Search Frictions, Bank Leverage, and Gross Loan Flows∗ Abeer Reza† Carleton University January 5, 2013 Job Market Paper ‡ Abstract This paper develops a search-theoretic banking model in a New Keynesian DSGE framework that can simultaneously explain cyclical movements in interest spreads and flows in gross loan creation and destruction, that were recently emphasized in the literature. The model features endogenous match separation, and allows bank loans for productive capital purchases to vary in both intensive and extensive margins. Search frictions in the banking sector generates a counter-cyclical interest spread that amplifies business-cycles. In addition, the model generates responses in gross loan destruction and net loan flows to a credit supply shock that can qualitatively match empirical responses estimated in a VAR framework. JEL classification: E43, E44, E51, G21 Key words: Real Financial Linkage; Search; Banking; Gross Loan Flows;
∗
I thank Huntley Schller, Till Gross, and Chris Gunn for important comments. I am especially grateful to my supervisor, Hashmat Khan, for his valuable support and direction. I am also indebted to Silvio Contessi for providing me with the data on U.S. gross loan flows. † Contact information: Ph.D. Candidate, Department of Economics, Carleton University, C870 Loeb Building, 1125 Colonel By Drive, Ottawa, ON, Canada, K1S 5B6. E-mail:
[email protected] ‡ The most recent version of this paper can be found at https://sites.google.com/site/abeerreza/
1
Introduction
During the 2007-09 financial crisis, a reduction in bank asset holdings led to an erosion in bank equity. This led to an increase in the spread between the loan interest rate and the risk-free rate, and a drop in bank lending. Since then, a growing stream of literature has focused on developing quantitative business cycle models that emphasize the bank leverage ratio (the ratio between total bank assets and bank equity) as a channel for generating counter-cyclical interest spreads that amplify and prolong recessions, and consider the banking sector as a potential source of shocks to the economy.1 At the same time, a second stream of inquiry has used disaggregated bank lending data to reveal important patterns within the banking sector that are not captured at the aggregate level.2 First, Ivashina and Scharfstein (2010) documents that bank loans vary both at the intensive margin (amount of loans), as well as the extensive margin (number of loans). Second, Contessi and Francis (2009) finds that during the 2008 and 1991 downturns, which featured an erosion of bank equity, gross loan destruction in US commercial banks superseded gross loan creation, resulting in a decline in net loan flows. In general, new loan creation moves pro-cyclically while loan destruction moves counter-cyclically.3 However, currently available business-cycle models featuring a banking sector cannot account for these movements in disaggregated loan flows. This paper fills this gap in the literature by developing a search-theoretic banking model that can simultaneously explain cyclical movements in interest spreads, as well as in disaggregated flows in loan creation and destruction. The model introduces costly search in a banking sector, a bank leverage ratio channel, and endogenous match separation to an otherwise standard New Keynesian DSGE model similar to Christiano et al. (2005) and Smets and Wouters (2007). Bank loans are used by firms to finance productive capital purchases, and are allowed to vary both in the extensive and intensive margins. I use the model to study responses to two shocks that affect credit supply 1
See, among others, the work in Gertler and Karadi (2011), deWalque et al. (2010), Meh and Moran (2010), Gerali et al. (2010), and references therein. 2 At the onset of the 2008 recession, Chari et al. (2008) argued that although there was little doubt that the U.S. was undergoing a financial crisis, aggregate data on bank lending showed no signs of the downturn. In response, Cohen-Cole et al. (2008) argued that a deeper look at disaggregated lending data shows evidence of the credit crunch. In particular, aggregate lending data hides movements in new loan creation, which had collapsed early in the recession. 3 Gross loan flows calculated using both Bank balance sheet data (Contessi and Francis (2009), Dell’Ariccia and Garibaldi (2005)) and firm-level compustat data (Herrera et al. (2011)) confirm this cyclical pattern.
1
– a one time decline in bank equity, and a one time increase in the match separation rate. I also look at responses to traditional technology and monetary shocks, as well as a capital quality shock that has been shown by Gertler and Karadi (2011) to replicate well important movements related to the bank leverage channel during the crisis.4 First, I find that the model generates a counter-cyclical interest spread that amplifies and prolongs recessions for all shocks considered.5 The intuition for this result is as follows. In this economy, loans are generated when a banking loan officer is matched with an unfunded project. Banks incur costs while searching for new funding opportunities, or in maintaining existing relationships. When a negative technology, monetary, or credit shock hits the economy, loan-demand falls, as does expected profits. Consequently, banks reduce their efforts in searching for new matches or in maintaining existing ones. This makes new matches scarcer, and increases the surplus from successful matches. Through Nash bargaining, this increase in match-surplus is translated to a higher loan interest rate. In the presence of an endogenous policy rate, the model generates a countercyclical interest spread. Overall, negative shocks generate deeper and more prolonged recessions in this model than the standard New Keynesian setup. Since the seminal contribution of Bernanke et al. (1999), asymmetric information setups have has provided a strong argument in motivating a financial accelerator effect through the banking sector, and has been widely used in the literature for this purpose.6 This paper contributes to the financial frictions literature by showing that costly search can also generate a counter-cyclical interest spread in a DSGE framework for a number of shocks, in the absence of any information 4
The intuition for the capital quality shock is as follows. A negative shock to the quality of capital reduces the productivity of capital, and hence, its market price. This reduction in asset values is translated through the bank balance sheet identity to an erosion of bank equity, and a consequent rise in the leverage ratio. This, in turn, reduces future lending and exacerbates the recession.Although a shock to capital quality leads to a recession on its own merit, it also provides a secondary effect by generating a persistent decline in asset values in the bank balance sheet, as seen during the sub-prime crisis. Following Gertler and Karadi (2011), I attempt to capture the effects of the financial crisis by considering this secondary effect that works through the banking system. 5 In contrast, Gerali et al. (2010) finds that the presence of the banking sector amplifies responses to financial shocks, but attenuates the effects of technology shocks. 6 In this vein, Gertler and Karadi (2011) introduces financial frictions in a workhorse DSGE model through limited commitments between bankers and depositors. Meh and Moran (2010) and Christensen et al. (2011) use costly state verification in a double moral hazard setup, while Dib (2010) uses the Bernanke et al. (1999) framework in a monopolistically competitive banking sector.
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asymmetries.7 Moreover, the narrative of the loan generation process in this model fits business practices in traditional banks. In addition, I find that the search-theoretic framework is useful in generating movements in loan creation and destruction flows that qualitatively match empirical evidence. First, the model generates pro-cyclical movements in loan creation, and counter-cyclical movements in loan destruction. Second, the model generates impulse responses that qualitatively match estimated responses of an identified credit supply shock. The idea that conditions in the financial sector can be an independent source of business cycle fluctuations has recently been emphasized in the literature. Gilchrist and Zakrajsek (2012a) and Boivin et al. (2012) estimate the effect of a credit shock on US data and find that a reduction in credit supply negatively affects the real economy. To see whether the model can generate empirically plausible movements in disaggregated loan flows, I first estimate responses to gross loan creation and destruction margins to a credit supply shock in a VAR framework. I find that interest rate spread and loan destruction margins rise, while loan creation falls after a credit supply shock. The model is able to generate responses to the capital quality and bank equity shocks that are qualitatively similar to empirical evidence, if investment is allowed to be as highly sensitive to capital prices as suggested by evidence from disaggregated data. Finally, I show that the model can be useful in policy analysis from a financial stability perspective. I find that a counter-cyclical leverage ratio regulation attenuates the responses to negative shocks if the policy instrument responds to the loan-to-output ratio. Early studies exploring the effect of search friction on credit markets include den Haan et al. (2003), and Wasmer and Weil (2004). However, none of these papers use search frictions to study business-cycle dynamics of bank loans. In that respect, the papers closest to this study are Dell’Ariccia and Garibaldi (2000) and Beaubrun-Diant and Tripier (2009). The former considers a search model only to match the second moments of gross loan flows, and the later explores 7
Other studies using a symmetric information setup for the banking sector includes Aliaga-D´ıaz and Olivero (2010) and Gerali et al. (2010). The former assumes deep-habits in loans, where it is costly for borrowers to switch banks during recessions. Banks are able to take advantage of their customers’ predicament and charge them a higher interest rate during downturns. The later imposes a binding borrowing constraint on the quantity of loans and generates interest rate spreads through counter-cyclical markups in a monopolistically competitive banking sector.
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the ability of a costly search setup in generating a counter-cyclical interest spread for technology shocks in an RBC model. On top of considering a New-Keynesian setting, my model differs from Beaubrun-Diant and Tripier (2009) by allowing an endogenous bank leverage channel and loans that are used for capital purchases to vary both in the intensive and extensive margins. In contrast, their model specifies loans used for intermediate good purchases, allows only movements in the extensive margin, and abstracts from both productive capital and bank equity. To the best of my knowledge, this is the first paper that considers a full-fledged banking model using search-frictions in a New-Keynesian setting, and explicitly models loan variation in both intensive and extensive margins. This is also the first paper to consider both simulated and empirical impulse responses of gross loan flows to financial shocks. Finally, although a number of recent papers study the effect of macro-prudential regulation (see Christensen et al. (2011) and references therein), this paper shows that counter-cyclical leverage regulations can be meaningful even in the absence of asymmetric information. The rest of the paper is organized as follows. Section 2 describes the benchmark model and calibration. Section 3 demonstrates the capacity of the model to amplify and propagate the effects of shocks to the economy, and explains the core search mechanism in generating a counter-cyclical interest spread. Section 4 determines the empirical responses for gross loan creation and destruction margins for a credit supply shock, and compares them with model responses. Section 5 shows that a counter-cyclical capital buffer regulation can attenuate shock responses, and section 6 provides concluding comments.
2
The Benchmark Model
In this section, I describe the benchmark model and calibration. The starting point is the workhorse New Keynesian DSGE model with nominal rigidities developed by Christiano et al. (2005) and Smets and Wouters (2007). To this canonical framework, I add a banking sector that intermediates loanable funds between households and firms. Banks face a Mortensen and Pissarides (1994) type search friction that creates a wedge between the loan and deposit interest rates. The mechanism parallels the creation of a wedge between wages and the marginal product of labor in the job-search
4
models of Pissarides (1985) and Andolfatto (1996). Precisely, household deposits are transferred to firms as loans used for capital asset purchases only when a banking loan officer is matched with a project that requires financing. The search process resulting in a matched banker-project pair generates a countercyclical wedge between the loan interest rate charged to the firm and the deposit interest rate paid by the bank. There are five types of private agents in the economy: households, banks, intermediate goods producers (referred to as firms here on), capital producers, and monopolistically competitive retailers. This setup closely follows Gertler and Karadi (2011), with the exception that the financing friction in this model is generated by search activity, rather than an agency problem stemming from information asymmetries between bankers and depositors. Households consume, supply labour to firms, and save in bank deposits. They own banks, intermediate and capital goods producing firms, and retail institutions. Income from these institutions are repatriated to households in the form of dividends. Capital, however, is owned by firms, is used along with labour to produce a homogeneous intermediate good, and can be bought only through funds secured from banks as loans. In this economy, firms, rather than households, take the investment decision. Financing for capital purchases varies across the business cycle both at the extensive margin as well as the intensive margin. The representative firm is best thought of as the head office of a continuum of projects in the unit interval. There is perfect capital and labour mobility across projects. The firm head office determines aggregate capital and labour demand, and therefore the intensive margin of financing. Production and financing, however, occurs at the individual project level, and only if the project is matched with a banker who provides financing. Similar to the firm, the representative bank is best thought of as the head office to a collection of loan officers, who can either be actively financing an existing project, or searching for potential projects to finance. The bank head office determines the total number of loan officers, both active and searching, in each period in accordance with a balance sheet constraint that equates total loans to total deposits plus bank equity, and a quadratic cost imposed on banks if the leverage ratio deviates from regulation. Following an aggregate shock, banks determine how many new projects to finance, and how many of the currently existing relationships to keep. Separation of
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existing relationships, therefore, is endogenous, and modeled by introducing an idiosyncratic cost of continuing an existing match, imposed on the individual loan officer. Each period, new matches occur between bankers looking for projects to finance, and unfunded projects. This generates an extensive margin for financing. Banks pay a deposit interest rate to households that equals the risk-free rate by arbitrage. Loan interest rates to firms are determined through Nash bargaining. At the end of the period, worn out capital is replaced by the capital goods producing sector, which, following Bernanke et al. (1999) and Gertler and Karadi (2011), is considered separately to keep the problem of intermediate goods producers tractable in the face of financial frictions. A monopollistically competitive retail sector introduces nominal price rigidities by costlessly differentiating the homogeneous intermediate good into a continuum of differentiated goods, and repackaging them to produce a final good. A central bank conducts conventional monetary policy to control inflation, and regulates the financial sector by setting bank capital adequacy rules. In the absence of financial frictions, the loan interest rate and the deposit rate are equal, and the question of matched banker-project pair is moot. In this case, the model reduces to the canonical New Keynesian model of Christiano et al. (2005) and Smets and Wouters (2007). The remainder of this section describes the benchmark model in detail. Appendix A at the end of the paper provides a summary of the timing of events.
