equations (13) and (14) imply that: (1) so long as β < β (bankers are impatient), the bankers will be credit constrained and; B H (2) so long as γ is smaller than one, there will be a positive spread between the return on loans E and the cost of deposits. The spread will increase with the tightness of the capital requirement constraint for the bank. Formally: β λ = 1(cid:0)β R = 1(cid:0) B > 0, (18) B B H β ( H) 1 1 1 R = (cid:0)γ (cid:0) > R . (19) E β E β β H B B H I turn now to entrepreneurs. Given the interest rates on loans R , a necessary condition E 8

for entrepreneurs to be constrained is that their discount factor is lower than the inverse of the return on loans above. When this condition is satisfied (that is, β R < 1), entrepreneurs will be E E constrained in a neighborhood of the steady state. Alternatively, this condition requires that the entrepreneurial discount rate is higher than a weighted average of the discount rates of households and bankers. 1 1 1 > γ +(1(cid:0)γ ) . (20) β Eβ E β E H B Both the bankers’ credit constraint and the entrepreneurs’ credit constraint create a positive wedge between the steady–state output in absence of financial frictions and the output when financial frictions are present. The credit constraint on banks limits the amount of savings that banks can transform into loans. Likewise, the credit constraint on entrepreneurs limits the amount of loans that can be invested for production. Both constraints lead to lower steady state–output. The same forces are also at work for shocks that move the economy away from the steady state, to the extent that these shocks tighten or loosen the severity of the borrowing constraints. 2.3 Calibration To illustrate the main workings of the model, I study the macroeconomic consequences of a shock that persistently reduces bank equity. In the full estimated model, I will also look at other shocks, and estimate using Bayesian methods the model’s structural parameters. The parameters chosen here are in line with the estimates and the calibration of the extended model. Thetimeperiodisaquarter. Isetthediscountfactorsofhouseholds,entrepreneursandbankers respectively at β = 0.9925, β = 0.94 and β = 0.945. Together with the choice of the leverage H E B parameters (described below), these numbers imply an annualized steady–state deposit rate R of H 3 percent and a steady–state lending rate R of 5 percent. As for adjustment cost parameters for E loans I set both ϕ and ϕ equal to 0.25. EE EB I set the weight on leisure in the household utility function, τ, at 2, implying a share of active timespentworkingclosetoonehalf, andaFrischlaborsupplyelasticityaround1. Isettheshareof housing in production ν is set at 0.05, and the the preference parameter for housing j in the utility function at 0.075. These choices imply a ratio of real estate wealth to output of 3.1 (annualized), of which 0.8 is commercial real estate and 2.3 is residential real estate. I next choose the parameters controlling leverage. I set m = 1, so that all labor costs must N be paid in advance. I set m , the entrepreneurial loan–to–value (LTV) ratio, to 0.9. The leverage H parameter for the bank is set at γ = 0.9: this number is consistent with historical data on bank E balance sheets that show capital–asset ratios for banks close to 0.1 (see for instance the evidence 9

in Van den Heuvel 2008). 2.4 The Dynamic Effects of a Financial Shock To gain intuition into the workings of the model, it is useful to consider how time–variation in the tightness of the bankers’ borrowing constraint can affect equilibrium dynamics. I begin with the price side. Abstracting from adjustment costs, the expression for the spread between the return on loans and the cost of deposits can be written as: λ E (R )(cid:0)R = B,t (1(cid:0)γ ). (21) t E.t+1 H,t m E B,t According to this expression, the spread between the return on entrepreneurial loans and the cost of deposits becomes larger whenever the banker’s multiplier on the borrowing constraint λ gets B,t higher. Whenthecapitaladequacyconstraintbecomestighter,forinstancebecausebanknetworth is lower, the bank requires a larger return on its assets in order to be indifferent between extending loans and issuing deposits. This occurs because loans are more illiquid than deposits: when the constraint is binding, a decline in deposits of 1 dollar requires a decline in loans by 1 > 1 dollars. γ E Accordingly, the rise in the spread will act as a drag on economic activity during periods of lower bank net worth. I move now to the quantity side. Whenever a shock causes a reduction in bank capital, the logic of the balance sheet requires the bank to contract its assets by a multiple of its capital, in order for the bank to restore its leverage ratio. The banker could avoid this by raising new capital or by reducing consumption. However, the bankers’ impatience makes this route impractical as well as insufficient. As a consequence, the bank reduces its lending. If the productive sector of the economy depends on bank credit to run its activities, the contraction in bank credit causes in turn a recession. How much do financial shocks affect the economy? Here I consider the effect of the shock ε t that transfers resources from the bank to the household. An interpretation of this shock is that it captures losses for the banking system caused, for instance, by a wave of loan defaults. Granted, loan defaults are not exogenous events, and they may have broader consequences than just hitting the balance sheet of lenders, for at least two reasons. First, there are large legal and social costs associated with defaults. Second, defaults are naturally the symptom of some primitive economic distress for those who default, which ideally one would like the capture in a richer model. With thesecaveatsin mind, I size the redistribution shocksbylooking at the data on loan losses – caused directly or indirectly by defaults –. 10

The particular type of shock that I emphasize here only captures one of the ways in which episodes of financial stress may ultimately redistribute resources across agents. In addition, both in the basic model of this section and in the estimated model of the next section, I place emphasis on a shock that redistributes wealth away from the banks towards the household sector. This is in keeping with the observation that the large losses suffered from banks during the Great Recession originated from household defaults. In the basic model presented here, there is only one household type (the savers), so that household–savers gain. In the extended model of the next section, which includesbothhousehold–saversandhousehold–borrowers, Iassumethathousehold–borrowersgain. For aggregate dynamics, whether the gains accrue to household who save or households to borrow is not crucial: what matters is that wealth gets redistributed away from a relatively productive sector (the banking sector that lends to entrepreneurs) to a relatively unproductive one. Figure 1 plots a dynamic simulation for the model economy in response to a sequence of redistribution shocks that hit the balance sheet of the bank. I assume that the stochastic process for ε follows t ε t = 0.9ε t−1 +ι t . (22) I feed into the model a sequence of unexpected shocks to ι , each quarter equal to 0.38 percent of t annual GDP, which lasts 12 quarters and causes losses for the banking system to rise from zero to 2.8 percent of GDP after 3 years, before loan losses gradually return to zero.7 Note that the losses for the banking system are equal to the gains of household sector, so no wealth is created or destroyed in aggregate by the shock. As such, the shock is a pure redistribution shock. From the standpoint of the banks, the loan losses closely mimic the losses of financial system during the Great Recession. Between 2007Q1 and 2009Q4, annualized loan charge–off rates on residential mortgages rose from 0.1 percent to 2.8 percent, and charge–off rates on consumer loans rose from 2.7 percent to 6.6 percent. Given a ratio of total household debt to GDP close to 1, the shockheremimicstheincreaseinloancharge–offsoftheGreatRecession. Notealsothatthroughout the paper, my maintained assumption is that banks cannot react to the shock by charging higher interest rates. The shock impairs the bank’s balance sheet, by reducing the value of the banks’ assets (total loans minus loan losses) relative to the liabilities (household deposits). Given the shock, in absence of any further adjustment to either loans or deposits, the bank would have a capital–asset ratio that is below target. The bank could restore such ratio either by deleveraging (reducing deposits 7In the experiment reported here, the cumulative loan losses for banks are about 9 percent of annual GDP after 5 years. These numbers are in the ballpark of the IMF estimates of total writedowns by banks and other financial institutions which were made during the financial crisis. See for instance Table 1.3 in IMF (2009). 11

