2/RT/16

Bank Lending, Collateral, and Credit Traps in a Monetary Union

Giuseppe Corbisiero

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Bank Lending, Collateral, and Credit Traps in a Monetary Union Giuseppe Corbisiero∗ March, 2016

Abstract This paper provides a theory to investigate the transmission of non-standard monetary policy to corporate lending in a monetary union where financial frictions limit firms’ access to external finance. The model incorporates a banking-sovereign nexus by assuming that sovereign default would generate a liquidity shock severely hitting domestic banks’ balance sheet. I find that this feature crucially impairs the transmission of monetary policy, generating asymmetric lending responses and the risk of contagion across economies. In particular I show that, in some circumstances, the liquidity injected into the risky country’s banks results in financing the sovereign rather than boosting lending, and sovereign risk in one country generates negative spillover effects on lending throughout the monetary union via the collateral channel. The model sheds light on the troubled transmission of the ECB’s policy measures to the economy of stressed countries during the euro sovereign debt crisis. KEYWORDS: Bank Lending, Sovereign Risk, Monetary Policy, Crisis, Euro Area. JEL Classification: E44, E52, F36, G01, G33.

∗ Monetary Policy Division, Central Bank of Ireland. Contact: [email protected]. Earlier versions of this paper, which is based on a chapter from my PhD dissertation at the University of Mannheim, circulated with the title “Banks’ Home Bias and Credit Traps in a Monetary Union”. I thankfully acknowledge the financial support of the Deutsche Forschungsgeimenschaft (DFG) for the whole duration of my PhD. I am especially grateful to Michèle Tertilt and Klaus Adam for continuous advice and encouragement. I would also like to thank Benjamin Born, Antonio Ciccone, Francesco Paolo Conteduca, Peter Dunne, Florian Exler, Gabriel Fagan, Tullio Jappelli, Matthias Kehrig, Bernard Kennedy, Niccolò Lomys, Vera Molitor, Tommaso Oliviero, Marco Pagano, Nicola Persico, Henning Roth, Annalisa Scognamiglio, Saverio Simonelli, Emanuele Tarantino, as well as seminar and conference participants at several institutions, in particular the Central Bank of Ireland, the University of Mannheim, and the University of Naples Federico II for their helpful comments. Views expressed in this paper are mine and do not necessarily reflect those of the Central Bank of Ireland or the ESCB. All errors are mine.

Non Technical Summary Since the beginning of the recent financial crisis, the ECB has responded to financial system impairments by complementing cuts in the policy interest rate with a wide range of non-standard measures, so injecting a large amount of liquidity at low cost. Nevertheless, bank lending hardly reacted, notably in countries where higher perceived risks of sovereign default emerged. At the same time, banks increased their domestic sovereign debt holdings to a much greater extent in stressed countries. This paper provides a model to explain these stylized facts by studying the transmission of central bank liquidity injections to corporate lending in a monetary union. In this model, countries differ in sovereign risk, and firms’ access to external finance can be constrained by financial frictions. The framework takes into account that the banking sector is very vulnerable to domestic sovereign risk, notably because of the high leverage of banks and their dependence on market confidence, which can disappear in a crisis. Specifically, I assume that the occurrence of sovereign default would generate a liquidity shock severely hitting a share of the country’s banks. Capturing the general equilibrium interplay between liquidity, financial frictions, firms’ collateral, and lending, the model shows that the banking-sovereign nexus crucially impairs the monetary transmission mechanism. In particular, I show that lending responses to monetary policy across countries are asymmetric, with liquidity injections mainly financing the sovereign rather than boosting lending in the risky country. This is because the banking-sovereign nexus prevents banks from fully taking into consideration the risk of their sovereign; hence, they respond to liquidity injections by purchasing domestic sovereign debt, to the detriment of private lending. This theoretical mechanism can shed light on the troubled transmission of the ECB’s policy measures to the economies of stressed countries during the euro sovereign debt crisis. I also show that sovereign risk in one country generates negative spillover effects that, through the ‘collateral channel’, can depress lending throughout the monetary union. Specifically, the possibility of a liquidity shock due to sovereign risk can reduce the expected price of assets used as loan collateral; therefore, to the extent that asset markets are integrated across countries, sovereign risk can undermine debt capacity of firms even in economies that do not suffer from high sovereign risk. This transmission mechanism provides new testable implications briefly discussed in the paper. This theory has the following policy implications. First, it can be beneficial to promote cross-border lending in the Euro Area, as well as weakening the link between a country’s banking and the health of its public finances. Second, a timely intervention in response to sovereign market turmoil would lessen banks’ search for sovereign yields and allow a more effective monetary stimulus to private lending in stressed countries. Third, nonstandard measures able to improve corporate sector liquidity circumventing the banking intermediation channel may enhance the monetary stimulus.

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Introduction

To what extent can monetary policy boost corporate lending in a monetary union suffering from a sovereign debt crisis? Since the beginning of the recent financial crisis, the ECB and all major central banks in the world’s developed economies have had to make recourse to new non-standard policy measures; this to overcome financial market impairments that were constraining the monetary transmission mechanism notwithstanding the reduction in the main policy interest rates (see e.g. Fahr et al. 2011, and Mishkin 2011). Nevertheless, this could not prevent firms from suffering from a strong reduction in the availability of bank loans, particularly in countries where higher perceived risks of sovereign default emerged since mid-2010. The left panel of Figure 1 shows variations in the stock of bank loans to domestic nonfinancial corporations (NFCs), comparing two groups of countries in the Euro Area (EA), ‘periphery’ (or ‘stressed countries’) – Greece, Ireland, Italy, Portugal, and Spain – versus ‘core’ – Austria, Belgium, Finland, France, Germany, and Netherlands. Since September 2008 (Lehman Brothers’ collapse), bank lending to NFCs has increased by 4% in the core but reduced by 29% in the periphery. The series started diverging as the euro sovereign debt crisis began: from September 2008 to June 2010, both the core and the periphery experienced a slight reduction, by 1% and 3% respectively; by contrast, from June 2010 to September 2015, bank loans massively reduced by 27% in the periphery but increased by 5% in the core. Total credit to NFCs displays similar trends (see Figure 6). At the same time, the sovereign bond portfolios of banks have been poorly diversified and largely ‘home biased’ throughout the EA. Since the financial crisis, however, banks have increased their domestic sovereign debt holdings to a much greater extent exactly in stressed countries, in spite of the emergence of high perceived risks of sovereign default. Since September 2008, banks’ sovereign holdings have increased by 172% in the periphery and by 63% in the core. A strong divergence has persisted from June 2010, with a 56% increase in the periphery vs. a 26% increase in the core (right panel of Figure 1). This paper provides a theory that aims at explaining these stylized facts. The model relies on the hypothesis that banks anticipate that the future occurrence of sovereign default will likely jeopardize liquidity of the domestic banking system. The purpose is to analyze whether this banking-sovereign nexus can explain the difference in bank lending responses to the ECB’s measures implemented during the euro sovereign debt crisis. The model builds upon the literature arguing that collateral eases financial frictions and enhances debt capacity of firms (Bernanke and Gertler 1989, Shleifer and Vishny 1992, Hart and Moore 1998, Bernanke et al. 1996, 1999, Kiyotaki and Moore 1997, Benmelech and Bergman 2012). In a two-country monetary union, governments issue sovereign debt, not repaid in the next period with an exogenous probability. Firms need external funds to undertake a profitable project but, as in Kiyotaki and Moore (1997), banks cannot verify project returns; hence, firms need to pledge their assets as collateral, with the asset value constraining their debt capacity. Collateral price is endogenously determined in a market