2.1
Households
There is a representative household that consumes, supplies labour and saves in bank deposits to maximize the following discounted sum of utilities: ∞ X i max Et β ln (Ct+i − hCt+i−1 ) − i=0
1 (LH )1+ϕ 1 + ϕ t+i
(1)
where Ct is consumption, LH t is labour supplied, 0 < β < 1 is the discount factor, 0 < ϕ is the inverse Frisch elasticity of labour supply, and 0 ≤ h < 1 determines the degree of habit formation. In each period, the household faces the following budget constraint H H Ct = Wt LH t + Rt Bt−1 − Bt + Divt
(2)
where BtH is this period’s savings deposited in banks, which earn real gross interest rate Rt in each period. Wt is the real wage rate, and Divt is the sum of dividends repatriated to households from
6
private enterprises in each period. As we will see below, the superscript H on aggregate household savings and labour supply helps distinguish them from labour demanded by individual projects, and deposits used by individual banker to fund projects. Let λt be the shadow value of income. The household’s first order conditions governing labour supply and savings can be given as follows: ϕ (LH = λ t Wt t )
(3)
λt = (Ct − hCt )−1 − hβEt (Ct+1 − hCt )−1 1 = βEt Λt,t+1 Rt Et Λt,t+1 = Et
(4) (5)
λt+1 λt
where βEt Λt,t+1 is the stochastic discount factor.
2.2
Matching
As mentioned earlier, the banking sector is a collection of individual loan officers, while the firm is a collection of a continuum of projects on the unit interval. A project can either be funded and productive, or looking for funding. Each period, the bank head office determines the number of loan officers, vt , that are actively searching for projects to fund. Let ut be the number of projects looking for funding. At the end of each period, after production takes place, and all factor payments and loan repayment commitments are completed, new matches, mt , are made between searching loan officers and unfunded projects according to the following Cobb-Douglas matching function: mt = muχt vt1−χ
(6)
where χ is the match elasticity. A banker-project pair matched in period t becomes active in period t + 1. Let qt be the probability with which an individual searching banker finds a match in period t, and pt be the probability of an unmatched project finding a match. Then we have the following
7
relationships: qt = pt = θt =
mt = mθt−χ vt mt = mθt1−χ ut pt vt = ut qt
(7) (8) (9)
where θt captures the tightness in the credit market. A low value for θt makes it more difficult for an unmatched project to secure funding.
2.3
Banks
A bank head office manages a continuum of loan officers. Although aggregate funding allocation decisions are taken by the head office, matching, lending and loan collection is undertaken by individual loan officers. The timing is as follows: the bank enters period t with nt−1 matched H . At the beginning of the period, the bank projects to fund, and household savings deposits of Bt−1
head office allocates a portion of deposits, Bj,t−1 , and net worth to each matched loan officer j. The active loan officer then lends out an amount Sj,t to the project with which it is matched, collects gross real loan interest rate Rtl and repays the head office Rt for use of deposit funds, which is then repaid to the household as deposit interest rate. After all loan commitments have been fulfilled and loan payments collected, an active loan officer is hit by an idiosyncratic ‘relationship shock’, ωj,t ∈ [ω, ω], representing the cost of continuing an existing relationship. The loan officer can either pay a cost Υωj,t and continue the relationship, or pay a fixed amount T , and separate the existing relationship. After separation takes place, the bank posts new loan vacancies at a unit cost of cv , each of which finds a match with probability qt . The pool of matched projects nt is then funded in the next period. In a symmetric equilibrium, all loan officers receive the same amount of deposits, Bt = Bj,t , and give out the same amount of loans, St = Sj,t . Since the shock hits the loan officer after all loan obligations are cleared, profits vary across loan officers ex-post. Let Πb,c t be the flow profit of a loan officer if the existing relationship continues to the next period, and Πb,x be the flow profit t
8
if the relationship separates. Then, in a symmetric equilibrium, we have that: i Rtl St − Rt Bt−1 − Υωj,t h i l Πb,x (ω ) = R S − R B −T j t t t−1 t t Πb,c t (ωj ) =
h
Let ω ˜ t be the reservation continuation cost, such that the existing relationship survives if ωj,t ≤ ω ˜ t and separates if ωj,t > ω ˜ t . The flow profit of the average loan officer, Πbt , is then given by: Πbt =
Z h i Rtl St − Rt Bt−1 − Υ
ω ˜t
Z
ω
ωdG(ω) −
ω
T dG(ω)
(10)
ω ˜t
where G(ω) is the distribution function for the idiosyncratic shock ωj,t . Two conditions restrict the total amount of loans given out by the banking sector. First, a balance sheet constraint equates total loans to the sum of deposits and bank equity: nt−1 St = nt−1 Bt−1 + Ntb
(11)
H is the amount of savings deposit available to the bank at period t, and N b where nt−1 Bt−1 = Bt−1 t
is bank equity. Second, a regulatory authority imposes a capital adequacy constraint on the bank. Specifically, the bank incurs a quadratic cost if its leverage ratio, defined as the ratio between bank loans (assets) and bank equity, exceeds a maximum regulated value. Precisely, the regulator wants nt−1 St ≤κ ¯ , and banks pay a deviation cost otherwise. Ntb Given the one-period lag between the time a match is created and loans are disbursed, the bank can only influence the number of matches that will become active in the next period. The bank searches for new matches by posting a loan vacancy at a fixed marginal cost of cv per unit, and finds one with probability qt each period. The head office also determines the number of existing matches that are separated.8 In every period, the aggregate banking sector receives an average profit of Πbt from each of the nt−1 active matches, and pays a loan vacancy posting cost of cv vt as well as a quadratic penalty if it deviates from the regulated leverage ratio of κ ¯ . The bank’s job 8
Note that if the separation decision were taken by the loan officer instead of the head office, then ω ˜t would equate the value functions between the two options – continuing and separating. To be precise, let Jtc (ωj,t ) = Πb,c t (ωj,t ) + βΛt,t+1 Jt+1 be the value function of the loan officer who continues the relationship, and Jtx (ωj,t ) = Πb,x t (ωj,t ) be that for the loan officer who separates her existing relationship. Here, Jt is the ex-ante value function. Then, the reservation ω ˜ t would satisfy Jtc (˜ ωt ) = Jtx (˜ ωt ).
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is to chose the number of loan vacancies, vt , and the reservation cost of continuation, ω ˜ t , in order maximize the following value function B
max V (nt−1 ) =
{vt ,˜ ωt }
nt−1 Πbt
2 b Ψ nt−1 St Nt − cv vt − −κ ¯ + βEt Λt,t+1 V (nt ) b 2 St Nt
subject to the law of motion for active matches ω ˜t
Z nt = nt−1
dG(ω) + qt vt
(12)
ω
= xt nt−1 + qt vt
(13)
where the endogenous survival rate, xt , is related to the threshold continuation shock by Z
ω ˜t
xt =
dG(ω) ω
and the match separation rate is given as 1−xt . The optimality conditions with respect to vt , nt , ω ˜t, and the envelope condition is as follows: cv = λbt qt βEt Λt,t+1
B (n
∂V t) ∂nt
(14)
= λbt
(15)
Υ˜ ωt = T + λbt B (n
∂V t−1 ) ∂nt−1
(16)
Z ω˜ t nt−1 St b b = Πt − Ψ −κ ¯ + λt dG(ω) Ntb ω
(17)
where λbt is the Lagrange multiplier for the constraint (13). The envelop condition (17) provides an expression for the value to the bank of an additional match, and represents the match surplus. Combining equations (14), (15) and the envelope condition (17), we get the BienvenisteScheinkman condition, which determines the optimal rule for posting new loan vacancies: Z ω˜ t+1 cv l = βEt Λt,t+1 Rt+1 St+1 − Rt+1 Bt − Υ ωdG(ω) − (1 − xt+1 )T qt ω " # ) nt St+1 cv −κ ¯ + xt+1 −Ψ b qt+1 Nt+1
(18)
Recall that qt = mt /vt . Equation (18) then implies that an expected increase in interest income will prompt the bank to post more loan vacancies in order to increase the number of active loans.
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Similarly, an expected increase in the actual leverage ratio from the regulated level of κ ¯ , and a subsequent penalty for deviation, will induce the bank to reduce the number of active loans. The optimal separation rule follows a similar logic and is found by combining equations (14) and (16): Υ˜ ωt = T +
cv qt
(19)
The bank adds its profits net of vacancy posting and regulatory costs to its capital base. Each period, the bank repatriates a fixed proportion δ n of its net worth to households as dividends. The law of motion determining bank equity is therefore given by: 2 b Nt Ψ nt−1 St b b b + (1 − δ n )Nt−1 − εnt −κ ¯ Nt = nt−1 Πt − cv vt − b 2 St Nt
(20)
where εnt is a direct shock to level of bank equity, and is meant to capture a financial shock that erodes the equity base of the banking sector.9 In this formulation, we abstract from capital issuance from the banking sector. The retention of profits in bank equity, however, is also present in Gertler and Karadi (2011). Note that this formulation implies that net bank profits are completely repatriated to households in the steady-state.
2.4
Intermediate Goods Firm
The representative firm manages a continuum of projects in the unit interval, and produces a homogeneous intermediate good that is sold to retailers at price Ptm . Capital and labour allocation decisions are taken by the firm head office, while search, matching and production activities take place at the level of individual projects. I assume perfect capital and labour mobility across projects.10 This implies that capital and labour allocation decisions by the firm head office does not depend on the number of firms that are matched. Capital allocation across projects is conducted in a competitive market, at the prevailing market price. The timing of events is as follows: the firm enters period t with nt−1 matched projects, and Y Kt−1 units of aggregate capital available for production. Each matched project i takes a loan of 9
This is similar to the net worth shock considered in Gertler and Karadi (2011). A similar shock for entrepreneur net worth has been shown to be more important in explaining output fluctuations in post-war US data than monetary shocks by Nolan and Thoenissen (2009). 10 This is similar to the assumption of consumption sharing across family members in models of labour search, such as Merz (1995) and Monacelli et al. (2010). With this assumption, there is no need to keep track of the match state of individual projects.