from households), or by reducing consumption in order to restore its equity cushion. If reducing consumption is costly, the bank cuts back on its loans, and begins a vicious, dynamic circle of simultaneous reduction both in loans and deposits, thus propagating the credit crunch. In particular, the decline in loans to the credit–dependent sector of the economy (entrepreneurs) acts a drag on both consumption and productive investment. It drags investment down because credit– constrained entrepreneurs reduce their real estate holdings and labor demand as credit supply is reduced. And it drags consumption down because the decline in labor demand and the reduction inentrepreneurialinvestmentinduceadeclineintotaloutput.8 Alltold, theshockproducesalarge and persistent decline in economic activity. After 3 years, output and asset prices are more than 2 percent below baseline, and the spread between lending and deposit rates, which equals 2 percent in steady state, rises to almost 6 percent. 3 Extended Model and Structural Estimation 3.1 Overview of the Model The basic model of the previous section assumes that real estate is the only input in production, that there is no heterogeneity across households, and that all the productive assets in the economy are held by firms that are credit constrained. In addition, the model lacks a horse race between “financial” shocks and other shocks that could be potentially important for explaining business fluctuations. In this section, I extend the basic model by relaxing the assumptions above. I then take the model to the data using likelihood–based techniques. An advantage of this approach is that the estimation provides an in–sample accounting of the forces driving recent U.S. business cycles in general, and the Great Recession in particular. Relative to the model of the previous section, I split the household sector into two types. Alongsidepatienthouseholds,thereisagroupofimpatienthouseholdsthatearnsafractionσ ofthe totalwageincomeintheeconomyandborrowsagainsttheirhomes. Inaddition,patienthouseholds accumulate a share 1(cid:0)µ of the economywide capital stock, while entrepreneurs accumulate real estate (as before) and the remaining fraction µ of the capital stock. Banks collect deposits and make loans to either impatient households or entrepreneurs. To capture the slow dynamics of many macroeconomic variables, I allow for quadratic adjustment costs for all assets, for habits in consumption, and for inertia in the borrowing constraints and in the capital adequacy constraint. With appropriate choices of the parameters, the model nests either the basic model of the previous 8Anadditionalforcethatreducesoutputinthewakeofaredistributionshockisanegativewealtheffectonlabor supply for the households who receive funds from the bank. This effect contributes to less than one quarter of the decline in output. 12

section or the standard RBC model as special cases. Finally, as in virtually every model that is estimated using likelihood–based techniques, I allow for a rich array of shocks to explain the variation in the data. 3.2 Main Model Features Below, I describe the main features of the model. The complete set of model equations can be found in Appendix B. Patient Households. The patient households objective is given by ∑∞ maxE 0 βt H (A p,t (1(cid:0)η)log(C H,t (cid:0)ηC H,t−1 )+jA j,t A p,t logH H,t +τ log(1(cid:0)N H,t )), t=0 subject to the following budget constraint: K C H,t + H,t +D t +q t (H H,t (cid:0)H H,t−1 )+ac KH,t +ac DH,t A ( K,t ) 1(cid:0)δ KH,t = R M,t z KH,t + K H,t−1 +R H,t−1 D t−1 +W H,t N H,t . (23) A K,t In the utility function above, the term A denotes a shock to preferences for consumption and p,t housing jointly (aggregate spending shock), the A term denotes a housing demand shock, and η j,t measuresexternalhabitsinconsumption. Inthebudgetconstraint,householdsownphysicalcapital K and rent capital services z K to entrepreneurs at the rental rate R (the utilization H,t KH,t H,t M,t rate is z ). The term A denotes an investment–specific technology shock. The terms ac KH,t K,t KH,t and ac denote convex, external adjustment costs for capital and deposits. The parameter DH,t δ denotes the depreciation function for physical capital, which assumes that depreciation is KH,t convex in the utilization rate of capital. The functional forms for the adjustment costs and for the depreciation function are in Appendix B. Impatient Households. The objective of the impatient households is given by ∑∞ maxE 0 βt S (A p,t (1(cid:0)η)log(C S,t (cid:0)ηC S,t−1 )+jA j,t A p,t logH S,t +τ log(1(cid:0)N S,t )), t=0 13

where β denotes their discount factor.9 Their budget constraint is: S C S,t +q t (H S,t (cid:0)H S,t−1 )+R S,t−1 L S,t−1 (cid:0)ε H,t +ac SS,t = L S,t +W S,t N S,t , (24) where L denotes loans made by banks to impatient households, paying a gross interest rate R , S,t S,t and the term ac denotes a convex cost of adjusting loans from one period to the next. The SS,t term ε in the budget constraint is an exogenous shock, similar to the redistribution shock of H,t the previous section, that transfers wealth from banks to households: I assume that impatient households can pay back less (more) than agreed on their contractual obligations when ε is H,t greater (smaller) than zero. From the households’ perspective, this redistribution shock represents – all else equal – a positive shock to wealth, since it allows them to spend more than previously anticipated. When I take the model to the data, I measure this shock by looking at data on loan losses on residential mortgages suffered by financial intermediaries. Impatient households are also subject to a borrowing constraint that limits their liabilities to a fraction of the value of their house: ( ) q L S,t (cid:20) ρ S L S,t−1 +(1(cid:0)ρ S )m S A MH,t E t R t+1 H S,t . (25) S,t The term ρ allows for slow adjustment over time of the borrowing constraint, to capture the idea S thatinpracticelendersdonotreadjustborrowinglimitseveryquarter. ThetermA denotesan MH,t exogenous shock to the borrowing capacity of the household, due to, for instance, looser screening practices of the banks that allow them to supply more loans for given amount of collateral. The borrowing constraint binds in a neighborhood of the steady state if β is lower than a weighted S average of the discount factors of patient households and bankers. Note that one could endogenize the default–redistribution shock in other ways: for instance, one could assume that if house prices fall below some value, borrowers could find it optimal to default rather than roll their debt over: defaulting would then be equivalent to choosing a value for R S,t L S,t−1 lower than previously agreed. Bankers. Bankers solve: ∑∞ maxE 0 βt B (1(cid:0)η)log(C B,t (cid:0)ηC B,t−1 ) t=0 9For impatient households to borrow and to be credit constrained in equilibrium, one needs to assume that their discount factor is lower than a weighted average of the discount factors of households and banks. See Appendix B for details. An analogous restriction applies to entrepreneurs. 14

subject to the following budget constraint: C B,t +R H,t−1 D t−1 +L E,t +L S,t +ac DB,t +ac EB,t +ac SB,t = D t +R E,t L E,t−1 +R S,t L S,t−1 (cid:0)ε E,t (cid:0)ε H,t . (26) Thelasttwotermsdenotetherepaymentshocks. Asbefore, thetermsac ,ac andac DB,t EB,t SB,t denote adjustment costs paid by the bank for adjusting deposits, loans to entrepreneurs L , and E,t loans to impatient households L . The bank is subject to a capital adequacy constraint of the S,t form: L t (cid:0)D t (cid:0)E t ε t+1 (cid:21) ρ D (L t−1 (cid:0)D t−1 (cid:0)E t−1 ε t )+(1(cid:0)γ)(1(cid:0)ρ D )(L t (cid:0)E t ε t+1 ), (27) where L = L +L are bank loans and ε = ε +ε are loan losses. This constraint posits t E,t S,t t E,t H,t that bank equity (after expected losses) must exceed a fraction of bank assets, allowing for partial adjustment in bank capital given by ρ . In this formulation, the capital–asset ratio of the bank D can temporarily deviate from its long–run target, γ, so long as ρ is not equal to zero. Such a D formulation allows the bank to take corrective action to restore its capital–asset ratio beyond one period. Entrepreneurs. The last group of agents are the entrepreneurs. They hire workers and combine themwithcapital(bothproducedbythemandsuppliedbypatienthouseholds)inordertoproduce the final good Y . Their utility function is t ∑∞ maxE 0 βt E (1(cid:0)η)log(C E,t (cid:0)ηC E,t−1 ) t=0 and they are subject to the following budget constraint: K E,t C E,t + +q t H E,t +R E,t L E,t−1 +W H,t N H,t +W S,t N S,t +R M,t z KH,t K H,t−1 +ac KE,t +ac EE,t A K,t 1(cid:0)δ KE,t = Y t + K E,t−1 +q t H E,t−1 +L E,t +ε E,t , (28) A K,t where ε denotes default–redistribution shocks, and ac and ac denote adjustment costs E,t KE,t EE,t for capital and loans. The production function is given by: Y t = A Z,t (z KH,t K H,t−1 )α(1−µ)(z KE,t K E,t−1 )αµH E ν ,t−1 N H (1 , − t α−ν)(1−σ) N S (1 ,t −α−ν)σ , (29) 15