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Bank holdings of domestic sovereign debt bln €

bln €

Bank loans to domestic NFC 3,000

900

2,500

750

2,000

600

1,500

450

1,000

300 Core

500

150

Periphery

0

Core Periphery

0

Figure 1: Loans to NFCs vs. Domestic Sovereign Holdings of Banks in the Euro Area The left panel shows monthly data on the outstanding amounts of bank loans to domestic NFCs. The right panel shows monthly data on the outstanding amounts of bank holdings of domestic sovereign debt. Data source: ECB Statistical Data Warehouse.

with a structure following Shleifer and Vishny (1992). As in Benmelech and Bergman (2012), non-standard measures are modeled in reduced-form as central bank injections of liquidity into commercial banks’ balance sheet, and financial instability is captured by a liquidity shock forcing a share of firms to liquidate their assets. For ease of exposition, I compare the full model with a benchmark model abstracting from any banking-sovereign nexus. In the latter, the monetary transmission mechanism is similar to Benmelech and Bergman (2012). Liquidity injections positively affect corporate lending through two interdependent channels: first, the interest rate on loans (or ‘lending rate’) is reduced and this, in turn, expands the discounted expected price of collateral – i.e. E(P ) 1+r

– by reducing its denominator. Consequently, debt capacity of firms and corporate

lending increase. Second, as firms are endowed with more liquidity, they will bid more aggressively for assets liquidated in the next period by firms in financial distress, boosting their price. Banks upgrade their expectations of the liquidation price of assets, E (P ), acknowledge a higher debt capacity of firms, and hence grant them even more loans. Thanks to this virtuous interplay, the central bank can successfully offset the lending reduction during an economic downturn throughout the monetary union. However, if the crisis is particularly severe – i.e. too many firms are forced to liquidate their assets – an excessive asset supply depresses its liquidation price, and corporate lending will be constrained at a sub-optimal level, regardless of the strength of the central bank intervention. The full model introduces a nexus between domestic banking and sovereign risk. Specifically, I assume that banks make their present investment decisions anticipating that, if sovereign default occurs in the next period, it will generate a liquidity shock forcing a share of domestic banks into bankruptcy. This feature impairs the monetary transmission mechanism, generating asymmetric responses across countries and the risk of contagion across economies. To clarify the mechanism, suppose that one sovereign is risky (in country R) while the other is not (in country S), and the share of domestic banks hit by the sovereign default

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shock equals one. Initially, liquidity injections lower the lending rate and boost corporate lending in both countries, as in the benchmark model. However, due to the investment behavior of country R’s banks, there is a level of liquidity beyond which further injections lower the lending rate in country S but not in R. Indeed, although firm loans guarantee a repayment up to the collateral value, banks’ profits do not increase with returns realizing in the future state of the world where sovereign default forces them into bankruptcy (and zero profit, as protected by limited liabilities). Once the lending rate equals the domestic sovereign yield, additional liquidity injections do not reduce it further – as long as there is a competitive investment, sovereign debt, which pays high yields and whose risk is not internalized by domestic banks. The collateral constraint prevents debt capacity of firms from increasing, and banks invest the liquidity injected purchasing domestic sovereign bonds. By contrast, the central bank intervention incessantly reduces the lending rate and expands corporate lending in country S; thus, monetary policy produces asymmetric effects on lending across the monetary union countries. Section 5 argues that this theoretical mechanism can shed light on the troubled transmission of the ECB’s policy measures to the economies of stressed countries during the euro sovereign debt crisis. In the model, the exposure of one country’s banks to domestic sovereign risk also generates the risk of negative spillover effects, depressing lending throughout the monetary union, through endogenous dynamics in the collateral price. This mechanism is due to the fact that banks in country S can rationally anticipate that, if the government in country R defaults in the next period, domestic firms holding bank deposits will have less funds to purchase liquidated assets. This fall in the demand can lower the asset price, which would lead banks to update their expectations of the value of collateral and downgrade debt capacity of firms today, even in country S. In some circumstances, the central bank is not able to offset this contraction in corporate lending regardless of the monetary policy stance. Therefore, the monetary transmission mechanism becomes impaired even in economies that are not directly subject to high sovereign risks. This transmission mechanism provides new testable implications briefly discussed in Section 5. The modeling framework in Benmelech and Bergman (2012) is the most closely related to the one outlined in Section 2. They study non-standard monetary policy in a closed economy with similar financial frictions and a similar structure of the market for liquidated assets, showing the existence of equilibria in which banks choose to hoard liquidity in spite of the monetary expansion. Within a different modeling framework, Buera and Nicolini (2014) also study the effect of collateral constraints in the transmission of monetary policy at the zero bound in a closed economy. To study the transmission of monetary policy in the EA, I propose instead a two-country framework with one central bank, sovereign risk, and a banking-sovereign nexus. So augmented, the model highlights new limitations and asymmetries encountered by monetary policy that can shed light on the diverging lending responses observed across EA’s countries during the sovereign debt crisis.

