Financial Fragility and Unconventional Central Bank Lending Operations

Transcription

1 Financial Fragility an Unconventional Central Ban Lening Operations Christiaan van er Kwaa April 3, 217 Abstract I analyze the effect of unconventional central ban lening operations on output through the creit provision channel, which is especially relevant in light of the European Central Ban s ECB s unconventional Longer-Term Refinancing Operations LTROs announce at the en of 211. I construct a DSGE moel containing balance-sheet-constraine commercial bans with a portfolio choice between private loans an government bons. Commercial bans have access to central ban funing, for which they must plege government bons as collateral, which creates a lin between central ban lening operations an commercial bans portfolio choice. I fin that the LTRO s cumulative impact on output is zero, irrespective of the haircut policy, i.e., the amount of central ban funing obtaine for one euro of collateral. The haircut policy, however, allows the central ban to shift output losses between perios. I fin that unlie central ban lening operations, a irect recapitalization by the fiscal authority oes not inuce a shift from private creit. Keywors: Financial Intermeiation; Macrofinancial Fragility; Unconventional Monetary Policy JEL: E32, E44, E2, G21 I acnowlege the generous support of the Dutch Organization for Sciences, through the NWO Research Talent Grant No I am grateful to Sweer van Wijnbergen, Wouter en Haan, Nicola Gennaioli, Jose Victor Rios-Rull, Ricaro Reis, Franlin Allen, Ethan Ilzetzi, Luas Schmi, Thomas Eisenbach, Toni Ahnert, Christian Stoltenberg, Bjoern Bruggeman, Petr Selace, Omar Rachei, Anatoli Segura, Agnese Leonello, Enrico Mallucci, Alex Clymo, Patric Tuijp, Oana Furtuna, Damiaan Chen, Lucyna Gornica an Egle Jaucionyte for helpful comments an suggestions. Affiliation: Rijsuniversiteit Groningen. Aress: Nettelbosje 2, 9747 AE Groningen. aress: c.g.f.van.er.waa@rug.nl. Telephone:

2 1 Introuction In December 211 an February 212, the European Central Ban ECB engage in unconventional lening operations with the European commercial baning system to prevent a creit contraction, which woul have ha serious conseuences for the macroeconomy European Central Ban, 212. These Longer-Term Refinancing Operations LTROs feature a long maturity 36 months an a promise by the ECB to provie as much funing to the commercial bans as emane against eligible collateral. 1 Commercial bans eventually too out more than AC1 billion in ECB funing, maing the LTROs the largest refinancing operation in the history of the ECB. The goal of this paper is to investigate the macroeconomic impact of such unconventional central ban lening by lining such a program to the creit transmission channel. Such a large program has the potential to affect aggregate investment, as this funing can potentially be use to provie new creit to the real economy. Effects on private creit provision are relevant in the Eurozone, as 8% of ebt-financing to non-financial corporations is intermeiate by commercial bans European Central Ban, In fact, expaning creit was one of the goals of the ECB, as state by Mario Draghi, presient of the ECB:...at least the bans will be more incline to use the money - which was our prime expectation really - to expan creit to the real economy. European Central Ban 212. It is not so clear, however, whether the ECB funing was use to provie new loans to the private sector. European commercial bans were unercapitalize at the time International Monetary Fun, 211; Hoshi an Kashyap, 214, which mae it more ifficult for them to expan the balance sheet to provie new creit. Empirical evience suggests that lening to the real economy i not expan in Italy, Spain an Portugal, which too out more than % of LTRO funing Bruegel, 21, while omestic bonholings sharply increase. In aition, Drechsler et al. 214 fin that wealy capitalize bans in the Eurozone borrowe more from the ECB, plege risier collateral, an actively investe in istresse sovereign ebt after the European sovereign ebt crisis began in 21. Crosignani et al. 21 fins that Portuguese bans purchase omestic bons uring the LTRO allotment. It is therefore not clear from an empirical point of view whether the funing was use to provie new creit to the real economy. In this paper I investigate the impact of unconventional central ban lening operations on creit provision to the real economy an, through that channel, on output. Following up on this uestion, I compare the effectiveness of this policy with that of a recapitalization by the fiscal authority. 1 Normally, the ECB provies cash loans to commercial bans uner the Main Refinancing Operations MROs an the Longer-Term Refinancing Operations LTROs. In exchange for cash loans, commecial bans must plege eligible collateral. MROs have a maturity of one wee, an LTROs of three months. 2 Throughout the paper, I use commercial bans an financial intermeiaries interchangeably to enote the same group of economic agents, which capture all ins of creit institutions: commercial bans, savings bans, postbans, an specialize creit institutions, among others. 2