where A is a shock to total factor productivity. Finally, entrepreneurs are subject to a borrowing Z,t constraint that acts as a wedge on the capital and labor demand. The constraint is given by: ( ( ) ) q L E,t (cid:20) ρ E L E,t−1 +(1(cid:0)ρ E )A ME,t m H E t R t+1 H E,t +m K K E,t (cid:0)m N (W H,t N H,t +W S,t N S,t ) . E,t+1 (30) In a manner similar to the impatient households problem, the term A denotes a shock to ME,t the borrowing capacity of the entrepreneur. Market Clearing and Equilibrium. MarketclearingisimpliedbyWalras’slawbyaggregating all the budget constraints. For housing, we have the following market clearing condition: H +H +H = 1. (31) H,t S,t E,t To compute the model dynamics, I solve a linearized version of the system of equations describing the equilibrium of the model under the maintained assumption that the constraints given by equations (25), (27) and (30) are always binding. I verify that, given the size of the estimated shocks, the Lagrange multipliers are always positive throughout a given simulation. 3.3 Estimation IuseBayesianmethodsasdescribedinAnandSchorfheide(2007)toestimatethemodelparameters. Data. The emphasis on financial factors of this paper leads me to consider for estimation several quantitieswhichareimportanttoidentifythevariousshocksgiventhedata. Accordingly,Iestimate the model using U.S. quarterly data from 1985Q1 to 2010Q4.10 The model allows for eight shocks. Following usual practice, I use as many shocks as observable variables. The observables are: real consumption, real nonresidential fixed investment, losses on loans to businesses, losses on loans to households,loanstobusinesses,loanstohouseholds,realhouseprices,andtotalfactorproductivity. AppendixCdescribesthedataconstruction. Exceptforloanlosses, Idetrendthelogarithmofeach variable independently using a quadratic trend.11 The detrended and demeaned data are plotted in Figure 2. 10The sample begins in 1985Q1, but the first 20 observations are used as a training sample for the Kalman filter, so that the estimation is effectively based on the observations from 1990Q1 to 2010Q4. 11AlthoughseveralrecentestimatedDSGEmodelsallowfordeterministicorstochastictrends,incorporatingsuch features into a model with financial variables such as loans is nontrivial. Several financial variables appear to have trends of their own which would require specific modeling assumptions to guarantee balanced growth: for instance, the ratio of household debt to GDP has been rising throughout the sample in question. I leave exploration of this topic for future research. 16

Calibration and Priors. Table 1 summarizes the calibrated parameters. These values are kept fixed because the data are demeaned and cannot pin down steady–state values in the estimation procedure. I set the variable capital share in production α at 0.35 and capital depreciation rate at 0.035. I choose a number for the depreciation rate which is slightly larger than the typical number in the literature – 0.025 – since my model also includes real estate as a factor of production which does not depreciate altogether. These numbers imply an investment to output ratio of 0.25 and a variablecapitaltooutputratioof1.8. Alltheleverageparametersaresetat0.9,andIassumelabor must be fully paid in advance, so that m = 1. Together with the discount factors, the leverage N parameters imply an annualized steady–state return on deposits of 3 percent and a steady–state return on loans of 5 percent. Tables 2.a and 2.b show the prior distributions for the model’s remaining parameters. I assume that all parameters are independent a priori. The domain of most parameters, whenever possible, covers a wide range of outcomes. In the prior, I choose to be conservative about the importance of financial shocks. In particular, my assumptions about the relative importance of the various shocks imply that, at the prior mean, the financial shocks (that is, the combination of housing price shocks, default–redistribution shocks, and loan–to–value ratio shocks) account for about 15 percent of the total variance of output, consumption and investment at business cycle frequencies (as implied by an HP–filter with a smoothing parameter of 1,600). Estimation Findings. The last three columns of Tables 2.a and 2.b report the means and 5% and95% ofthe posteriordistribution for theestimated modelparameters. All shocksareestimated to be quite persistent, with autocorrelation coefficients ranging from 0.84 to 0.994. The share of constrained entrepreneurs, µ, is found to be 0.46, slightly lower than its 0.5 prior. The wage share of constrained households, σ, is found to be 0.33, slightly higher than its 0.3 prior. The elasticity of output to entrepreneurial real estate (ν) is estimated at 0.04, implying a steady–state ratio of commercial real estate to annual output of about 0.4. I find substantially more inertia in the household and entrepreneurs’ borrowing constraints (around 0.7) than in the capital adequacy constraint of the bank. Interestingly, the inertia in the borrowing constraints lines up with the well–known observation that various indicators of the quantity of credit tend to lag the business cycle, rather than lead it. The estimated standard deviation of the household default shock is only 0.13 percentage points. Seen through the lenses of the model, the experience of the financial crisis, when charge–offs rates on loans to households rose by more than 2 percentage points (see Figure 2), appears a remarkably rare event. 17

4 The Transmission of Financial Shocks 4.1 Financial Shocks and the Great Recession An important question that one can ask of the estimated model is: how important were financial shocks in shaping the recent U.S. macroeconomic experience? Figure 3 provides an answer by providing historical decompositions of output, total loans, house prices and investment over the estimation sample (at the mean of the estimated parameters). In the data – consistent with the model–outputisdefinedasthesumoftotalconsumptionandnonresidentialfixedinvestment,thus excluding the foreign and the government sector. As the figure shows, movements in output and investmentdonotappeartobedrivenmuchbyfinancialshocksuntil2007, buttheGreatRecession offers a remarkably different picture, as also shown in Table 3. During the Great Recession, about two–thirds of the decline in output and investment is driven by the combined effect of default shocks, housing demand shocks, and LTV shocks. The timing of the shocks, in particular, is of independent interest. Early during the Recession in 2007 and 2008, the decline in output and investment is mostly driven by negative housing demand shocks. Lower collateral values reduce the borrowing capacity of entrepreneurs and lead to lower investment and output. Next, default shocks take center stage. Default shocks account for 1.2 percentage points of the 3.6 percent decline in output in 2008, and for 1.4 percentage points of the 9 percent decline in output in 2009. Last, LTV shocks become important. In 2010, with output growth nearly recovering, tighter credit – in the form of negative LTV shocks – subtracts 1.5 percent from output growth. All told, the three financial shocks combined can explain about two–thirds (9 percentage points out a 13 percent decline) of the output decline from 2007 to the end of 2010. In order to judge the success of the model, at least from a statistical standpoint, I run a formal comparison between the estimated model and an estimated version of the model without banks. To this end, I estimate (using the same priors and data) a version of the model without banks, and perform a standard Bayesian model comparison between the two models. In the model without banks, there is no capital adequacy constraint, savings can be transformed into loans at no cost, andfinancialintermediationisperformedbyhouseholdsaversdirectly. Asaconsequence,quadratic adjustment costs aside, interest rate spreads equal zero at all times. Under the assumption that both models are viewed as equally likely a priori, I obtain a posterior odds ratio of about e4.5 that strongly favors (in the sense Kass and Raftery 1995) the model with banks. As an additional test of the empirical fit of the model, I conduct an external validation exercise to assess the reliability of the model in fitting time series that were not used as inputs in the estimation. Such an exercise is of particular interest since it addresses the critique that DSGE 18

models can do a good job at fitting the data in sample, but have poor performance otherwise. In particular, given the estimated shocks, I contrast in Figure 4 the model’s simulated time series for interestratespreads,capacityutilizationandbankers’consumptionagainsttheirdatacounterparts. The top panel plots the two–year ahead interest rate spread against the C&I Loan Rate Spread for all loans from the Fed Survey of Terms of Business Lending.12 Both in the model and in the data, the interest–rate spread rises markedly during the 2007–2009 period, although the increase – in percentage terms – is slightly larger in the data than in the model.13 In the middle panel, the behavior of capital utilization in the model mimics its data analogue,14 with both the model and the data pointing to a large and persistent decline in utilization around the financial crisis. The bottom panel compares bankers’ consumption with a measure of the health of the banking system in the data, namely corporate profits of the financial sector.15 Both measures tank during the Great Recession. 4.2 The Transmission Mechanism of Financial Shocks Figure 5 illustrates the model’s transmission mechanism for three key markets, at the model’s parameter estimates, by plotting the model–consistent demand and supply curves derived from the relevant Euler equations. I focus on how resources are transferred from the savers (the patient households) to the ultimate users of them (the final good firms), and on how a given size financial shock affect the functioning of these markets. I focus on a redistribution shock that leads to a rise in charge–off rates for household loans from 0 to 2 percent, a magnitude in line with the Great Recession. In the market for deposits D , household–savers set aside resources, and supply them to t thebank. Thebankdemandsdepositsfromthehousehold. Theslopesofdemandandsupplycurves are a function of the estimated parameters ϕ and ϕ which measure the convex adjustment DB DH, cost of changing deposits for banks and households. The linearized demand and supply schedules are plotted in the figure. The negative financial shock hits the financial position of the bank and – holding everything else the same – reduces the bank’s ability to borrow from the household at a given deposit rate. The deposits demand curve shifts to the left, thus reducing equilibrium deposits 12TheseriesnameinthedataisFCIRS@USECON.Iconstructthemodelinterestspreadasthedifferencebetween the lending rate for entrepreneurs (R ) and the deposit rate (R ). I construct a model–consistent two–year spread E H using the expectations hypothesis to match the average duration of C&I Loans in the Survey of Terms of Business Lending. 13In the model, spreads rise when banks’ financial conditions worsen, since they signal the unwillingness of banks to lend funds. In the data, the rise in spreads reflects default risk that is not priced in the model. 14There is no satisfactory counterpart to the model’s capital utilization in the data. Existing data refer only to manufacturing, and are calculated by comparing actual production with a measure of full-capacity production. The proxy I use is the total industry capacity utilization is the Board of Governors of the Federal Reserve System (Industrial Production and Capacity Utilization Summary Table, CUT@USECON). 15The data source for corporate profits is the BEA GDP release. The series name is YCPDF@USECON. 19