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Si,t from the bank at loan rate Rtl , and purchases Ki,t−1 units of capital at price Qt . The head office hires labour at wage Wt and allocates Li,t amount per project. Production occurs only in matched projects according to the following Cobb-Douglas function: Yi,t = zt (ξt Ki,t−1 )α (Li,t )1−α
(21)
where zt is a standard technology shock and ξt is a capital quality shock common to all projects, similar to Gertler and Karadi (2011), making ξt Ki,t−1 the effective quantity of productive capital at time t. α is the capital share of output. Once production is complete, project i repays the loan and interest to the bank, and sells the capital back to the market at price Qt for reallocation in the next period amongst projects that will be in production. Depending on the match-specific continuation cost ωi,t that each project’s loan officer faces, the project either continues the match into the next period (if ωi,t < ω ˜ t ) or separates (otherwise). Separated projects start looking for another match in the same period. The number of unmatched projects looking for funding at the end of period t is denoted by ut and defined as: Z
ω ˜t
ut = 1 −
nt−1 dG(ω)
(22)
ω
Each period, a proportion δ of capital is depreciated, and is replaced at unit cost. Firms do not face capital adjustment costs.11 The flow benefit of a matched project, Πei,t takes into account the marginal product of capital, the value of capital stock sold back to the market after production (Qt − δ)ξt Ki,t−1 , and the loan cost: Πei,t =
αPtm
Yi,t + (Qt − δ) ξt Ki,t−1 − Rtl Si,t ξt Ki,t−1
(23)
where the loan amount is spend only on purchasing capital: Si,t = Qt Ki,t−1
(24)
Let Htc (ωi,t ) be the value function of a project that continues its match, and Htx (ωi,t ) be the value 11
Following Gertler and Karadi (2011), adjustment costs occur on net rather than gross investment, and is borne by capital goods producers.
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function of a project that separates after production in period t. Then we have that: Hts (ωi,t ) = Πei,t + βEt Λt,t+1 Ht+1
(25)
Htn (ωi,t ) = Πei,t + Ut
(26)
where Ht+1 is the ex-ante or average match value in period t + 1, and Ut is the value function of an unmatched project. An unmatched project find a match with probability pt , and remains unmatched with probability 1 − pt . The value of an unmatched project is then given by: Ut = pt βEt Λt,t+1 Ht+1 + (1 − pt )βEt Λt,t+1 Ut+1
(27)
In a symmetric equilibrium, all projects receive the same amount of labour, Lt = Li,t , and capital inputs, Kt−1 = Ki,t−1 , and consequently produce the same amount of output Y = Yi,t . Defining the surplus from the match as VtF , we have that: VtF
Z
ω
Ht (ωt )dG(ω) − Ut
= ω
=
Ptm α
Yt F + Qt (1 − δ)ξt Kt−1 − Rtl St + xt (1 − pt ) βEt Λt,t+1 Vt+1 Kt−1
(28)
Since the firm head office makes the labour allocation decision, the optimality condition for labour demand is standard: Wt = (1 − α)Ptm
Yt Lt
(29)
where Wt is the real wage rate. Capital is owned by the firm head office, and is transferred intertemporally. The optimal condition for capital demand equates the return of capital to the cost of financing: h Rtl = Et
t αPtm KYt−1 + (Qt+1 − δ)ξt
i
Qt
(30)
Note that the value of capital stock left over after production takes into account the unit replacement cost of depreciated capital, and is given by Et (Qt+1 − δ)ξt Kt−1 . The capital quality shock ξt generates variation in the return to capital, as well as in the price of capital Qt .
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2.5
Nash Bargaining
At the beginning of the period, the loan interest rate Rtl is determined via Nash bargaining by maximizing the joint match surpluses accruing to the bank and the firm: max {Rtl }
η VtF
∂V (nt−1 ) ∂nt−1
1−η
where η is the firm’s bargaining power. The optimality condition is given by (1 − η) VtF
= η
∂V (nt−1 ) ∂nt−1
(31)
Replacing the expressions for the match surpluses from equations (28) and (17), and simplifying, we get the following condition for the loan interest rate: Rtl St
Z ω˜ t Yt m = (1 − η) Pt α ωdG(ω) + (Qt − δ)ξt Kt−1 + ηRt Bt−1 + ηΥ Kt−1 ω nt−1 St pt +η(1 − xt )T + ηΨ −κ ¯ − ηcv xt b qt Nt
(32)
where the following equality has been taken into account: e (1 − η) βEt Λt,t+1 St+1 = ηβEt Λt,t+1
∂V (nt ) cv =η ∂nt qt
Equation (32) specifies that the loan interest rate, Rtl , increases when firm profits go up, or if the cost to the bank for servicing the loan goes up. In particular, an increase in the cost of funding for banks, Rt , or in the leverage ratio will be (at least partially) transferred to firms through higher loan rates. Finally, a tighter credit market, implied by a fall in θt =
pt qt ,
will prompt banks to charge
a higher rate to firms.
2.6
Capital Producing Firms
At the end of period t, capital producing firms buy capital from intermediate goods producing firms, repair depreciated capital at unit cost, build new capital and sell it at price Qt . Following Gertler and Karadi (2011), I assume that there is no adjustment cost associated with refurbishing capital, but there are flow adjustment costs with producing new capital. These adjustment costs are imposed on net investment flow, rather than gross investment flow, to make capital decisions
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independent of the price of capital. The capital producing firms’ problem is to chose net investment to maximize the following sum of discounted profits: n ∞ X It+τ + I¯ n n t+τ n ¯ β Λt,t+τ Qt+τ It+τ − It+τ − f max Et n ¯ (It+τ + I) It+τ {Itn } −1 + I τ =0 where It is gross capital created, Itn is net capital created, and I¯ is the steady-state investment. The adjustment cost function satisfies f (1) = f 0 (1) = 0, f 00 (1) > 0. The definition of net new capital and the law of motion of capital stock is given by: Y Itn ≡ It − δξt Kt−1
(33)
Y KtY = ξt Kt−1 + Itn
(34)
where aggregate capital KtY = nt Kt . Any profits from the capital producing firms are rebated back to the household. The optimal condition for the capital producing sector gives the following relation for net investment: Qt
2.7
n 2 It+1 + I¯ Itn + I¯ 0 = 1 + f (·) + n f (·) − Et βΛt,t+1 f 0 (·) It−1 + I¯ Itn + I¯
(35)
Retail Sector
Following Bernanke et al. (1999) and Gertler and Karadi (2011), I model the retail sector in two steps. First, a continuum of monopolistically competitive retail firms indicated by i ∈ [0, 1] purchases the homogeneous intermediate good at price Ptm and costlessly differentiates them to a continuum of retail goods. Second, these differentiated goods Yi,t are combined into a composite final good YtF by a packaging firm using a Dixit-Stiglitz aggregating technology : Z 1 −1 −1 F ε Yt = Yi,t , > 0 0
where 1/( − 1) > 0 is the constant elasticity of substitution between differentiated retail goods. Cost minimization by the final good packer gives the following demand for each type of retail good Pi,t − F Yi,t = Yt Pt where Pt is the price of a unit of final good determined by the zero profit condition: Z 1 1/(1−) 1− Pt = Pi,t 0
15
The marginal cost faced by the monopolistically competitive retail firms is the price, Ptm , of intermediate goods. Following Calvo (1983), nominal price stickiness is introduced by assuming staggered price setting by the retail firm. Each period a fraction, 0 < 1 − Θ < 1, of retail firms re-sets their sales price optimally, while the remaining fraction Θ keeps their prices unchanged. The retail firm’s problem is to chose the optimal sales price given the staggered price setting mechanism max Et ∗ pt
∞ X
m Λt,t+j Θj Pt∗ Yf,t+j − Pt+j Pt+j
j=0
subject to a sequence of demand curves Yi,t+j =
Pt∗ Pt+j
−
F Yt+j
The optimal price, Pt∗ , satisfies the first-order condition ∞ X m j ∗ P Pt+j = 0 Et Λt,t+j Θ Yi,t+j Pt − − 1 t+j
(36)
j=0
where the aggregate price level is given by i 1 h ∗(1−) 1− 1− + (1 − Θ)Pt Pt = ΘPt−1
(37)
Log-linearizing equations (36) and (37) around a steady-state inflation rate of 1, we get the following expression for the New-Keynesian Philips curve π ˆt = βEt π ˆt+1 +
(1 − βΘ)(1 − Θ) ˆ m Pt Θ
(38)
where πt = Pt /Pt−1 is the inflation rate, and hats represent variables that are log-linearized around their respective steady-states.
2.8
Resource Constraint and Policy
Final output is the sum of output from each individual project, and is divided between consumption, investment, adjustment costs, and costs incurred by banks for separation and search for new projects. YtF
Z ω˜ Itn + I¯ n ¯ = Ct + I t + f (I + I) + c v + n Υ ωdG(ω) v t t−1 t n + I¯ It−1 ω Z ω nt−1 St +nt−1 T dG(ω) + Ψ − κ ¯ Ntb ω ˜
≡ nt−1 Yt
16
(39)
A central bank determines monetary policy by setting the nominal gross interest rate it , according to the following simple Taylor rule, expressed in log-linearized form ˆit ≡ Rˆt + π ˆt+1 = %π π ˆt + %y YˆtF + εm t
(40)
where εm t is an i.i.d. shock to the nominal interest rate, and the link between nominal and real interest rates follow a Fisher relationship. We also assume that the central bank is tasked with macro-prudential stabilization of the economy, and does so by setting the bank loan to capital ratio κ ¯ t according to the following simple Taylor-type rule: κ ¯t = κ ¯
$ % κ t
$
(41)
where $t can be any economic variable of the regulator’s choice, and $ its steady state value. Banks pay a quadratic cost with elasticity Ψ if total loans exceed a multiple κ ¯ t of bank equity: nt−1 St >κ ¯ t . A counter-cyclical leverage ratio implies that the bank is allowed to have a higher Ntb leverage ratio during downturns, while they are required to lower the leverage ratio, and build up equity capital during upturns. This concludes the description of the model. Appendix B summarizes the list of non-linear equations defining the model.
2.9
Calibration
I log-linearize the model around its steady-state12 and solve using Dynare13 The system of loglinearized equations is presented in appendix C. Tables 3 and 4 summarize the choice of parameter values and steady-state ratios for the benchmark model. Calibration value of the discount factor, β, the depreciation rate, δ, and the capital share of income, α, are standard. I set the habit parameter to 0 in the benchmark, and the inverse Frisch elasticity of labour supply to 1. The elasticity of net investment to capital price parameter is set to 1.728, following Gertler and Karadi (2011). The elasticity of substitution among retail goods, , is chosen to match a markup of 15 per cent. 12
Note that the steady-state value of net investment Itn is zero. I linearize the equations containing Itn and normalize by output. All log-linearized variables presented in appendix C are denoted by a hat, and linearized variables denoted by a tilde. 13 See Adjemian et al. (2011) and http://www.dynare.org/.
17
The Calvo parameter for the frequency of price adjustment is set to 0.8, which is common in the literature. I use the simplest form of the Taylor rule and set %π equal to 1.5, and %Y to zero, implying that there is no response by the monetary authority to deviations in output. The capital to output ratio is set to deliver an investment to output share of 0.1. There are no standard values prescribed in the literature for the parameters and steady-state values pertaining to the matching variables. I follow Beaubrun-Diant and Tripier (2009) and set the match probability of searching projects, p, to 0.4 and the loan market tightness, θ, to 0.6. The former value implies an average search duration of two-and-half quarter for projects. The match elasticity parameter, χ, is set to 0.5 and the bargaining power of the firm, η, is equated to this value in order to observe the Hosios (1990) condition of match efficiency. The steady state annual gross loan interest rate is set to 1.05. Using disaggregated quarterly data from the US banking system from 1999 through 2008, Contessi and Francis (2009) calculate a net growth rate in gross loans, denoted by N ET , of 4.67 per cent, and in loan reductions, denoted by N EG, of 2.42 per cent. To account for the trend in gross loans, I set the loan survival rate, x, to match the following x =
1 − N EG 1 + N ET
This gives a separation rate of 0.95. I assume a uniform distribution for the ‘relationship shock’ on a unit spread (i.e., ω − ω = 1 ), and set the threshold value for ω ˜ such that total cost to maintaining loan relationships in the steady-state equals zero.14 I set the steady-state capital price to equal 1 , and the total loan to output ratio to equal the capital to output ratio. The parameter κ ¯ is set such that bank equity is equal to 8 per cent of total assets. This matches the requirements set out in the 1988 Basel-I accord. In the steady-state, bank equity matches this requirement. I set the bank dividend payout rate, δ n , such that dividends equal net profits of the banking sector, including interest income, loan vacancy posting cost, and 14
Z
ω ˜t
A uniform distribution implies
ωdG(ω) = ω
ω ˜ t2 − ω . So, ω ˜ must follow the following two conditions 2(ω − ω)
ω ˜ −ω ω ˜ 2 − ω2 x= and 0 = . ω−ω 2(ω − ω)
18
separation cost.15 The dynamics of the search mechanism depends importantly on the loan vacancy posting cost, cv , and the parameters determining the cost of continuing or separating existing relationships, Υ and T . The benchmark values for these parameters are chosen to give reasonable impulse responses to the four types of shocks considered. In particular, the values are chosen to give a non-negative interest spread response on impact for technology and monetary shocks. I check the sensitivity of model results to the calibration of these parameters in section 3.2. Beaubrun-Diant and Tripier (2009) provides a discussion on the importance of similar parameters in generating a positive spread response in a search model of credit in an RBC framework.