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Recent empirical works show the relevance of collateral constraints for debt capacity of firms (see Shleifer and Vishny 2011 for a review of the literature on fire sales in macroeconomics and finance). Benmelech and Bergman (2011), and Hertzel and Officer (2012) show that bankruptcies raise industries’ cost of capital by deteriorating collateral market conditions. Ortiz-Molina and Phillips (2014) find that collateral market liquidity reduces firms’ cost of capital. Adelino et al. (2015) find that the recent real estate boom-and-bust affected employment in small businesses through the collateral channel. Several recent papers address the large exposure of the EA’s banks to domestic sovereign debt. Battistini et al. (2014) find that banks in stressed countries increase the home share of their sovereign debt portfolios as the country risk increases. Acharya and Steffen (2015) investigate the “carry trade” by the EA’s banks, which fund themselves in the wholesale market and invest the proceeds in risky sovereign bonds, partly because of the ECB funding of these positions. Acharya et al. (2015) find that firms exposed to banks affected by the sovereign debt crisis became financially constrained and reduce their business. This literature provides evidence that banks in the EA’s periphery increased domestic sovereign holdings during the euro crisis, to the detriment of domestic lending. From a theoretical viewpoint, Livshits and Schoors (2009) argue that banking crises are due to inadequate prudential regulations, providing evidence from the Russian 1998 crisis. In Uhlig (2014), risky countries’ regulators promote banks’ exposure to domestic sovereign debt, getting to borrow more cheaply and shifting sovereign risk onto the central bank. Crosignani (2015) argues that undercapitalized banks act as buyers of last resort for home public debt, so providing incentive to governments not to recapitalize the financial sector during a sovereign crisis. While these papers investigate the reasons behind the banks’ exposure to domestic sovereign debt, my analysis incorporates a banking-sovereign nexus to mainly focus on its consequences for the transmission of monetary policy. Broner et al. (2014) address the euro sovereign debt crisis with a model relying on creditor discrimination and crowding-out effects, showing that domestic debt purchases reduce growth and welfare, possibly leading to self-fulfilling crises. Compared to the latter paper, a microfoundation of financial frictions and an endogenous market for collateral allows my analysis to investigate spillover effects of sovereign risk through the collateral channel. Corsetti et al. (2014) calibrate a two-country New Keynesian model to the euro area, showing that a combination of sovereign risk and procyclical fiscal policy generate the risk of belief-driven deflationary downturns. In contrast to the present paper, their transmission channels do not rely on bank lending. The rest of this paper is organized as follows. Section 2 presents the model setup and Section 3 describes the monetary transmission in the benchmark case. Section 4 contains the main analysis and studies the impact of the banking-sovereign nexus on the effectiveness of monetary policy. Section 5 discusses the model predictions in the light of the ECB’s policy and the lending response during the euro sovereign debt crisis. Section 6 concludes.

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2

Model Setup

In a stylized 3-period general equilibrium framework, two countries (R and S) constitute a monetary union. Each country is populated by firms, commercial banks, and a government issuing sovereign bonds that do not repay in the next period with an exogenous probability. The following features constitute the building blocks of this model. Financial Frictions and Firms’ Access to External Finance. As in Kiyotaki and Moore (1997), lenders cannot verify returns on firms’ projects; then, in an optimal financial contract, debt cannot exceed the value of assets pledged as collateral. So, this theory relies on the hypothesis that the collateral constraint binds debt capacity of at least some firms in the economy – which can be particularly relevant in the current juncture to the extent that the crisis generated higher uncertainty about firms’ solvency, leading to increases in collateral requirements for bank loans.1 Non-Standard Monetary Policy. As in Benmelech and Bergman (2012), the central bank controls the total liquidity in the system through non-standard measures, modeled in reduced-form as liquidity injections into commercial banks’ balance sheet. Market for Funds. Absent any segmentation in the market for funds, the law of one price would imply equal lending rates across countries; moreover, deposits in the riskier banking system would be entirely moved to banks in the safer country. To prevent the model from displaying such unrealistic features, I assume two types of segmentation: first, banks face an operating cost of lending funds abroad, which allows a band within which lending rates can differ across countries; second, firms cannot deposit their wealth in foreign banks. Market for Firms’ Assets. Asset price dynamics capture Shleifer and Vishny’s hypothesis (1992) that fire sales due to financial distress depress debt capacity of other industry participants. As in Benmelech and Bergman (2012), a liquidity shock, capturing the crisis’ severity, forces a share of firms to liquidate their assets. Proposition 3 (spillover effects of sovereign risk) relies on the hypothesis that asset markets are sufficiently integrated to let the price in country i being affected by a drop in the demand in country j. Banking-Sovereign Nexus. There is a positive probability that, at least in one country, sovereign default will occur at time-1. Making their time-0 investment decisions, banks anticipate that the occurrence of sovereign default in the next period will force a share of domestic banks into bankruptcy, regardless of their portfolio composition. The rest of this section describes the model setup in details. For convenience, maximization problems provide a simpler, but equivalent, formulation than in Hart and Moore (1998), incorporating the contract theory problem through budget constraints. Figure 2 comprehensively summarizes the timing of events. 1

Evidence in this direction is provided by the ECB’s survey on the access to finance of enterprises (SAFE), according to which since 2009 entrepreneurs constantly registered, on average, increases in collateral requirements for bank loans (see Figure 8).

