Understanding Bank and Nonbank Credit Cycles: A Structural Exploration

Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. Understanding Bank and Nonbank Credit Cycles: A Structural Exploration C. Bora Durdu and Molin Zhong 2019-031 Please cite this paper as: Durdu, C. Bora, and Molin Zhong (2019). “Understanding Bank and Nonbank Credit Cycles: A Structural Exploration,” Finance and Economics Discussion Series 2019-031. Washington: Board of Governors of the Federal Reserve System, https://doi.org/10.17016/FEDS.2019.031. 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.

Understanding Bank and Nonbank Credit Cycles: A Structural Exploration∗ C. Bora Durdu Molin Zhong Federal Reserve Board Federal Reserve Board March 2019 Abstract We explore the structural drivers of bank and nonbank credit cycles using an estimated medium-scale macro model that allows for bank and nonbank financial intermediation. We posit economy-wide aggregate and sectoral disturbances to potentially drive bank and nonbank credit growth. We find that sectoral shocks affecting the balance sheets of entrepreneurs who borrow from the financial sector are important for the business cycle frequency fluctuations in bankandnonbankcreditgrowth. Economy-wideentrepreneurialriskshocksgainpredominance for explaining the longer-horizon comovement between the two series. JEL Classification: E3, E44, G01, G21 Keywords: banks, nonbanks, credit cycles, leverage, DSGE models, capital requirements 1 Introduction The U.S. financial intermediation system has experienced significant changes over the last three decades with the increasing role of nonbank sector activity. Indeed, since the late 1990s, nearly 60 percent of total credit extended to the nonfinancial business sector has been from nonbanks as ∗We would like to thank Elena Afanasyeva, Levent Altinoglu, Luca Guerrieri, Jose Lopez, Caterina Mendicino, Wayne Passmore, Pau Rabanal, Alex Vardoulakis, and seminar participants at the Federal Reserve Board, Federal ReserveResearchScrum2018,IAAE2018,NASMES2018,andSED2018forhelpfuldiscussionsandHoltDwyer,Alex Martin, and Skeet Singleton for excellent research assistance. All remaining errors are exclusively our responsibility. Correspondence: bora.durdu@frb.gov and molin.zhong@frb.gov, mailing address: 20th Street and Constitution Ave NW, Washington, DC 20551, phone numbers: 202-452-3755 (Bora Durdu) and 202-973-6126 (Molin Zhong). The views expressed in this paper are those of the authors and should not be attributed to the Board of Governors of the Federal Reserve System or its staff.

opposedtotraditionalbanksources. Thesedevelopmentsraisethequestionsofwhatisthenatureof disturbances driving the bank and nonbank credit cycles, and how do these disturbances propagate to the wider macroeconomy? We provide answers to these questions through the lens of an estimated dynamic equilibrium model that accounts for bank and nonbank lending to the nonfinancial business sector. Our model posits two main classes of structural shocks that could drive the credit cycles. First, we allow for the usual economy-wide disturbances such as technological progress, aggregate demand, or financial shocks that most of the extant literature on business cycles have considered (Smets and Wouters, 2007; Justiniano et al., 2010; Jermann and Quadrini, 2012; Christiano et al., 2014; Iacoviello, 2015). Second, on top of the economy-wide shocks, we also allow for sector-specific shocks, which only directly impact either bank or nonbank lending. These sectoral shocks–examples of those shocks includethedisturbancestocommercialbankingintheSavingsandLoanCrisis,thecollapseofshadow banking in the Great Recession, or changes in bank regulatory policy–could play an important role alongside aggregate shocks in understanding the macro-financial cycle.1 Our model builds off the previous contributions of Bernanke et al. (1999); Sandri and Valencia (2013); Clerc et al. (2015); Begenau and Landvoigt (2017). It allows for two types of financial intermediaries: banks and nonbanks. Both financial institutions intermediate credit between saving households and borrowing entrepreneurs. Following Begenau and Landvoigt (2017), deposits from both institutions produce partially substitutable liquidity services and there is competition for deposit funds. Both institutions combine deposits with inside equity accumulated through retained earnings to make loans to entrepreneurs. Banks and nonbanks have the option to default. The key difference is that upon default, banks have access to deposit insurance while nonbanks do not. Banks face capital requirements set by a regulator while nonbanks set leverage based on market forces. We estimate our model using sectoral and aggregate financial and macro data. To construct our bank and nonbank lending data, we follow Gallin (2013) and allocate all lending passing through the long intermediation chains in the U.S. financial sector to institutions that, broadly speaking, borrow from households and lend to the productive nonfinancial sector. We think of bank lending as encompassing all lending to the nonfinancial business sector from commercial banks, savings 1Onefeaturethatourmodeldoesnotinclude,however,isshiftsinregimethatmaychangestructuralparameters withinthemodelalongthelinesofBianchi(2013). Therefore,wedonotcapturepotentialswitchesinthestructureof theeconomythatmayimpactthepropagationofthestructuralshocks. Partofthereasonforthisiscomputational; since we are already estimating a rich structural model, it would be computationally challenging to feature regime shifts as well. 1

institutions, and credit unions. We think of nonbank lending as encompassing all other providers of nonfinancial business credit outside of banks, including money market mutual funds, mutual funds, pensionfunds, andinsurancecompanies. WethenuseBayesianmethodstomatchmacroaggregates and lending quantities and rates in the bank and nonbank sectors on quarterly U.S. data from 1987 – 2015. Wefindaquantitativelydominantroleforsectoralfinancialshocksindrivingbankandnonbank lending growth. Over 70 percent of bank and nonbank lending growth are driven by sectoral shocks. Especially important are shocks to the net worth position of the entrepreneurs who borrow from banks and nonbanks. A decline in the net worth of entrepreneurs in one sector impairs their ability to take on debt and purchase capital, which leads to further declines in net worth and the price of capital. These fire sale dynamics encourage entrepreneurs in the other sector to demand loans to take advantage of the low capital prices. We find this to be the main mechanism driving lending growth dynamics in the estimated model. Interestingly, the single most important structural shock driving lending growth in the banking sector are shocks to the net worth position of entrepreneurs borrowing from the nonbank sector, and vice versa. Through historical decompositions, we find entrepreneur net worth shocks to be important in understanding the deep decline in bank lending growth in the early 1990s and the dynamics of bank and nonbank lending entering into the Great Recession. Together, they account for around half of the declines in bank and nonbank lending growth during those two periods. All this is not to say, however, that aggregate shocks within the model are estimated to be unimportant for bank and nonbank lending growth. We find an important frequency dimension to our results on the importance of sectoral versus aggregate shocks. Specifically, at lower frequencies, economy-wide fluctuations in the variance of idiosyncratic risks entrepreneurs face (risk shocks) become important, especially in driving the low-frequency positive comovement between the bank and nonbank credit cycles. At business cycle frequencies, however, their effects are negligible. Historically, this entrepreneurial risk operating at low frequencies helps us understand the slow lending growth recoveries following the three credit growth downturns – the Savings and Loans Crisis, the early 2000s recession, and the Great Recession – found in the data. Additionally, entrepreneur risk shocks are the most important driver of investment growth dynamics among the financial shocks, accounting for around 30 percent of its movements, and play an important role for nonfinancial lending spreads and deposit rate movements. Our estimated model is consistent with several empirical facts on bank and nonbank lending 2

growth in the U.S. First, the model can generate that nonbank lending growth is less volatile than bank lending growth over the cycle. Second, despite the important role of sectoral shocks in driving lending growth dynamics, the model can replicate the positive correlation between bank and nonbank lending growth. Third, the model-generated data is also consistent with the low observed correlation between lending growth and investment growth. Moreover, our estimated model additionally generates historical series of nonbank leverage and financial sector credit supply shocks that are consistent with broker-dealer leverage (Adrian et al., 2014) and the excess bond premium (Gilchrist and Zakrajsek, 2012) data, respectively. Both of these data were not used in the estimation of the model, lending further external credence to the model estimates. Our work closely relates to the literature on macro models with a financial sector. Jermann and Quadrini (2012); Christiano et al. (2014); Ajello et al. (2018) estimate medium-scale macro models on macro and financial data. They all find important roles for financial shocks in driving businesscyclefluctuations. Differentlyfromourwork,thesepapersdonotmodelaseparatefinancial intermediationsector. Geralietal.(2010);SandriandValencia(2013);Iacoviello(2015);Clercetal. (2015); Ajello (2016); Hirakata et al. (2017); Afanasyeva and Guntner (2018) all formulate models with financial intermediaries, but they do not distinguish between bank and nonbank lending. To model our heterogeneous financial sector, we combine the banks featured in Clerc et al. (2015) with the financial intermediaries featured in Sandri and Valencia (2013). A burgeoning literature incorporates unregulated or shadow banking into macroeconomic models. Begenau and Landvoigt (2017) and Moreira and Savov (2017) are focused on modeling shadow banks that introduce financial fragility into the macroeconomy in the form of run risk or liquidity crunches, respectively. Gertler et al. (2016); Meeks et al. (2017); Nelson et al. (2017); Fève and Pierrard (2017) focus on the wholesale funding aspect of shadow banks. The shadow banks are either modeled as borrowing funds primarily from retail banks funded by the households as in Gertler et al. (2016), or as securitizers of bank loans that relax regulatory constraints on commercial banks as in Meeks et al. (2017); Nelson et al. (2017); Fève and Pierrard (2017). Mendicino et al. (2018) studiestheoptimaldynamiccapitalrequirementsinamodelthatallowsforbanklendinganddirect household financing of investment. While we share certain modeling elements with this work, none of them look at structurally understanding the drivers of bank and nonbank credit cycles. Other papers have also considered a dichotomy between bank versus bond finance, but without estimating the structural shocks driving bank versus nonbank credit cycles. Fiore and Uhlig (2011, 2015) present models that can endogenously generate a division between firms using market-based bond 3

finance versus bank finance. Firms trade off more information about their idiosyncratic shocks at a cost via bank finance with the more uncertain but costless market-based finance. Crouzet (2018) studies a model where firms have the option to substitute between bank and bond finance, thereby speaking to both the extensive and intensive margin of firm finance. Bank finance allows restructuring in times of stress at a higher cost during normal times. Finally, there have been more empirical studies measuring the bank and nonbank credit cycles Becker and Ivashina (2014); Herman et al. (2017); Kemp et al. (2018); FSB (2018). These papers takeanentirelyreduced-formapproachinmeasuringbankandnonbanklendingandininvestigating their financial and macro effects. They do not attempt to model these fluctuations. The rest of the paper is organized as follows. Section 2 describes how we measure the bank and nonbank credit cycles and key empirical facts that we find in the data. Section 3 describes the model environment in detail. Section 4 discusses our estimation strategy. Section 5 presents our main results decomposing bank and nonbank credit cycles with the estimated model. Section 6 presents two model external validation exercises. Finally, Section 7 summarizes our conclusions. 2 Empirical Facts on the Bank and Nonbank Credit Cycle We begin by documenting the empirical regularities on the bank and nonbank credit cycle in the U.S. from 1987Q2 to 2015Q1. We focus on lending to the nonfinancial business sector and from domestic private financial entities to be consistent with our modeling approach. 2.1 Defining bank and nonbank lending We define bank lending as all loans from commercial banks, savings institutions, and credit unions. We take a broad approach in thinking about nonbank lending. Our definition includes all lending to the nonfinancial business sector outside of the traditional banking sector, government, and foreign entities. This is comprised of a mix of financial institutions such as mutual funds, pension funds, insurance companies, and money market mutual funds. Before moving on, it is important to emphasize that in measuring the nonbank credit cycle, we consider a larger class of financial intermediaries than what several authors have referred to as shadowbanks(Pozsaretal.,2010;Gallin,2013). Forexample,Gallin(2013)iscarefultodistinguish between shadow bank and nonbank lending, of which the former is defined as institutions relying on short-term funding and have "inherent susceptibility to runs." Our definition of nonbank lending 4