3
Results
In this section, I analyze the responses of the benchmark model to three different shocks affecting the economy – a negative technology shock, a contractionary monetary shock, and a negative shock to productive capital quality. First, I show that the banking model amplifies and propagates the responses to all shocks considered. The amplification is due to a counter-cyclical spread between the loan rate and the deposit rate. I then explain the core mechanism of the search framework that generates the interest spread, and highlight how the bank leverage ratio helps in this process. Finally, I consider alternate calibration values for a few key parameters.
3.1
Comparison with the standard New Keynesian Model
Figure 1 compares impulse responses from the benchmark model with those from a standard New Keynesian one. The first three columns show responses for a one percent shock to technology, interest rate and capital quality, respectively. The persistence parameter of the technology shock, ρz , is set to 0.8, and that of the capital shock, ρξ , is set to 0.66, following Gertler and Karadi (2011). Figure 2 shows responses of selected financial market variables to the same shocks, presented in the same order. The presence of a banking sector amplifies and propagates the responses to all shocks. In 15
b
1 S T cv l Precisely, δ is set such that δ =n R −R 1− − n(1 − x) − v . Y κ ¯ Y Y Y n
nN
19
contrast, using exogenous borrowing constraints in a monopolistically competitive banking model, Gerali et al. (2010) find that the presence of banks attenuates the economy’s responses to monetary and technology shocks. Moreover, all negative shocks generate a counter-cyclical interest rate spread and a persistent recession. Importantly, the banking model generates a persistent recession following an i.i.d. increase in short-term interest rates. In contrast, the simple NK model generates a short-lived recession following a monetary shock. Usually, persistent responses to monetary shocks are achieved in the DSGE literature by assuming interest smoothing by the monetary authority, and inflation indexation in the New Keynesian Philips curve. In the banking model, however, a persistent recession is generated in the absence of these assumptions. In comparison to a technology shock, the effects of monetary shocks are more strongly amplified by the financial friction. This is because, ceteris paribus, an increase in the interest rate distorts the relative costs of input in production, and disproportionately affects the firm’s investment choices and capital price vis-`a-vis a technology shock. Following Gertler and Karadi (2011), I consider a negative shock to capital quality in an attempt to capture the effects of a financial crisis. A decline in capital quality reduces the productivity of capital and, in itself, can generate a recession. However, the resulting decline in capital prices also induces a persistent decline in the value of bank assets, as seen during the sub-prime crisis. It is this secondary effect that works through the financial system that is of interest here. Figure 1 shows that a reduction in the effectiveness of capital induces a modest recession in the NK model. In the presence of a banking sector, however, this decline is greatly amplified. The fall in capital value reduces the size of banking assets. This loss in assets is translated to a strong and persistent reduction in bank equity through the balance sheet identity. Interest spreads rise on impact, further reducing the demand for capital and investment by the firm. Capital prices fall even further, exacerbating the balance sheet position of banks. As a result, the overall contraction in the economy is magnified.
20
3.2
Explanation of the core mechanism
How do the banking sector and the credit search mechanism amplify shock responses? At the heart of the amplification is the counter-cyclical interest rate spread generated by movements in the extensive margin of loans. This mechanism is fortified by two additional channels considered here: endogenous separation and the bank leverage ratio. The intuition is as follows. The bank incurs search costs when looking for new projects to fund. When a negative technology, monetary, or capital quality shock hits the economy, loan demand goes down, as does expected profit. The bank will then reduce its efforts in searching for new matches, or in continuing existing ones. As a result, more existing matches will separate, and fewer new matches will be created. From the firm’s perspective, the scarcity of matches means that the probability of finding a new match, pt , will decline. On the other hand, as more and more projects go unmatched, the probability of finding a new match from the banker’s perspective, qt , will rise. The net effect is captured by a reduction in the market tightness variable θt =
pt qt .
Since
a match is now scarcer, it will be valued more by both the firm and the bank. Nash bargaining on loan rates will then ensure that this increase in the surplus from the match gets translated to an increase in loan interest rates. If the fall in θt is sufficiently large, the rise in loan rates will surpass any movement in the risk-free interest rate, and the interest rate spread will increase. This counter-cyclical spread, in turn, exacerbates the reduction in aggregate loans. Two additional channels in this model contribute to generating a counter-cyclical spread. First, the bank leverage ratio imposes a restriction on the amount of funding that each loan officer is able to generate. If a shock reduces the level of bank equity, the bank will have to rely more on household deposits to generate new loans. In this model, household deposits are pre-determined. A reduction in bank equity then provides a supply-side constraint that further increases credit market tightness by reducing θt and consequently increasing interest rate spreads. Second, endogenous match separation introduces another channel for the extensive margin of banks loans to vary. In contrast to Beaubrun-Diant and Tripier (2009) who consider a Nashbargaining approach where banks and firms jointly decide whether to separate or not, I model match separation as exclusively the banker’s decision. As a result, separation is triggered by the
21
same mechanisms as search effort, and ends up enhancing the movement in θt described above. The core search mechanism can be explained through equations (18) and (32). Using equations (8) and (7) to express the match probabilities pt and qt by the credit market tightness variable θt , imposing the balance sheet constraint nt−1 St = nt−1 Bt−1 + Ntb to replace household borrowing, and log linearizing, we get: χ cv ˆ 1 S ˆ S l χ cv ˆ l S ˆl θt = βR Rt+1 + βR 1 − Rt+1 + β R − R Sˆt+1 + βx θt+1 qY Y κ ¯ Y Y qY Nb R ˆb Ψ ˆ cv 1 Υ T ˆ + β Nt+1 − n ˆ t − β¯ κ + − ω ˜ x ˆt+1 (42) ℵt+1 − κ ¯ t+1 + βx Y n Y Y Y q Y S ˆl 1 S ˆ K ˆ m ˆm ˆ ˆ Rl R = ηR 1 − R + (1 − η)αP P + Y + (1 − η)(1 − δ) K + ξ t t t−1 t t Y t κ ¯ Y Y S cv K ˆ l Sˆt − ηxθ θˆt +(1 − η) Q t−η R −R Y Y Y b Ψ ˆ cv Υ RN T b ˆ ˆ Nt − n ˆ t−1 − η¯ κ +θ − ω ˜ x ˆt (43) − η ℵt − κ ¯ t + ηx n Y Y Y Y Y ˆ t,t+1 term has been omitted, where for convenience of exposition, the expectations operator and the Λ ˆt = n ˆtb . Variables and movement in the bank asset to capital ratio is expressed by ℵ ˆ t−1 + Sˆt − N without a time subscript represent steady-state values. Equation (42) says that θt would rise and banks will increase their search effort for new matches if future profits for the bank is expected to increase. Equation (43) says that any increase in profits to banks or firms would be shared between both parties through an increase in the loan rate. If, however, θt drops, then the loan rate would go up. Consider the limiting case of exogenous separation and a constant bank capital. In this case, there would be no penalty for deviating from the regulated bank asset to capital ratio. We would then have x ˆt = 0, and Ψ = 0. Consequently, the expressions within braces in the last lines of both equations would disappear. In this case, all else equal, a fall in expected future loans, St+1 or in θt+1 would induce a fall in the current tightness variable, θt , signaling a reduction in search efforts by the bank and lower number of matches. This, in turn, will raise the loan interest rate, Rtl . The problem, however, is that some shocks that induce a decline in borrowing, end up affecting the loan interest rate in the opposite direction. A negative technology shock reduces Yt , while a negative capital quality shock reduces ξt , and consequently, Qt – both of which provide downward pressure on the loan interest rate. The reduction in θt , therefore needs to be sufficiently large to
22
induce an overall increase in spreads Rtl − Rt . The calibration value of the loan vacancy posting cost is important in determining the dynamic response of θt . Figure 4 shows the sensitivity of impulse responses to changes in the parameter determining the ratio of vacancy posting cost to output,
cv Y .
A higher cost of vacancy posting
reduces the magnitude of the movement in θt , and generates a smaller initial response in interest spreads. However, spreads remain positive for a longer time, and the persistence of the recession increases. The benchmark value of
cv Y
= 1.5 was chosen to generate a positive spread response to
technology and monetary shocks. Calibrating this value to 3 ends up generating a negative spread response on impact. Both endogenous separation and the bank leverage ratio help generate persistence and amplification of shock responses. First, consider endogenous separation. Log-linearizing equation (19) around its steady-state, we get: x
Υ x ˆt = Y
χ cv ˆ θt qY
(44)
This shows that xt moves in the same direction as θt and acts to amplify its effect. The importance of this support is visible in figure 3, which compares a model with endogenous separation to one without. The model with exogenous separation produces a milder recession in response to technology and bank capital shocks, and a negative spread on impact for technology and monetary shocks. Referring back to the expression within braces in equation (42), note that movements in the separation rate xt amplifies the dynamics of θt only when
T Y
+
cv Yq
>
Υ ˜. Yω
Denote by φx the
T Y
+ Ycvq − YΥ ω ˜ . Figure
difference between the right and left hand sides of the inequality above: φx =
5 shows the sensitivity of the impulse responses to variations in φx . A low value of φx creates insufficient variation in θt and generates a negative response in interest spreads for technology and monetary shocks. Finally, and importantly, the leverage ratio in the banking sector also augments the dynamic responses of θt and the interest spread. First, note that bank deposits are pre-determined for the current period. Since the number of active matches are also pre-determined, it follows that any unexpected reduction in the asset side of the bank balance sheet is translated to a reduction in bank equity. Precisely this sensitivity of bank capital to the variations in bank assets has been at
23
the heart of the sub-prime crisis, and has prompted much of the asset-relief efforts from various governments, as well as the recent regulatory interest in capital buffers. Equations (42) and (43) show that an unexpected reduction in bank capital directly increases the loan interest rate, while an expected reduction in future bank capital lowers θt , which, in turn, brings a second round increase in the loan interest rate. The sizable increase in spreads following a one-time reduction in bank equity is generated precisely through this mechanism. There is a second round of amplification provided by the leverage ratio. To see this, denote nt−1 St the leverage ratio as ℵt = . In the steady state, ℵ = κ ¯ . The balance sheet identity implies Ntb that a fall in bank assets will result in a fall in bank equity of similar magnitude. It follows that the leverage ratio ℵt will rise. Equations (42) and (43) show that this will further amplify the interest spread. The model assumes that deviating from the required leverage ratio imposes a cost to the bank. This may be loosely motivated as a reputation cost internal to bank management, or an external cost payable to the regulator. The parameter Ψ controls the magnitude of this cost. Figure 12 shows impulse responses to different magnitudes of deviation cost. As expected, a high cost to deviation induces a smaller movement in θt and hence results in a less volatile spread over the cycle.