and the deposit interest rate.16 In the market for loans L , the dynamics reflect two forces. On the supply side, as bankers E are forced to deleverage, they reduce the supply of loans, which shifts inwards. On the demand side, at the going interest rate, entrepreneurs would like to borrow more: given their high discount factor and their binding borrowing constraint, the drop in consumption growth increases their loan demand. At the model’s estimates, the inward shift in loan supply is far larger than the increase in loan demand, the equilibrium lending rate rises, and total loans decline. In the market for capital K , as equilibrium borrowing drops, entrepreneurs are less able to E supply funds to final good firms, and the supply of capital drops. Capital demand also drops because wealthier borrowers decide to work less, and because factor complementarities reduce the marginal product of capital as real estate demand and utilization rates fall, even as total factor productivity remains unchanged. In turn, the decline in the demand for other factors lowers the marginal product of capital, thus further exacerbating the decline of output. 4.3 Impulse Response Analysis Figure 6 offers a summary picture of the model dynamics in response to the estimated shocks, at the mean of estimated parameter values. To better highlight the role of banks, I compare the model responses to those of a model without banks that retains financial frictions on households and firms. Thetoptworowsshowtheimpulseresponsetorepaymentshocksofentrepreneursandimpatient households respectively, and illustrate how the presence of leveraged banks amplifies such shocks. In particular, the second row shows how a one standard deviation household repayment shock (corresponding to a persistent rise in charge–off rates for the banks of 0.13 percentage points) leads to a protracted decline in output and investment, whereas the effects would be more muted in a frictionlessmodelwithoutbanks. Inotherwords, thepresenceofconstrainedbanksproduceslarger negative effects on output for given redistribution shocks that transfer resources away from banks. These effects are present both when the redistribution works in favor of entrepreneurs – first row – and when it works in favor of household borrowers – second row –, but they are weaker in the first case. For when resources are transferred to entrepreneurs, the reduction in loan supply stemming from the reduction in bankers’ net worth is partly offset by the increase in investment and capital accumulation due to higher entrepreneurial net worth, thus mitigating the output decline. 16As general equilibrium repercussions affect wages and consumption, the household’s supply of deposits – which dependsoninterestratesandexpectedconsumptiongrowth–movestoo. Inparticular,dependingonthepersistence oftheshockandthehabitcoefficient,thesupplyofdepositsmayeitherincreaseordecrease. Atthemodel’sestimates, the supply of deposits is reduced, thus partly mitigating the decline in deposit rates. 20

As for the responses to other shocks, the dynamics in the model with banks are not drastically different from those of the model without banks. This implies that financial frictions on banks work mostly to amplify shocks affecting banks’ net worth, but matter relatively less for traditional business–cycle shocks. To understand this result, it is useful to consider that capital-constrained bankscreateastaticanddynamicwedgethatlimitstheamountofsavingsthatcanbetransformed intoinvestmentgoods. Whengivenshocksmovethiswedgebylittle,thedynamicsofthetwomodels are similar. However, the redistribution shocks directly affect the wedge through their strong effect on bank net worth. There are some additional, subtle differences between the two models that do notshowupinthedynamics, butareimportantforthesteady-stateimplicationsofthetwomodels. The capital requirement on banks constrains the amount of savings that can be transformed into investment goods. This constraint is absent in the model without banks, which implicitly assumes that all savings can be transformed into investment goods at no cost (except for the standard quadratic adjustment costs). For this reason, at the estimated parameters’ mode, steady–state consumption, investment and output are, respectively, 0.5, 4.5 and 1.5 percent higher in the model without banks than in the model with banks. Figure 7 illustrates the strength of the various channels in shaping output dynamics in response to an estimated one standard deviation household default shock. I compare three models: the RBC model; a model with traditional financial frictions on both firms and households; and my model, which combines financial and banking frictions. TheRBCmodelhasonlytwohouseholdtypes, allinvestmentisdonebythepatienthouseholds, and the entrepreneurial sector is shut off (by setting µ and ν to zero). The only friction pertains to the fact that households who borrow are financially constrained: if this friction was missing, there would be no heterogeneity, and no way to think about redistribution shocks (the shock would wash out in the aggregate, in an accounting and behaviorial sense). In the RBC version, the redistribution shock transfers wealth from the savers to the borrowers. Accordingly, borrowers consume more. Patient households, instead, consume less, but reduce their saving in order to smooth their consumption. All told, the decline in savers’ consumption does not fully offset the rise in borrowers’ consumption, and aggregate consumption rises. In turn, lower savings lead to a decline in investment that more than offsets the rise in consumption, so that aggregate output falls, although the total effects are very small. A one standard deviation shock leads to a 0.02 percent decline in output after one year. In the model with financial frictions both on households and on entrepreneurs, but without banks, the decline in households’ saving following the repayment shock reduces the supply of available funds for the entrepreneurs, and causes a knock–on effect on borrowing and investment that 21

further magnifies the output decline. The decline in output after one year is about 0.05 percent, twice as large than in the RBC case. The largest negative effects on economic activity from the repayment shock occur when both the banking channel and the collateral channel are at work, thus restoring the benchmark model with leveraged banks. By putting direct pressure on the bank’s balance sheet, the repayment shock further strengthens the drop in output. At the trough, the output decline is 0.15 percent, almost one order of magnitude larger than in the model without financial frictions. 5 Concluding Remarks In this paper I have presented and estimated a DSGE model where losses sustained by banks can produce sizeable, pronounced and long–lasting effects on business activity. The key ingredients of the model are constraints on the leverage of the banks and a business sector that is bank– dependent for its operations. In an estimated version of the model, financial shocks account for about two–thirds of the decline in output during the Great Recession. Despite its complexity, my model precludes an examination of certain aspects that may be important to understand the role of banks and leveraged agents in business fluctuations. First, banks offer the important benefit of maturity transformation by intermediating across needs and projects with different termination dates. However, while the simple model of this paper features loans and deposits with different adjustment costs, it abstract from a richer examination of the liquidity role provided of banks through this function. Second, because of the illiquid nature of many of the bank’s assets, banks can be subject to runs, especially in periods when their balance sheets are weak or perceived as such. Third, default episodes are obviously the consequence of some negative shocks hitting elsewhere in the economy, and one would love to have a parsimonious macro framework that explains defaults without losing the tractability of a stylized model that can be taken to the data. The recent papers by Andreasen, Ferman, and Zabczyk (2013), Forlati and Lambertini (2011) and Gertler and Kiyotaki (2013) contain interesting examples of models that have begun to address these issues. 22

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Table 1: Calibrated Parameters for the Extended Model Parameter Value Household–saver (HS) discount factor β 0.9925 H Household–borrower (HB) discount factor β 0.94 S Banker discount factor β 0.945 B Entrepreneur (E) discount factor β 0.94 E Total capital share in production α 0.35 Loan–to–value ratio on housing, HB m 0.9 S Loan–to–value ratio on housing, E m 0.9 H Loan–to–value ratio on capital, E m 0.9 K Wage bill paid in advance m 1 N Liabilities to assets ratio for Banker γ ,γ 0.9 E S Housing preference share j 0.075 Capital depreciation rates δ ,δ 0.035 KE KH Labor Supply parameter τ 2 25