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2.1

Firms’ Problem

Each country is populated by a continuum of firms Bi of measure one. Each firm is endowed with an identical preexisting asset and different initial wealth levels A, which are i.i.d. draws according to probability measure PA over [0, I], with associated cumulative distribution function F (A). Each firm can undertake a project, which requires a monetary investment of I at time-0, and generates returns X1 at time-1 and X2 at time-2, with I < X1 < X2 . Firms can borrow from domestic or foreign banks to finance the project. For convenience, a firm’s borrowing requirement B is defined as the difference between the cost of the project and the firm’s initial wealth, B ≡ I − A. Let F (B) be the cumulative distribution function according to which firms’ borrowing requirements B are distributed over the interval [0, I]. If firms do not obtain sufficient funds from banks, they can deposit their initial wealth in domestic banks, earning a return determined by the equilibrium interest rate. The assumption that firms cannot deposit their wealth in foreign banks prevents country R’s bank deposits from being entirely moved abroad; moreover, it represents the fact that the vast majority of firms in the EA operate with domestic banks.2 As in Benmelech and Bergman (2012), firms face an idiosyncratic liquidity shock: at time-1, a fraction γi of country i’s firms, whose identity is ex-ante unknown, are forced to liquidate their asset and to consume all their available wealth. A higher γi proxies for a higher aggregate liquidity shock hitting the economy or, in other words, for a more severe impact of the financial crisis.3 The price of the liquidated asset, P , is endogenously determined in a union-level market, whose suppliers are firms hit by the liquidity shock and operators are the others. Purchasing an additional asset unit generates a return Y > 0 at time-2, while holding 0

it generates a return X2 > Y at time-2 (the latter implies that firms do not voluntarily liquidate assets at time-1). The return guaranteed by an additional asset does not exceed the project’s cost, Y < I (as the asset price is bounded from above by Y , this inequality implies that the collateral constraint binds at least for some firms). Ignore for the moment the bank exposure to the sovereign default shock (i.e. δ = 0). Given a lending rate rf and a deposit rate rid , a country i’s firm with initial wealth A obtains by borrowing an amount b ∈ R+ and undertaking the project (lower index ‘P ’) the following time-0 expected payoff:

 

E VPδ=0 = γi 1I X1 + E (P ) − 1 + rf b + (1 − γi ) 1I X2 + y 1I X1 − 1 + rf b 

Y 0 + (1 − y) 1I X1 − 1 + rf b + X2 E (P )

(1)

where 1I is an indicator function assuming value 1 if the firm obtains sufficient funds to invest in the project, b + A ≥ I, and 0 otherwise. With probability γi , at time-1 the firm is hit by a liquidity shock, forced to liquidate assets and consume its wealth, constituted by 2 In the EA, the cross-border share of total deposits has been consistently around 1% for households and 7% for NFCs over the last decade, absent significant variations during the financial crisis or the sovereign debt crisis (see ‘balance sheet items’, Statistical Data Warehouse, ECB). 3 One market for collateral implies that results apply unchanged regardless of differences in γ.

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the return on project, X1 , plus the expected liquidation value of the asset, E (P ), minus the bank loan repayment, 1 + rf b. With probability 1 − γi , the firm can continue its 0

business until time-2, when the project generates X2 and the asset generates X2 . In this case, the firm can allocate a share 1 − y, with y ∈ [0, 1], of its time-1 wealth to asset purchases, with expected price E (P ) and time-2 return Y . Alternatively, given a deposit rate rid , a firm depositing its initial wealth A in the banks (lower index ‘N P ’) will obtain the following expected payoff:

 E VNδ=0 = γi 1 + rid A + E (P ) P  

0 Y + (1 − γi ) y 1 + rid A + (1 − y) 1 + rid A + X2 . E (P )

(2)

Also in this case, with probability γi a liquidity shock forces the firm to consume its 

time-1 wealth, constituted by the gross return on deposits, 1 + rdi A, and the expected liquidation value of the asset, E (P ). With probability 1 − γi , the firm can continue its 0

business until time-2, when the asset generates X2 , and the additional assets possibly   bought in the previous period guarantee a gross return equal to 1 + rid

Y E(P )

(1 − y) A.

Banks’ exposure to domestic sovereign default risk (i.e. δ > 0) does not modify the 

firm’s expected payoff from undertaking the project; namely, E (VP ) = E VPδ=0 . By

contrast, the probability δρi of bankbankruptcy affects returns on deposits, given that in   d this case banks only repay α 1 + ri A at time-2, with α ∈ (0, 1], rather than 1 + rid A at time-1 (see the banks’ problem below for more details), Hence, in the ‘sovereign default shock’ scenario, a firm’s expected payoff from depositing its initial wealth in the banks is given by: 

 E (VN P ) = γi (1 − δρi ) 1 + rid A + δρi α 1 + rid A + E (P )    

Y
0 + (1 − γi ) (1 − δρi ) y 1 + rid + (1 − y) 1 + rid A + δρi α 1 + rid A + X2 E (P )

(3)

Financial frictions require that the financial contract is incentive compatible, and this can limit the firm’s ability to obtain funds from banks and hence to undertake the project. Define Ξ as a financial contract – a three-dimensional vector specifying: (i) time-0 debt, b, (ii) time-1 repayment, and (iii) penalty in case of no repayment – and Ξ as the set of optimal financial contracts (which is characterized in Section 3.1.1). The financial friction constrains the amount of obtainable funds b to be an element of an optimal financial contract, b : Ξ ∈ Ξ. Therefore, the profit maximization problem of a firm whose wealth is A is given by:4 max

ξ∈{0,1}, b, y∈[0,1]

ξE (VP ) + (1 − ξ) E (VN P ) (

s.t.

b: Ξ∈Ξ,

if ξ=1

b=0,

otherwise

(4)

So formulated, the maximization problem does only allow firms to choose between 4

I assume that firms can borrow only to undertake the project. This is without loss of generality, given that in any equilibrium the deposit rate and the lending rate coincide.

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t=0 CB liquidity injection Issue of government bonds Bank investment decision Firm investment decision

t=1

t=2

Returns on investment: X1 or (1 + r) A

Returns on investment: X2

Firms pay back debt

Returns on asset holding: 0 Y , X2

γi firms liquidate asset: market for collateral

Bankrupt banks’ liquidation: α (1 + r) A

If sovereign default: δ banks go bankrupt

Figure 2: Timing of Events This figure describes the timing of events. As time is discrete, in each period all events take place simultaneously.

the project and bank deposit; as robustness check of the results, the proof of Lemma 2 considers the case in which firms can also choose to keep their initial wealth.