4
Credit Supply Shock and Gross Loan Flows
In this section, I show that the model produces empirically plausible responses in loan creation and destruction flows for a credit supply shock. First, I estimate the empirical response of gross loan flows and loan levels to an orthogonal credit supply shock in a VAR framework. Second, I show that a negative shock to bank equity generates counter-cyclical spreads, and movements in loan creation and destruction margins that qualitatively match VAR results. However, quantitatively, the model generates insufficient variations in gross loan flows compared to data. The empirical effect of credit supply shocks on the real economy has recently been studied by Gilchrist and Zakrajsek (2012b) and Boivin et al. (2012). Both studies find that a shock to credit supply has a substantial effect on the real economy. Gilchrist and Zakrajsek (2012a) finds that a negative shock to credit supply reduces aggregate bank lending to firms using a VAR framework.
24
However, whether this decline in aggregate loans is carried through by a reduction in new loan creation, or by destroying existing lending relations has not been studied. Creation and destruction margins may respond differently to shocks affecting the economy for several reasons. First, extending new loans and retiring existing ones are two distinct activities involving different costs. The former may involve the cost of information acquisition, searching for new clients, or evaluating new projects. On the other hand, contractions in loans may depend on the liquidity of borrowers or on the legal steps involved in ensuring repayment or separation of relationships. Second, loan expansion and contraction decisions may vary differently across banks. Regional and sectoral differences in both borrowers and lenders may result in overall loan contraction in some banks and expansion in others. Moreover, these idiosyncratic differences may depend on the type of shock affecting the economy. The 2008-09 recession was brought forth by a shock to the entire financial system. All banks were more-or-less negatively affected by the crisis.16 This is not necessarily the case for other recessions. Finally, Contessi and Francis (2009) finds that gross loan flows followed a unique pattern during the 2008 and 1990-91 recessions – both of which coincide with an erosion of bank equity. During most recessions, loan destruction increases and creation decreases. However, the magnitude of the changes are such that net loans, defined as expansion minus contraction, usually remains a small positive in level terms. Moreover, loan destruction does not usually persist beyond the initial quarter of the recession. In contrast, during the two recessions involving stress on the financial system, loan destruction exceeded creation so that the net loan flow became negative. This suggests that credit shocks may have a unique effect on the dynamics of these two variables. The goal of this section is to capture this pattern of response from a credit shock and to see whether the benchmark model is able to match it. In the remainder of the section, I first provide a quick summary of the data construction methodology for gross loan flows. I then describe the empirical findings and compare them with model results. 16
See Brunnermeier (2009) for a summary of the economic mechanisms that characterized the financial crisis.
25
4.1
Data
I use quarterly data series on gross loan flows calculated for 1979 through 1999 by Dell’Ariccia and Garibaldi (2005) and extended from 1999 through 2008 by Contessi and Francis (2009). Loan creation at time t is denoted by P OSt , and defined as the weighted sum of changes in credit for banks that increased loans in any given quarter. Loan destruction at time t is denoted by N EGt and defined as the absolute value of the weighted sum of changes in credit for all banks that decreased their loans since the previous quarter. This approach of constructing gross credit flows mirrors the calculation of gross job flows in Davis et al. (1998), where net employment changes in the economy is decomposed into the two components of gross job creation and gross job destruction. The two gross loan series are constructed using quarterly bank-level balance sheet information publicly available in the Reports of Condition and Income database (commonly called Call Report Files). Consolidation, entry and exits of banks during the time period is corrected for by matching the data with the National Information Center’s (NIC) transformation table to avoid double counting. The two series are calculated as follows: PN
˜
∆lit i|˜ l ≥0
P OSt = PNit
i=1 lit−1
PN
˜
∆lit i|˜ l <0
N EGt = PNit
i=1 lit−1 N ETt = P OSt − N EGt
where ∆˜lit is adjusted change in total loans, accounting for mergers and acquisitions, and lit is unadjusted loans. See Contessi and Francis (2009) for a full description of the data construction methodology. I join the series calculated by Contessi and Francis (2009) to the numbers form Dell’Ariccia and Garibaldi (2005) and consider an unbroken series running from 1979:Q2 through 2008:Q2. Note that the data represents all types of loans extended by commercial banks, including mortgages, lines of credit, and commercial and industrial loans. The model considered in the remainder of the paper, however, considers only commercial and industrial loans. Although this difference may be non-trivial for shocks to technology or monetary policy, it is not unreasonable to expect the general response of aggregate loans to carry through for other loan categories for a
26
financial shock that affects bank balance sheets on a systemic scale.
4.2
Estimation
I estimate the effect of a bank credit supply shock in a VAR framework. Identifying a credit supply shock, however, is complicated by the fact that many shocks that affect the supply of credit, including a tightening in monetary policy, can also have an independent effect on economic activity. To overcome this identification problem, I follow Gilchrist and Zakrajsek (2012b) and consider an orthogonal shock to the ‘GZ excess-bond premium’. This variable is constructed to measure the deviation in the pricing of corporate debt claims relative to the expected default risk of the issuer, and captures shifts in risk attitudes of financial intermediaries. Using a large panel of corporate bonds issued by non-financial firms, credit spreads associated with individual firms are decomposed into two components: one capturing the risk of default, and another capturing the cyclical-fluctuations of the relationship between default risk and credit spreads. Gilchrist and Zakrajsek (2012b) and Gilchrist and Zakrajsek (2012a) show that the majority of the information contained in credit spreads commonly used in the literature is attributable to movements in the excess bond premium, and that shocks to the excess bond premium that are orthogonal to current macroeconomic conditions have significant effects on the real economy, as well as on outstanding bank loans. To examine the effect of credit market disturbances on disaggregated loan flows, I consider a VAR with two lags that includes the following variables, ordered accordingly: (1) the log-difference in real investment, (2) the log-difference in real GDP, (3) log-difference in the GDP deflator, (4) the excess bond-premium, (5) the log-difference in real business loans outstanding in all commercial banks, (6) the effective (nominal) federal funds rate, (7) real loan creation (POS) and (8) real loan destruction (NEG).17 This ordering follows Gilchrist and Zakrajsek (2012a), and allows the first three variables, which are traditionally viewed as ‘slow moving’, to respond to a shock in credit supply only after a quarter. The variables ordered after the excess bond-premium, however, are allowed to respond contemporaneously to a shock in credit supply. The data are in quarterly 17
Real values of aggregate business loans, and disaggregated flows in loan creation and destruction is calculated by dividing the relevant variables with the GDP deflator.
27
frequency, and span the period from 1979:Q2 through 2008:Q2, for which information on loan creation and destruction are available. Figure 7 shows the impulse responses to a Cholesky-ordered shock to the excess bond-premium, along with their 68th and 95th percentile Monte Carlo confidence bands. An increase in the excess bond-premium generates a recession driven by a reduction in investment. Aggregate commercial and industrial loans outstanding at all banks decline. Most importantly, loan creation falls and loan destruction rises a few quarters after the initial shock. Therefore, in so far as the excess bond-premium captures information about the supply of bank credit, we can say that a negative supply shock increases loan destruction, and reduces loan creation. A more direct measure of bank credit supply, however, can be gathered from survey results on banks’ willingness to lend. The Federal Reserve Board’s Senior Loan Officer Opinion Survey on Banking Lending Practices, conducted each quarter on 60 US banks, asks senior officers whether banks have changed their credit standards over the past three months. The data, available from 1990:Q2, is plotted in figure 6, along with the excess bond premium. The solid line represents the net percentage of banks that reported tightening their credit standards on commercial and industrial loans to large and medium-sized firms. The net percentage is calculated as the percentage of banks that report tightening less the percentage that report not tightening lending standards.18 As the figure shows, banks tighten their lending standards counter-cyclically, and at the height of the financial crisis, almost all banks reported doing so. Indeed, one of the merits of the GZ excess bond-premium listed in Gilchrist and Zakrajsek (2012a) is its strong co-movement properties with the change in lending standards, clearly demonstrated in the figure. With this arguably more direct measure of bank credit supply, I run a VAR with two lags that includes the following variables, ordered accordingly: (1) the log-difference in real investment, (2) the log-difference in real GDP, (3) net percentage of banks tightening lending standards, (4) the excess bond-premium, (5) the log-difference in real business loans outstanding in all commercial banks, (6) the effective (nominal) federal funds rate, (7) real loan creation (POS) and (8) real loan destruction (NEG). The impulse responses from an orthogonalized shock to bank lending standards 18
See http://www.federalreserve.gov/boarddocs/SnLoanSurvey/ for a description of the questions and more information on the survey.
28
is reported in figure 8. An tightening of lending standards increases the excess bond premium on impact. Consequently, outstanding commercial and industrial bank loans fall gradually, as do investment and output. Loan creation declines with a lag, and loan destruction rises on impact. Overall, I take the above evidence to suggest that a reduction in bank credit supply has a negative effect on the real economy, driven by a rise in interest spreads, and a consequent fall in loans to firms. Moreover, following a credit supply shock, disaggregated loan destruction rises and loan creation falls.19
4.3
Model Analysis
In this subsection, I compare model results on loan creation and destruction flows from a credit supply shock with empirical evidence outlined above. Note that the empirical definition of these flows include changes in loans from both the intensive and extensive margins. To conform with data, I derive the following parallel in the benchmark model: P OSt =
mt−1 St nt−2 St−1
N EGt = (1 − xt )
St St−1
where 1 − xt is the separation rate. I find that the model can generate impulse responses for loan creation and destruction flows to a credit supply shock that qualitatively match evidence, if investment is allowed to be less sluggish than usually assumed in the literature. To capture the concept of a shock to credit supply, I consider an i.i.d. shock to Bank equity, as well as an i.i.d. increase to the match separation rate. Figure 9 shows impulse responses for both these shocks for the benchmark calibration. For comparison, the ‘crisis experiment’ case of a negative capital quality shock is also included in the figure. We see that all three shocks result in a counter-cyclical rise in the interest spread, and an ensuing recession. However, apart from the rise on impact for NEG, and the eventual decline in POS for the capital 19
In an earlier version of this paper, I considered estimating the effects of financial shocks in a FAVAR framework, following Boivin et al. (2012). Identification was achieved through the following sign restrictions: the volatility of the S&P index increases, the level of the S&P index falls, the spread between corporate BAA bonds and treasury yields rises, the treasury yield falls, and both GDP and investment fall on impact. Using this framework, I found qualitatively similar results to those reported here. This analysis is available upon request, but not included in this version of the paper.
29
quality shock, the response for disaggregated flows do not conform with data. To see why this may be the case, note that net loan flows, which equal loan creation less loan destruction, captures changes in loan levels. For each of the shocks considered, we see a large temporary drop in capital prices, followed by a gradual decline in capital stock. Since loans are used in this model to purchase capital, the impulse response of total real loans reflect both the large initial drop in real capital prices as well as the small gradual decline in capital levels. As such, the impulse response for loans does not match the smooth response seen in the data. Since responses in disaggregated loan flows capture the curvature of the response in loan levels, we see the counter-factual result shown in figure 9. If however, investment were allowed to be more responsive to capital prices, we may generate loan responses of the shape seen in the data. In the benchmark model, the parameter capturing the inverse of the elasticity of net investment to the price of capital was set to 1.728, as adopted by Gertler and Karadi (2011). This is representative of the values commonly assumed in the macro literature. However, using disaggregated data from 18 U.S. manufacturing industries, Groth and Khan (2010) estimate the weighted average of the elasticity of investment to the current shadow price of capital to be 15.2, suggesting a value of the inverse elasticity parameter of around 0.067. Figure 10 shows impulse responses of investment, aggregate loans, real capital price, and capital levels for credit supply shocks for two calibrations. The dashed line represents the benchmark calibration with a high inverse elasticity parameter, and the solid line represents a calibration of 0.11, a value between the two extremes mentioned above. We see that with a more elastic investment, the impulse response for loans are smoother, with a much higher drop in investment for a credit supply shock. Figure 11 shows the responses for output, spreads, and both aggregate loans and disaggregated loan flows to the same three shocks for the highly elastic investment case. We see now that both for the bank equity shock, as well as the capital quality shock, loan destruction increases on impact, and loan creation falls persistently. This evidence is more in tune with the empirical results seen in figures 7 and 8. A one-time reduction in the separation rate, however, does not generate impulse responses of disaggregated loan flows that match evidence, despite the smooth reaction of investment. Loan destruction rises due to the shock to the separation rate. However, in light of
30
an increased interest spread, and in the absence of a shock affecting loan demand, banks have no reason to continue reducing loans. Rather, banks increase their efforts to find new matches, which in turn, increases loan creation. This result suggests that a more meaningful representation of credit supply shocks are needed to match movements in disaggregated loan flows seen in the data. From a quantitative perspective, I find that the model generates empirically plausible cyclical comovements in gross loan flows. The data calculated from bank balance sheet information shows that loan creation is mildly pro-cyclical, while loan destruction is mildly counter-cyclical. Herrera et al. (2011) calculate similar flows using non-financial firm-level data from S&P full coverage Compustat tapes, and find cyclical correlations of a similar magnitude. Table 1 compares the correlation of gross loan flows with output from the Dell’Ariccia and Garibaldi (2005) and Contessi and Francis (2009) dataset and those derived from model simulations for each of the shocks considered in the model for the benchmark calibration.20 For all shocks considered, the correlation of gross loan flows with output are comparable to evidence.