Table 2.a: Estimation, Structural Parameters Parameter Prior distribution Posterior Distribution Density Mean St.dev. 5% Mean 95% Habit in Consumption η beta 0.5 0.15 0.36 0.46 0.56 D adj cost, Banks ϕ gamm 0.25 0.125 0.05 0.14 0.26 DB D adj cost, Household Saver (HS) ϕ gamm 0.25 0.125 0.04 0.10 0.20 DH K adj. cost, Entrepreneurs (E) ϕ gamm 1 0.5 0.23 0.59 1.41 KE K adj. cost, Household Saver (HS) ϕ gamm 1 0.5 0.88 1.73 2.95 KH Loan to E adj cost, Banks ϕ gamm 0.25 0.125 0.03 0.07 0.13 EB Loan to E adj cost, E ϕ gamm 0.25 0.125 0.02 0.06 0.11 EE Loan to HB adj cost, Banks ϕ gamm 0.25 0.125 0.24 0.47 0.72 SB Loan to HB adj cost, HH Borrower HB ϕ gamm 0.25 0.125 0.14 0.37 0.66 SS Capital share of E µ beta 0.5 0.1 0.34 0.46 0.58 Housing share of E ν beta 0.04 0.01 0.03 0.04 0.05 Inertia in capital adequacy constraint ρ beta 0.25 0.1 0.10 0.24 0.41 D Inertia in E borrowing constraint ρ beta 0.25 0.1 0.53 0.65 0.79 E Inertia in HB borrowing constraint ρ beta 0.25 0.1 0.64 0.70 0.76 S Wage share HB σ beta 0.3 0.1 0.22 0.33 0.45 Curvature for utilization function E ζ beta 0.2 0.1 0.20 0.42 0.63 E Curvature for utilization function HS ζ beta 0.2 0.1 0.18 0.38 0.58 H Table 2.b: Estimation, Shock Processes Parameter Prior distribution Posterior Distribution Density Mean St.dev. 5% Mean 95% Autocor. E default shock ρ beta 0.8 0.1 0.886 0.932 0.971 be Autocor. HB default shock ρ beta 0.8 0.1 0.944 0.969 0.988 bh Autocor. housing demand shock ρ beta 0.8 0.1 0.986 0.992 0.997 j Autocor. investment shock ρ beta 0.8 0.1 0.840 0.916 0.973 k Autocor. LTV shock, E ρ beta 0.8 0.1 0.750 0.839 0.917 me Autocor. LTV shock, HB ρ beta 0.8 0.1 0.781 0.873 0.948 mh Autocor. preference shock ρ beta 0.8 0.1 0.989 0.994 0.998 p Autocor. technology shock ρ beta 0.8 0.1 0.973 0.988 0.997 z St.dev., Default shock, E σ invg 0.0025 0.025 0.0009 0.0011 0.0012 be St.dev., Default shock, HB σ invg 0.0025 0.025 0.0012 0.0013 0.0015 bh St.dev., housing demand shock σ invg 0.05 0.05 0.0248 0.0346 0.0473 j St.dev., investment shock σ invg 0.005 0.025 0.0049 0.0081 0.0161 k St.dev., LTV shock, E σ invg 0.0025 0.025 0.0129 0.0204 0.0366 me St.dev., LTV shock, HB σ invg 0.0025 0.025 0.0090 0.0115 0.0150 mh St.dev., preference shock σ invg 0.005 0.025 0.0179 0.0205 0.0237 p St.dev., technology shock σ invg 0.005 0.025 0.0062 0.0070 0.0080 z Note: The posterior density is constructed by simulation using the Random-Walk Metropolis algorithm (with 250,000 draws) as described in An and Schorfheide (2007). 26

Table 3: Historical Decomposition Contribution to Output 2007 2008 2009 2010 2007-2010 Default shocks -0.2 -1.2 -1.4 0.1 -2.7 Housing Demand shock -1.3 -1.7 -1.0 0.0 -4.1 LTV shocks 1.1 0.2 -2.2 -1.5 -2.4 Preference shock 2.9 -0.1 -4.9 2.6 0.5 TFP shocks -2.2 -0.8 0.3 -1.3 -4.0 All shocks (data) 0.3 -3.6 -9.3 -0.1 -12.6 Contribution to Investment 2007 2008 2009 2010 2007-2010 Default shocks -0.5 -2.7 -3.0 0.7 -5.5 Housing Demand shock -2.1 -3.4 -2.8 -0.9 -9.1 LTV shocks 3.5 1.7 -6.8 -5.7 -7.3 Preference shock 2.5 -0.9 -5.7 5.1 1.0 TFP shocks -0.5 1.1 -4.9 2.2 -2.1 All shocks (data) 3.0 -4.2 -23.3 1.4 -23.1 Contribution to Consumption 2007 2008 2009 2010 2007-2010 Default shocks -0.1 -0.7 -0.9 -0.1 -1.7 Housing Demand shock -1.1 -1.1 -0.4 0.3 -2.3 LTV shocks 0.2 -0.3 -0.6 -0.1 -0.7 Preference shock 3.1 0.1 -4.6 1.8 0.4 TFP shocks -2.7 -1.4 2.0 -2.5 -4.7 All shocks (data) -0.6 -3.4 -4.5 -0.6 -9.1 Note: Contribution of each estimated shock to year-on-year growth in Annual Output (sum of consumption and non-residential fixed investment), Annual Investment and Annual Consumption. 27

Figure 1: Dynamics of the Basic Model after Default Shock Output 0 −0.5 −1 −1.5 −2 −2.5 0 10 20 30 .s.s morf noitaiveD tnecreP Spread lending−borrowing rate 6 5 4 3 2 0 10 20 30 level dezilaunna ,stnioP egatnecreP 15 10 5 0 0 10 20 30 PDG launna fo % 0 −0.5 −1 −1.5 −2 −2.5 0 10 20 30 quarters .s.s morf noitaiveD tnecreP Housing Prices Cumulated Losses Loan Losses quarters Note: The plots show the responses of macroeconomic variables to a shock that leads after 3 years to (flow) loan losses for banks equal to 2.8 percent of GDP. The cumulated losses are the cumulative sum of the flow loan losses, divided by 4 to express as a fraction of annual GDP. 28

Figure 2: Data Used in Estimation Consumption 2 0 −2 −4 1985 1990 1995 2000 2005 2010 dnert.dauq morf .ved % Investment 20 10 0 −10 −20 1985 1990 1995 2000 2005 2010 dnert.dauq morf .ved % Losses on Loans to Entrepreneurs 3 2 1 0 1985 1990 1995 2000 2005 2010 )denaemed( PDG fo % Losses on Loans to Households 3 2 1 0 1985 1990 1995 2000 2005 2010 )denaemed( PDG fo % Loans to Entrepreneurs 10 0 −10 −20 1985 1990 1995 2000 2005 2010 dnert.dauq morf .ved % Loans to Households 10 5 0 −5 −10 −15 1985 1990 1995 2000 2005 2010 dnert.dauq morf .ved % House Prices 10 0 −10 1985 1990 1995 2000 2005 2010 dnert.dauq morf .ved % Technology 2 0 −2 −4 1985 1990 1995 2000 2005 2010 dnert.dauq morf .ved % Note: The model parameters are estimated using data from 1990Q1 to 2010Q4. The 1985-1989 period is used to initialize the Kalman filter. 29

Figure 3: Historical Decomposition of the Estimated Model Output 2 0 −2 −4 −6 −8 1990 1995 2000 2005 2010 egnahc % YOY Loans 5 0 −5 −10 Loan Default Shock Housing Demand Shock LTV shock −15 1990 1995 2000 2005 2010 egnahc % YOY House Prices 5 0 −5 −10 1990 1995 2000 2005 2010 egnahc % YOY Investment 5 0 −5 −10 −15 −20 1990 1995 2000 2005 2010 egnahc % YOY Note: The solid lines plot actual data. The bars show the contributions of the estimated financial shocks. Data are expressed in deviation from their mean. 30

Figure 4: External Validation: Historical Decomposition of Model Series Interest Rate Spreads 3 2.5 2 1.5 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 )ledoM( daerpS raeY 2 4 3 2 1 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 RFF revo daerpS snaoL I%C Utilization 110 100 90 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 noitazilitU latipaC )001=5891 :xednI ,ledoM 80 60 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 :noitazilitU yticapaC )ataD( yrtsudnI latoT Banking Profits 1.5 1 0.5 0 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 noitpmusnoC ‘sreknaB )ledoM( PDG fo tnecreP 4 2 0 −2 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 :stiforP etaroproC )PDG fo tnecrep( yrtsudnI laicnaniF model data model data model data Note: The solid lines plot model simulated (smoothed estimates) series. The dashed lines plot similar objects from actual data. 31

Figure 5: Transmission Mechanism of Default Shock 3.1 3 2.9 2.8 2.7 −1 −0.5 0 D (% change from steady state) )% ,launna( R D DEPOSITS LOANS (demand=BANK, supply=HOUSEHOLDS) (demand=ENTREPRENEURS, supply=BANK) 5.6 5.4 5.2 5 −0.8 −0.6 −0.4 −0.2 0 0.2 L (% change from steady state) E )% ,launna( R L 9 8.9 8.8 8.7 −0.3 −0.2 −0.1 0 0.1 K (% change from steady state) E )% ,launna( R EK ENTREPRENEURIAL CAPITAL (demand=FIRM, supply=ENTREPRENEURS) Demand Demand, after shock Supply Supply, after shock Note: Each panel plots the linearized demand and supply curves for deposits, loans to entrepreneurs, and entrepreneurial capital in steady state and away from it, in the first period when a redistribution shock (that transfers 2 percent of GDP from banks to impatient households) hits. 32