2.2

Banks’ Problem

Each of the two economies includes a large number n of competitive commercial banks, all identical, whose balance sheet is composed of the following elements. Define Ai as the subset of Bi constituted by firms ı applying for deposits in that bank, ´ Ai : {ı ∈ Bi : a (ı) > 0}. Total deposit applications to that bank equal Ai a (ı) dı, and ´ the bank decides how much to accept, h Ai a (ı) dı, with h ∈ [0, 1]. In addition, the bank obtains liquidity from the central bank, l = LIABILITIESi,0

L n,

for total time-0 liabilities equal to: ˆ =h a (ı) dı + l. Ai

Define Bi (Bj ) as the subset of Bi (Bj ) constituted by domestic firms ı (foreign firms ) 



applying for loans from that bank, Bi : {ı ∈ Bi : b (ı) > 0} (Bj :  ∈ Bj : b () > 0 ). For each loan application, b (ı) and b (), the bank decides how much to grant, x (ı) , x () ∈ [0, 1]. As in the firm’s profit maximization problem, the amount of funds supplied to each firm, x (ı) b (ı) and x () b (), must be elements of optimal financial contracts, Ξ ∈ Ξ. In addition, a bank can underwrite an amount gi (gj ) of domestic (foreign) government debt and deposit funds in the central bank, C, for total time-0 assets equal to: ˆ ˆ ASSETSi,0 = R + x (ı) b (ı) dı + x () b () d + gi + gj + C, Bi

Bj

where R is initial capital to be deposited as reserves in the central bank at zero interest rate. Ignore for the moment the bank exposure to the sovereign default shock (i.e. δ = 0). Given the cost of foreign lending, c,5 rates on domestic loans, rifD , and on foreign ones, 5

This interprets operating and/or informational advantages in lending funds to a domestic firm, and produces a segmentation in the capital market that allows lending rates to possibly differ across countries.

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rifF , government bond yields, rgD and rgF , sovereign default risks, ρi and ρj , and a zero interest rate on central bank deposits and liabilities, a country i’s bank has the following time-1 expected payoff: ˆ  x (ı) b (ı) dı + 1 + rifF − c

ˆ  E (Π1,i,δ=0 ) = R + 1 + rifD

x () b () d

Bj

Bi

ˆ


+ (1 − ρi ) (1 + rgD ) gi + (1 − ρj ) (1 + rgF ) gj + C − 1 + rid h

(5) a (ı) dı − l ,

Ai

which the bank maximizes at time-0 over the decision variables: x (ı) ∈ [0, 1] , x () ∈ [0, 1] , gi , gj , h ∈ [0, 1], subject to the following resources constraint: ˆ ˆ ˆ x (ı) b (ı) dı + x () b () d + gi + gj + C ≤ h a (ı) dı + l , Bi

Bj

(6)

Ai

and the following financial contract optimality constraints: x (ı) b (ı) : Ξ ∈ Ξ, ∀ı, and x () b () : Ξ ∈ Ξ, ∀.

(7)

In the benchmark model (Section 3), the banks’ problem analyzed is exactly as described above. The full model (Section 4) includes instead a banking-sovereign nexus through the following assumption. Assumption: Sovereign Default Shock The occurrence at time-1 of sovereign default generates a liquidity shock S that hits the balance sheet of a fraction δ > 0 of domestic banks so large as to force them into bankruptcy, regardless of their portfolio composition. As described above, firms are subject to a shock capturing the effects of the financial crisis; similarly, banks are subject to a shock that captures the effects of the sovereign debt crisis (and, as for firms, the identity of banks hit by this shock is ex-ante unknown). Specifically, if sovereign default occurs in country i at time-1, domestic banks are subject to the following idiosyncratic shock: (

s=

S, with probability δ 0,

with probability 1 − δ

Conditional on the occurrence of sovereign default in the next period, the present expected payoff of a domestic bank is given by: E (Π1,i | sdefi = 1) = max {ASSETSi,1,sdefi =1 − LIABILITIESi,1 − δS, 0} , where the max operator applies because of banks’ limited liabilities. The ‘sovereign default shock’ assumption implies that: S ≥ ASSETSi,sdefi =1 − LIABILITIESi , ∀x (ı) , x () , gi , gj , h, which, in turn, implies that: E (Π1,i | sdefi = 1, s = S) = 0. 12

(8)

Therefore, the time-1 expected payoff of a bank in country i is given by: ˆ  E (Π1,i ) = (1 − ρi δ) R + 1 + rifD "

ˆ  x (ı) b (ı) dı + 1 + rifF − c

Bi

+ (1 − ρj ) (1 + r

gF

) gj + C − 1 +

ˆ rid




x () b () d

Bj

 a (ı) dı − l + (1 − ρi ) (1 + r

h

(9) gD

) gi ,

Ai

which the bank maximizes over the decision variables x (ı) ∈ [0, 1], x () ∈ [0, 1], gi , gj , h ∈ [0, 1], and is subject to the resources and financial contract optimality constraints (6) and (7) above. Note that this formulation of the problem implicitly assumes that, if sdefi = 1 and s = 0, bank reserves R are sufficient to compensate for losses due to no repayment of sovereign bonds. The ‘sovereign default shock’ assumption conjectures that the future occurrence of sovereign default will likely produce systemic developments – e.g. a bank run – irreparably deteriorating the assets of at least a share of domestic banks, regardless of their portfolio composition. A very similar hypothesis is shared, for instance, by rating agencies: Standard & Poor’s (2004, 2011) explain that banks are rarely rated above their sovereign, as banking is a leveraged industry more likely than any other to be directly or indirectly affected by any sovereign default or other such crisis; several past episodes of sovereign default are mentioned in support of this view. The relevance of this theory relies exactly on the extent to which the ‘sovereign default shock’ hypothesis is shared by economic agents – rather than on the extent to which, during a sovereign default episode, it turns out to be actually correct. Indeed, the model mechanisms are based on the agents’ expectations of future outcomes, but produce their effects at time-0, one period ahead the possible occurrence of sovereign default. While ρ interprets the probability of sovereign default, δ – the share of domestic banks hit by the sovereign default shock – can reflect the strength of the banking-sovereign nexus. In the model, the residual assets of a bankrupt bank are used to satisfy the creditors, who, however, do not have immediate access to recoverable funds. Specifically, a firm that deposited its wealth in a bankrupt bank cannot use the recoverable funds to purchase liquidated assets at time-1. This assumption captures the hypothesis that, through the banking system, the sovereign default shock also affects liquidity available to the domestic demand for liquidated assets. For simplicity, I do not explicitly model a market for distressed banks’ assets, assuming instead that at time-2 creditor firms recover a fraction of the gross return on deposit they would have obtained in case of no bankruptcy, i.e. α(1 + rid )A, with α ∈ (0, 1). The model mechanisms rely on the expectation that sovereign default will jeopardize liquidity of the domestic banking system, but not on the destruction of resources. Therefore, while S can interpret the severity of the sovereign default shock in terms of liquidity, α can interpret how much it destroys resources beyond its temporary effects.