3 European commercial bans have been unercapitalize since the financial crisis of International Monetary Fun, 211; Hoshi an Kashyap, 214. The Gertler an Karai 211 framewor enables me to capture this feature, which I exten in two irections. First, commercial bans have a portfolio choice between government bons an private loans, which are use by non-financial corporations to purchase prouctive physical capital. For etails, see Gertler an Karai 213 an Bocola 21. Secon, I introuce the possibility of collateralize central ban lening, which represents an alternative form of funing for commercial bans besies net worth an eposits. To obtain central ban funing, commercial bans have to plege collateral, for which only government bons are eligible. In line with LTRO policy at the time, the central ban has two instruments for its lening policy: the nominal interest rate on central ban funing an the collateral or haircut policy, which etermines how much central ban funing is obtaine for one euro of collateral. The haircut is the ifference between the two. I moel the LTRO by temporarily ecreasing the interest rate on central ban funing with respect to the interest rate on eposits. The main contribution of my paper is lining private creit provision an central ban lening operations by incluing a collateral constraint that etermines how much central ban funing is obtaine for one euro of government bons. The reuirement to plege government bons as collateral affects the portfolio ecision between private loans an government bons. This setup allows me to investigate the effect of unconventional central ban lening to commercial bans, such as the LTROs of December 211 an February 212. Within this framewor I am also able to investigate the impact of the haircut policy on the creit provision channel an to explore the role of financial fragility in such operations. My first result is that unconventional central ban lening to balance-sheet-constraine commercial bans has a contractionary short-run effect an an expansionary long-run effect. I istinguish two competing effects. First is the collateral effect, which has a contractionary effect on output. The LTRO increases the collateral value of government bons. Commercial bans shift into government bons an, conseuently, must she private loans. Creit provision to the real economy falls, with a contractionary effect on output. Secon is the subsiy effect, which has an expansionary effect on output. Because the interest rate on central ban funing is below the interest rate on regular eposits, the LTRO reuces funing costs an increases commercial ban profits. Bans balance sheets recover more uicly, leaing to a creit expansion. The collateral effect ominates the short-run effect, but isappears once the LTRO has ene. The subsiy effect is still present an ominates the long-run effect, which leas to an expansion of output. My secon an main result is that unconventional central ban lening oes not have a cumulative effect on output. This result hols for ifferent values of the haircut parameter. Interestingly, the haircut policy oes have a pronounce effect on the time-pattern of output. A smaller haircut leas to a stronger collateral effect an a steeper short-run output contraction. At the same time, the smaller haircut leas to a stronger economic recovery in the long run through 3

4 the subsiy effect. The mechanism is as follows. The smaller haircut increases the collateral value an leas to a larger shift into government bons. More government bons allow commercial bans to obtain more low-interest-rate central ban funing, thereby increasing commercial ban profits. Through the resulting faster balance sheet recovery, I obtain the expansionary effect that offsets the contractionary collateral effect. A thir result is that the provision of central ban funing, which amounts to an inirect recapitalization of the financial sector, is less effective in stimulating output than a irect recapitalization by the fiscal authority. A irect recapitalization provies commercial bans with new net worth an alleviates bans balance sheets constraints. Contrary to central ban lening operations, a irect recap oes not involve crowing out private loans by government bons. My paper is relate to several strans of the literature. First, it relates to recent papers that stuy the transmission to the macroeconomy of shocs to the balance sheets of financial intermeiaries Gertler an Kiyotai, 21; Gertler an Karai, 211, 213. In all these moels, financial intermeiaries face an enogenous leverage constraint that limits the size of the balance sheet for a given amount of net worth. Kirchner an van Wijnbergen 212 exten this framewor by introucing a portfolio choice between private loans an government ebt. A ebt-finance fiscal expansion increases commercial bans bonholings, which crows out private creit. My framewor also features crowing out through an alternative mechanism: the provision of central ban funing at an interest rate below that on eposits increases the collateral value of government bons an maes government bons more attractive. Gertler an Kiyotai 21 an Bocola 21 allow for central ban lening to financial intermeiaries, in an otherwise similar setup as my paper. Bocola 21, who explicitly loos at the LTRO, fins a small positive effect on lening an output because central ban funing relaxes ban balance sheet constraints in this setup. My paper iffers in two imensions: first, central ban funing oes not irectly relax ban balance sheet constraints, but oes so only inirectly by proviing ebt financing at an interest below that on regular eposit funing. Secon, commercial bans must plege government bons as collateral, giving rise to the collateral effect, which is absent in Gertler an Kiyotai 21 an Bocola 21. Contrary to Bocola 21, I fin a contractionary short-run effect on private creit provision an output ue to the collateral effect. Contrary to Gertler an Kiyotai 21 an Bocola 21, Schabert 21 an Hörmann an Schabert 21 inclue the reuirement to plege collateral to access central ban lening facilities. These papers fin that a smaller haircut has an expansionary effect on output. My paper iffers along two imensions: first, Schabert 21 an Hörmann an Schabert 21 explicitly incorporate money holings, as househols face a cash-in-avance constraint for which they can borrow at the central ban. Instea, I consier a cashless economy in which central ban lening is an alternative form of ebt financing at an interest rate possibly below that on eposits. Secon, instea of proviing central ban funing to unconstraine househols, commercial bans in my moel are the only agents in the economy with access to central ban funing. Because commercial bans are balance-sheet-constraine, forcing them to plege col- 4

5 lateral to obtain central ban funing affects the portfolio ecision between private loans an government bons, giving rise to the collateral effect. Contrary to Schabert 21 an Hörmann an Schabert 21, I fin that the haircut policy oes not have a cumulative impact on output, because the expansionary subsiy effect is offset by the short-run collateral effect. Finally, my paper connects to the literature on government bon accumulation by commercial bans. Becer an Ivashina 214 fin empirical evience for the crowing out of private loans by increase holings of government bons an for financial repression by governments. Crosignani 214 evelops a general euilibrium moel in which bans shift into omestic sovereign ebt when unercapitalize. Domestic sovereign ebt has the highest payoff in the goo state of the worl, which is the only state bans care about. Bans have limite liability, an therefore o not care about being banrupt in the ba state of the worl. Hence, government bon accumulation by commercial bans arises because of ris shifting. Government bon accumulation in my moel arises because commercial bans nee government bons for collateral purposes when the central ban engages in special lening operations with commercial bans. I escribe some stylize facts in section 2. The moel escription can be foun in section 3, while section 4 iscusses the calibration of my moel. Section presents the results from my simulations, an section 6 conclues the paper. 2 Stylize facts Creit institutions in the Eurozone play a crucial role in the provision of creit to the real economy, as they intermeiate approximately 8% of ebt financing to non-financial corporations European Central Ban, 21. The LTROs of December 211 an February 212 provie creit institutions with fresh liuiity amounting to approximately 1% of Eurozone GDP. However, i the creit institutions use this funing to provie new loans to the real economy? Di they expan their balance sheets? In this section, I present some stylize facts regaring the aggregate balance sheets of Monetary Financial Institutions MFIs at the time of the LTROs of December 211 an February 212. Data about the refinancing operations of the ECB were collecte from Bruegel 21, while balance sheet ata of MFIs were collecte from the ECB s statistical warehouse European Central Ban, 21. The time series have a monthly freuency. Balance sheet ata of MFIs, excluing the European System of Central Bans, are available at a country level. 3 The vast majority of euro-area MFIs are creit institutions i.e., commercial bans, savings bans, postbans, specialize creit institutions, among others European Central Ban, 211b. 3 MFIs inclue creit institutions an non-creit institutions mainly money maret funs whose business is to receive eposits from entities other than MFIs an to grant creit an/or invest in securities European Central Ban, 211b.