Figure 6: Impulse Responses to all Shocks, Estimated Banking Model and Counterfactual Model without Banks 0.1 0.05 0 )eb(ε tluafed E Output Consumption Investment Loans House Prices 0.1 0.1 0.2 0.05 0.05 0 0 0 0 −0.1 −0.2 −0.05 0 −0.1 −0.2 )hb(ε tluafed HH 0 0 0 0 −0.05 −0.2 −0.2 −0.1 −0.1 −0.4 −0.4 −0.2 0.5 0 −0.5 )j(ε .ferp gnisuoH 0.5 0.5 1 1.4 0 0 0.5 1.3 −0.5 −0.5 0 0.4 0.2 0 )k(ε kcohS.vnI 0.5 2 0.5 0.5 0 1 0 0 −0.5 0 −0.5 −0.5 1 0 −1 )em(ε .pertnE VTL 0.2 2 4 0.4 0 0 2 0.2 −0.2 −2 0 0 0.1 0 −0.1 )hm(ε HH VTL 0.05 0.5 0.2 0.1 0 0 0.1 0.05 −0.05 −0.5 0 0 1.5 1 0.5 )p(ε ecnereferP 1.5 2 1 0.5 1 1.5 0.5 0.45 0.5 1 0 0.4 1 0.9 0.8 0 10 20 )z(ε PFT 1 2 1 0.8 0.8 1.5 0.5 0.75 0.6 1 0 0.7 0 10 20 0 10 20 0 10 20 0 10 20 Estimated Model Estimated Model taking out Banking Friction Note: horizontal axis: quarters from the shock; vertical axis: percent deviation from the steady state. The solid lines plot, for each row, the responses to each estimated shock, one standard deviation in size. The dashed lines plot the same model shutting off the banking sector. 33

Figure 7: Impulse Responses to Estimated Household Default Shock Output 0 −0.1 −0.2 0 5 10 15 20 tnecrep Consumption 0.1 0 −0.1 0 5 10 15 20 tnecrep Investment 0 −0.2 −0.4 0 5 10 15 20 tnecrep Hours 0 −0.1 −0.2 0 5 10 15 20 tnecrep House Prices 0 −0.1 −0.2 0 5 10 15 20 tnecrep Loans to Output Ratio 0.5 0 −0.5 0 5 10 15 20 PDG launna fo tnecrep Spread Lending Borrowing Rate 0.4 0.2 0 −0.2 0 5 10 15 20 stniop egatnecrep launna Cumulated Losses 1 0.5 0 0 5 10 15 20 quarters PDG launna fo tnecrep quarters RBC Frictions E,HH Benchmark: Frictions E,HH,Bank Note: horizontal axis: quarters from the shock; vertical axis: percentage deviation from the steady state. Loans and loan losses are percentages of annualized output. The Spread between the Loan and Deposit Rate is expressed in annualized percentage points. The shock is one standard deviation in size. 34

Appendix Appendix A Complete Set of Equations of the Basic Model The basic model is described by the following set of equations. I denote with u the marginal ij utility of good i for agent j. C H,t +D t +q t (H H,t (cid:0)H H,t−1 ) = R H,t−1 D t−1 +W H,t N H,t +ε H,t , (A.1) u = β E (R u ), (A.2) CH,t H t H,t CH,t+1 τ W u = , (A.3) H,t CH,t 1(cid:0)N H,t q u = u +β E (q u ), (A.4) t CH,t HH,t H t t+1 CH,t+1 C B,t +R H,t−1 D t−1 +L E,t +ac EB,t = D t +R E,t L E,t−1 (cid:0)ε H,t , (A.5) D = γ(L (cid:0)E ε ), (A.6) ( ) t Et t H,t+1 ∂ac 1(cid:0)γ + EB,t u = β E ((R (cid:0)γR )u ), (A.7) ∂L CB,t B t E,t+1 H,t CB,t+1 E,t C E,t +q t (H E,t (cid:0)H E,t−1 )+R E,t L E,t−1 +W H,t N H,t = Y t +L E,t +ac EE,t , (A.8) Y = Hν N1−ν, (A.9) ( t E,t−1 )H,t q L = m E t+1 H (cid:0)m W N , (A.10) E,t H t E,t N H,t H,t R ( (( ) )) E,t+1 (( ) ) ∂ac m q Y q (cid:0)E 1(cid:0) EE,t H t+1 u = β E q (1(cid:0)m )+ν t+1 u , t t ∂L R CE,t E t t+1 H H CE,t+1 E,t E,t+1 E,t (A.11) ( ( )) ∂ac u (1(cid:0)ν)Y = W N E 1+m 1(cid:0) EE,t (cid:0)β R CE,t+1 , (A.12) t H,t H,t t N ∂L E E,t+1 u E,t CE,t H +H = 1. (A.13) H,t E,t The model endogenous variables are Y, H , H , N , C , C , C , L , D, q, W , R , and R . E H H B E H E H E H The exogenous repayment shock is ε . H,t 35

Appendix B Complete Set of Equations of the Extended Model This section describes in detail the extended model. Unless stated otherwise, the absence of subscript from a variable denotes the steady state of that variable. For instance, K is household H,t capital at time t, and K is the steady–state value of household capital. H Patient Households. Patient households solve: ∑∞ maxE 0 βt H (A p,t (1(cid:0)η)log(C H,t (cid:0)ηC H,t−1 )+jA j,t A p,t logH H,t +τ log(1(cid:0)N H,t )) t=0 subject to: K C H,t + H,t +D t +q t (H H,t (cid:0)H H,t−1 )+ac KH,t +ac DH,t A ( K,t ) 1(cid:0)δ KH,t = R M,t z KH,t + K H,t−1 +R H,t−1 D t−1 +W H,t N H,t , (B.1) A K,t where the adjustment costs take the following form ac = ϕ KH (K H,t (cid:0)K H,t−1 )2 , KH,t 2 K H ac = ϕ DH (D t (cid:0)D t−1 )2 , DH,t 2 D and the depreciation function is ( ( ) ( )) δ = δ +b 0.5ζ ′ z2 + 1(cid:0)ζ ′ z + 0.5ζ ′ (cid:0)1 , KH,t KH KH H KH,t H KH,t H ′ ζ where ζ = H is a parameter measuring the curvature of the utilization rate function. ζ = H 1−ζ H ′ H ′ 0 implies ζ = 0; ζ approaching 1 implies ζ approaches infinity and δ stays constant. H H H KH,t b = 1 +1(cid:0)δ and implies a unitary steady–state utilization rate. ac measures a quadratic KH β KH t adjustme H nt cost for changing the quantity i between time t (cid:0) 1 and time t. Both habits and adjustment costs are assumed to be external. Denote with u = Ap;t(1−η) and u = jAj;tAp;t the marginal utilities of consumption CH,t CH;t −ηCH;t(cid:0)1 HH,t HH;t and housing. The optimality conditions yield equations for deposit supply, labor supply, supply of capital, housing demand, and for the optimal utilization rate: ( ) ∂ac DH,t u 1+ = β E (R u ), (B.2) CH,t ∂D H t H,t CH,t+1 t τ W u = , (B.3) H,t CH,t 1(cid:0)N ( ) (( H,t ) ) 1 ∂ac 1(cid:0)δ KH,t KH,t+1 u 1+ = β E R z + u , (B.4) A CH,t ∂K H t M,t+1 KH,t+1 A CH,t+1 K,t H,t K,t+1 q u = u +β E (q u ), (B.5) t CH,t HH,t H t t+1 CH,t+1 ∂δ KH,t R = , (B.6) M,t ∂z KH,t 36