13

2.3

Governments

In each country there is a government that issues sovereign debt in fixed supply, Gi ≥ 0. This theory abstracts from strategic default considerations and an objective function is not assigned to governments. There is instead an exogenous probability, ρi , that country i’s government is forced to declare insolvency, with ρR > ρS ≥ 0. In this case, the government does not repay bondholders. I assume that sovereign risks are uncorrelated; this is trivially without loss of generality in the most relevant case that the monetary union is composed of a risky country and a safe one – reflecting ‘stressed’ countries and ‘core’ ones of the EA. If one wants to consider that both countries suffer from a positive sovereign risk, it can be easily verified that the results are valid but reduced in magnitude for a positive smaller than one correlation, and they are amplified for a negative correlation. Outside the monetary union, there are international investors willing to underwrite gi sovereign bonds at an interest rate just compensating their risk, rint =

ρi 1−ρi .

This demand

establishes an upper-bound on sovereign yields that rule out equilibria with no real investment. Whilst such upper-bound is important, the generality of results does not depend on the level specifically assumed.6

2.4

Central Bank

As in Benmelech and Bergman (2012), the central bank directly injects liquidity into commercial banks’ balance sheet. As banks are identical, apart from the cross-country difference in the sovereign risk they are exposed to, I assume that liquidity injections are equal across banks. Hence, for an aggregate level of 2L, L is the liquidity injection in each country, and l =

L n

the liquidity injected in each single bank.

Central banks actually provide liquidity to credit institutions against collateral. In the model, although not collateralized in-advance, banks’ net liabilities versus the central bank are fully employed in collateralized firm loans and/or sovereign bonds. Liquidity injections into commercial banks’ balance sheet capture non-standard monetary policy, which has been largely used by all major central banks in the world’s developed economies since the financial crisis. To analyze the effects of non-standard measures over a wider range of policy intervention, an objective function is not assigned to the central bank, and the model considers instead the equilibrium lending response for any level in the aggregate liquidity.

3

Benchmark Case: No Banking-Sovereign Nexus

To underline how the banking-sovereign nexus impacts the monetary transmission mechanism, I compare the full model in Section 4 with a benchmark model in which sovereign gi ρi If rint > 1−ρ , lending rates shifts upward both in the benchmark model and in the full model within a i certain liquidity range – without affecting the comparison between the two, hence the generality of results. 6

14

default does not hit domestic banks’ balance sheet. This benchmark model can also interpret how monetary policy is expected to work in the absence of a sovereign debt crisis. In the benchmark model, monetary policy only encounters the limitation shown in Benmelech and Bergman (2012). If the share of firms forced to liquidate assets is too large, an excess supply prevents asset prices from increasing beyond a certain level. Hence, bank lending is sub-optimal, in spite of the monetary policy stance. Concerning the transmission of monetary policy across countries, however, Proposition 1 shows that lending responses are equal, regardless of differences in sovereign default risk and/or in the magnitude of the liquidity shock hitting the two economies. The following analysis first considers the asset liquidation value as exogenous; thereafter, it includes an endogenous market for collateral, so as to take into consideration the full interplay between liquidity injections, collateral price, and lending.

3.1

Equilibrium for a Given Asset Price

Financial Frictions and Firms’ Demand for Funds A firm with initial wealth A needs to borrow an amount b ≥ I − A to undertake the project, but its debt capacity is limited, given that bank claims on project returns cannot be enforced. Each firm is endowed with a real asset that can be pledged as loan collateral, with the bank able to foreclose on it in case of no debt repayment. Given the returns scheme, there are positive values of debt such that the threat of liquidation exerted by the creditor bank induces the firm to repay at time-1, and the parties can write an incentive compatible financial contract. However, banks anticipate that no repayment exceeding the asset liquidation value P will take place in equilibrium;7 then, at time-0 a financial contract is optimal if and only if it specifies a repayment smaller than or equal to the liquidation price of asset:  b 1 + rf ≤ P .8 Hence, given a lending rate rf , the maximum amount of funds that a firm can borrow at time-0 equals: P . (10) 1 + rf Firms differ in their initial wealth, and only those with borrowing requirement satisfyb≤

ing the ‘collateral-in-advance constraint’ (10) can obtain sufficient funds to undertake the project. Whether they do so also depends on the expected return on deposits. The profit maximization problem trivially implies that both b > B and 0 < b < B are dominated choices; then, in equilibrium it must be either b = B or b = 0. Moreover, for any asset price P < Y , any firm spared by the liquidity shock optimally invests the whole time-1 wealth in liquidated asset purchases, i.e. y = 0. These conditions allow us to simplify the problem as follows: given a lending rate rf and a deposit rate rid , a firm with borrowing requirement B will prefer to undertake the project if the following condition – 7 Following Benmelech and Bergman (2012), I assume that at time-1 the firm has all the bargaining power in renegotiating its debt obligation with the bank. This implies that the firm will always bargain down its repayment to the bank’s outside option, that exactly equals the liquidation value of the asset P . 8 See, e.g., Hart and Moore (1994, 1998) for more details. Note that, as P is considered exogenous, there is no expected value operator.