6 Country use of ECB funing Figure 1 shows the stoc of total refinancing operations in the Eurozone, as well as the country use by MFIs in Italy, Spain an Portugal. Total refinancing operations consist of Main Refinancing Operations MROs an Longer-Term Refinancing Operations LTROs, which iffer in their respective maturity. MROs have a maturity of one wee, while regular LTROs feature a maturity of three months. Contrary to regular LTROs, the LTROs of December 211 an February 212 feature a maturity of 36 months. I show the sum of MROs an LTROs because part of the LTROs of December 211 an February 212 were use to repay outstaning MROs an/or roll over outstaning LTROs IT ES PT RE Country use of ECB funing Total Refinancing Operations EUR billion /1/211 1/1/212 1/1/213 Figure 1: Country use of outstaning MROs an LTROs by MFIs in Italy IT, Spain ES, Portugal PT an the rest of the Eurozone RE in AC billion from January 211 to January 213. The two vertical lines refer to December 1st, 211 an March 1st, 212, which mar the beginning of the perio in which the two LTROs too place an the en, respectively. Source: Bruegel 21. Figure 1 suggests three main observations. First, the stoc of total refinancing operations increase by approximately AC3 billion uring the perio in which the two unconventional LTROs were unertaen. The net increase is smaller than the gross increase of AC1 billion, which was mentione in the introuction, because part of the gross increase has been use to 6

7 repay outstaning MROs an/or roll over outstaning LTROs. Secon, a isproportionate share of the funing went to MFIs in Italy, Spain an Portugal. By March 1st, 212, more than % of total ECB funing ha been borrowe by MFIs from these countries, while their cumulative share in Eurozone GDP is less than one-thir. Apparently, the LTROs of December 211 an February 212 were especially attractive for MFIs in Italy, Spain an Portugal. Thir, the use of ECB funing by MFIs from these three countries amounte to a large share of their respective GDP. On March 1st, 212, ECB funing accounte for AC2 billion of ebt funing for Italian MFIs, which is close to 2% of Italian GDP. For Spain, this number is as high as AC4 billion, which amounts 6 x Total MFI assets 16 to 4% of Spanish GDP. To sum up, ECB funing constitute a significant source of ebt funing for IT MFIs in Italy, Spain an Portugal. ES 4 PT Balance sheet composition MFIs Figure 2 shows the total asset holings of MFIs in Italy, Spain an Portugal. I normalize total asset holings to 1 on December 1st, 211 which is one wee before the unconventional LTROs were announce by the ECB European Central Ban, 211a. The figure suggests a small expansion 1/1/211 in total MFI assets uring the perio 1/1/212 in which the two LTROs too1/1/213 place. 1 1 IT ES PT Total assets MFIs in Italy, Spain an Portugal Total MFI assets 9 9 1/1/211 1/1/212 1/1/213 Figure 2: Total assets of Monetary Financial Institutions MFI s excluing the European System of Central Bans in Italy IT, Spain ES, an Portugal PT from January 211 to January 213. Levels were rescale with respect to total assets on December 1st, 211, which has a value of 1 in all three plots. Source: ECB. A more important uestion from a macroeconomic point of view is whether creit to nonfinancial corporations an househols expanewith oubts raise by Panel 3a, which epicts private creit to the real economy as a percentage of total MFI assets: creit fell by one to two percentage points in all three countries uring the perio in which the two LTROs too place. There seems to be a clear brea between creit levels as a percentage of MFI assets in the perio before December 211 an those in the perio after March 212 in Portugal an Spain. Although creit as a percentage of total MFI assets also fell in Italy uring this perio, creit ha alreay been falling in the months before the first intervention, an it is less clear whether 7

8 the fall can be attribute to the two LTROs. Given that balance sheets expane very little Figure 2, the ata suggest that private creit intermeiation measure in euros fell. The ata clearly inicate that a creit expansion, as envisage by ECB Presient Draghi, i not occur. At the same time, Panel 3b shows an increase in omestic government bonholings of one to one-an-a-half percentage points of total MFI assets for all three countries uring the perio, amounting to a striing increase of 3% in euros of government bonholings. This result is in line with the finings of Drechsler et al. 214 an Crosignani et al. 21. There is a clear brea between government bonholings in the perio before December 211 an those in the perio after March 212. These figures give a mixe message: while balance sheets slightly expane in the irect aftermath of the LTROs, MFIs shifte from private creit to government bons, given the fraction of total assets investe in a particular asset class. One possible explanation for this fining is that government bons can easily be plege as collateral to obtain funing from the ECB. In aition, haircuts, i.e., the amount of central ban funing obtaine for one euro of collateral, are usually small for government bons. Loans to non-financial corporations an househols, however, are usually ifficult to convert into eligible collateral, an usually come with a larger haircut. 8