is closer to the "Monitoring Universe of Non-bank Financial Intermediation" as defined in the FSB (2018), which contains all nonbank financial intermediation. This broad definition is also in line with recent papers measuring the nonbank credit cycle, such as Kemp et al. (2018). 2.2 Measurement issues We use the Federal Reserve Board’s Z.1 statistical release to construct our measures of bank and nonbank lending. Our goal is to decompose a measure of total nonfinancial business sector lending into that done by banks and nonbanks. Pozsar et al. (2010) and Gallin (2013) emphasize the difficultyofthisexercise,astherearecomplexintermediarychainswithinfinancialsectorinstitutions that may lead to a drastic overstatement of the size of nonbank lending. To overcome this issue, we follow a procedure outlined in Gallin (2013) for netting out the financial intermediary chains. Gallin (2013) decomposes the credit from nonfinancial sector lenders to nonfinancial sector borrowers as flowing through five categories of financial intermediaries: traditional banks (commercial banks, savings institutions, and credit unions), government (federal government and the monetary authority), foreign entities, long-term funders (mutual funds, pension funds, insurance companies), and short-term funders (money market mutual funds). He calls these financial intermediaries "terminal funders." Broadly speaking, these terminal funders borrow from the nonfinancial sector and fund both other financial intermediaries and nonfinancial sector borrowers. There are also intermediate funders, such as private-label issuers of asset-backed securities, funding corporations, and real estate investment trusts, which are entities along the intermediation chain.2 The objective of Gallin (2013) is to trace each unit of debt provided to nonfinancial sector borrowers through the intermediation chains in the financial system back to one of these terminal funders. The paper does so by assigning all nonfinancial sector debt listed in the Z.1 tables as held by the intermediate funders to terminal funders proportionately to the holders of the intermediate funders’ liabilities. For the purposes of our paper, this measure is appropriate as it resolves any double counting in the amount of credit provided by the financial system to the nonfinancial sector from grossing up the aggregate debt holdings of different financial intermediary entities. We define banks as the traditional banks in Gallin (2013). Nonbanks are the sum of long-term funders and short-term funders. An important additional distinction to make is that while Gallin (2013)isinterestedintotalnonfinancialsectorlending,wearefocusedonlendingtothenonfinancial 2A full list of the definitions for each category can be found in Table 4.1 of Gallin (2013). 5

Figure 1: Growth Rates of Bank and Nonbank Lending 4 Bank 3 Nonbank 2 1 tn e c 0 r e P -1 -2 -3 -4 1990 1995 2000 2005 2010 2015 Date NOTE:Thisfigureshowspercapitabankandnonbanklendinggrowth. Thedataareconstructedusingthemethodologyof Gallin(2013)andcovertheperiodfrom1987Q2to2015Q1. business sector.3 2.3 Empirical facts Figure 1 shows the bank (blue) and nonbank (red) lending growth dynamics in the U.S. Both bank and nonbank lending growth tend to comove over the credit cycle. Since the late-1980s, they have gone through three distinct swings. In the early- to mid-1990s, bank lending growth persistently declined following the Savings and Loan Crisis. This decline was steeper and much longer lasting than the corresponding slowdown in nonbank lending growth. A second milder credit crunchoccurredfollowingtheearly-2000srecession. Thisdeclineinlendingincontrast,ledtoamore sluggish nonbank lending growth recovery. Finally, the Great Recession produced sharp declines and sluggish recovery in both bank and nonbank lending growth to the nonfinancial business sector, although again the depths of the decline in bank lending growth was more severe. Table 1 shows several statistics that highlight the empirical regularities that we would like to investigatewithourstructuralmodel. Weareinterestedinthreefactsofthebankandnonbankcredit cycles. First, nonbank lending growth is less volatile than bank lending growth. In the data, the standard deviation of bank lending growth fluctuations is 1.59, while it is 1.12 for nonbank lending 3Further details about our implementation of the procedure can be found in the appendix. 6

Table 1: Key summary statistics on bank and nonbank lending growth Statistic Data Std bank gr 1.59 Std nonbank gr 1.12 Corr bank and nonbank gr 0.48 Corr bank and inv gr 0.16 Corr nonbank and inv gr 0.17 NOTE:Thistableshowsthestandarddeviationsandcorrelationsstatisticsforaselectedsetofvariables. Thedatarunfrom 1987Q2to2015Q1. growth. Second, bank and nonbank lending growth are positively correlated, with a correlation of nearly 0.5. Finally, both bank and nonbank lending growth are at best weakly positively correlated with real activity, which we measure in this case with investment growth.4 2.4 Discussion Our empirical facts largely align with the literature. Kemp et al. (2018) measure the bank and nonbankcreditextendedtotheentirenonfinancialsectorformanydevelopedandemergingmarkets. Their results on the coherence and relative magnitudes of the bank and nonbank credit cycles differ across countries, but they do find that for the U.S., bank and nonbank credit growth are positively correlated with bank lending growth more volatile than nonbank lending growth. Becker and Ivashina (2014) look at bank and bond credit growth in the U.S., finding that bank debt is more volatile than bond debt. At face value, the second empirical fact – that bank and nonbank credit growth is strongly positively correlated – points to the importance of an economy-wide factor in driving fluctuations. As emphasized in Foerster et al. (2011), however, inter-sectoral linkages may propagate sectoral shocks to the wider system as a whole, potentially allowing them to also explain positive sectoral comovement. This issue necessitates the development of a structural model through which to filter the data, to which we turn next. 3 Model Environment Our goal is to structurally decompose fluctuations in bank and nonbank lending growth. To this end, we employ a medium-scale model that allows for bank and nonbank lending and can be taken 4Aswearefocusingoncreditextensiontothenonfinancialbusinesssector,wefinditmostusefultouseinvestment growthasourrealindicator. Ourexactdefinitionofinvestmentgrowthandtheothervariablesweuseinestimating the model can be found in Section 4. 7

to the data. The model builds off of the previous contributions of Bernanke et al. (1999); Sandri and Valencia (2013); Clerc et al. (2015); Begenau and Landvoigt (2017). At the heart of our model is a friction driven by asymmetric information that prevents the direct flow of funds from the saving householdstotheborrowingentrepreneurs. Financialintermediarieshavethetechnologytomonitor the entrepreneurs at a cost, and they take deposits from households and lend to entrepreneurs. Importantly, our model specifies financial frictions that operate on both the productive nonfinancial sector and the financial sector. This feature implies that the net worth positions of the financial intermediaries and the nonfinancial sector both matter, allowing our paper to speak to the literature on the relative importance of nonfinancial versus financial sector net worth (Sandri and Valencia, 2013; Clerc et al., 2015; Hirakata et al., 2017). In contrast to those papers, in our model, there are two types of intermediaries: banks whose deposits are insured and face capital requirements and nonbanks whose deposits are risky and have leverage ratios governed by market discipline. Our modeling of banks largely draws from Clerc et al. (2015) whereas our modeling of nonbanks follows from Sandri and Valencia (2013). We allow for a rich set of interactions between banks and nonbanks that can propagate sectoral shocks to the wider economy. First, on the funding side, banks and nonbanks compete for deposits fromhouseholdsandinsideequityfrominvestoragents. Second, theentrepreneurswhoborrowfrom banksandnonbankscompeteincommoncapitalgoodsandfinalgoodsmarkets. Therefore,financial conditions of banks and nonbanks are important in the determination of the overall equilibrium. Our model is populated by households, entrepreneurs, investors, two types of credit intermediaries, and final goods and capital goods producers. We first give a brief summary of the economy. Then, we provide further details about the characteristics of the agents. 3.1 Structure of the economy In our economy, households are the main saving agents. They have an option to save in riskless bank deposits or risky nonbank deposits. We assume that households derive utility from both types of deposits, motivated by the benefits from liquidity services. Banks and nonbanks are two-period lived agents funded by deposits and inside equity capital provided by investor agents. Banks and nonbanks lend out funds to entrepreneurs, who then combine these funds with inside net worth to purchase capital to rent to final goods producers. We assume that a certain class of entrepreneurs borrow from banks exclusively and another class borrow from nonbanks exclusively. 8

There are aggregate and idiosyncratic shocks that hit the economy. The aggregate shocks can be economy-wide or sectoral in nature. The idiosyncratic shocks impact the capital returns of entrepreneurs and the portfolio returns of the financial intermediaries and generate an asymmetric information problem between the borrowers and lenders. Upon realization of the aggregate and idiosyncratic shocks, payoffs from the borrowers to lenders occur. We allow for limited liability and strategic default of entrepreneurs and intermediaries. 3.2 Agents in the economy Households. Households are risk-averse, infinitely-lived agents, who derive utility from consumption and liquidity services and disutility from working. They can save in deposits in banks and nonbanks. Households maximize ∞ (cid:20) (cid:21) max E (cid:88) βt+iβ˜ log(c −hc )− χ l1+ψ +χ log(h ) ct,lt,dB t ,dN t t i=0 t+i t+i t+i−1 1+ψ t+i h t+i (1) s.t. c +dB +dN ≤ w l +RD dB +R˜D,NdN −T +Π t t t t t t−1 t−1 t t−1 t t h = (cid:104) Λ (cid:0) dN(cid:1)α h + (cid:0) dB(cid:1)α h (cid:105)1/α h t N,t t t where c denotes consumption, l denotes labor supply, and h denotes the liquidity services derived t t t from credit intermediary deposits. The deposits can take two forms: dB and dN, representing t t deposits in banks and nonbanks, respectively, with corresponding returns RD and R˜D,N. Due to t−1 t the presence of deposit insurance, the return from holding deposits in banks is risk-free from the perspective of the households and RD is predetermined, whereas the return from holding deposits t−1 in nonbanks are risky and therefore R˜D,N may be affected by contemporaneous shocks. T denotes t t lump-sum taxes paid to the government, Π denotes profits from the capital good producers, which t are owned by households, and dividend transfers from the investors and entrepreneurs who borrow from banks and nonbanks. Theliquidityservicesh isaCESfunctionofdepositsatthebanksandnonbanks. Theparameter t ψ is the inverse of the Frisch elasticity of labor supply. The parameters χ and χ are respective h utility parameters for labor and liquidity services. The parameter α denotes the elasticity of h substitution between banks and nonbanks deposits.5 5Wehavealsotriedspecificationsoftheliquidityaggregatorthatallowtheamountofliquidityserviceprovidedby nonbankdepositstobeafunctionoftheamountofnonbankdefault. Estimatessettheelasticityofthatrelationship 9