whereA isaninvestmentshock,A isaconsumptionpreferenceshock,A isahousingdemand K,t p,t j,t shock. Impatient Households. Impatient households solve: ∑∞ maxE 0 βt S (A p,t (1(cid:0)η)log(C S,t (cid:0)ηC S,t−1 )+jA j,t A p,t logH S,t +τ log(1(cid:0)N S,t )), t=0 where ( ) 1(cid:0)β R β < 1(cid:0)((1(cid:0)β )ρ +(1(cid:0)ρ )γ ) B H β , S B D D S 1(cid:0)β ρ B B D subject to C S,t +q t (H S,t (cid:0)H S,t−1 )+R S,t−1 L S,t−1 (cid:0)ε H,t +ac SS,t = L S,t +W S,t N S,t , (B.7) and to ( ) q L S,t (cid:20) ρ S L S,t−1 +(1(cid:0)ρ S )m S A MH,t E t R t+1 H S,t , (B.8) S,t where ε is the borrower repayment shock, A is a loan-to-value ratio shock. The adjustment H,t MH,t cost is: ac = ϕ SS (L S,t (cid:0)L S,t−1 )2 . SS,t 2 L S Thefirstorderconditionsare, denotingwithu = Ap;t(1−η) andu = jAj;tAp;t themarginal CS,t CS;t −ηCS;t(cid:0)1 HS,t HS;t utilities of consumption and housing, and with λ the multiplier on the borrowing constraint S,t normalized by the marginal utility of consumption: ( ) ∂ac 1(cid:0) SS,t (cid:0)λ u = β E ((R (cid:0)ρ λ )u ), (B.9) ∂L S,t CS,t S t S,t S S,t+1 CS,t+1 S,t τ S W u = , (B.10) S,t CS,t 1(cid:0)N ( ) S,t q q (cid:0)λ (1(cid:0)ρ )m A E t+1 u = u +β E (q u ). (B.11) t S,t S S MH,t t R CS,t HS,t S t t+1 CS,t+1 S,t Bankers. Bankers solve: ∑∞ maxE 0 βt B (1(cid:0)η)log(C B,t (cid:0)ηC B,t−1 ) t=0 where β < β , B H subject to C B,t +R H,t−1 D t−1 +L E,t +L S,t +ac DB,t +ac EB,t +ac SB,t = D t +R E,t L E,t−1 +R S,t L S,t−1 (cid:0)ε E,t (cid:0)ε H,t , (B.12) 37

where ε is the entrepreneur repayment shock. The adjustment costs are: E,t ac = ϕ DB (D t (cid:0)D t−1 )2 , DB,t 2 D ac = ϕ EB (L E,t (cid:0)L E,t−1 )2 , EB,t 2 L E ac = ϕ SB (L S,t (cid:0)L S,t−1 )2 . SB,t 2 L S Denote ε = ε + ε . Let L = L + L . The banker’s constraint is a capital adequacy t E,t H,t t E,t S,t constraint of the form: (L t (cid:0)D t (cid:0)E t ε t−1 ) (cid:21) ρ D (L t−1 (cid:0)D t−1 (cid:0)E t−1 ε t )+(1(cid:0)γ)(1(cid:0)ρ D )(L t (cid:0)E t ε t+1 ), bankequity bankassets stating that bank equity (after expected losses) must exceed a fraction of bank assets, allowing for a partial adjustment in bank capital given by ρ . Such constraint can be rewritten as a leverage D constraint of the form D t (cid:20) ρ D (D t−1 (cid:0)(L E,t−1 +L S,t−1 (cid:0)E t−1 (ε E,t +ε H,t )))+ (1(cid:0)(1(cid:0)γ)(1(cid:0)ρ ))(L +L (cid:0)E (ε +ε )). (B.13) D Et S,t t E,t+1 H,t+1 The first order conditions to the banker’s problem imply, choosing D, L , L and denoting E S with λ be the multiplier on the borrowing constraint normalized by u , the banker’s marginal B,t CB,t utility of consumption: ( ) ∂ac 1(cid:0)λ (cid:0) DB,t u = β E ((R (cid:0)ρ λ )u ), (B.14) B,t ∂D CB,t B t H,t D B,t+1 CB,t+1 ( t ) ∂ac 1(cid:0)(γ (1(cid:0)ρ )+ρ )λ + EB,t u = β E ((R (cid:0)ρ λ )u ), (B.15) E D D B,t ∂L CB,t B t E,t+1 D B,t+1 CB,t+1 ( E,t ) ∂ac 1(cid:0)(γ (1(cid:0)ρ )+ρ )λ + SB,t u = β E ((R (cid:0)ρ λ )u ). (B.16) S D D B,t ∂L CB,t B t S,t D B,t+1 CB,t+1 S,t Entrepreneurs. Entrepreneursobtainloansandproducegoods(includingcapital). Entrepreneurs hire workers and demand capital supplied by the household sector. They maximize ∑∞ maxE 0 βt E (1(cid:0)η)log(C E,t (cid:0)ηC E,t−1 ) t=0 where ( ) 1(cid:0)β R β 1(cid:0)((1(cid:0)β )ρ +(1(cid:0)ρ )γ ) B H < β , E B D D E 1(cid:0)β ρ B B D 38

subject to: K E,t C E,t + +q t H E,t +R E,t L E,t−1 +W H,t N H,t +W S,t N S,t +R M,t z KH,t K H,t−1 +ac KE,t +ac EE,t A K,t (B.17) 1(cid:0)δ KE,t = Y t + K E,t−1 +q t H E,t−1 +L E,t +ε E,t , A K,t and to Y t = A Z,t (z KH,t K H,t−1 )α(1−µ)(z KE,t K E,t−1 )αµH E ν ,t−1 N H (1 , − t α−ν)(1−σ) N S (1 ,t −α−ν)σ , (B.18) where A is a shock to total factor productivity. The adjustment costs are Z,t ac = ϕ KE (K E,t (cid:0)K E,t−1 )2 , KE,t 2 K E ac = ϕ EE (L E,t (cid:0)L E,t−1 )2 . EE,t 2 L E Note that symmetrically to the household problem entrepreneurs are subject to an investment shock, can adjust the capital utilization rate, and pay a quadratic capital adjustment cost. The depreciation rate is governed by ( ( ) ( )) δ = δ +b 0.5ζ ′ z2 + 1(cid:0)ζ ′ z + 0.5ζ ′ (cid:0)1 , KE,t KE KE E KE,t E KE,t E where setting b = 1 +1(cid:0)δ implies a unitary steady state utilization rate. KE β KE E Entrepreneurs are subject to a borrowing/pay in advance constraint that acts as a wedge on the capital and labor demand. The constraint is ( ) q L E,t = ρ E L E,t−1 +(1(cid:0)ρ E )A ME,t E t m H R t+1 H E,t +m K K E,t (cid:0)m N (W H,t N H,t +W S,t N S,t ) . E,t+1 (B.19) Letting u be the marginal utility of consumption and λ the borrowing constraint nor- CE,t E,t malized by the marginal utility of consumption u , the first order conditions for loans, capital CE,t and real estate are: ( ) ∂ac 1(cid:0)λ (cid:0) EE,t u = β E ((R (cid:0)ρ λ )u ), (B.20) E,t ∂L CE,t E t E,t+1 E E,t+1 CE,t+1 ( E,t ) ∂ac 1+ KE,t (cid:0)λ (1(cid:0)ρ )m A u = β E ((1(cid:0)δ +R z )u ), ∂K E,t E K ME,t CE,t E t KE,t+1 K,t+1 KE,t+1 CE,t+1 E,t (B.21) ( ( )) q q (cid:0)λ (1(cid:0)ρ )m A E t+1 u = β E (q (1+R )u ). (B.22) t E,t E H ME,t t R CE,t E t t+1 V,t+1 CE,t+1 E,t+1 Additionally, these conditions can be combined with those of the production arm of the firm, 39

giving: αµY t = R K,t z KE,t K E,t−1 , (B.23) α(1(cid:0)µ)Y t = R M,t z KH,t K H,t−1 X t , (B.24) νY t = R V,t q t H E,t−1 , (B.25) (1(cid:0)α(cid:0)ν)(1(cid:0)σ)Y = W N (1+m A λ ), (B.26) t H,t H,t N ME,t E,t (1(cid:0)α(cid:0)ν)σY = W N (1+m A λ ), (B.27) t S,t S,t N ME,t E,t ∂δ KE,t R = . (B.28) K,t ∂z KE,t Equilibrium. Market clearing is implied by Walras’s law by aggregating all the budget constraints. For housing, we have the following market clearing condition H +H +H = 1. (B.29) H,t S,t E,t The model endogenous variables are Y, H , H , H , K , K , N , N , C , C , C , z , E H S E H H S B E H KH z , L , L , D, q, W , W , R , R , R , R , R , R , λ , λ , λ , together with the definition KE E S H S K M V E S H E S B of the depreciation rate functions and the adjustment cost functions given in the text above. Shocks. Thefollowingzero-mean,AR(1)shocksarepresentintheestimatedversionofthemodel: ε , ε , A , A , A , A , A , A . The shocks follow the processes given by: E H j K ME MH p z ε E,t = ρ be ε E,t−1 +υ E,t , υ E (cid:24) N(0,σ be ), ε H,t = ρ bh ε H,t−1 +υ H,t , υ H (cid:24) N(0,σ bh ), logA j,t = ρ j logA j,t−1 +υ j,t , υ j (cid:24) N(0,σ j ), logA K,t = ρ K logA K,t−1 +υ K,t , υ K (cid:24) N(0,σ k ), logA ME,t = ρ me logA ME,t−1 +υ ME,t , υ ME (cid:24) N(0,σ me ), logA MH,t = ρ mh logA MH,t−1 +υ MH,t , υ MH (cid:24) N(0,σ mh ) logA p,t = ρ p logA p,t−1 +υ p,t , υ p (cid:24) N(0,σ p ), logA Z,t = ρ z logA Z,t−1 +υ z,t , υ z (cid:24) N(0,σ z ). 40