9 Balance sheet composition MFIs in Italy, Spain an Portugal Loans to NFC an HH % of MFI assets IT ES PT 4 4 1/1/211 1/1/212 1/1/213 a 9 8 IT ES PT Dom. government bons % of MFI assets /1/211 1/1/212 1/1/213 b Figure 3: Balance sheet composition of Monetary Financial Institutions MFIs excluing the European System of Central Bans in Italy IT, Spain ES, an Portugal PT from January 211 to January 213. Panel 3a shows loans to non-financial corporations NFC an househols HH as a percentage of total MFI assets. Panel 3b shows omestic government bonholings as a percentage of total MFI assets. The two ashe vertical lines refer to December 1st, 211 an March 1st, 212, respectively, which mar the beginning an the en of the perio in which the two LTROs too place, respectively. Source: ECB. 9

10 3 Moel 3.1 Moel overview I consier a stanar New-Keynesian moel, which inclues commercial bans that are balancesheet-constraine, as in Gertler an Karai 211, an have a portfolio choice between private loans an government bons, as in Gertler an Karai 213. The asset sie is finance by net worth, eposits an central ban funing. Commercial bans nee to plege collateral in the form of government bons to obtain funing from the central ban, while private loans are not eligible as collateral. The central ban etermines the interest rate on both regular eposits an central ban funing an how much funing commercial bans receive for one euro in government bons, i.e., the haircut applie to collateral. The central ban can ecrease the interest rate on central ban funing in times of financial crises, compare with the interest rate on regular househol eposits, an finances its lening operations by issuing eposits to househols. Central ban profits an losses are transferre perio by perio to the fiscal authority. In aition to commercial bans an a central ban, the economy contains househols, a prouction sector, an a fiscal authority. Each househol consists of worers an baners. Worers supply labor to intermeiate goos proucers, while baners run the commercial bans. Intermeiate goos proucers borrow from commercial bans to purchase physical capital from capital goos proucers, who face convex ajustment costs. Labor is hire the next perio, together with capital use for the prouction of the intermeiate goo. Intermeiate goos proucers sell their goos to retail goos proucers an sell the use capital bac to the capital goos proucers. Retail goos proucers face monopolistic competition an price-sticiness, as in Calvo 1983 an Yun Final goos proucers operate in a perfectly competitive maret an purchase from retail goos proucers while taing prices as given. The final goo is sol to househols for consumption, to capital goos proucers as investment, an to the government. The government honors outstaning obligations, potentially provies financial sector support, covers possible central ban losses, an finances these expenitures by raising lump-sum taxes an issuing long-term ebt, in a way similar to Woofor 1998, 21. Fiscal policy is etermine via exogenous fiscal rules. 3.2 Househols A continuum of househols with measure one are infinitely live, an exhibit ientical preferences an asset enowments. Each househol consists of baners an worers. There is perfect consumption insurance within the househol, which allows me to eep the representative agent representation. Househols obtain utility from consumption c t, while labor h t provies isutility. Househols receive income from labor at wage rate w t. Househols can invest in one perio ebt a t, which consists of eposits t an loans to the central ban CB cb t, which can be treate as perfect substitutes from the househol s point of view by assumption, i.e. a t = t + cb Investment of a t 1 in perio t 1 yiels repayment of principal a t 1 an interest r t t. in perio 1

11 t. Househols can also invest in government bons with return r b t on their holings b t 1s b,h where t 1 b is the bon price in perio t 1, an s b,h t 1 the number of bons purchase in perio t 1. Besies that, they receive income from profits Π t from the prouction sector an the financial sector. Income is use for consumption c t, investment in one perio ebt a t an investment in government bons s b,h t at price t b. Househols pay a cost for the intermeiation of government bons, which is uaratic in the eviation of the number of bons from the level ŝ b,h to capture in a simple way the limite participation in asset marets by househols Gertler an Karai, 213. The government levies lump sum taxes τ t. Househol members erive utility from consumption an leisure, with habit formation in consumption to more realistically capture consumption ynamics, as in Christiano et al. 2.Househols maximize expecte life-time utility subject to the buget constraint: c t + τ t + a t + b t s b,h t max E t {c t+i,h t+i,a t+i,s b,h t+i} i= + κ s b,h 2 s.t. { [ ]} β i log c t+i υc t 1+i Ψ h1+ϕ t 1 + ϕ i= This will give rise to the following first orer conitions: 2 s b,h t ŝ b,h = w t h t rt at rt b b t 1 s b,h t 1 + Π t t 1, c t : λ t = c t υc t 1 1 βυe t [c t+1 υc t 1], 1 h t : Ψh ϕ t = λ t w t, 2 [ ] a t : E t βλt,t r t+1 = 1, r b t : E t βλ t+1 b t t,t+1 = 1, 4 t b + κ sb,h s b,h t ŝ b,h s b,h where λ t is the marginal utility of consumption. The househol s stochastic iscount factor is βλ t,t+1 = βλ t+1 /λ t. Euation 1 enotes the marginal utility from an aitional unit of consumption, while euation 2 euates the marginal cost from an aitional unit of labor in the form of isutility with the marginal benefit from aitional wage income. Euation 3 an 4 weigh the benefit from an aitional unit of consumption tomorrow from investing in eposits respectively government bons, with the cost of lower consumption toay. 3.3 Financial intermeiaries Optimization problem Financial intermeiaries channel funs from savers to borrowers. They invest in two asset classes: private loans to intermeiate goos proucers s,p j,t an government bons s b,p j,t. Total assets p j,t 11