There are two shocks: β˜ are preference shocks, and Λ are nonbank liquidity demand shocks. t N,t Positive nonbank liquidity demand shocks increase the liquidity service provided by nonbank deposits while decreasing the liquidity service provided by bank deposits. Entrepreneurs. There are two classes of entrepreneurs, which we call B-sector and N-sector entrepreneurs. Each class of entrepreneurs belongs to a sequence of overlapping generations of twoperiod-livedrisk-neutralagentswhoownandmaintainthecapitalstockforeachsector. Withineach generation of entrepreneur, there is an ex-ante identical continuum of agents. We specify that the B-sector entrepreneurs only borrow from banks and that the N-sector entrepreneurs only borrow from nonbanks. Within each class of entrepreneurs, the modeling of their problem closely follows Clerc et al. (2015), which, in turn, follows Bernanke et al. (1999) and Townsend (1979). Each generation of entrepreneurs inherits net worth in the form of bequests, ne,i, where i ≡ B,N. They purchase t capital from capital goods producers in a common market and then rent it to the producers of the consumption good in each of the B and N-sectors frictionlessly. Entrepreneurs finance the capital holdings with their initial net worth and loans bi for each of the B and N sectors. In line with t previous work such as Clerc et al. (2015); Sandri and Valencia (2013); Bernanke et al. (1999), we assumethatentrepreneurshaveallthebargainingpowerinthecontractualrelationship. Inaddition to aggregate shocks, each entrepreneur is also hit by private idiosyncratic productivity shocks that the intermediary cannot observe in the second period and faces a default decision. As discussed in Clercetal.(2015), theidiosyncraticshocksareasimplewaytogenerateanasymmetricinformation problem between lenders and borrowers in the model, rationalize the existence of differences in the entrepreneurs’ performance, and generate a nontrivial default decision on entrepreneurial loans. Upon default, the lending intermediary monitors the entrepreneur at a cost. An entrepreneur in each sector born in time t therefore has a sequence of decisions over the two dates. At time t, she is endowed the previous generation’s bequests and takes out loans to purchase capital to maximize expected time t+1 wealth. After aggregate and idiosyncratic shocks realize, each entrepreneur has a default decision with limited liability. If the entrepreneur defaults, her time t+1 wealth level is 0 with no additional penalty. Finally, conditional on a time t+1 wealth level, each entrepreneur must allocate the resources into dividends to households and bequests to the future generation of entrepreneurs. It is convenient to work backwards to solve the entrepreneur’s problem. Given a wealth level to 0, so we did not pursue that extension further. 10

We,i , the time t + 1 optimization problem for an entrepreneur born in period t in each of the t+1 i ∈ {B,N} sector is given by (cid:16) (cid:17)χe,i (cid:16) (cid:17)1−χe,i max ce,i t+1 ne,i t+1 t+1 t+1 ce t+ ,i 1 ,ne t+ ,i 1 (2) s.t. ce,i +ne,i ≤ We,i . t+1 t+1 t+1 Optimizing behavior yields the following dividend payment and earnings retention rules ce,i = χe,i We,i , t+1 t+1 t+1 (3) ne,i = (1−χe,i )We,i , t+1 t+1 t+1 χe,i are entrepreneur dividend policy shocks. They change the fraction of overall wealth alt+1 located as dividends to households (ce,i ) versus bequeathed to the following generation of ent+1 trepreneurs. Positive entrepreneur dividend policy shocks therefore reduce the net worth passed on to the future generation. These shocks can account for the unmodeled investor equity flows into and out of the nonfinancial sector. Taking one step back, we look at the default decision of the entrepreneur. Conditional upon the realization of aggregate variables and idiosyncratic shocks, as well as the previously-made time t decisions on the amount of capital to purchase, amount of borrowing, and contractual borrowing rate, the entrepreneur faces the following default decision: (cid:104) (cid:16) (cid:17) (cid:105) We,i = max ωe,i rk,i +(1−δ)qK ki−Ribi,0 (4) t+1 t+1 t+1 t+1 t t t where qK is the price of capital, ki is the capital stock held by the entrepreneur, bi is the amount t t t borrowed from the corresponding type of financial intermediary, rk,i is the rental rate of capital, t and Ri is the contractual gross interest rate of loans. The term ωe,i denotes the idiosyncratic shocks t t to the entrepreneur’s efficiency units of capital. If the entrepreneur’s revenues from holding capital are exceeded by the promised payment to the financial intermediary, she defaults and ends up with a wealth of 0. The time t decision problem of the entrepreneur can be written as 11

(cid:16) (cid:17) max E We,i t t+1 ki,bi,Ri t t t s.t. qKki−bi = ne,i (5) t t t t Bank or nonbank participation constraint. The entrepreneur chooses the amount of capital to purchase ki, amount of loans to take on bi, t t and contractual interest rate on the loans Ri to maximize expected wealth subject to the budget t constraint and incentive compatibility of the intermediary from which the entrepreneur borrows. Thestructureofthisoptimizationproblemcomesfromtheassumptionthattheentrepreneurhasall of the bargaining power in the contractual relationship. The intermediary participation constraint will be specified below. To compute the expected value of wealth We,i , we must specify the distribution of the idiosynt+1 cratic shocks. These shocks are independently and identically distributed across entrepreneurs and follow a log-normal distribution with an expected value of one and density and cumulative distribution function denoted fe,i(·) and Fe,i(·), respectively. Following Christiano et al. (2014), we allow for risk shocks σe,i that impact the cross-sectional volatility of the idiosyncratic shocks. t The entrepreneurs face limited liability if they default on their loans. In case of default, the intermediary can only recover a fraction, 1−µe,i of the gross return of capital, where µe,i denotes verification costs. Defining the gross return per efficiency unit of capital as rK,i +(1−δ)qK RK,i = t+1 t+1, t+1 qK t the cutoff threshold above which the entrepreneur repays the loan equals Ribi ωe,i = t t . (6) t+1 RK qKki t+1 t t As in Bernanke et al. (1999) and Clerc et al. (2015), we can define the expected gross fraction (not including intermediary monitoring costs on defaulted loans) of entrepreneurial returns from capital going to intermediaries as: Γe,i (cid:16) ω¯e,i (cid:17) = (cid:90) ω¯ t e + ,i 1 ωe,i fe,i (cid:16) ωe,i (cid:17) dωe,i +ω¯e,i (cid:90) ∞ fe,i (cid:16) ωe,i (cid:17) dωe,i . (7) t+1 t+1 t+1 t+1 t+1 t+1 t+1 0 ω¯e,i t+1 12

Intuitively, this term depends on the expected values of the idiosyncratic shock, taking into account the entrepreneur’s default decision. The first term in this expression is the component of theexpectedvalueconditionalonentrepreneurialdefaultwhereasthesecondterminthisexpression is the component of the expected value conditional on entrepreneurial repayment. We call the share of gross return for each intermediary that comes from defaulted loans as: Ge,i (cid:16) ω¯e,i (cid:17) = (cid:90) ω¯ t e + ,i 1 ωe,i fe,i (cid:16) ωe,i (cid:17) dωe,i . (8) t+1 t+1 t+1 t+1 0 (cid:16) (cid:17) The net share of the total gross returns that each bank appropriates then becomes Γe,i ω¯e,i − t+1 (cid:16) (cid:17) µe,iGe,i ωe,i . t+1 With these definitions, we can reformulate the entrepreneurs’ optimization problem as follows: (cid:34)(cid:32) (cid:32) (cid:33)(cid:33) (cid:35) xe,i(·) max E 1−Γe,i t RK,iqKki ki,bi,Ri t RK,i t+1 t t t t t t+1 s.t. qKki−bi = ne,i (9) t t t t (cid:34) (cid:32) (cid:32) (cid:33) (cid:32) (cid:33)(cid:33) (cid:35) E (cid:0) 1−Γi(cid:0) ωi (cid:1)(cid:1) Γe,i xe t ,i(.) −µe,iGe,i xe t ,i(.) RK,iqKki ≥ ρ φibi, t t+1 RK,i RK,i t+1 t t t t t t+1 t+1 where xe,i(·) = R t ibi t. The intermediary participation constraint contains an additional term 1− t qKki t t Γi(cid:0) ωi (cid:1) that represents the expected fraction of total intermediary loan returns going to the int+1 side equity investors. This value depends on a yet to be specified term ωi , which is the threshold t+1 between default and repayment for the idiosyncratic shock that hits the intermediary. The entrepreneur takes this value as given. The intermediary participation constraint says that the total expected return to intermediary inside equity investment must be greater than or equal to a required return to equity ρ that the t entrepreneur takes as given. There is no superscript on ρ due to the presence of a no-arbitrage t condition that equalizes expected returns across the two sectors. The term φi is the equity-tot assets ratio of the intermediary, so φibi is the total inside equity position of the investors in the t t intermediary. Finally, before we move on, we define R˜i , which is the time t+1 realized return of loans from t+1 the intermediary of type i. 13

(cid:18) (cid:18) (cid:19) (cid:18) (cid:19)(cid:19) Γe,i xe t ,i(.) −µe,iGe,i xe t ,i(.) RK,iqKki RK,i RK,i t+1 t t R˜i = t+1 t+1 (10) t+1 bi t Investors. There are an ex-ante identical continuum of investors belonging to a sequence of overlapping generations of risk-neutral, two-period-lived agents. Investors are the only agents who can invest net worth as bank and nonbank equity capital. Each generation of investors inherits net worth, nb in the form of bequests, and has the utility function (cid:0) cb (cid:1)χb t+1 (cid:0) nb (cid:1)1−χb t+1. This form t t+1 t+1 of the utility function implies that at time t+1, conditional on a level of investor wealth, the agents allocate a fraction χb of total wealth to household dividends (cb ) and the rest as bequests to t+1 t+1 the next period of investors. Asinvestorsonlyallocatefundsbetweeninsideequityofbankandnonbankcreditintermediaries, they equalize the expected returns of investing in both sectors. ρ = E ρ˜B = E ρ˜N (11) t t t+1 t t+1 Hence, investors’ net worth evolves according to the following law of motion (cid:16) (cid:17) nb = 1−χb (cid:0) ρ˜B eB +ρ˜N eN(cid:1) , (12) t+1 t+1 t+1 t t+1 t whereρ˜B denotesex-postgrossreturnonbankequity,andρ˜N denotesex-postreturnonnonbank t+1 t+1 equity. There are investor dividend policy shocks χb . These shocks shift around the fraction of t+1 wealth allocated to consumption versus bequests, similar to the redistribution shocks considered in Iacoviello (2015). The shocks can be interpreted as capturing unmodeled investor inside equity flows or unmodeled housing loan losses from default (as in Iacoviello (2015)). Intermediaries. There are an ex-ante identical continuum of two types of intermediaries: banks (B) and nonbanks (N). The B intermediaries lend to a well-diversified portfolio of B entrepreneurs and N intermediaries lend to a well-diversified portfolio of N entrepreneurs. Both banks and nonbanks are two-period lived projects financed by inside equity provided by the investors as well as deposits from the households. The shareholders of the intermediaries - the investor agents have limited liability, hence the payoffs from investing into intermediaries are nonnegative. Both banks and nonbanks receive idiosyncratic private portfolio return shocks, creating an asymmetric 14

information problem between intermediaries and households. There are two key differences between the banks and nonbanks. First, banks have deposit insurance whereas nonbanks do not. Second, banks face capital requirements whereas nonbanks do not. The monitors of the banks are the deposit insurance fund whereas the monitors of the nonbanks are the households. Wefirstdiscusstheproblemofthebanksandthenmoveontothenonbanks. Fortheproblemof banks,webeginwiththet+1decisionproblemaftertherealizationoftheaggregateandidiosyncratic shocks, the time t lending and borrowing levels, and the previously agreed upon contractual deposit rate. Conditional on those variables, the banks have the following default decision: (cid:104) (cid:105) πB = max ωB R˜B bB −RDdB,0 (13) t+1 t+1 t+1 t t t where R˜B is the aggregate return on B entrepreneurial loans, bB is the quantity of entrepreneurial t+1 t loans held by the banks, RD is the contractual deposit rate, dB is the amount of bank deposits, t t and ωB is the idiosyncratic portfolio return shock. In the event of a default, the deposit insurance t+1 fund monitors the banks. Now we move on to the timet decision. Because of deposit insurance, the deposit rate the banks face is not sensitive to their leverage positions, which is defined as eB φB = t (14) t bB t Therefore, the banks always find it optimal to lever up to the maximum allowed by the capital requirements, which is set on φB. The capital requirement directly determines the leverage position t of the banks. They take the amount of equity invested, eB, by the investor agents as given. t The nonbanks face the same default decision as the banks at time t+1: (cid:104) (cid:105) πN = max ωN R˜N bN −RD,NdN,0 (15) t+1 t+1 t+1 t t t where the definitions of the variables are the same, except now with a N instead of B superscript to denote that the N intermediaries take nonbank deposits from households and lend to N-sector entrepreneurs. RD,N is the contractual deposit rate agreed at time t (specified below), which t distinguishes it from the realized deposit rate R˜D,N that the household receives taking into account t+1 15