15

the ‘investment participation constraint’ (IPC) – is satisfied:   


Y 0 γ X1 + P − 1 + rf B + (1 − γ) X2 + X1 − 1 + rf B + X2 P   

0 Y ≥ γ 1 + rid (I − B) + P + (1 − γ) 1 + rid (I − B) + X2 . P

(11)

The left hand side represents the expected payoff from undertaking the project, and right hand side the one from depositing wealth in the banks; rearranging terms, we obtain:     

 Y Y X1 γ + (1 − γ) + X2 (1 − γ) ≥ B rf − rid + I 1 + rid . γ + (1 − γ) P P

(12)

From equation (12), we find that if the lending rate and the deposit rate are equal, i.e. rf = rid , the IPC does not depend on the firm’s borrowing requirement B. On the other side, if rf > rid , the IPC is tighter as B is higher. From the banks’ point of view, operating with domestic firms is profit maximizing only if the lending rate is at least as big as the deposit rate, rifD ≥ rid . This must hold in equilibrium; hence, banks accept all deposits and incentive compatible loan applications from domestic firms – i.e. h = 1 and x (ı) = 1, ∀ı : b ≤

P f . 1+ri D

Furthermore, as banks are perfectly competitive, in equilibrium the lending rate and the deposit rate coincide, i.e. rifD = rid = ri ; foreign loans must include instead the cost of foreign lending, i.e. rifF = ri + c. Lemma 1 below shows that, in equilibrium, firms only demand domestic loans, and the relevant lending rate coincides with the domestic one, rf = rifD . Hence, rf = ri . This allows us to further simplify the IPC as follows: ri ≤

X1 (1 − γ) X2 i − 1 = ri . +h I γ + (1 − γ) YP I

(13)

The threshold ri determines whether it is convenient to undertake the project and, together with condition (10), allows us to obtain the effective private demand for funds in each country. If ri > ri , all firms find it optimal to deposit wealth in the banks. By contrast, if ri ≤ ri , undertaking the project maximizes firms’ profit. Nevertheless, the collateral-in-advance constraint (10) limits the debt capacity of firms. Firms with binding collateral constraint cannot collect sufficient funds to undertake the project, i.e. A+

P 1+ri

< I; hence, they deposit their wealth in the banks. All firms for which the

collateral constraint does not bind will instead demand loans, for a total amount equal to: ˆ

P/(1+ri )

Dii (ri , rj ) =

BdF (B),

(14)

0

where Dii indicates the total demand from country i’s firms (lower index) for funds supplied by country i’s banks (upper index). Governments’ Demand for Funds The effective demand for funds from governments is affected by the international investors, who are willing to purchase sovereign bonds at gi an interest rate rint =

ρi 1−ρi .

At this rate, the expected return on sovereign bonds is zero. 16

As long as the lending rate is positive, the expected return on firm loans is positive and banks do not underwrite sovereign debt, which is totally purchased by foreign investors. By contrast, if the total liquidity is sufficiently large to lead to a zero lending rate, banks may purchase sovereign bonds in equilibrium (see Lemma 1). Banks’ Supply of Funds and Equilibrium Domestic banks’ supply of funds is constituted by firms’ deposits plus liquidity injected by the central bank, L. If ri ≤ ri , the firms’ IPC is satisfied. All domestic firms with borrowing requirement B ≤ P/ (1 + ri ) undertake the project, while those with borrowing requirement B > P/ (1 + ri ) deposit their wealth in the domestic banks. Aggregating over country i’s banks, the total supply of funds is given by: ˆ

I

(I − B) dF (B).

Si (ri , rj ) = L +

(15)

P/(1+ri )

The following lemma characterizes the equilibrium on the market for funds for any exogenous asset liquidation value, P , and aggregate liquidity injection, L. Lemma 1

Assume δ = 0. Given an exogenous asset value P , in equilibrium:

(i) The interest rate on government i’s bonds satisfies rgi =

ρi 1−ρi ,

∀i. Bank purchases of

government bonds can be positive only if rj = 0, ∀i, j. (ii) Lending rates are equal across countries, ri = rj , regardless of differences in sovereign default risks. Country i’s banks do not lend funds to country j’s firms, ∀i, j. (iii) For any liquidity level L, the firms’ IPC (11) does not bind in both countries. Firms with borrowing requirement B ≤

P 1+ri

undertake the project, while the others deposit

their wealth in the banks. (iv) There is a threshold Lmax such that lending rates equal zero in both countries. Up to that threshold, an increase in L constantly reduces lending rates. Proof See Appendix A. Liquidity injections expand the supply of funds and reduce the equilibrium lending rate: the collateral-in-advance constraint relaxes, and more firms obtain sufficient funds to invest. As sovereign risks are correctly internalized by banks, they have no effect on the transmission of monetary policy to corporate lending, regardless of cross-country differences. As a loan does not exceed the time-0 collateral value, regardless of the firms’ liquidity risk, the asset liquidation guarantees full repayment of the loan. By contrast, country i’s sovereign bonds do not repay at time-1 with probability ρi . Hence, banks underwrite them only if their yield guarantees at least the loans’ expected return, rgi ≥ ri +ρi 1−ρi .

As the demand from international investors fixes an upper-bound on sovereign

17

yields equal to lending rate is

3.2

ρi 1−ρi , sovereign zero.9

debt does not grant a sufficient expected return unless the

Equilibrium with Endogenous Asset Price

As a collateral constraint applies, the effects of liquidity on asset price dynamics crucially affect the transmission of monetary policy to lending. Before analyzing those, it is convenient to provide a definition of the equilibrium in the economy analyzed. Equilibrium Definition An equilibrium in the economy described in Section 2 is a vector {L, rR , rS , rgR , rgS , P (σ)} such that: (i) Firms optimally make their borrowing and investment decisions, given lending rates rR and rS , and the asset liquidation value P (σ); (ii) Banks optimally make their lending choices knowing that, given the time-1 realization of shocks {σ}, firms will repay no more than the asset liquidation value P (σ); (iii) Lending rates rR and rS , and sovereign yields rgR and rgS , are equilibrium values such that, at time-0, markets for loanable funds and for sovereign bonds clear; (iv) Given the time-1 realization of shocks {σ}, P (σ) is an equilibrium price such that the market for liquidated assets clears. The equilibrium requirements (i) to (iii) simply state that firms and banks optimize in their choices, conditional on the financial contract being optimal; interest rates adjust in equilibrium such that markets for loans and for sovereign bonds clear – as characterized by the market clearing conditions provided in Section 3.1 above. The requirement (iv) takes into consideration the endogenous market for liquidated assets, analyzed in this section. Note that P can be function of {σ}, the time-1 realization of the liquidity shock hitting firms – and, in the full model below, of the sovereign default shock hitting banks. As banks know that P (σ) sets an upper-bound on the firms’ ability to repay at time-1 (and given the linearity of the banks’ problem), the stochastic equivalent of the collateral-in-advance constraint (10) is simply given by: b≤

E(P ) . 1 + ri

(16)

At time-1, a share of firms is hit by a liquidity shock and forced to sell their asset, which can be bought by other firms. Purchasing an additional asset generates return Y in the next period. Assets are freely traded across the monetary union countries. Perfect competition between bidders would lead to a price equal to the asset return Y ,10 but firms are liquidity constrained; hence, depending on their time-1 wealth, the equilibrium asset price can be strictly lower than Y . 9

It is straightforward to verify that a higher upper-bound on sovereign yields would generate a greaterthan-zero lower bound for lending rates without producing cross-country different lending responses. 10 Y is not discounted given that no alternative investment can be undertaken at time-1.