12 are given by: p j,t = t s,p j,t + b t s b,p j,t, where t is the price of private loans, an b t the price of government bons. Intermeiaries fun their assets through net worth n j,t, ris-free househol eposits j,t an central ban funing cb j,t : p j,t = n j,t + j,t + cb j,t, New net worth is the ifference between the return on assets an the return on ebt funing. Net worth can be increase through financial sector support by the government, which is proportional to previous perio net worth n g j,t = τ n t n j,t 1. Net worth ecreases when the financial sector has to repay previously aministere support, which is also proportional to previous perio net worth, ñ g j,t = τ n t n j,t 1. τ n t an τ n t will be efine in section 3.. The law of motion for iniviual net worth is given by: n j,t+1 = 1 + rt+1 t s,p j,t rt+1 b b t s b,p j,t 1 + rt+1 j,t 1 + rt+1 cb cb j,t + n g j,t+1 ñg j,t+1 = 1 + rt+1 + τt+1 n τ t+1 n t s,p j,t rt+1 b + τt+1 n τ t+1 n b t s b,p j,t 1 + rt+1 + τt+1 n τ t+1 n j,t 1 + rt+1 cb + τt+1 n τ t+1 n cb j,t, where r t is the net real return on private loans in perio t, r b t the net real return on government bons, rt the net real return on eposits an rt cb the net real return on central ban funing. Following Gertler an Karai 211, I assume intermeiaries are force to shut own with probability σ, which is i.i.. an exogenous, both in time an the cross-section. When the intermeiary is force to stop operating, all net worth is pai out to the househol, the ultimate owners of the financial intermeiary. iscounte profits: V s,p j,t 1, sb,p j,t 1, j,t 1, cb j,t 1 = max E t { βλ t,t+1 [1 σ n j,t+1 + σv The financial intermeiary maximizes expecte future ]} s,p j,t, sb,p j,t, j,t, cb j,t Househols face an agency problem when eciing on the amount of funs to save through eposits, as in Gertler an Karai 211, 213: financial intermeiaries have the capability to ivert assets when moving from the current to the next perio. Depositors can force the intermeiary into banruptcy in that case, but will only recoup a fraction 1 λ a of asset class a = {, b}. The remaining fraction λ a of each asset class is pai out as a ivien to the househol owning the intermeiary. Depositors, however anticipate this possibility, an will in euilibrium only provie eposits up to the point where the continuation value of the intermeiary is larger 12

13 or eual than the opportunity cost of iverting the assets. V s,p j,t 1, sb,p j,t 1, j,t 1, cb j,t 1 λ t s,p j,t + λ bt b s b,p j,t. Financial intermeiaries have access to central ban funing cb j,t, but are reuire to plege collateral in the form of government bons. The commercial ban remains the legal owner of the bon, an will receive the interest payments from the bon after repayment of cb j,t to the central ban in perio t + 1, unless the financial intermeiary becomes insolvent, a case I abstain from through a proper calibration. The collateral constraint has the following functional form: cb j,t θ t b t s b,p j,t, 6 where θ t is the haircut parameter that regulates the collateral policy of the central ban, see section 3.. A low θ t, or a high haircut, inicates that a commercial ban will obtain little central ban financing for a euro of government bons. The optimization problem of the financial intermeiary can now be formulate: V j,t = max {s,p j,t,sb,p j,t,j,t,cb s.t. V j,t λ t s,p j,t + λ b b t s b,p j,t, j,t} E t {βλ t,t+1 [1 σ n j,t+1 + σv j,t+1 ]}, n j,t + j,t + cb j,t = t s,p j,t + b t s b,p j,t, n j,t = 1 + rt + τt n τ t n t 1 s,p j,t rt b + τt n τ t n b t 1 s b,p 1 + rt + τt n τ t n j,t rt cb + τt n τ t n cb j,t 1, θ t b t s b,p j,t cb j,t, where I have abbreviate the value function of the financial intermeiary by: V j,t = V s,p j,t 1, sb,p j,t 1, j,t 1, cb j,t 1. j,t 1 13

14 3.3.2 First orer conitions Appenix A.1 shows that the problem of the financial intermeiary leas to the following firstorer conitions: λ b [ E t Ωt,t+1 r λ t+1 r ] t+1 µt λ 1 + µ t [ = E t Ωt,t+1 r b t+1 rt+1 ] ψt + θt, µ t = E t [ Ωt,t+1 r t+1 r t+1], 8 ψ t 1 + µ t = E t [ Ωt,t+1 r t+1 r cb t+1], 9 η t = E t [ Ωt,t r t+1 + τ n t+1 τ n t+1], 1 where µ t is the Lagrange multiplier on the ban s balance sheet constraint, an ψ t the Lagrangian multiplier on the collateral constraint 6. η t enotes the shaow value of an aitional unit of net worth. Ω t,t+1 = βλ t,t+1 [1 σ + σ 1 + µ t+1 η t+1 ] is the intermeiaries stochastic iscount factor, an can be interprete as the househol s stochastic iscount factor βλ t,t+1, augmente by an aitional term to incorporate the effect of the financial frictions. First orer conition 7 pins own the ban s portfolio choice on the asset sie of the balance sheet. The left han sie enotes the marginal benefit to the financial intermeiary from investing an aitional unit of private loans, value by the intermeiaries stochastic iscount factor, an correcte by the term λ b /λ to reflect the fact that the financial friction is more severe for private loans than for government bons. The right han sie enotes the marginal cost of giving up an aitional unit of government bons, measure by the creit sprea between government bons an the eposit rate. But government bons also erive value from the fact that they serve as collateral with which intermeiaries can obtain central ban funing, which is reflecte by the secon term on the right han sie of euation 7. Euation 8 is the first orer conition for private loans. We clearly see that the presence of a bining ban balance sheet constraint µ t > in euation limits the ability of commercial bans to arbitrage away the ifference between the expecte rate of return on private loans an eposits, since commercial bans cannot expan the balance sheet. The portfolio choice on the liabilities sie of the balance sheet is given by euation 9: an increase in the creit sprea between eposits an central ban funing rt+1 rt+1 cb increases the collateral value of government bons ψ t everything else eual, an leas to a shift into government bons, see 7, which allows the commercial ban to increase the amount of central ban funing. Euation 1 shows the shaow value of an aitional unit of net worth η t, which is eual to the expecte gross return on eposits, iscounte by the intermeiaries stochastic iscount factor Ω t,t+1. The expecte return is augmente by the financial sector support per unit of net worth τ n t+1 an the repayment per unit of net worth τ n t+1. Using these first orer conitions, I can erive the following proposition: 14