nonbank default. The time t decision problem of the nonbanks is more involved. Although the government does not impose a capital requirement, a leverage constraint arises endogenously from a contractual problem between the households and the nonbanks. We assume that the nonbanks have all of the bargaining power in setting the contract with the household. (cid:34)(cid:32) (cid:32) (cid:33)(cid:33) (cid:35) xN max E 1−ΓN t R˜N bN xN,bN t R˜N t+1 t t t t+1 s.t. Λ (cid:0) dN(cid:1)α h −1 (16) λ −β˜χ N,t t = ... t t h Λ (cid:0) dN (cid:1)α h + (cid:0) dB (cid:1)α h N,t t t (cid:34) (cid:32)(cid:32) (cid:32) (cid:33) (cid:32) (cid:33)(cid:33) (cid:33)(cid:35) xN xN bN βE β˜ λ ΓN t −µNGN t R˜N t t t+1 t+1 R˜N R˜N t+1bN −eN t+1 t+1 t t where xN = R t D,N(bN t −eN t ) . Here we have already substituted out the balance sheet constraint of the t bN t intermediaries bN = eN +dN. t t t Given an amount of inside equity eN, the N intermediaries choose the amount of lending bN t t and leverage position xN (implicitly the contractual deposit rate RD,N) to maximize the expected t t returns to the inside equity holders, making sure to satisfy the incentive compatibility constraint of the household. The incentive compatibility constraint comes from the first order condition of the household with respect to the nonbank deposits. It says that the discounted expected return the nonbanks offer the household on their deposits must at least make up for the foregone cost of consumption today. Relative to a standard Euler equation, there is an extra term on the left hand side of the equality that accounts for the fact that households have direct utility services from holding deposits, which the intermediaries take into account. The time t return to households from depositing in the N-type intermediaries is the following: R˜D,NdN = (cid:0) ΓN (cid:0) ωN(cid:1) −µNGN(ωN) (cid:1) R˜NbN (17) t t−1 t t t t−1 whereωN istheidiosyncraticshockdefaultthresholdforthenonbanks. Wecanrewritethisreturnin t termsofnonbankdeposits,dN . UsingthebalancesheetconstraintbN = eN+dN andthedefinition t−1 t t t for nonbank leverage eN = φNbN, where φN is determined by the contract and households take it t t t t 16

as given, bN is nonbank intermediary lending, eN is nonbank intermediary equity, we can derive t t dN bN = t t 1−φN t R˜D,N = (cid:0) ΓN (cid:0) ωN(cid:1) −µNGN(ωN) (cid:1) R˜ t N t t t t 1−φN t−1 Capital good production. Thecapitalgoodproducerspurchaseallundepreciatedcapitalfrom the old generation of entrepreneurs and combine it with the new capital from investment to sell to the new generation of B and N entrepreneurs in a common market. Therefore, they solve the following maximization problem ∞ (cid:26) (cid:20) (cid:18) (cid:19)(cid:21) (cid:27) maxE (cid:88) βiβ˜ λ t+i qK I −EK 1+g I t+i I . (18) It+i t t+i λ t t+i t+i t I t+i−1 t+i i=0 The optimality condition would yield (cid:34) (cid:35) (cid:18) I (cid:19) λ (cid:18) I (cid:19)2 β˜qK = β˜EK 1+g + t g(cid:48) −E β˜ t+1 t+1 EK g(cid:48) (19) t t t t t I t t t+1 λ I t+1 t+1 t−1 t t (cid:16) (cid:17) where g = g It . t It−1 EK denotes marginal efficiency of investment (MEI) shocks, as in Justiniano et al. (2010). t Positive MEI shocks increase the price of capital by making it more expensive to produce. Final goods production. The homogeneous final good is produced by both the B and N sectors, indexed by the type of entrepreneur from which they rent capital. Each sector i has its respective following production function yi = (cid:0) ki (cid:1)αi(cid:0) A li(cid:1)1−αi (20) t t−1 t t A is a TFP shock, which is common across sectors and drives long-run growth in the model. t The optimality conditions for each sector implies the following rental rate and the wage rate yi rK,i = αi t , t ki t−1 (21) yi wi = (1−αi) t. t li t 17

Market clearing conditions. The following market clearing conditions must be satisfied in equilibrium. The consumption good market clearing implies (cid:20) (cid:18) (cid:19)(cid:21) I (cid:16) (cid:17) (cid:16) (cid:17) y =c + 1+g t I +µe,BGe,B ωe,B RK,BqK kR +µe,NGe,N ωe,N RK,NqK kN + t t I t t t t−1 t−1 t t t−1 t−1 t−1 µBGB(cid:0) ωB(cid:1) R˜BbB +µNGN (cid:0) ωN(cid:1) R˜NbN . t t t−1 t t t−1 (22) The consumption good market clearing implies that total output must equal total consumption, total investment taking into account adjustment costs, and monitoring costs from the defaulting entrepreneurs and intermediaries in both the B and N sectors. Labor market clearing implies yB (1−αB) t = lB, wB t t yN (1−αN) t = lN. (23) wN t t lB +lN = l t t t Capital market clearing implies yB αB t = kB rB t t yN αN t = kN rN t (24) t kB +kN = k t t t k = (1−δ)k +I , t t−1 t Market clearing in the bank and nonbank deposit markets implies the following conditions dB = (1−φB)bN, t t t (25) dN = bN −eN. t t t 18

Market clearing in the entrepreneurial loan markets implies qKkB −bB = ne,B, t t t t (26) qKkN −bN = ne,N. t t t t The intermediary equity market clearing condition implies (cid:16) (cid:17) 1−χb Wb = φBbB +bN −dN (27) t t t t t t Finally, the deposit insurance agency needs to have a balanced budget, hence the taxes collected from households need to be equal to the insurance provided to the regulated intermediary deposits, e.g., T = (cid:2) ωB −ΓB(cid:0) ωB(cid:1) +µBGB(cid:0) ωB(cid:1)(cid:3) R˜BbB . (28) t t t t t t t−1 Capital Requirements. In addition to the market clearing conditions highlighted so far, a capital requirement also needs to be satisfied by banks. We consider the following capital requirement: φB = φ B +η (29) t 0 φ,t where η is the capital requirements shock, meant to capture bank regulatory capital changes. φt 3.3 Shocks We specify several candidate drivers of the bank and nonbank credit cycles. These shocks can be divided along two interesting dimensions. The first dividing line is between macro and financial shocks. The second is between economy-wide and sectoral shocks. Let us begin with the economy-wide macro shocks in the model. We specify aggregate TFP shocks that affect both sectors.6 The TFP shocks are an AR(1) in growth rates. ∆logA = Λ (1−ρ )+ρ ∆logA +(cid:15) ,(cid:15) ∼ N(0,σ2) (30) t A A A t−1 A,t A,t A MEI shocks are specified as AR(1):7 6In our explorations, we also tried specifications with sectoral TFP level shocks. They ended up being estimated as unimportant. 7The 1−ρ term ensures that the shocks are centered around a mean of 1. EK 19

EK = (1−ρ )+ρ EK +(cid:15) ,(cid:15) ∼ N(0,σ2 ) (31) t EK EK t−1 EK,t EK,t EK Preference shocks are also specified as AR(1): β˜ = (1−ρ )+ρ β˜ +(cid:15) ,(cid:15) ∼ N(0,σ2) (32) t β β t−1 β,t β,t β Financial shocks in the model can be economy-wide or sectoral. The economy-wide shocks are the economy-wide components of the entrepreneur risk and dividend policy shocks and the investor dividend policy shocks. The sectoral shocks are the nonbank liquidity demand shocks, the sectoral componentsoftheentrepreneurriskanddividendpolicyshocks,andthecapitalrequirementsshocks. The nonbank liquidity demand shocks are specified as AR(1): Λ˜ = (1−ρ )+ρ Λ˜ +(cid:15) ,(cid:15) ∼ N(0,σ2 ) U,t Λ,U Λ,U U,t−1 Λ,U,t Λ,U,t Λ,U,t (33) Λ = Λ Λ˜ U,t U U,t We decompose entrepreneur risk shocks and entrepreneur dividend policy shocks into an aggregate and sectoral component. Our specification for the entrepreneur risk shocks is as follows: σe,i = σe,iσe,Aggσe,i t t t σe,Agg = (1−ρ )+ρ σe,Agg +(cid:15) ,(cid:15) ∼ N(0,σ2 ) (34) t σ,e,Agg σ,e,Agg t−1 σ,e,Agg,t σ,e,Agg,t σ,e,Agg σe,i = (1−ρ )+ρ σe,i +(cid:15) ,(cid:15) ∼ N(0,σ2 ) t σ,e,i σ,e,i t−1 σ,e,i,t σ,e,i,t σ,e,i Our entrepreneur dividend policy shocks are specified as follows: χe,i = χe,i+χe,Agg +χe,i t t t χe,Agg = ρ χe,Agg +(cid:15) ,(cid:15) ∼ N(0,σ2 ) (35) t χ,e,Agg t−1 χ,e,Agg,t χ,e,Agg,t χ,e,Agg χe,i = ρ χe,i +(cid:15) ,(cid:15) ∼ N(0,σ2 ) t χ,e,i t−1 χ,e,i,t χ,e,i,t χ,e,i The investor dividend policy shocks are specified as AR(1): 20

χb = χb+χ˜b t t (36) χ˜b = ρ χ˜b +(cid:15) ,(cid:15) ∼ N(0,σ2 ) t χ,b t−1 χ,b,t χ,b,t χ,b Finally, the capital requirements policy shocks are also AR(1): η = ρ η +(cid:15) ,(cid:15) ∼ N (cid:0) 0,σ2(cid:1) (37) φ,t η φ,t−1 η,t η,t η 4 Empirical Strategy To measure the importance of the structural shocks for the bank and nonbank credit cycles, we estimate our model using Bayesian methods. In this section, we discuss the additional data we use to inform the model and our estimation strategy. 4.1 Data We use the following data to inform our empirical analysis: per capita consumption and investment growth, commercialbankandmoneymarketmutualfunddepositrates, BAA-10yearspreads, bank equity-to-lending ratio, and per capita bank and nonbank debt growth. With the exception of the bank equity-to-lending ratio data, all of the data are quarterly from 1987Q1 to 2015Q1. The bank equity-to-lending ratio data is available at an annual frequency from 1987 to 2015. Further details about the data can be found in the appendix. 4.2 Calibration and Estimation Procedure We take a two-step approach to setting the parameters in the model. For a block of parameters that have important implications for steady state values, we either set them to commonly accepted values in the literature or use them to target important moments of interest. Theparameterswecalibratebasedonthepastliteraturearethediscountfactor,Frischelasticity of labor, substitutability between bank and nonbank deposits in the household liquidity utility function, depreciation rate, and the persistence of the capital requirements shock. One important calibrated parameter to discuss is α , or the substitutability between bank and nonbank deposits h in the household utility function. We use the same value of 0.745 as in Begenau and Landvoigt 21