Table 1: Correlation of gross loan flows with output Variables
data
technology
monetary
capital quality
bank equity
POS
0.20
0.17
0.31
0.47
0.35
NEG
-0.21
-0.19
-0.34
-0.12
-0.24
NET
0.20
0.38
0.37
0.51
0.30
The model fails, however, to generate volatilities in gross loan flows comparable to evidence. Dell’Ariccia and Garibaldi (2005) find that both variations in loan destruction and loan creation are larger in magnitude than variations in output. Moreover, destruction is more volatile than creation of loans. Table 2 summarizes the standard deviations of creation and destruction flows relative to output for each of the shocks considered in the model for the benchmark calibration, along with the relevant empirical values for aggregate loans. We see that for each shock, the model is able to generate gross loan creation that is more volatile than output. However, the volatility of loan creation is an order of magnitude smaller than seen in the data. Moreover, the volatility of N EGt is smaller than output. This suggests, if anything, 20
i.e. the relative standard deviation if the economy were subject to one type of shock only.
31
Table 2: Standard deviation of gross loan flows relative to output Variables
data
technology
monetary
capital quality
bank capital
POS
23.85
1.57
2.36
1.97
2.10
NEG
26.71
0.10
0.39
0.14
0.39
that the model requires an even stronger variation in endogenous separation.
5
Countercyclical Leverage Ratio Regulations
In this section, I show that the benchmark model is still useful in analyzing aggregate policy outcomes. In particular, I show that a countercyclical bank leverage regulation reduces the magnitude of a recession following a negative shock. The Basel III regulatory standards that came out as a reaction to the financial crisis features a countercyclical bank capital buffer. The idea is that banks would build up extra capital during periods of strong credit increase. The required leverage ratio would consequently be reduced during times of financial stress. To capture such a counter-cyclical regulation, I specify the following rule for the regulated leverage ratio: κ ¯t = κ ¯
$ % κ t
$
where $t can be any economic variable that the regulator chooses, and $ its steady state value. Following Christensen et al. (2011), I chose the ratio of bank credit to GDP as the target economic variable. This is consistent with the fact that the Basel III regulations also require each country to publish a credit-to-GDP ratio to guide the operation of the capital buffer. A countercyclical leverage ratio requirement implies a value of %κ < 0. Figure 13 compares impulse responses between an economy with fixed leverage ratio regulation, and one facing a counter-cyclical leverage ratio regulation. The counter-cyclical leverage regulation diminishes the responses to all negative shocks.
32
6
Conclusion
In this paper, I develop a search-theoretic banking model in a New-Keynesian DSGE framework that can simultaneously explain movements in gross flows in loan creation and destruction, and the interest rate spread. The model demonstrates that the presence of the banking sector amplifies and propagates the economy’s response of a number of shocks by generating a counter-cyclical interest rate spread. Shocks that disproportionately affect the balance sheets of banks are particularly amplified. Moreover, shocks originating within the banking sector also lead to a prolonged recession. I show that the model generates responses in gross loan creation and destruction flows to a credit supply shock that qualitatively match empirical evidence. I estimate the effect of a credit supply shock on loan creation and destruction margins in a VAR framework. I then consider two shocks that can proxy the effects of a credit supply shock – a one time reduction in bank equity, and a one time increase in the match separation rate. I also consider a negative shock to the quality of productive capital, which works through the bank balance sheet identity and reproduces well important movements related to the bank leverage channel observed during the recent crisis. I show that both the capital quality shock, as well as the shock to bank equity can produce impulse responses that qualitatively match evidence, provided investment sensitivity to capital prices is allowed to be high enough to match levels estimated from disaggregated data, rather than the low values usually assumed in aggregate macro models. An exogenous increase in the separation rate, however, does not produce empirically plausible responses for disaggregated loan flows. Finally, the model predicts that banks naturally respond to negative shocks by varying their leverage ratio in a counter-cyclical manner. This, in turn, raises interest spreads even further. Regulatory authorities can diminish this channel of financial acceleration by imposing a higher cost of deviation from the regulated leverage ratio, or a counter-cyclical capital buffer where the policy instrument responds to the loan-to-output ratio. The model fails, however, to quantitatively match the business cycle volatilities of gross loan creation and destruction flows. In particular, volatilities of these two margins are far lower than seen in the data. Overall, however, the paper demonstrates that a search-theoretic banking model is a step in the right direction in jointly explaining movements in the interest rate spread and gross
33
loan flows, while keeping the model useful for aggregate policy analysis.
34
References Adjemian, S., Bastani, H., Juillard, M., Mihoubi, F., Perendia, G., Ratto, M. and Villemot, S.: 2011, Dynare: Reference manual, version 4, Dynare Working Papers 1, CEPREMAP. Aliaga-D´ıaz, R. and Olivero, M. P.: 2010, Macroeconomic implications of deep habits in banking, Journal of Money, Credit and Banking 42(8), 1495–1521. Andolfatto, D.: 1996, Business cycles and labor-market search, American Economic Review 86(1), 112–32. Beaubrun-Diant, K. E. and Tripier, F.: 2009, The credit spread cycle with matching friction, Working Papers hal-00430809, HAL. URL: http://ideas.repec.org/p/hal/wpaper/hal-00430809.html Bernanke, B. S., Gertler, M. and Gilchrist, S.: 1999, The financial accelerator in a quantitative business cycle framework, in J. B. Taylor and M. Woodford (eds), Handbook of Macroeconomics, Vol. 1 of Handbook of Macroeconomics, Elsevier, chapter 21, pp. 1341–1393. Boivin, J., Giannoni, M. P. and Stevanovi´c, D.: 2012, Dynamic effects of credit shocks in a data-rich environment, Manuscript. Brunnermeier, M. K.: 2009, Deciphering the liquidity and credit crunch 2007-2008, Journal of Economic Perspectives 23(1), 77–100. Calvo, G.: 1983, Staggered pricing in a utility maximizing framework, Journal of Monetary Economics 12, 383–96. Chari, V., Christiano, L. J. and Kehoe, P. J.: 2008, Facts and myths about the financial crisis of 2008, Technical report. Christensen, I., Meh, C. and Moran, K.: 2011, Bank leverage regulation and macroeconomic dynamics, Technical report.
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Christiano, L. J., Eichenbaum, M. and Evans, C. L.: 2005, Nominal rigidities and the dynamic effects of a shock to monetary policy, Journal of Political Economy 113(1), 1–45. Cohen-Cole, E., Duygan-Bump, B., Fillat, J. and Montoriol-Garriga, J.: 2008, Looking behind the aggregates: a reply to facts and myths about the financial crisis of 2008, Technical report. Contessi, S. and Francis, J.: 2009, U.s. commercial bank lending through 2008:q4: new evidence from gross credit flows, Technical report. Davis, S. J., Haltiwanger, J. C. and Schuh, S.: 1998, Job Creation and Destruction, Vol. 1 of MIT Press Books, The MIT Press. Dell’Ariccia, G. and Garibaldi, P.: 2000, Gross credit flows, CEPR Discussion Papers 2569, C.E.P.R. Discussion Papers. URL: http://ideas.repec.org/p/cpr/ceprdp/2569.html Dell’Ariccia, G. and Garibaldi, P.: 2005, Gross credit flows, Review of Economic Studies 72(3), 665– 685. den Haan, W. J., Ramey, G. and Watson, J.: 2003, Liquidity flows and fragility of business enterprises, Journal of Monetary Economics 50(6), 1215–1241. deWalque, G., Pierrard, O. and Rouabah, A.: 2010, Financial (in)stability, supervision and liquidity injections: A dynamic general equilibrium approach, Economic Journal 120(549), 1234–1261. Dib, A.: 2010, Capital requirement and financial frictions in banking: Macroeconomic implications, Technical report. Gerali, A., Neri, S., Sessa, L. and Signoretti, F. M.: 2010, Credit and banking in a DSGE model of the euro area, Journal of Money, Credit and Banking 42(s1), 107–141. Gertler, M. and Karadi, P.: 2011, A model of unconventional monetary policy, Journal of Monetary Economics 58(1), 17–34.
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Gilchrist, S. and Zakrajsek, E.: 2012a, Bank lending and credit supply shocks, in F. Allen, M. Aoki, N. Kiyotaki, R. Gordon, J. E. Stiglitz and J.-P. Fitoussi (eds), The Global Macroeconomy and Finance, Palgrave Macmillan, pp. 154–176. Gilchrist, S. and Zakrajsek, E.: 2012b, Credit spreads and business cycle fluctuations, American Economic Review 102(4), 1692–1720. URL: http://ideas.repec.org/a/aea/aecrev/v102y2012i4p1692-1720.html Groth, C. and Khan, H.: 2010, Investment adjustment costs: An empirical assessment, Journal of Money, Credit and Banking 42(8), 1469–1494. URL: http://ideas.repec.org/a/mcb/jmoncb/v42y2010i8p1469-1494.html Herrera, A. M., Kolar, M. and Minetti, R.: 2011, Credit reallocation, Journal of Monetary Economics 58(6), 551–563. Hosios, A. J.: 1990, On the efficiency of matching and related models of search and unemployment, Review of Economic Studies 57(2), 279–98. Ivashina, V. and Scharfstein, D.: 2010, Bank lending during the financial crisis of 2008, Journal of Financial Economics 97(3), 319–338. Meh, C. A. and Moran, K.: 2010, The role of bank capital in the propagation of shocks, Journal of Economic Dynamics and Control 34(3), 555–576. Merz, M.: 1995, Search in the labor market and the real business cycle, Journal of Monetary Economics 36(2), 269–300. Monacelli, T., Perotti, R. and Trigari, A.: 2010, Unemployment fiscal multipliers, Journal of Monetary Economics 57(5), 531–553. Mortensen, D. T. and Pissarides, C. A.: 1994, Job creation and job destruction in the theory of unemployment, Review of Economic Studies 61(3), 397–415. Nolan, C. and Thoenissen, C.: 2009, Financial shocks and the us business cycle, Journal of Monetary Economics 56(4), 596–604.
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Pissarides, C. A.: 1985, Short-run equilibrium dynamics of unemployment vacancies, and real wages, American Economic Review 75(4), 676–90. Smets, F. and Wouters, R.: 2007, Shocks and frictions in us business cycles: A bayesian DSGE approach, American Economic Review 97(3), 586–606. Wasmer, E. and Weil, P.: 2004, The macroeconomics of labor and credit market imperfections, American Economic Review 94(4), 944–963.