15 Proposition 1. central ban lening an the collateral policy only have a first orer effect when both the ban balance sheet constraint is bining an the interest rate on eposits r t+1 is not eual to the interest rate on central ban funing r cb t+1. Lemma 1. If the ban balance sheet constraint is not bining, then there is no first orer effect from central ban lening on private creit. Proof. Consier optimal choices for the financial intermeiary. When euation is not bining, µ t is eual to zero. From euation 8, we see that the expecte return on private loans must eual the expecte rate on eposits. The term on the left han sie of euation 7 is zero, an is not affecte by ψ t, which captures the effects from central ban lening. Lemma 2. When the interest rate on eposits r t+1 an central ban funing r cb t+1 are eual, there is no effect from central ban lening an/or the haircut parameter θ t. Proof. When r t+1 = r cb t+1, we fin from euation 9 that ψ t =. This implies that the secon term on the right han sie of euation 7 rops out. This is the only first orer conition where ψ t, which measures the collateral value of government bons, an the haircut parameter θ t show up. Hence, central ban lening oes not affect the portfolio ecision between private loans an government bons. Proof of Proposition 1. To have an effect from central ban lening, lemma 2 shows that the interest rate on eposits an central ban funing has to iffer. Lemma 1 shows that even when the interest rate on eposits an central ban funing is ifferent capture by ψ t >, there is no first orer effect unless the ban balance sheet constraint is bining µ t >. Note that when the interest rate on eposits an central ban funing is the same ψ t =, commercial bans are inifferent between the two funing sources, since the collateral value of government bons is now zero. Deposits an central ban funing are perfect substitutes. Hence I can tae the collateral constraint to be bining in my simulations, irrespective of the ifference between the interest rate on eposits an that on central ban funing. Because of the proposition, an the fact that European commercial bans have been unercapitalize since the financial crisis of International Monetary Fun, 211; Hoshi an Kashyap, 214, I will tae both the ban s balance sheet constraint an the collateral constraint 6 to be bining in my simulations. When the ban s balance sheet constraint is bining, I can rewrite it into the following euation: 1 + µ t η t n j,t = λ t s,p j,t + λ b b t s b,p j,t, 11 It is clear from euation 11 that the size of the balance sheet is limite by the amount of current net worth n j,t. 1

16 3.3.3 Aggregate law of motion net worth The law of motion for aggregate net worth consists of the net worth of the baners that are allowe to continue operating, together with the aggregate net worth given to new baners, which is eual to a fraction χ of previous perio assets p t 1. Together with net government support n g t ñ g t, I obtain the following law of motion: n t = σ [ r t r t t 1 s t 1 + r b t r t b t 1 s b t 1 + rt rt cb cb t rt ] nt 1 + χp t 1 + n g t ñ g t. 12 I introuce the variable ω t to enote the fraction of assets investe in private loans: ω t = t s t /p t Prouction sector The prouction factor is moele in stanar New-Keynesian fashion. I will shortly outline the setup below, with a more etaile exposition in appenix A Intermeiate Goos Proucers A continuum of intermeiate goos proucers, that face perfect competition, acuire capital i,t 1 from capital proucers at the en of perio t 1 for a price t 1 through a state-contingent loan s i,t 1 = i,t 1 from the financial intermeiaries. Next perio s profits can creibly be plege to the intermeiaries, as in Gertler an Kiyotai 21. After realization of the shocs, the proucers hire labour h i,t at a wage w t, an start proucing intermeiate goos with previous perio capital i,t 1 an labor h i,t as input. After prouction, the intermeiate goos proucers pay a state-contingent net real return rt prouction technology: over claims issue in perio t, with the following y i,t = z t ξ t i,t 1 α h 1 α i,t. Quality of capital ξ t an total factor prouctivity z t are riven by exogenous AR1 processes. Output y i,t is sol to retail firms for a price m t. The effective capital stoc after epreciation is sol to the capital proucers for a price t an the procees are use to pay bac the loans an a net return to the financial intermeiaries, after paying wages set in a perfectly competitive labor maret: w t = 1 α m t y i,t /h i,t, rt = αm ty i,t / i,t 1 + t 1 δ ξ t t