(2017). We fix the persistence of the capital requirements shock to be 0.999 as we think of these policy changes as permanent. The rest of the parameters we calibrate are chosen to target important moments of interest. Table 2 shows the moments that we target. We target the mean levels of our two deposit rate data to set the steady states for the contractual deposit rates charged to the households in each sector. The spread between bank and nonbank entrepreneur lending rates targets the spread between bank and bond borrowing rates used by Fiore and Uhlig (2011). The size of bank to nonbank lending targets the mean relative sizes implied by our constructed sectoral lending growth data. Nonbank sector entrepreneur default rates come from Bernanke et al. (1999). We leave the bank sector entrepreneur default rate untargeted. It is disciplined in part by information on the average spreads between the lending rates to bank and nonbank sector entrepreneurs. Our justification for this choice is that Bernanke et al. (1999) was focused more on the default of entrepreneurs borrowing from the corporate debt markets, not the traditional banking markets. For bank default rates, we use the average percentage of assets defaulted in the commercial banking sector from the FDIC for our sample period. For nonbank default, we look at Vazza and Kraemer (2017), who report that the average default rates for financial institutions as a whole is around the same as those we calculate from the FDIC data for banks from 1981-2016. We target an average inside investor equity return of 2.87% quarterly, in line with U.S. commercial bank equity return data from 1987Q1−2015Q1 (FRED). The steady state equity-to-lending ratio of banks is calculated from the mean equity-tolending ratio data we obtained from the FDIC. For the steady state equity-to-lending ratio of the nonbanks, we use the value computed by Hirakata et al. (2017) for financial intermediaries. Finally, we discuss our nonbank lending rate target. We target a quarterly value of 1.0093% in our calibration. This is below the mean of the BAA rate of 1.0135% (quarterly) in our sample, which is our proxy for the nonbank lending rates. It is difficult for our model to simultaneously match the high leverage in the financial sector, net worth levels implied by the return to investor inside equity, and high lending spreads. This is because the combination of the net worth and high leverage of the financial sector imply high levels of lending, which make it difficult to square with a high lending rate.8 We then linearize the model around the nonstochastic steady state and estimate the rest of the parameters using Bayesian methods (An and Schorfheide, 2007), which include the parameters 8One in theory could match a high lending rate by assuming an unreasonably high level of entrepreneur default monitoring cost. We check to ensure our entrepreneur default monitoring is within the range deemed reasonable by Carlstrom and Fuerst (1997). 22

Table 2: Calibration Targets RD(N) B(N) inter dep rate (Bank time and Inst only MMF rates) 1.003(1.004) RB −RN B and N ent lend spreads (Fiore and Uhlig (2011)) 0.000675 RN N inter lend rate 1.0093 L Labor share 1/3 bB Size B to N inter lending (Z.1. Tables) 0.72 bN def Qtrly default rates of N ent (Bernanke et al., 1999) 0.75% e,N def Qtrly default rates of B (N) inter (FDIC, S&P) 0.17(0.17)% B(N) ρ Qtrly return inv equity (U.S. Commercial bank equity returns, FRED) 2.87% φ Equity-to-lending ratio B inter (FDIC data) 0.088 B φ Equity-to-lending ratio N inter (Hirakata et al. (2017)) 0.1084 N NOTE:Thesearethecalibrationtargetsforthemodel. Thefirstcolumnshowsthevariableinthemodelbeingtargeted,the middlecolumnshowsthesourceofthetarget,andthelastcolumnshowsthevalueofthetarget. Numbersinparenthesesare thecorrespondingvaluesfortheNsector. governing the exogenous shocks, degree of habits, and investment adjustment costs.9 We use the following data to estimate the model: 3-month rates of commercial bank time deposits, 3-month rates of institutional only money market funds to inform the annualized contractual bank and nonbank bank deposit rates (400(RD−1) and 400(RD,N −1)), BAA-10 year spreads to inform the t t annualized spread of the N sector entrepreneur borrowing rates over the risk-free rate (400(RN − t Rf))10, per capita consumption growth and investment growth data, equity-to-lending ratio data to t inform the level of the capital requirements (φB), and per capita bank and nonbank lending growth t data. As the equity-to-lending ratio data is only available at the annual frequency, there is an issue ofamixedfrequencyofobservations. WefollowworkbyDelNegroandEusepi(2011)onestimating DSGE models allowing for missing observations. We assume that the equity-to-lending ratio data informs the 4th quarter observation of the corresponding year. 4.3 Estimated parameters and model fit Table 3 lists the parameters and their calibrated/estimated values. We focus our empirical results ontheposteriormodeparameters.11 Weestimateahighdegreeofhabitsandamoderateamountof investmentadjustmentcosts. Ourestimatesforthemacroshocksarefairlyinlinewiththeliterature. We estimate a low degree of persistence for the TFP growth shock. Relative to Justiniano et al. 9The full set of equilibrium conditions can be found in the appendix. 10Rf istheriskfreerateinthemodel,whichisderivedfromtheEulerequationofthehouseholdoverahypothetical t riskfreeassetthatdoesnothaveliquidityservices. WedemeantheBAA-10yearspreaddataandmatchittomodelbaseddeviationsof400(RN−Rf)fromsteadystate. Thisisbecauseoftheaforementionedissuethatthemodelhas t t matching the average BAA rate. 11Additional estimation details, including on the prior specifications and posterior distributions, can be found in the appendix. 23

(2010), our MEI shocks are less important due to the inclusion of financial data, more in line with the results of Christiano et al. (2014). Among the financial shocks, we estimate highly persistent economy-wide entrepreneur risk and nonbank liquidity demand shocks. The sectoral risk shocks are estimated to be much less important. On the other hand, the sectoral entrepreneur dividend policy shocks are estimated to be important while the economy-wide entrepreneur dividend policy shocks are estimated to be unimportant. Therefore, in looking at the estimates, it seems both economywide and sectoral shocks could play an important role in understanding the macro-financial cycle in this model. We list in Table 4 the model-implied steady state values. Overall, we think the model does a good job at matching our calibration targets. One issue that is worth pointing out is that the model hasahardtimesimultaneouslymatchingtheequity-to-lendingratiovaluesinthebankandnonbank intermediary sectors. We choose to hit the equity-to-lending ratio in the bank sector exactly at the cost of calibrating the equity-to-lending ratio in the nonbank sector at slightly too low of a value. Tables 5 and 6 show model-implied standard deviations and autocorrelations for our observable variables and compare them with the data. Our model does a decent job at matching both the volatility and persistence of the macro and financial data. In terms of volatility, the variable that the model does not do well in matching is the N-sector entrepreneur lending spread volatility, although it does do a good job at matching the volatility of the deposit rates in both sectors. The estimated model understates the persistence of the deposit rates and lending growth. All in all, we believe that the model does do a good job at simultaneously matching moments for macro and financial data, given the well-known difficulties DSGE models have in simultaneously matching macro quantities and asset prices (Rouwenhorst, 1995; Fernández-Villaverde, 2010). 5 Decomposing Bank and Nonbank Credit Cycles With our estimated model in hand, we are now in a position to decompose the bank and nonbank credit cycles. We first look at simulations of our model to determine the main drivers of bank and nonbank credit growth. Then, we move on to a historical decomposition of the two credit cycles. Finally, we close by looking at the relationship between credit and business cycles implied by the model. 24

β Discount factor* 0.9965 h Habits 0.9693 η Frisch elasticity of labor* 1 α Substitutability between regulated and unregulated deposits* 0.745 h χ Importance of labor disutility* 8.32 χ Importance of liquidity service* 0.013 h Λ Importance of nonbank deposits in liquidity* 1.04 N χ (N) Entrepreneur dividend policy* 0.019(0.020) e,B χ Banker dividend policy* 0.024 b αB(N) Capital share in prod* 0.33 δ Dep rate* 0.025 K Φ Inv adj cost 3.09 I µ (N) Monitoring cost entrepreneur B(N)* 0.31(0.36) e,B µ (N) Monitoring cost B(N) intermediary* 0.3(0.35) B σ (N) Std of idio shock B(N) ent* 0.54(0.41) e,B σ (N) Std of idio shock B(N) bank* 0.032(0.035) B B φ B Bank capital requirement* 0.088 0 Λ Steady state TFP growth* 0.004 A ρ Persistence TFP growth 0.12 A ρ Persistence MEI 0.52 EK ρ Persistence pref 0.49 β ρ Persistence nonbank liquidity demand shock 0.93 Λ,N ρ Persistence economy-wide entrepreneur risk shock 0.99 σ,e,Agg ρ (N) Persistence bank (nonbank) sector entrepreneur risk shock 0.51(0.5) σ,e,B ρ Persistence aggregate entrepreneur dividend policy shock 0.5 χ,e,Agg ρ (N) Persistence bank (nonbank) sector entrepreneur dividend policy shock 0.58(0.65) χ,e,B ρ Persistence investor dividend policy shock 0.58 χ,b ρ Persistence cap req shock* 0.999 η σ Std TFP 0.013 A σ Std MEI 0.005 EK σ Std preference 0.15 β σ Std nonbank liquidity demand shock 0.11 Λ,N σ Std aggregate entrepreneur risk shock 0.02 σ,e,Agg σ (N) Std bank (nonbank) sector entrepreneur risk shock 0.01(0.0) σ,e,B σ Std aggregate entrepreneur dividend policy shock 0.0 χ,e,Agg σ (N) Std bank (nonbank) sector entrepreneur dividend policy shock 0.005(0.005) χ,e,B σ Std investor dividend policy shock 0.016 χ,b σ Std cap req shock 0.002 η Table 3: Baseline Parameters: * denotes that the parameter is calibrated. The rest of the parameters are estimated. 25

Table 4: Implied steady state values for a selected variables RD(N) B(N) inter dep rate 1.003(1.004) RB(N) B(N) inter lend rate 1.0099(1.0093) L Labor share 1/3 bB Size B to N inter lending 0.72 bN def Qtrly def rates of B (N) ent 1.18(0.74)% e,B(N) def Qtrly def rates of B (N) inter (FDIC) 0.17(0.17)% B(N) φ (N) Equity-to-lending ratio B (N) inter 0.088(0.097) B NOTE:Thistableshowsthesteadystatevaluesimpliedbythemodelforaselectedsetofvariables. Numbersinparentheses denotethecorrespondingvaluesfortheNsector. Table 5: Standard deviations of observables in the data and the model at posterior mode parameters Variable Data Model B Deposit rates 2.05 2.10 N Deposit rates 2.40 2.76 N Ent lend spr 0.75 1.39 Cons gr 0.51 0.55 Inv gr 2.29 2.03 B Lend gr 1.59 1.77 N Lend gr 1.12 1.37 NOTE:Thesearethestandarddeviationsoftheobservablesinthedataandimpliedbythemodel. Table 6: Autocorrelation of observables in the data and the model at posterior mode parameters Variable Data Model B Deposit rates 0.90 0.69 N Deposit rates 0.92 0.81 N Ent lend spr 0.89 0.80 Cons gr 0.43 0.51 Inv gr 0.53 0.43 B Lend gr 0.74 0.45 N Lend gr 0.59 0.31 NOTE:Thesearetheautocorrelationsoftheobservablesinthedataandimpliedbythemodel. 26