38
A
Timing
State variables: • nt−1 : number of projects that receive funding in period t. • Kt−1 : symmetric equilibrium capital used for production in each project in period t. b : bank capital at the beginning of period t. • Nt−1
• Bt−1 : amount of deposits saved in the banking sector the end of period t − 1 by households that make up loans for the purchase of capital in period t. Timing: • Time t begins with the number of funded projects, total productive capital quantity, and bank deposits to be used in period t as given. • Aggregate shocks hit the economy. • Firms and Banks determine loan interest rate Rtl through Nash bargaining. • Firms chose symmetric equilibrium loan level St = Qt Kt−1 for each funded project, given the loan interest rate Rtl . Each funded project receives capital Kt−1 purchased at price Qt for production this period. • Labour demand / supply and wage setting takes place. • Production occurs in funded projects according to Yt = zt (ξt Kt−1 )α Lt1−α . • Firms repay Rtl St to banks. • After loans are repaid for the period, each project / loan officer relationship suffers an idiosyncratic ‘relationship shock’ ωt from a uniform distribution. This is a cost to maintaining the relationship from the bank’s perspective. If ω ≤ ω ˜ , the relationship survives, banks pay ωt and keep the match. If ω > ω ˜ , banks pay a fixed penalty amount T in lieu of the ω relationship cost and severe the relationship.
39
• Banks determine how many currently active relationships to sever (separation rate xt ) and how many new credit relationships to open. Accordingly, they hire loan officers at a cost of cv per hire and look for new relationships, keeping in mind the penalty to be paid if the capital adequacy ratio is not met. • Match between unfunded projects and open credit lines occur, and the number of funded projects for t + 1 is determined. • Firms sell worn out capital to the capital producing sector, where new capital is created for use in t + 1. • Firms sell intermediate goods to the retail sector. Prices are determined. The monetary authority reacts to inflation by setting the nominal policy rate Rt + πt+1 . • Banks repay households for their deposits Bt−1 at real interest rate Rt , and pay any penalties for deviating from the capital adequacy ratio κ ¯ . Aggregate bank profits are realized, dividends δ n Ntb are paid out, and Bank net worth is determined. • Period t ends.
40
B
Non-linear system of equations Ct = Wt LYt + Rt nt−1 St − Ntb − nt St+1 − Ntb + Divt ϕ LY t = λt Wt λt = (Ct − aCt )−1 − aβ (Ct+1 − aCt )−1
(48)
λt+1 λt
(49)
b nt−1 St = nt−1 Bt−1 + Ntb
(50)
St = Qt Kt−1
(51)
ω ˜t − ω ω−ω cv = T+ qt
xt = Υ˜ ωt
(52) (53)
nt = xt nt−1 + qt vt Ntb = nt−1 Πbt − cv vt −
(54)
Ψ nt−1 St −κ ¯ 2 Ntb
2
Ntb b + (1 − δ n )Nt−1 − nt St
nt−1 St = nt−1 Bt−1 + Ntb Z ω˜ t+1 cv l ωdG(ω) − (1 − xt+1 )T = βΛt,t+1 Rt+1 St+1 − Rt+1 Bt − Υ qt ω " # ) nt St+1 cv −Ψ −κ ¯ + xt+1 b qt+1 Nt+1 Z ω˜ t Yt b l m Rt St = (1 − η) Pt α + (Qt − δ)ξt Kt−1 + ηRt Bt−1 + ηΥ ωdG(ω) Kt−1 ω nt−1 St pt +η(1 − xt )T + ηΨ −κ ¯ − ηcv xt b qt Nt Yt = zt (ξt Kt−1 )α (Lt )1−α
t αPtm KYt−1
(55) (56)
(57)
(58) (59)
Yt Lt + (Qt+1 − δ)ξt
Wt = (1 − α)Ptm Rtl =
(46) (47)
1 = βΛt,t+1 Rt Λt,t+1 =
(45)
(60) (61)
Qt
41
ut = 1 − xt nt−1
(62)
vt = θt [1 − xt nt−1 ]
(63)
qt = mθ ¯ t−χ
(64)
qt vt = mθ ¯ t1−χ [1 − xt nt−1 ]
(65)
pt = mθ ¯ 1−χ
(66)
Y Itn ≡ It − δξt Kt−1
(67)
KtY
Y = ξt Kt−1 + Itn
KtY
= nt Kt
(68) (69)
Qt = 1 + f (·) + π ˆt ˆt + π R ˆt+1 YtY
n + I¯2 It+1 f 0 (·) n ¯ It + I
Itn + I¯ 0 f (·) − Et βΛt,t+1 n + I¯ It−1 (1 − βθ)(1 − θ) ˆ m = βEt π ˆt+1 + Pt θ = %π π ˆt + %y Yˆt + m t n Z ω˜ It+τ + I¯ n ¯ = Ct + I t + f n ¯ (It+τ + I) + cv vt + nt−1 Υ ω ωdG(ω) It+τ −1 + I Z ω +nt−1 T dG(ω)
(70) (71) (72)
(73)
ω ˜
YtY
= nt−1 Yt
(74)
LYt
= nt−1 Lt
(75)
KtY
= nt Kt
(76)
BtY
= nt Bt
(77)
ˆ ω ˜t = x ˆt
(78)
zˆt = ρz zˆt−1 + zt
(79)
ξˆt = ρξ ξˆt−1 + ξt
(80)
42
C
Log-linearized System of Equations b W LY ˆ ˆt + R n S − N R ˆ t + Rn S n Wt + n ˆ t−1 + L ˆ t−1 + Sˆt Y Y Y Y b b b N ˆb S N ˆb N ˆb −R Nt − n Nt+1 + δ n N n ˆ t + Sˆt+1 + Y Y Y Y t−1 ˆ t) = W ˆ t − Cˆt ϕ(ˆ nt−1 + L C Y
=
ˆt Cˆt+1 − Cˆt = R
(82) (83)
ˆ t = Cˆt − Cˆt+1 Λ ω ˜ 1 ˆ x ˆt = ω ˜t x ω−ω χ cv ˆ Υ ˆt = θt x x Y qY
(84) (85) (86)
n ˆ t = x(1 − p)(ˆ xt + n ˆ t−1 ) + (1 − χ)
p(1 − xn) ˆ θt n
(87)
ˆt + K ˆ t−1 Sˆt = Q Nb
(81)
(88)
Nb
S ˆ T cv Υ ˆ b = nRl S R ˆl + R N −n Rt + nx +θ − ω ˜ x ˆt t t Y Y Y Y Y Y Y S l Nb ˆb cv Nb ˆb +n R − R Sˆt + R Nt − (1 − xn)θ θˆt + (1 − δ n ) N Y Y Y Y t−1 S T cv +n Rl − R − (1 − x) + xθ n ˆ t−1 − εnt (89) Y Y Y χ cv ˆ 1 cv ˆ 1 Nb S ˆ S Ψ ˆ l S ˆl l θt = Λt + βR Rt+1 + βR − Rt+1 + β R − R − n b St+1 qY qY Y n Y Y Y N b cv 1 Υ RN Ψ S T + − ω ˜ x ˆt+1 − β +n b n ˆt +βx Y Y q Y n Y N Y Nb R Ψ S ˆb Ψ χc ˆ¯ t+1 + βx v θˆt+1 +β + n b b Nt+1 + β κ ¯κ (90) Y n Y qY N N S ˆl ˆ K ˆ Rl Rt + St = (1 − η)αP m Pˆtm + Yˆt + (1 − η)(1 − δ) Kt−1 + ξˆt Y Y b Ψ S K ˆ RN Ψ S ˆ +n n ˆ t−1 + η R + n b St +(1 − η) Qt + η Y n Y Y Nb N Y R Ψ S Nb ˆb S 1 Nb ˆ −η +n b b Nt + ηR − Rt n Y Y n Y N N cv Υ Ψ c T ˆ¯ t − ηxθ v θˆt −ηx +θ − ω ˜ x ˆt − η κ ¯κ (91) Y Y Y Y Y ˆ t−1 ) + (1 − α)L ˆt Yˆt = zˆt + α(ξˆt + K (92) ˆ t = Pˆtm + Yˆt − L ˆt W
(93)
43
n o ˆ t = f 00 (·) (1 + β)I˜n − I˜n − β I˜n Q t t−1 t+1 K ˆ ˆ ˆ t−1 It − ξt − K I˜tn = δ Y ˆ t = (1 − δ)(K ˆ t−1 + ξˆt ) + δ Iˆt K π ˆt = β π ˆt+1 +
(1 − βθ)(1 − θ) ˆ m Pt θ
ˆt + π R ˆt+1 = %π π ˆt + rt Yˆt =
C ˆ K Ct + δ Iˆt Y Y
(94) (95) (96) (97) (98) (99)
zˆt = ρz zˆt−1 + zt
(100)
ξˆt = ρξ ξˆt−1 + ξt
(101)
ˆ t = m P OS ˆ t−1 + Sˆt − n ˆ t−2 − Sˆt−1
(102)
ˆ t = x N EG ˆt−1 + Sˆt − Sˆt−1
(103)
ˆ t = N ET
D
Calibration Tables
E
Figures
m ˆ ˆ t P OS t + xN EG n
44
(104)
Table 3: Calibration of parameters and steady-state ratios Households β
Discount rate
0.99
h
Habit parameter
0
ϕ
Inverse Frisch elasticity of labour supply
1
Intermediate Firms α
Capital share of output
0.33
δ
Capital depreciation rate
0.025
Elasticity of net investment to capital price
1.728
Capital Producing Firms f 00 (·) Retailers Θ
Calvo price setting parameter
0.8
Elasticity of substitution
7.5
Consumption to output ratio
0.6
Aggregation and Policy C Y K Y %π
Inflation coefficient on Taylor rule
1.5
%Y
Output coefficient on Taylor rule
0.5
ρz
Persistence of technology shock
0.09
ρξ
Persistence of capital quality shock
0.66
Capital to output ratio
2.04 × 4
Shocks
45
Table 4: Calibration of parameters and steady-state ratios contd. Matching p
Match probability of searching projects
0.4
θ
Loan market tightness
0.6
χ
Elasticity of match
0.5
η
Bargaining power of firm
0.05
Banks Rl
SS loan interest rate
R
SS deposit interest rate
x
SS match survival rate
ω ˜
Threshold continuation shock
n
SS number of matches
κ ¯
SS bank loan to capital ratio
δn S Y Nb cY
Bank dividend payout rate
v
Y T Y Υ Y Ψ Y
1.051/4 1 β 0.95
SS loan to output ratio SS bank capital to output ratio Loan vacancy posting cost to output Separation cost to output
x/2 p 1 − x(1 − p) 1 0.08 0.37 1 K × n Y 1 S × κ ¯ Y 1.5 6
Marginal continuation cost to output
9.43
Quadratic cost for deviating from capital adequacy
0.1
46
Figure 1: Impulse responses for benchmark and new Keyenesian models. Technology
Monetary
Output
0
Capital Quality
0
0
−0.05
−0.2
−0.02 −0.04 −0.06
−0.1
Investment
5
10
15
20
−0.4 5
10
15
20
0
0
0
−0.1
−0.1
−0.5
−0.2
−1
−0.2
5
10
15
20
5
10
15
20
5
10
15
20
5
10
15
20
−0.3 5
10
15
20
5
10
15
20
Spread
0.8 6
6
0.4
4
4
0.2
2
2
0.6
0
Policy Rate
5
10
15
20
0
0 5
10
15
20 0.02
0.08
0.02 0.01 0 5
10
15
20
0.06
0
0.04
−0.02
0.02
−0.04
0
−0.06 5
10
15
20
Notes: Solid lines represent the benchmark model with a banking sector, broken line represents a standard New Keynesian model. The first column represents impulse responses to a negative technology shock, the second to a contractionary monetary shock, and the third to a negative capital quality shock.
47
Figure 2: Impulse responses for selected banking sector variables.