17 A capital uality shoc ξ t ecreases the return on capital for two reasons: prouction ecreases, as capital becomes less prouctive, reucing the first term of 1. But the capital price t will fall, leaing to a further ecrease in the return on capital because of the secon term in Capital Proucers Capital proucers purchase the effective capital stoc that is left after prouction incluing epreciation, 1 δξ t t 1, from the intermeiate goos proucers. They also purchase an amount i t of final goos, an convert the ol capital stoc an newly purchase final goos into new capital. The newly prouce capital stoc t is subseuently sol to the intermeiate goos proucers at the same price t that was pai for the capital after prouction. The capital proucers face convex ajustment costs, so that for every unit i t only 1 Ψι t units of capital are prouce, with ι t = i t /i t 1 representing the change in the investment level. The expression for the capital stoc after the capital proucers have prouce or output of capital proucers is then: t = 1 δξ t t 1 + [1 Ψι t ] i t, with Ψι t = γ 2 ι t Retail Firms A continuum of ifferentiate retail firms inexe by i [, 1] transform intermeiate goos y i,t into ifferentiate retail goos y f,t = y i,t uner monopolistic competition. Each perio, only a ranom portion 1 ψ of retail firms is allowe to reset their prices P f,t, while the other firms must eep their prices fixe, see Calvo 1983 an Yun Retail firms face the eman function y f,t = P f,t /P t ɛ y t, with ɛ > 1 an price inex Pt 1 ɛ = 1 f Final Goos Proucers P 1 ɛ f,t Final goos proucers purchase the ifferentiate retail goos y f,t to prouce final goos. They face the following technology constraint: y ɛ 1/ɛ t = 1 y ɛ 1/ɛ f,t f, where ɛ represents the elasticity of substitution between goos bought from the retail firms. Final goo proucers operate in a perfectly competitive maret. Hence they tae prices as given, an sell their goos for the same price P t. Final goos are sol to househols an government for consumption, an to capital proucers as input for investment. 17

18 3. Government 3..1 Fiscal authority The government issues b t long term bons in perio t, an raises t b b t in revenue, with t b the maret price of bons. I parametrize the maturity structure of government ebt lie Woofor 1998, 21. A bon issue in perio t 1 pays a cash flow r c in perio t, ρr c in perio t + 1, ρ 2 r c in perio t + 2, etc. The rate of return rt b on a bon purchase in perio t 1 is given by: 1 + r b t = r c + ρ b t b t 1, 16 where ρ pins own the maturity 4 of government ebt, see for more etails Van er Kwaa an Van Wijnbergen 214. The government also raises revenue by levying lump sum taxes τ t on the househols an receives profits Π cb t from the central ban. Government purchases are constant in real terms: g t = G. Furthermore, the government may provie assistance to the financial sector by injecting new net worth n g t. The government also receives repayment from previously aministere support ñ g t. The buget constraint is given by: b t b t + τ t + ñ g t + Π cb t = g t + n g t r b t b t 1 b t The tax rule of the government is given by a rule which maes sure the intertemporal government buget constraint is satisfie Bohn, 1998: where b is the steay state level of ebt. κ n controls the way government transfers to the financial sector are finance. If κ n =, support is finance by new ebt. κ n = 1 implies that the aitional spening is completely finance by increasing lump sum taxes. I parametrize government support as follows: n g t = τ n t n t 1, ζ, l, 18 τ n t = ζε ξ,t l. Thus the government provies funs to the financial sector if ζ < a negative shoc ε ξ,t l to the uality of capital. Depening on the value of l, the government can provie support instantaneously l =, or with a lag l >. Furthermore, ϑ inicates the extent to which the government nees to be repai: ñ g t = ϑn g t e, ϑ, e ϑ = means the support is a gift from the government. In case ϑ = 1, the government ai is a zero interest loan, while a ϑ > 1 implies that the financial intermeiaries have to pay interest 4 The uration of the bon is eual to j=1 jβ j ρ j 1 r c j=1 β j ρ j 1 r c 18

19 over the support receive earlier. The parameter e enotes the amount of time after which the government ai has to be pai bac Central Ban Conventional Interest Rate Policy The Central Ban sets the nominal interest rate on eposits rt n rule, in orer to minimize output an inflation eviations: accoring to a stanar Taylor r n t = 1 ρ r [ r n + κ π π t π + κ y log y t /y t 1 + κ ξ ξt ξ ] + ρ r r n t 1 + ε r,t, 2 where ε r,t N, σr, 2 an κ π > 1 an κ y > active monetary policy. The parameter π is the target inflation rate. The term κ ξ ξt ξ can be interprete as a conventional monetary stimulus in times of financial crises. The real interest rate on eposits then euals: 1 + rt = 1 + rt 1/π n t Central Ban Balance Sheet Policy Besies conventional interest rate policy, the central ban lens cb t to the commercial baning system. In orer to obtain access to this facility, commercial bans are reuire to provie collateral in the form of government bons, see euation 6. Collateral is neee in orer for the creitor to recoup the principal in case of a ebtor s banruptcy. A haircut is applie to protect the creitor from capital losses on the collateral. The central ban has two instruments for its balance sheet policy. It controls the nominal interest rate r n,cb t on central ban funing provie to commercial bans, an the haircut parameter θ t applie to the collateral. For a given interest rate r n,cb t an haircut parameter θ t, the central ban provies as much funing as emane by the commercial bans, in line with the Fixe Rate Full Alotment policy of the ECB after October The central ban can lower the nominal interest rate r n,cb t in times of crisis with respect to the interest rate on regular eposit funing rt n by increasing the creit sprea Γ cb t : r n,cb t = r n t Γ cb t. 22 The creit sprea Γ cb t between the nominal rate on eposits an the nominal rate on central ban funing is given by: Γ cb t = Γ cb + κ cb ξt ξ, 23 The case where ϑ > 1 happene in the Netherlans, where financial intermeiaries receive government ai with a penalty rate of percent. EU state support rules usually reuire financial intermeiaries to repay previously receive state support with a penalty rate. 6 Before October 28, the ECB use to auction a given amount of funing against eligible collateral, with the interest rate being etermine in the auctioning process. In October 28, the ECB switche to a Fixe Rate Full Alotment policy, uner which the ECB sets the collateral haircuts an the interest rate, an provies commercial bans with the funing emane European Central Ban,