Table 7: Unconditional variance decomposition of bank and nonbank lending growth Variable TFP gr Liq N Ent risk EW Ent risk B Ent div B Ent div N Cap req Bank lend gr 4 13 9 13 11 49 0 Nonbank lend gr 10 9 19 9 37 8 1 NOTE:Thistableshowstheunconditionalvariancedecompositionofbankandnonbanklendinggrowthattheposterior modeparametersforaselectedsetofstructuralshocks. EWdenoteseconomy-wide. Theshockswhicharenotincludedhere wereestimatedtobeunimportant. 5.1 Which shocks are important in driving bank and nonbank lending growth? Table 7 shows an unconditional variance decomposition of bank and nonbank lending growth at the posterior mode parameters. Several interesting results emerge. First, it is clear that our model interprets credit cycles in general as primarily driven by financial shocks. Indeed, for both bank and nonbank credit cycles, the macro shocks make up at most less than 15 percent of fluctuations. The most important among the macro shocks is the TFP growth shock, which drives around 4 percent of bank lending growth and 10 percent of nonbank lending growth, respectively. The lack of importance of macro shocks for credit cycles should not be surprising given the lack of empirical comovement between investment growth and lending growth in either sector. Second, among the financial shocks, it seems that sector-specific, as opposed to economy-wide shocks play a dominant role. The sector-specific shocks, which are the nonbank liquidity demand, bank entrepreneur risk shocks and dividend policy shocks, and nonbank entrepreneur dividend policy shocks, drive over 80 percent of bank lending growth and nearly 70 percent of nonbank lending growth. On the other hand, the economy-wide shocks, most importantly the entrepreneur risk shock, play a less of a role. Nevertheless, the model can still generate positive correlation between bank and nonbank lending growth. Model-simulated bank and nonbank lending growth has a correlation of 0.22. Third, the sectoral entrepreneur dividend policy shocks seem to be the most important drivers of bank and nonbank lending growth. Interestingly, our results suggest that exogenous shocks to the balance sheet conditions of entrepreneurs who borrow from banks mainly drive nonbank lending growth dynamics and vice versa. In the next subsection, we will give some intuition as to why this is the case. There is additionally an important frequency dimension to our second and third results mentionedabove. Thiscanbeseenfromcomparingvariancedecompositionsatbusinesscyclefrequencies (6-32 quarters) and medium-frequency cycles (32-200 quarters as in Comin and Gertler (2006)), as shown in Table 8. 12 At business cycle frequencies, the sectoral shocks – and specifically the bank 12The frequency decomposition is done by applying a bandpass filter to isolate the fluctuations at the relevant 27

Table 8: Variance decompositions at business cycle (6-32 qtrs) and medium-frequency cycle (32-200 qtrs) frequencies Variable Ent risk EW Ent div B Ent div N 6-32 qtrs Bank lend gr 4 13 66 Nonbank lend gr 4 61 11 32-200 qtrs Bank lend gr 34 13 40 Nonbank lend gr 34 30 15 NOTE:Thistableshowsthevariancedecompositionsattheposteriormodeparametersatbusinesscycle(6-32quarters)and medium-frequencycycle(32-200quarters)frequencies. Theisolationofthefrequenciesisdonebyapplyingabandpassfilter. EWmeanseconomy-wide. and nonbank entrepreneur dividend policy shocks – gain even more importance, driving over 70 percent of fluctuations in both sectors. The economy-wide entrepreneur risk shocks become more importantatlongerhorizons,drivingover30percentofcreditfluctuationsinbothsectorsatmedium frequencies. Apersistentriseineconomy-wideentrepreneurialriskincreasesentrepreneurialdefault, which leads to lending spreads rising, investment growth declining, and both bank and nonbank lending growth persistently falling.13 Therefore, in our model, credit fluctuations at business cycle frequencies are best characterized as responses to sectoral financial shocks, but an important economy-wide financial shock drives their lower frequency comovement. Finally, a point of independent interest is the importance of bank capital requirement changes on bank and nonbank lending growth behavior. We find in our estimated model that this effect is negligible, mainly due to the fact that free investor equity flows between financing banks and nonbankscanlargelyunduethecreditsupplyrestrictionsorlooseningsfromthecapitalrequirements shocks. 5.2 Understanding the mechanism behind sectoral entrepreneur dividend policy shocks Figure 2 shows the responses of bank and nonbank lending growth, as well as other quantities of interest, to positive bank and nonbank sector entrepreneur dividend policy shocks, which lowers the net worth of the respective entrepreneur. Interestingly, despite the sectoral nature of the shocks, both disturbances lead to positive comovement between bank and nonbank lending growth. Let us first begin with the bank sector entrepreneur dividend policy shocks. Positive bank entrepreneur dividend policy shocks decrease the amount of wealth bank entrepreneurs allocate to net worth and increase the amount allocated as dividends for households. This decline in net worth frequencies. 13As this shock is a more standard financial shock in the literature, we discuss its effects in more detail in the appendix. 28

Figure 2: Impulse responses of bank and nonbank sectoral entrepreneur dividend policy shocks Shocks Bank lending gr Nonbank lending gr Price of capital 30 1 0.8 0.1 0 25 0.8 0.6 -0.1 20 0.6 0.4 -0.2 tn tn tn tn e c15 e c 0.4 e c e c-0.3 re re re re P P P 0.2 P -0.4 10 0.2 -0.5 0 5 0 -0.6 0 -0.2 -0.2 -0.7 0 20 40 0 20 40 0 20 40 0 20 40 Quarters Quarters Quarters Quarters Nonbank lending rate Bank equity/nonbank equity Nonbank leverage Inv gr 0.2 3 3 0.2 2.5 0.1 0.15 2 0 2 0.1 1 -0.1 tp g tc P 0.05 tn e c re P 1.5 1 tn e c re P 0 tn e c re P - - 0 0 . . 3 2 0.5 -0.4 0 -1 0 -0.5 Bank ent Nonbank ent -0.05 -0.5 -2 -0.6 0 20 40 0 20 40 0 20 40 0 20 40 Quarters Quarters Quarters Quarters NOTE:Thesearetheresponsestoonestandarddeviationbank(bluesolid)andnonbank(orangedashed)positive entrepreneurdividendpolicyshocksattheposteriormodeparameters. They-axisisinpercentandthex-axisisinquarters. 29

impairs the ability of the bank sector entrepreneurs to purchase capital. Therefore, in the short run, they purchase less capital but borrow more from banks to partially make up for the lost purchasing power. Investor equity flows into the banking sector from the nonbanking sector to support this extra lending. Nonbank lending growth increases at an even faster pace than bank lending growth. This is because the lack of capital purchasing power from bank sector entrepreneurs decreases the price of capital, making it a good time to invest in capital to take advantage of the expected capital appreciation. Therefore,thenonbanksectorentrepreneursborrowtofinancetheircapitalpurchases. Nonbank leverage rises as a result of the relaxed constraints from higher lending rates. In the longer run, nonbank leverage continues to be high as bank sector entrepreneurs build back their net worth. Overall, these shocks generate a short-run decline in investment growth. Nonbank sector entrepreneur dividend policy shocks have much the same effects, except operating in the opposite direction. Now, it is the bank lending growth that increases more than the nonbank lending growth, as bank sector entrepreneurs have stronger net worth positions. Indeed, the nonbank lending growth response is muted on impact, as a combination of the weak net worth positions of the nonbank entrepreneurs and weak financial position of nonbanks interfere with the freeflowofcredit. Nonbankscontinuetoleveruponimpactbecauseofthefire-salepricesofcapital, butoncethepriceofcapitalreturnstonearitssteadystatebyquarter10,nonbankleveragedeclines below its steady state as nonbank sector entrepreneurs continue to build back their net worth. Taken together, these shocks are important drivers of bank and nonbank credit cycles. The combined shocks lead to bank lending growth being more volatile than nonbank lending growth and a positive comovement between bank and nonbank lending growth. A negative comovement between lending growth and investment growth is an important driver of the dynamics, but as we saw in the empirical facts above, this lack of comovement between real and debt quantities is not inconsistent with the data. The amplification of bank relativeto nonbank lending growth primarily comes fromtwo sources: one exogenous and one endogenous. The estimated nonbank sector entrepreneur dividend policy shocks are slightly more persistent than the bank sector entrepreneur ones. This fact, along with a similar estimated volatility of the innovations, does mechanically lead to a more volatile bank lending growth series. The endogenous factor is important as well. As can be seen in Figure 2, troubles in the balance sheets of the entrepreneurial sector always lead to investor flows to the bank sector. This is because in response to the two shocks, the bank sector entrepreneurs always demand more loans, which the 30

banks must fund by extra equity. The negative effects on nonbank lending of the resulting outflows of inside equity from the nonbank sector are partially offset by an increase in nonbank leverage. When the shocks originate with the bank sector entrepreneurs, the investor equity inflows help to support the modest rise in bank lending growth and limit the rise in nonbank lending growth. When the shocks originate with the nonbank sector entrepreneurs, however, the equity flows from the nonbank to bank sector amplifies the increase in bank lending growth and adds further distress to the nonbank sector, which counteracts the positive demand for loans from the nonbank sector entrepreneurs. Therefore, even if the two shocks were of the same magnitude, the nonbank sector entrepreneur balance sheet shocks would have larger effects on bank lending growth compared to the bank sector entrepreneur balance shocks’ effects on nonbank lending growth. 5.3 Historically decomposing bank and nonbank credit cycles We now give a historical perspective on the drivers of bank and nonbank credit cycles. Figure 3 shows the historical movements of bank and nonbank lending growth implied by just the entrepreneurial dividend shocks (red) and all sectoral shocks in yellow. As was alluded to in the variance decomposition results, the entrepreneur dividend policy shocks are by far the most important sectoral shocks in driving bank and nonbank lending growth. This can be seen by noting that the red and yellow lines closely hug each other. The sectoral shocks are most important in understanding the higher frequency movements in bank and nonbank lending growth, in line with the observation that they are most important at the business cycle frequencies. Entrepreneur dividend policy shocks can help to explain around half of the drop in bank and nonbank lending growth during the Savings and Loans Crisis and the Great Recession. They can also explain almost all of the strong lending growth in the late 1990s and before the Great Recession. For understanding all three dips in lending growth found in the data, however, an important part of the story is missing. This fact is most evident when looking at the slow recoveries in lending growth following the Savings and Loan Crisis and the Great Recession. Figure 4 shows the credit cycle movements implied by just economy-wide shocks. The economywide shocks drive the lower frequency movements in bank and nonbank lending growth, capturing thethreedistinctwavesinlendinggrowththatweseeinthedata. Theydoabetterjobatexplaining the slower recoveries in lending growth, especially after the Savings and Loans Crisis and the Great Recession. Among the economy-wide shocks, the entrepreneur risk shocks are by far the most important for the bank and nonbank credit cycles. 31

Figure 3: Bank and nonbank credit growth implied by only sectoral shocks Bank lending growth Nonbank lending growth 5 4 Data 4 Ent div shocks 3 Sectoral shocks 3 2 2 tn 1 tn 1 e e c c re P 0 re P 0 -1 -1 -2 -2 -3 -4 -3 1990 1995 2000 2005 2010 2015 1990 1995 2000 2005 2010 2015 Date Date NOTE:Thesefiguresshowthehistoricalbank(left)andnonbank(right)lendinggrowthseriesimpliedbyonlyentrepreneurial dividendshocksaswellasallsectoralshocksfrom1987Q2to2015Q1. Weusethesimulationsmootherforthesecalculations. Figure 4: Bank and nonbank credit growth implied by only economy-wide shocks Bank lending growth Nonbank lending growth 4 4 Data 3 Ent EW risk shocks 3 EW shocks 2 2 1 1 tn tn e c 0 e c re re P P 0 -1 -1 -2 -2 -3 -4 -3 1990 1995 2000 2005 2010 2015 1990 1995 2000 2005 2010 2015 Date Date NOTE:Thesefiguresshowthehistoricalbank(left)andnonbank(right)lendinggrowthseriesimpliedbyonly entrepreneurialeconomy-wideriskshocksaswellasalleconomy-wideshocksfrom1987Q2to2015Q1. Weusethesimulation smootherforthesecalculations. 32