Appendix C Estimation: Data Construction The model is estimated with U.S. quarterly data. I use the following time series as observables. Series mnemonics are from Haver Analytics. ConsumptionandInvestmentdataarefromNIPA.LoandataarefromtheFlowofFundsAccounts. Loan charge-offs data are from the Federal Reserve Board. 1. Consumption Model Variable: C . t Data: CH@USECON: Real Personal Consumption Expenditures (SAAR, Bil.Chn.2005$, Source: BEA). The series is log transformed, and detrended with a quadratic trend. 2. Investment Model Variable: I = KE;t −(1−δKE;t )KE;t(cid:0)1+KH;t −(1−δKH;t )KH;t(cid:0)1. t AK;t Data: FNH@USECON:RealPrivateNonresidentialFixedInvestment(SAAR,Bil.Chn.2005$, Source: BEA). The series is log transformed, and detrended with a quadratic trend. 3. Losses on Loans to Entrepreneurs Model Variable: ε . E,t Data: ε = DYRM (cid:2)OL14MOR5+DYI (cid:2)(OL14OTL5+OL14BLN5), Et where: DYRM@USECON: Loan Charge-Off Rate: Commercial Real Estate Loans: All Comml Banks (SAAR,%) (Source: H8 Release, Federal Reserve Board); OL14BLN5@FFUNDS:Nonfinancialbusiness;totalmortgages;liability(Source: TableL.101, Flow of Funds Accounts); DYI@USECON: Loan Charge-Off Rate: C&I Loans: All Insured Comml Banks (SAAR,%) (Source: H8 Release, Federal Reserve Board); OL14OTL5@FFUNDS: Nonfinancial business; other loans and advances; liability (Source: Table L.101, Flow of Funds Accounts); OL14BLN5@FFUNDS: Nonfinancial business; depository institution loans n.e.c.; liability (Source: Table L.101, Flow of Funds Accounts). The data series is constructed multiplying commercial bank charge-off rates by the volume of loans (C&I loans, mortgages and loans not elsewhere classified) held by nonfinancial businesses. Both in the model and in the data, charge-offs rates are scaled by steady–state GDP. In the data, liabilities are in dollars and steady-state GDP is measured by a cubic trend in the sum of nominal consumption and investment. Notes: When a bank loan is securitized and sold to another bank or GSE, it shows as a loan in the liability side of the nonfinancial business sector balance sheet, while it shows as a security in the asset side of the bank balance sheet. Charge-offs are measured in the data by looking at reported losses of banks on loans on the asset side of the balance sheet. By multiplying charge-off rates by the total amount of liabilities of the business sector in the form of loans, one is implicitly allocating losses to all loans and securities held by banks or institutions who purchased securities whose underlying asset are these loans (alternatively, 41

one is consolidating GSE, commercial banks and ABS issuers into one single, big, financial institution). More detail is provided in Appendix D. Charge-offs for commercial mortgages (DYRM) are available starting in 1991Q1, whereas charge-offs for C&I Loans (DYI) begin in 1985Q1. I use the regression coefficients of a regression of DYRM on a constant and DYI for the 1991-2010 period and data on DYI in order to backcast the missing data for DYRM for the 1986-1990 period. 4. Losses on Loans to Households Model Variable: ε . H,t Data: ε = DYRR(cid:2)XL15HOM5+DYU (cid:2)HCCSDODNS, Ht where DYRR@USECON: Loan Charge-Off Rate: Residential Real Estate Loans: All Comml Banks (SAAR,%); (Source: H8 Release, Federal Reserve Board); XL15HOM5@FFUNDS: Households and nonprofit organizations; home mortgages; liability (Source: Table L.100, Flow of Funds Accounts); DYU@USECON LoanCharge-OffRate: ConsumerLoans: AllInsuredCommlBanks(SA,%) (Source: H8 Release, Federal Reserve Board); HCCSDODNS@FFUNDS:Households andnonprofit organizations; consumer credit; liability (Source: Table L.100, Flow of Funds Accounts). Both in the model and in the data, charge-offs rates are scaled by steady–state GDP. In the data, liabilities are in dollars and steady-state GDP is measured by a cubic trend in the sum of nominal consumption and investment. Notes: Charge-offs for mortgages (DYRR) are available starting in 1991Q1, whereas chargeoffs for Consumer Loans (DQU) begin in 1985Q1. I use the regression coefficients of a regression of DYRR on a constant and DQU for the 1991-2010 period and data on DYI in order to backcast the missing data for DYRR for the 1986-1990 period. 5. Loans to Entrepreneurs Model Variable: L . E,t Data: L = OL14MOR5+OL14OTL5+OL14BLN5. The series is converted in real terms E,t using the GDP deflator, log transformed and detrended with a quadratic trend. 6. Loans to Households Model Variable: L . H,t Data: L = XL15HOM5+HCCSDODNS. The series is converted in real terms using H,t the GDP deflator, log transformed and detrended with a quadratic trend. 7. House Prices Model Variable: q . t Data: USHPI@USECON: FHFA House Price Index, United States (NSA). The series is converted in real terms using the GDP deflator, log transformed and detrended with a quadratic trend (Source: FHFA). 8. Technology (TFP) Model Variable: A . Z,t 42

Data: Utilization–adjustedquarterlygrowthrateofTFP(DTFP UTIL@SFFED)constructed by Fernald (2012). The series is integrated back to levels, log transformed, and detrended with a quadratic trend. Notes: Fernald corrects the Solow residual (a measure of TFP) by utilization (and other adjustments)toarriveatameasureofthegrowthrateoftechnology. Theutilization-adjusted quarterly series is an improvement over more “na¨ıve” measures of TFP as a high-frequency indicator of technological change”. As shown in the bottom right panel of Figure 2, it is hard to characterize the behavior of TFP during the financial crisis is simple terms: TFP is weak around the 2005-2008 period, rises in 2009 in the midst of the financial crisis, and drops again around 2010 (by contrast, TFP without the utilization adjustment does not rise in 2009, as utilization drops substantially at the peak of the financial crisis). 43

Appendix D Additional Notes on Charge-offs Charge-off rates are the flow of a bank’s net charge-offs (gross charge-offs minus recoveries) during a quarter divided by the average level of its loan outstanding over that quarter multiplied by 400 to express the ratio as an annual percentage rate. Charged-off loans are reported on schedule RI-B and the average levels of loans on schedule RC-K of a bank’s quarterly Consolidated Report of Condition and Income (generally referred to as the call report). Charge-off rates on loans are then computed dividing bank’s net charge-offs by average outstanding loans of banks. For the purpose of computing total losses of all financial intermediaries, I apply bank charge-off rates to the entire stock of mortgage debt held by households and businesses in the U.S. Note, in fact, that bank loans are only a fraction of total loan payables of households and businesses, since many loans are sold after origination to GSE and secondary market investors. For instance, as shown in Table L.217 of the Flow of Funds data, the total stock of mortgage debt (held by households and businesses) in the U.S. at the end of 2010 was $13.7 tn. Out of this amount, $4.2tn is held by banks (largely, U.S. chartered depository institutions) which file the call reports, whereas the rest is held by GSEs and Agency- and GSE-backed mortgage pools ($6.2tn), by ABS issuers ($2tn), and a smaller fraction by REITs, Finance Companies, Credit Unions. By allocating all losses to banks, I am effectively consolidating GSE, commercial banks and ABS issuers into one single, big, financial institution. Note also that GSEs may issue liabilities to finance issuance of ABS, and some of their liabilities are in turn owned by banks. How big were the charge-offs during the financial crisis? If one considers charge-offs at all insured commercial banks, net charge-offs were $150bn above baseline per year for about 3 years, for a total cumulative loss of around $450bn. Charge-offs of $176bn in 2009 against a loan volume of $6,647bn in the same year (broken down into $966bn of consumer loans, $2,099bn of residential real estate loans, and $1,344bn of commercial real estate loans) indicate a charge-off rate of 2.5 percent, and a ratio of charge-offs to GDP of around 1.5 percent. If one now takes the same chargeoff rate but applies it to all debt instruments of households and businesses in the United States, cumulative loan losses in dollars become much larger, since they now apply to a stock of household debt of $13,394 bn in 2009, and a stock of nonfinancial business debt of $6,416 bn. Hence the resulting losses are about $1.2tn. 44