Theta
Technology 0 −0.1
0.2
−0.2
0
10
15
20
−0.2 5
0
0
−0.01
−0.1
10
15
20
5
10
15
20
5
10
15
20
5
10
15
20
5
10
15
20
0
−0.2
−0.02
−0.2
−0.03
−0.3 5
10
15
20
0 Int Margin
Capital Quality 0.4
−0.3 5
Bank Equity
Monetary
0.04 0.02 0 −0.02 −0.04 −0.06
5
10
15
20
0
0
−0.02
−0.2
−0.05
−0.04
−0.4
−0.1 5
10
15
20
−0.4
5
10
15
20
−3
Ext Margin
x 10
0.08 0.06 0.04 0.02 0 −0.02
0
5
−0.01
0
−0.02
−5 5
10
15
20
5
10
15
20
Notes: Solid lines represent the benchmark model with a banking sector, broken line represents a standard New Keynesian model. The first column represents impulse responses to a negative technology shock, the second to a contractionary monetary shock, the third to a negative capital quality shock.
48
Figure 3: Impulse responses highlighting the importance of endogenous match separation.
Output
Technology
Monetary
0 −0.02 −0.04 −0.06 −0.08
0 −0.05 −0.1 −0.15 5
Spread
Capital Quality
10
15
20
0
0
−0.2
−0.05
−0.4
−0.1 −0.15
−0.6 5
10
15
20
5
10
10
5
5
0
0
10
15
20
5
10
15
20
5
10
15
20
5
10
15
20
20
0.5 0 −0.5
10 0
−5 5
Tightness
Bank Capital
10
15
20
0.04 0.02 0 −0.02 −0.04
5
10
15
20
0
−0.3 15
20
15
20 0 −0.1
0
−0.2 10
10
0.2
−0.1
5
5
−0.2
−0.2 5
10
15
20
5
10
15
20
Note: Solid line represents a model with endogenous match separation, broken line represents a model with exogenous match separation. The first column represents impulse responses to a negative technology shock, the second to a contractionary monetary shock, the third to a negative capital quality shock, and the fourth to a negative shock to bank capital.
49
Figure 4: Sensitivity to the cost of posting loan vacancies. Technology
Monetary
Output
0 −0.02 −0.04 −0.06
Capital Quality
Bank Capital
0
0
0
−0.05
−0.2
−0.01
−0.1
−0.4
−0.02
−0.08
Spread
5
15
20
5
10
15
20
6 4 2 0 −2
1 0.5 0 5
Tightness
10
10
15
20
0.05
−0.1 10
15
20
15
20
10
15
20 0.5
−0.2
0
10
15
20
10
15
20
20
0
5
10
15
20
5
10
15
20
0 −0.02 −0.04 −0.06 −0.08
−0.5 5
15
2 5
0
10
4
0 5
5 6
5
−0.4 5
10
10
0 −0.05
5
5
10
15
20
Note: Solid line represents benchmark value of cYv = 1.5, broken line represents a bigger value of cYv = 3, and dotted line represents a lower value of cYv = 0.8. The first column represents impulse responses to a negative technology shock, the second to a contractionary monetary shock, the third to a negative capital quality shock, and the fourth to a negative shock to bank capital.
50
Figure 5: Sensitivity to the cost of adjusting the separation rate.
Output
Technology
Monetary
0 −0.02 −0.04 −0.06 −0.08
0
−0.05
−0.2
−0.01
−0.4
−0.02
−0.15 10
15
20
1.5 Spread
Bank Capital
0
−0.1 5
5
10
15
20
8 6 4 2 0 −2
1 0.5 0 5
Tightness
Capital Quality
0
10
15
20
0.04 0.02 0 −0.02 −0.04 −0.06 −0.08
5
10
15
6
5
4
0
2 5
10
15
20
5
10
15
20
10
15
20
5
10
15
20
5
10
15
20
−0.02 −0.04
−0.2 −0.4
0
5
0
0
−0.3 20
20
0.2
−0.2 15
15
0.4
−0.1
10
10
10
20
0
5
5
5
10
15
20
Note: Solid line represents benchmark value of φx = 3.75, broken line represents a bigger value of φx = 4.5, and dotted line represents a lower value of φx = 1.5. The first column represents impulse responses to a negative technology shock, the second to a contractionary monetary shock, the third to a negative capital quality shock, and the fourth to a negative shock to bank capital.
51
Figure 6: Net percentage of banks tightening lending and the excess bond premium. 100.0
2.5 2
80.0
1.5
60.0
1
40.0 0.5 20.0 0
0.0
-0.5
Net Tightening Standards
2010-Q3
2009-Q4
2009-Q1
2008-Q2
2007-Q3
2006-Q4
2006-Q1
2005-Q2
2004-Q3
2003-Q4
2003-Q1
2002-Q2
2001-Q3
2000-Q4
2000-Q1
1999-Q2
1998-Q3
1997-Q4
1997-Q1
1996-Q2
1995-Q3
1994-Q4
1994-Q1
1993-Q2
1992-Q3
-1.5 1991-Q4
-40.0 1991-Q1
-1
1990-Q2
-20.0
Excess Bond Premium
Note: Solid line represents the net percentage of banks reported as tightening lending standards for commercial and industrial loans to large and medium firms. Marked line represents the Gilchrist and Zakrajsek (2012b) excess bond premium.
52
Figure 7: VAR Impulse responses to an increase in the excess bond premium.
Investment
GDP
0
1
−1
0
−2
−1 5
10
15
20
5
Prices
10
15
20
Excess Bond Premium
2
0.8 0.6 0.4 0.2 0 −0.2
0 −2 5
10
15
20
5
C&I Loans
10
15
20
15
20
15
20
Funds Rate
0
0
−2
−2
−4
−4
−6 5
10
15
20
5
POS
10 NEG
0.1
0.2
0
0.1
−0.1
0
−0.2
−0.1 5
10
15
20
5
10
Note: Dashed lines represent 68th percentile and dotted lines represent 95th percentile Monte Carlo confidence bands. 53
Figure 8: VAR impulse responses to an increase in the net percentage of banks tightening lending standards.
Investment
GDP
0
0
−1
−1
−2 5
10
15
20
−2
Tighten Lending
5
10
15
20
Excess Bond Premium 0.5
0.5 0
0 −0.5 5
10
15
20
−0.5
5
C&I Loans
10
15
20
15
20
15
20
Funds Rate 0
0 −2
−10
−4 −20
−6 5
10
15
20
5
POS
10 NEG
0.4
0.1 0 −0.1 −0.2 −0.3
0.2 0 −0.2 5
10
15
20
5
10
Note: Dashed lines represent 68th percentile and dotted lines represent 95th percentile Monte Carlo confidence bands. 54
Figure 9: Benchmark model impulse responses to credit supply shock
Output
Capital Quality
−3
Bank Equity
0
0
−0.2
−0.01
−0.4
x 10
−0.02 5
10
15
Separation
2 0 −2 −4 −6 −8
20
5
10
15
20
5
10
15
20
5
10
15
20
10
15
20
10
15
20
6 Spread
6 4 2 0 5
10
15
20
4
1
2
0.5
0
5
10
15
20
0
−4
−3
POS
x 10 0
20
−0.02
10
x 10 4 2
0
−0.04
0 5
10
15
20
5
10
15
20
5 −3
NEG
x 10 0.15 0.1 0.05 0 −0.05
4 0.01 2
0 5
10
15
20
−0.01
0 5
10
15
20
5
Note: First column represents a negative shock to productive capital quality, second column represents an i.i.d. reduction in bank equity, and the third column represents an i.i.d. increase in the separation rate. Benchmark calibration implies an inverse investment elasticity to capital price of 1.728.
55
Figure 10: Comparison of impulse responses to credit supply shock for different investment elasticities Investment
Capital Quality
Bank Equity
Separation
0
0
0 −0.02
−2
−0.2
−0.04 −0.06
−4
−0.4
−0.08
5
10
15
20
5
10
15
20
5
10
15
20
10
15
20
10
15
20
10
15
20
Loans
−3
0
0
−0.2
−0.01
0
x 10
−2 −4
−0.4
−0.02
−6
−0.6 5
10
15
20
5
10
15
20
5
−3
−3
Capital Price
x 10 0
0
−0.05
−5
−0.1
−10
−0.15
−15 5
10
15
20
x 10 0 −2 −4
5
10
15
20
5
Capital
−3
0
0
−0.2
−0.01
0
x 10
−2 −4
−0.4
−0.02
−6
−0.6 5
10
15
20
5
10
15
20
5
Note: First column represents a negative shock to productive capital quality, second column represents an i.i.d. reduction in bank equity, and the third column represents an i.i.d. increase in the separation rate. Dashed lines represent the benchmark calibration of an inverse investment elasticity to capital price of 1.728. Solid line represents an inverse investment elasticity to capital price of 0.11.
56
Figure 11: Model impulse responses to credit supply shock for elastic investment
Output
Capital Quality
Bank Equity
Separation
0
0
0
−0.5
−0.05
−0.01 −0.02
Spread
5
10
15
20
2 1 0 −1 5
10
15
20
5
10
15
20
4
1
2
0.5
0
5
10
15
20
0
5
10
15
20
5
10
15
20
10
15
20
10
15
20
10
15
20
−3
Loans
0
0
0
−0.01 −5
−0.02
−0.5 5
10
15
20
5
10
15
20
5
−3
POS
0
0
−3
x 10
x 10 4
−1
2
−2
−0.05 5
10
15
20
0
−3
5
10
15
20
5
−3
−3
x 10 NEG
x 10
0.1 0.05 0 −0.05 5
10
15
20
x 10
10
4
5
2
0
0 5
10
15
20
5
Note: First column represents a negative shock to productive capital quality, second column represents an i.i.d. reduction in bank equity, and the third column represents an i.i.d. increase in the separation rate. The inverse investment elasticity to capital price is set to 0.11.
57
Figure 12: Sensitivity to the cost deviating from the regulated asset to capital ratio Technology
Monetary
Capital Quality
Output
0.1 0
0 −0.1
−0.05
−0.2
Spread
−0.1
5
15
20
0.5 0 −0.5 −1
5
10
15
20
10
10
5
0
10
15
20
0.02 0 −0.02 −0.04 −0.06 10
15
20
0.02 0 −0.02 −0.04 −0.06 −0.08 5
10
15
20
5
10
15
20
5
10
15
20
5
10
15
20
6
2 0
−10 5
10
15
20
0 −0.1 −0.2 −0.3 5
Bank Capital
4
0 5
Tightness
10
0.4 0.2 0 −0.2 −0.4 −0.6 −0.8
5
10
15
20 0.02 0 −0.02 −0.04 −0.06
0.2 0 −0.2 5
10
15
20
5
10
15
20
Note: Solid line represents benchmark value of YΨ = 0.1, broken line represents a bigger value of YΨ = 1, and dotten line represents no penalty for deviating from regulated asset to capital ratio YΨ = 0. The first column represents impulse responses to a negative technology shock, the second to a contractionary monetary shock, the third to a negative capital quality shock, and the fourth to a negative shock to bank capital.
58
Figure 13: Countercyclical leverage ratio Technology
Monetary
Output
0 −0.02 −0.04
Spread Tightness
0.8 0.6 0.4 0.2 0 −0.2
0
−0.05
−0.2
Bank Capital 0 −0.02 −0.04
−0.06 −0.08
Capital Quality
0
−0.1 5
5
10
10
15
15
20
20
−0.4 5
10
15
20
−0.06 5
10
15
20
6
6
15
4
4
10
2
2
5
0
0 5
10
15
20
5
10
15
20
0
0.02 0 −0.02 −0.04 −0.06 5
10
15
20
−0.2
0
−0.3
−0.2 5
10
15
20
10
15
20
5
10
15
20
5
10
15
20
0
0.2
−0.1
0
5
−0.05 −0.1 −0.15 5
10
15
20
Note: Impulse responses to different negative shock for two models with banking. Solid line represents the case with countercyclical leverage ratio. Broken line represents the benchmark banking model with static bank capital requirement. %κ = −1.5
59