Table 9: Unconditional variance decomposition of investment growth Variable TFP gr Ent risk EW Ent div B Ent div N Inv gr 27 30 16 24 NOTE:Thistableshowstheunconditionalvariancedecompositionofinvestmentgrowthattheposteriormodeparametersfor interestingstructuralshocks. EWmeanseconomy-wide. Theshocksnotonthislistwereestimatedtobeunimportant. 5.4 The relationship between credit cycles and business cycles Finally, we discuss the linkages between financial fluctuations and their real effects. The variance decompositions show that the credit cycles estimated by the model are almost entirely a financial phenomenon. Even at lower frequencies, structural macro shocks do not have much of a role. Therefore, we focus on the effects of our important sectoral and economy-wide financial shocks on real aggregates. Table 9 shows the unconditional variance decomposition of investment growth. Investment growth is primarily driven by four shocks: a TFP growth shock and three financial shocks. In line with Christiano et al. (2014), the entrepreneur risk shocks play an important role in understanding investment growth fluctuations. The sectoral dividend policy shocks play a factor as well, together accounting for 40 percent of fluctuations. The model is consistent with the low observed correlation between lending growth in both sectors and investment growth. Model simulations at the posterior mode parameters produce a correlation between bank lending growth and investment growth of −0.34 and a correlation between nonbank lending growth and investment growth of −0.14. 6 Validating the Estimated Model In this section, we present some external evidence supporting the validity of the estimated model. First, we compare the measure of broker-dealer leverage computed in Adrian et al. (2014) to our smoothed nonbank leverage series in Figure 5. Although our nonbank sector covers a larger group of nonbank intermediaries, collecting leverage data for the nonbank intermediaries as a whole is difficult. We follow Gertler et al. (2016) and use broker-dealer leverage to proxy for overall nonbank leverage. Our model can capture several important features of the data, including the rise in nonbank leverage from the late 1980s to 2003, as well as the drop in 2004 and subsequent peak in the Great Recession. Overall, the correlation between the two series is 0.77. We view this as an important validation of a key mechanism of the model, especially considering we do not use this data to inform nonbank leverage in our estimation. Figure 6 shows a comparison of the excess bond premium data from Gilchrist and Zakrajsek 33

Figure 5: Broker-dealer leverage vs smoothed nonbank leverage 4 Broker-dealer lev Model nonbank lev 3 2 s n 1 o it a iv e d 0 g o L -1 -2 -3 1990 1995 2000 2005 2010 2015 Date NOTE:Thisfigureshowsnormalizedlogbroker-dealerleveragefromAdrianetal.(2014)andourmodel-impliednonbank leveragefrom1987Q2to2015Q1. Weusethesimulationsmootherforthesecalculations. 34

Figure 6: Excess bond premium vs smoothed investor dividend shock 5 EBP Investor div shock 4 3 2 1 0 -1 -2 -3 1990 1995 2000 2005 2010 2015 Date NOTE:ThisfigureshowsnormalizedexcessbondpremiumfromGilchristandZakrajsek(2012)andourmodel-implied investordividendshockfrom1987Q2to2015Q1. Weusethesimulationsmootherforthesecalculations. (2012) (blue) and our model’s smoothed investor dividend shocks (red). The excess bond premium measures the willingness to provide credit to nonfinancial sector borrowing firms over and above the expected default conditions of those firms. It is generally a credit supply indicator and viewed as a proxy for financial sector shocks. The investor dividend shock in the model is the key credit supply shock. A positive investor dividend policy shock reduces the amount of inside equity available for banks and nonbanks to draw from, thereby raising lending spreads and contracting credit. The two series move especially closely around the Great Recession. The model correctly estimates the relative magnitude and timing of the credit supply contraction. Indeed, the two series comove more closely after 2000, with a correlation of 0.53. Before 2000, the series comove less closely. Overall, the correlation is 0.29. 35

7 Conclusion Inthispaper,weexaminedtheroleofmacro,financial,economy-wide,andsectoralstructuralshocks in driving fluctuations in the bank and nonbank credit cycles through the lens of a medium-scale DSGE model. Overall, we find that sectoral shocks are the more important than economy-wide shocks in understanding bank and nonbank lending growth, especially at business cycle frequencies. The bank and nonbank entrepreneur dividend policy shocks are the most predominant. At lower frequencies, the economy-wide entrepreneur risk shocks become important. 36

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Appendix A Data For our deposit rate data, we use 3-month deposit rates for commercial bank time deposits collected from call reports and 3-month rates of institutional only money market funds from iMoneyNet. We turnthesenominalratestorealratesbysubtractingtheGDPpricedeflatorinflationfromFRED.We use the Moody’s Seasoned BAA Corporate bond yield over the 10 year treasury constant maturity data from FRED to inform our unregulated intermediary lending spreads (see Figure 7).14 Figure 7: Spreads on Entrepreneurial Loans and Real Rates on Deposits 7 6 5 4 ) d e z 3 ila u n 2 n a ( tn 1 e c r e 0 P -1 BAA-10yr -2 3-Mo Inst money fund 3-Mo Bank time deposit -3 1990 1995 2000 2005 2010 2015 Date NOTE:MMF:iMoneyNet,Inc.,iMoneyNetBulkData-OffshoreAnalyzerandGoldAnalyzer,BAA:Moody’s,Moody’s SeasonedBaaCorporateBondYield[BAA],Commercialbanktimedeposits: BoardofGovernorsoftheFederalReserve System(US),Callreportdata. Ourdepositratedataisarealrate,aswesubtracttheGDPpricedeflatorinflation. Our consumption and investment growth data both come from FRED. Consumption is defined as the sum of PCE services and nondurables whereas investment is the sum of PCE durables and domestic private investment. We deflate the series using the GDP price deflator and turn them into per capita values by dividing by the civilian noninstitutional population aged 16 or over from FRED (see Figure 8). 14Notethatasweareconstructingrealdepositrates,the3-MoInstmoneyfundand3-MoBanktimedepositseries can go negative. 41

Figure 8: Growth Rate of Consumption and Investment 2 6 1.5 4 1 2 0.5 0 tn 0 e c -2 r e-0.5 P -4 -1 -6 -1.5 -2 Cons (left) -8 Inv (right) -2.5 -10 1990 1995 2000 2005 2010 2015 Date NOTE:ThisdataistherealpercapitaconsumptionandinvestmentgrowthseriesfromFRED.Consumptionisdefinedasthe sumofPCEservicesandnondurableswhereasinvestmentisthesumofPCEdurablesanddomesticprivateinvestment. We deflatetheseriesusingtheGDPpricedeflatorandturnthemintopercapitavaluesbydividingbythecivilian noninstitutionalpopulationaged16oroverfromFRED. Thebankequity-to-lendingratiodataisconstructedastheratiobetweenthetotalequitycapital of commercial banks and savings institutions (defined as the sum of perpetual preferred stock, common stock, surplus, undivided profits, and other capital) and the total equity capital and liabilities (liabilities are the sum of total deposits, borrowed funds, subordinated notes, and other liabilities, see Figure 9). This data is from the FDIC. A.1 Details on the calculation of bank and nonbank debt growth The construction of our bank and nonbank nonfinancial business debt growth data closely follows the methodology of Gallin (2013), which uses the Z.1. Financial Accounts of the United States. Gallin (2013) decomposes the credit from nonfinancial sector lenders to nonfinancial sector borrowers as flowing through five categories of financial intermediaries: traditional banks (commercial banks, savings institutions, and credit unions), government (federal government and the monetary authority), foreign entities, long-term funders (mutual funds, pension funds, insurance companies), and short-term funders (money market mutual funds).15 He calls these financial intermediaries as "terminal funders." Broadly speaking, these terminal funders borrow from the nonfinancial sector 15A full list of the definitions for each category can be found in Table 4.1 of Gallin (2013). 42

Figure 9: Equity-to-lending Ratio Commercial Bank Lending 12 11 10 9 tn e c r e P 8 7 6 5 1990 1995 2000 2005 2010 Date NOTE:Thisannualdataoftotalequitycapitalofcommercialbanksandsavingsinstitutions(sumofperpetualpreferred stock,commonstock,surplus,undividedprofits,andothercapital)andthetotalequitycapitalandliabilities(liabilitiesare thesumoftotaldeposits,borrowedfunds,subordinatednotes,andotherliabilities). ThedataisfromtheFDIC. and fund both other financial intermediaries and nonfinancial sector borrowers. The objective of Gallin (2013) is to trace each unit of debt provided to nonfinancial sector borrowers through the intermediationchainsinthefinancialsystembacktooneoftheseterminalfunders. Forthepurposes of our paper, this measure is especially appropriate as it attempts to resolve any double counting in the amount of credit provided by the financial system to the nonfinancial sector from grossing up the aggregate debt holdings of different financial intermediary entities. Relative to Gallin (2013), which constructs this decomposition for the nonfinancial sector as a whole, we do so for only the nonfinancial business sector. We define banks as the traditional banks inGallin(2013). Thenonbanksarethesumoflong-termfundersandshort-termfunders. Asweare primarily concerned with the domestic private provision of credit, we exclude from our calculations the government and foreign entities. We give a short description of our implementation of the empirical strategy of Gallin (2013). Further details can be found in that paper. TheZ.1. Tablesgiveabreakdownoftotalnonfinancialsectorliabilitiesintoseveralinstruments. Theyalsoprovideinformationontheholdersofeachinstrument. Gallin(2013)allocatestheholders of each instrument into terminal funders and intermediate funders. Intermediate funders include 43

financial institutions that are generally thought of as borrowing from other financial institutions (e.g. government-sponsored enterprises, private-label issuers of asset-backed securities). For the nonfinancial sector liabilities held by the intermediate funders, Gallin (2013) uses information on the funding structure of the intermediate funders to allocate these liabilities further along the intermediationchain. Specifically,thenonfinancialsectorliabilitiesheldbytheintermediatefunders are allocated proportionally to the holders of the liabilities issued by the intermediate funders. The process abstracts away from the equity claims issued by the intermediate funders. It finishes when all nonfinancial sector liabilities are allocated to only terminal funders. We follow the same strategy, but focus on the nonfinancial business sector. A complication, however, is that we only have terminal and intermediate funders’ holdings by instrument of the overall nonfinancial sector liabilities, but not the nonfinancial business sector components of these instruments from the Z.1. Tables. We do, however, have data on the total liabilities of the nonfinancial business sector broken down by instrument. Therefore, an assumption we make is that each type of funder (terminal and intermediate) holds the same fraction of each instrument for the nonfinancial business sector as it does for the overall nonfinancial sector. This allows us to back out the amount of nonfinancial business sector liabilities by instrument held by each funder from only the total nonfinancial business sector liabilities by instrument and terminal and intermediate funders’ holdings of total nonfinancial sector liabilities by instrument. Our bank and nonbank lending data therefore captures differences in the importance of terminal funders for the nonfinancial business sector relative to the nonfinancial sector due to the differing mix of the liability instruments issued. For example, the nonfinancial business sector is funded by commercial paper and corporate bonds whereas the household sector is not. What our assumption misses, however, is any differences in the importance of terminal funders due to differing terminal funder holdings of nonfinancial business versus household debt instruments. For instance, we would not capture any relative differences in traditional bank holdings of household mortgages versus business mortgages. B Model equations We list here the full set of detrended equilibrium conditions implied by the model. The variables that are trending are detrended by A . t 44

Households (cid:34) (cid:35) β˜ β˜ exp(−∆logA ) t t+1 t+1 λ = −hβE t t C −hC exp(−∆logA ) C −hexp(−∆logA ) C t t−1 t t+1 t+1 t UL = χβ˜ Lη t t t UL = w λ t t t β˜ (cid:0) dB(cid:1)α h −1 (cid:104) (cid:105) λ = χ t t +βE β˜ exp(−∆logA )λ RD t h Λ (cid:0) dN (cid:1)α h + (cid:0) dB (cid:1)α h t t+1 t+1 t+1 t N,t t t β˜Λ (cid:0) dN(cid:1)α h −1 (cid:104) (cid:105) λ = χ t N,t t +βE β˜ exp(−∆logA )λ R˜D,N t h Λ (cid:0) dN (cid:1)α h + (cid:0) dB (cid:1)α h t t+1 t+1 t+1 t+1 N,t t t (cid:104) (cid:105) λ = βE β˜ exp(−∆logA ) λ Rf t t t+1 t+1 t+1 t (cid:0) ΓN −µN GN(cid:1) R˜N RD,N = t t t t 1−φN t−1 c +dB +dN = w l +RD dB +R˜D,NdN −T +Π t t t t t t−1 t−1 t t−1 t t Entrepreneurs (cid:16) (cid:17) We,B = 1−Γe,B exp(−∆logA ) RK,BqK KB t t t t t−1 t−1 (cid:16) (cid:17) ne,B = 1−χe,B We,B t t t (cid:34) (cid:32) (cid:33)(cid:35) (cid:16) (cid:17) 1−ΓB (cid:16) (cid:17) E 1−Γe,B RK,B +λe,B t+1 Γe,B −me,BGe,B RK,B −ρB = 0 t t+1 t+1 t φB t+1 t t+1 t+1 t+1 t (cid:34) (cid:35) (cid:104) (cid:105) 1−ΓB (cid:16) (cid:17) E −Γe,B,1 +λe,BE t+1 Γe,B,1−me,BGe,B,1 = 0 t t+1 t t φB t+1 t t+1 t 45