20 where Γ cb is the steay state creit sprea. When κ cb <, a financial crisis increases the interest rate sprea between eposits an central ban funing, ecreasing funing costs for commercial bans. The secon policy instrument is the haircut parameter θ t that is applie to the collateral. From euation 6 we see that a commercial ban elivering t b s b j,t in government bons, provies the commercial ban θ t t b s b j,t units of central ban funing. Hence the collateral haircut is 1 θ t. A higher value of θ t allows the commercial ban to obtain more central ban funing for the same number of government bons, which increases the collateral value of government bons. The haircut parameter θ t is possibly time-varying, an is given by the following process: θ t = θ + κ,cb ξt ξ, 24 where θ is the steay state haircut parameter, which increases in a financial crisis by setting κ,cb <. The asset sie of the central ban balance sheet consists of loans cb t to commercial bans on which it receives a nominal interest rate r n,cb t. The liabilities consist of househol eposits 7 on which it pays the nominal eposit rate rt n. Central ban profits or losses are passe on to the fiscal authority perio by perio. Hence central ban net worth is zero, an liabilities consist solely of househol eposits. Real central ban profits or actually losses, since r n,cb t 1 rn t 1, are given by: Π cb t = 1 + r n,cb t 1 cb t 1 π t 1 + r n t 1 π t cb t 1 = rt cb rt cb t 1, 2 where π t is the gross inflation rate, an the net real return on central ban funing rt cb by: 1 + r cb t is given = 1 + rn,cb t 1 π t. 26 Note that without the central ban intervention, commercial bans woul have to pay the interest rate rt. Hence the central ban losses Π cb t ban to the commercial bans. can be interprete as the subsiy given by the central 3.6 Maret clearing In euilibrium, the total number of private loans t must eual the total number of loans provie by the financial intermeiaries. Similarly, the total bon supply must eual the bons purchase 7 Central bans in most avance economies are not irectly finance through eposits, but through interest bearing commercial ban reserves. I coul moel this by incluing commercial ban reserves on the asset sie of commercial bans. Commercial bans woul not be capable of iverting commercial ban reserves in such a setup because the central ban is in charge of the reserve system. Commercial bans are not balance-sheet-constraine in financing commercial ban reserves in such a setup. Hence explicitly moelling commercial ban reserves is euivalent to letting the central ban be finance irectly by househol eposits, see also Gertler an Karai 211 2

21 by the househol sector an financial intermeiaries: t = s,p t, 27 b t = s b,h t The aggregate resource constraint is given by: + s b,p t. 28 y t = c t + i t + g t κ s b,h s b,h t ŝ b,h Euilibrium The resulting euilibrium efinition can be foun in appenix D.2, which gioves a complete escription of the moel can be foun incluing the stanar first orer conitions that have been left out in the main text. 4 Calibration I calibrate the moel on a uarterly freuency. I solve the moel using a perturbation metho that solves for the policy function with a first-orer approximation aroun the non-stochastic steay state. The parameter values can be foun in Table 1. Most of the parameter values are common in the literature on DSGE moels, or freuently use in moels containing financial frictions. I follow Gertler an Karai 211 for these parameters. Stanar parameter values are the subjective iscount factor β, the habit formation parameter υ, the inverse Frisch elasticity ϕ, the elasticity of substitution for final goos proucers ɛ, the Calvo probability of eeping prices fixe ψ, the capital share in output α, the investment ajustment parameter γ, an the smoothing parameters for prouction ρ z an the uality of capital ρ ξ. Parameters regaring conventional monetary policy are set at relatively stanar values. The interest rate smoothing parameter ρ r is set at.4, to reflect a more aggressive response of conventional monetary policy, which is in normal times in the range of.8.9. Other coefficients are calibrate to match specific targets: the relative utility weight of labor Ψ is calibrate to have the steay state labor supply eual 1/3. A crucial parameter in my analysis is the intermeiation cost for househols on bon holings κ sb,h. This affects the elasticity of househol eman for government bons in response to changes in the bon price. When commercial bans want to increase their bon holings because of central ban funing provie at an attractive interest rate, this parameter inicates how willing househols are to sell government bons to commercial bans. I set κ sb,h eual to.2. For this parameter value, a ecrease in the interest rate on central ban funing of basispoints on impact with respect to the interest rate on eposits leas to an increase recourse to central ban funing of apprxoimately % of annual steay state GDP, which is on the conservative sie in comparison with the cumulative tae up of LTRO funing in December 211 an February 212, as was 21

22 Parameter Value Definition Househols β.99 Discount rate υ.81 Degree of habit formation Ψ Relative utility weight of labor ϕ.276 Inverse Frisch elasticity of labor supply κ sb,h.2 Constant portfolio ajustment cost function ŝ b,h Reference level portfolio ajustment cost function Financial Intermeiaries λ.3861 Fraction of private loans that can be iverte λ b.193 Fraction of gov t bons that can be iverte χ.26 Proportional transfer to entering baners σ.9 Survival rate of the baners Intermeiate goo firms ɛ Elasticity of substitution ψ.779 Calvo probability of eeping prices fixe α.33 Effective capital share Capital goo firms γ Investment ajustment cost parameter δ.92 Depreciation rate Autoregressive components ρ z.9 Autoregressive component of prouctivity ρ ξ.66 Autoregressive component of capital uality ρ r.4 Interest rate smoothing parameter Policy r c.4 Real payment to government bonholer ρ.96 Parameter government ebt uration yrs κ b. Tax feebac parameter from government ebt κ π 1. Inflation feebac on nominal interest rate κ y.12 Output feebac on nominal interest rate Shocs σ z.1 Stanar eviation prouctivity shoc σ ξ. Stanar eviation capital uality shoc σ r.2 Stanar eviation interest rate surprise shoc Table 1: Moel parameters. 22