(cid:0) 1−ΓB(cid:1) R˜B ρe,B = t t t φB t−1 xe,B ω¯e,B = t−1 t RK,B t (cid:16) (cid:17) RB qKKB −ne,B t t t t xe,B = t qKKB t t rK,B +qK (1−δ) RK,B = t t t qK t−1 (cid:16) (cid:17) We,N = exp(−∆logA ) 1−Γe,N RK,N qK KN t t t t t−1 t−1 (cid:16) (cid:17) ne,N = 1−χe,N We,N t t t (cid:34) (cid:35) (cid:16) (cid:17) 1−ΓN (cid:16) (cid:17)(cid:16) (cid:17) E 1−Γe,N RK,N +λe,N t+1 Γe,N −me,N Ge,N RK,N −ρN = 0 t t+1 t+1 t φN t+1 t t+1 t+1 t+1 t (cid:34) (cid:35) (cid:16) (cid:17) 1−ΓN (cid:16) (cid:17) E −Γe,N,1 +λe,N t+1 Γe,N,1−me,N Ge,N,1 = 0 t t+1 t φN t+1 t t+1 t R˜N (cid:0) 1−ΓN(cid:1) ρe,N = t t t φN t−1 xe,N ω¯e,N = t−1 t RK,N t (cid:16) (cid:17) RN qKKN −ne,N t t t t xe,N = t qKKN t t rK,N +qK (1−δ) RK,N = t t t qK t−1 46

(cid:16) (cid:17) KB qK RK,B Γe,B −me,BG_eC t−1 t−1 t t t t R˜B = t q_K KC −n_eC t−1 t−1 t−1 (cid:16) (cid:17) KN qK RK,N Γe,N −me,N Ge,N t−1 t−1 t t t t R˜N = t qK KN −ne,N t−1 t−1 t−1  log (cid:16) ω¯e,i (cid:17) − (σ t e,i)2   log (cid:16) ω¯e,i (cid:17) + (σ t e,i)2 Γe,i = Φ t 2 +ω¯e,i 1−Φ t 2  t  σe,i  t   σe,i  t t     Γe,i,1 = 1−Φ   log (cid:16) ω¯ t e,i (cid:17) + (σ t e 2 ,i)2 + φ log(ω¯ t e,i σ ) t e − ,i (σt e 2 ,i)2 −ω¯ t e,iφ log(ω¯ t e,i σ ) t e + ,i (σt e 2 ,i)2  t  σe,i  ω¯e,iσe,i t t t  log (cid:16) ω¯e,i (cid:17) − (σ t e,i)2 Ge,i = Φ t 2  t  σe,i  t   log(ω¯e,i)− (σt e,i)2 φ t 2  σe,i t Ge,i,1 = t ω¯e,Bσe,B t t Investors (cid:16) (cid:17) Wb = exp(−∆logA ) ρBφB bB +ρN eN −nb t t t t−1 t−1 t t−1 t−1 nb = bN +φBbB −dN t t t t t (cid:16) (cid:17) nb = 1−χb Wb t t t E (cid:2) ρN (cid:3) = E (cid:2) ρN (cid:3) t t+1 t t+1 Intermediaries RD (cid:0) 1−φB (cid:1) ω¯B = t−1 t−1 t R˜B t 47

RD,N (cid:0) 1−φN (cid:1) ω¯N = t−1 t−1 t R˜N t eN φN = t t bN t (cid:104) (cid:105) (cid:104) (cid:16) (cid:17)(cid:105) E ΓN,1 = βλNE β˜ exp(−∆logA ) λ ΓN,1 −µN GN,1 t t+1 t t t+1 t+1 t+1 t+1 t+1   Et (cid:104)(cid:16) 1−ΓN t+1 (cid:17) R˜ t N +1 (cid:105) +λN t        χhΛN,tβ˜ t (cid:0)   − d Λ N t N Λ ,t N (cid:1)− ,t (cid:16) + 1 d − N t α (cid:18) h(cid:17) d d N t B t (cid:18) (cid:19) d d N t B t αh (cid:19)   α 2 h +βEt   R˜ t N +1 exp(cid:0)−∆logAt+1 (cid:1)β˜ t+1λ (cid:0)d N t+ N t 1 (cid:1)2 (cid:16) ΓN t+1−µNGN t+1 (cid:17)(cid:16) dN t −bN t (cid:17)         =0  log (cid:0) ω¯i(cid:1) − (σ t i)2   log (cid:0) ω¯i(cid:1) + (σ t i)2 Γi t = Φ t σi 2 +ω¯ t i 1−Φ t σi 2  t t      log (cid:0) ω¯i(cid:1) + (σ t i)2 φ log(ω¯ t i) σ − t i (σ 2 t i)2 −ω¯ t iφ log(ω¯ t i) σ + t i (σ 2 t i)2  Γi,1 = 1−Φ t 2 + t σi ω¯iσi t t t  log (cid:0) ω¯i(cid:1) − (σ t i)2 Gi t = Φ t σi 2  t   log(ω¯i)− (σt i)2 φ t 2  σi t Gi,1 = t ω¯iσi t t Final goods production YB = exp(−αyB∆logA ) (cid:0) KB (cid:1)αyB (cid:0) LB(cid:1)1−αyB t t t−1 t YB rK,B = αyB exp(∆logA ) t t t KB t−1 YB w = (1−αyB) t t LB t 48

YN = exp(−αyN∆logA ) (cid:0) KN (cid:1)αyN (cid:0) LN(cid:1)1−αyN t t t−1 t YN rK,N = αyN exp(∆logA ) t t t KN t−1 YN w = (1−αyN) t t LN t Capital goods production ψi (cid:18) I (cid:19)2 gI = exp(∆logA ) t −exp(∆logA ) t 2 t I t t−1 (cid:18) (cid:19) I gI,1 = ψi exp(∆logA ) t −exp(∆logA ) t t I t t−1 K = I +(1−δ) exp(−∆logA ) K t t t t−1 (cid:34) (cid:35) (cid:18) I (cid:19) λ (cid:18) I (cid:19)2 β˜ qK = β˜ EK 1+gI +exp(∆logA ) t gI,1 −βE β˜ exp(∆logA ) EK t+1 t+1 gI,1 t t t t t t I t t t+1 t+1 t+1 λ I t+1 t−1 t t Market Clearing dB = (cid:0) 1−φB(cid:1) bB t t t dN = bN −eN t t t bB +bN = b t t t Y = YB +YN t t t K = KB +KN t t t 49

L = LB +LN t t t qKKB −bB = ne,B t t t t qKKN −bN = ne,N t t t t Deposit Insurance −Tr +exp(−∆logA ) bB R˜B (cid:0) ω¯B −ΓB +µBGB(cid:1) = 0 t t t−1 t t t t Observation equations Cgr = 100(∆logA +log(C )−log(C )) t t t t−1 Igr = 100(∆logA +log(I )−log(I )) t t t t−1 bCgr = 100(∆logA +log(bC )−log(bC )) t t t t−1 bSgr = 100(∆logA +log(bS )−log(bS )) t t t t−1 (cid:16) (cid:17) RB,N,spr = 400 RB,N −Rf obs,t t t RD = 400 (cid:0) RD −1 (cid:1) obs,t t (cid:16) (cid:17) RD,N = 400 RD,N −1 obs,t t φC = 100φC obs,t t 50

C Prior distributions Our prior for the habits parameter is Beta with mean of 0.5 and standard deviation of 0.2. For the investment adjustment costs, it is normal with mean 4 and standard deviation 1.5. For the exogenous processes, we use normal distributions centered at 0.5 and with standard deviation of 0.1. The exception is the TFP growth persistence parameter, which we center around 0. For the standard deviations of the shocks, we use flat priors. As we specify more structural shocks than observables, we think it is important for us to allow for negligible effects from certain structural shocks. D Posterior distributions We use a two-step procedure to estimate the model. In the first step, we find the posterior mode parameters. There are several shocks that are estimated to be negligible, which means that the standard deviations of the innovations on these shocks are estimated to be 0. In the second step, we shut off all of the shocks estimated to be unimportant and take 250,000 draws from the posterior distribution of the parameters. The first 125,000 we take as burn in. Table 10 shows the resulting 10%and90%quantilesoftheestimatedparameters. Wefindthatthenonbanksectoralentrepreneur risk shocks and aggregate entrepreneur dividend policy shocks are unimportant.16 E Effects of economy-wide entrepreneur risk shocks Figure 10 shows the effects of a one standard deviation economy-wide entrepreneur risk shock. An increase in economy-wide entrepreneurial risk increases the probability of default for both bank and nonbank entrepreneurs. This leads to a spike in both the bank and nonbank lending rates, which depresses lending in both sectors. The resulting decline in credit decreases the price of capital. Investment growth therefore declines as well. 16Additionally, in the first stage estimates, the persistence of the economy-wide entrepreneur risk shocks was estimatedtobeneartheupperboundofitsstationarylevelat0.998. Therefore,wefixedthispersistenceparameter at that level and did not draw from its posterior distribution. 51

Figure 10: Impulse responses of economy-wide entrepreneur risk shocks Shocks Bank lending gr Nonbank lending gr 2 0.05 0.2 0.1 0 1.5 0 -0.05 tn tn tn -0.1 e c 1 e c e c re P re P -0.1 re P-0.2 -0.3 0.5 -0.15 -0.4 0 -0.2 -0.5 0 10 20 30 40 0 10 20 30 40 0 10 20 30 40 Quarters Quarters Quarters Price of capital Nonbank lending rate Inv gr 0.2 0.5 0.2 0 0.4 0 -0.2 0.3 -0.2 tn e c -0.4 tp g 0.2 tn e c re P-0.6 tc P re P-0.4 0.1 -0.8 -0.6 0 -1 -1.2 -0.1 -0.8 0 10 20 30 40 0 10 20 30 40 0 10 20 30 40 Quarters Quarters Quarters NOTE:Thisfigureshowstheresponsestoonestandarddeviationeconomy-wideentrepreneurriskshocksattheposterior modeparameters. They-axisisinpercentandthex-axisisinquarters. 52

Table 10: Posterior distribution parameters Parameter 10% 90% h 0.95 0.98 Φ 2.15 4.22 I ρ 0.10 0.15 A ρ 0.41 0.68 EK ρ 0.48 0.49 β ρ 0.89 0.97 Λ,N ρ 0.37 0.63 σ,e,B ρ 0.50 0.64 χ,e,B ρ 0.58 0.71 χ,e,N ρ 0.49 0.66 χ,b σ 0.011 0.014 A σ 0.003 0.007 EK σ 0.10 0.19 β σ 0.10 0.12 Λ,N σ 0.015 0.019 σ,e,Agg σ 0.009 0.015 σ,e,B σ 0.005 0.006 χ,e,B σ 0.005 0.006 χ,e,N σ 0.014 0.019 χ,b σ 0.002 0.003 η NOTE:Thistableshowsthe10%/90%quantilesoftheposteriordistribution. 53