18

Define for each country Bi as the borrowing requirement of the marginal borrowing firm, Bi ≡

E(P ) 1+ri ,

and the vectors B ≡ (BR , BS ), r ≡ (rR , rS ). Total time-1 wealth of firms

spared by the liquidity shock equals: "ˆ Q(B, r) =

X

(1 − γi )

E(P ) 1+ri

ˆ (X1 − B(1 + ri )) dF (B) +

0

i

#

I E(P ) 1+ri

(I − B)(1 + ri )dF (B) ,

which is the cross-country sum of the wealth of firms who invested in the project (first integral in parenthesis) and the wealth of those who deposited in the banks (second integral in parenthesis). Consequently, the aggregate demand for assets is:  h i  0, Q(B,r) Y D(P ; B, r) = Q(B,r)  P

if P = Y if P ∈ (0, Y )

The total supply of asset is simply γR + γS . By market clearing, D(P ; B, r) = γR + γS , and the equilibrium asset price is: 

P (B, r) = min Define γ ≡

γR +γS . 2

Q(B, r) ,Y γR + γS



.

Proposition 1 shows that, if γ if sufficiently small, a sufficient

liquidity injection will enable P ∗ = Y . In this case, banks lend the whole liquidity injected up to Lmax , threshold at which rates are zero and lending is maximal in each country, i.e. ´Y 0 BdF (B). Monetary policy is fully effective: as the central bank injects liquidity, the interest rate is reduced, relaxing the collateral constraint. More firms invest, which increase the time-1 wealth used to buy liquidated assets: the asset price increases, which relaxes further the collateral constraint. Anticipating this dynamic, at time-0 banks acknowledge a higher debt capacity of firms and grant more loans. Thanks to this virtuous interplay, a sufficiently forceful intervention from the central bank will enable maximum lending in ´Y both countries, 0 BdF (B), and all firms with B ≤ Y will be able to invest. By contrast, there exists a γˆ > 0 such that, for all γ > γˆ ,11 the equilibrium price of asset P ∗ is strictly smaller than Y , regardless of the size of liquidity injection. Lending rates reach the zero bound at L∗ < Lmax , and liquidity injections beyond L∗ neither enhance the asset price nor reduce the interest rate. Aggregate lending does not respond, ´ P∗ ´Y remaining constrained at a sub-optimal level, 0 BdG(B) < 0 BdF (B). Intuitively, an injection of additional liquidity is ineffective because banks rationally anticipate that lending any incremental fund does not boost collateral values sufficiently to support the additional lending.12 The following proposition summarizes these results. Proposition 1

Assume δ = 0. In equilibrium:

(i) There is a threshold γ¯ > 0 such that, for all γ ≤ γ¯ , lending is constantly increasing 11 γ¯ and γˆ do not necessarily coincide. For some distribution functions F (B), intermediate levels in γ lead to equilibria in which monetary policy has discontinuous effects; see Benmelech and Bergman (2012). 12 The equilibrium described can be considered as the multi-country equivalent of the ‘credit trap’ equilibrium characterized in Benmelech and Bergman (2012).

19

in L up to Lmax . At Lmax , corporate lending is at the maximum level, and the asset price satisfies

P∗

´Y 0

BdF (B),

=Y.

(ii) There is a threshold γˆ > 0 such that, for γ ≥ γˆ , the collateral price does not reach the full value, P ∗ < Y , ∀L. The amount of lending and the share of firms able to invest are sub-optimal. (iii) An increase in L equally affects lending across countries even if ρi 6= ρj . Moreover, one market for collateral in the monetary union implies that lending responses coincide even if γi 6= γj . Proof See Appendix A. As discussed above, Proposition 1 shows that, in the benchmark model, monetary policy only encounters the limit highlighted by Benmelech and Bergman (2012). Namely, if the liquidity shock hits a too large share of firms, an excess in the asset supply prevents liquidity injections from increasing debt capacity of firms beyond a sub-optimal level. Nevertheless, monetary policy equally affects both countries; moreover, an integrated market for collateral guarantees an equal transmission of monetary policy even if the magnitude of the liquidity shock hitting firms differs across countries. These results are no longer valid once the model includes the banks’ exposure to the sovereign default shock.

4

Full Model: Sovereign Default Shock

This section contains the main analysis of the paper; compared with the benchmark model, domestic banks are exposed to a liquidity shock forcing a share of them into bankruptcy if sovereign default occurs at time-1. The introduction of this banking-sovereign nexus generates two mechanisms that crucially impair the transmission of monetary policy. First, the central bank liquidity injected into the risky country’s banks will finance the domestic sovereign rather than boosting corporate lending in some circumstances; this implies that, as long as countries differ in sovereign risk, the response of corporate lending to non-standard measures is asymmetric across the monetary union countries (Proposition 2). It is noteworthy that asymmetric responses result in a framework in which countries neither differ in their real sector nor in their financial system, apart from the difference in sovereign risk which banks are exposed to. Second, the risk of sovereign default in one country generates negative spillover effects on corporate lending throughout the monetary union via the collateral channel. In some circumstances, these effects will persist regardless of the monetary policy stance (Proposition 3). I follow a similar solution strategy as in the benchmark model. First, I characterize the equilibrium on the market for funds when the liquidation value of assets is given. Thereafter, I include an endogenous market for liquidated assets, which allows the analysis

20

of the full impact that monetary policy has on the interplay between liquidity, collateral value, banks’ investment decisions, and lending. The equilibrium definition and the characterization of the optimal financial contract provided in Section 3 also applies here.

4.1

Equilibrium for a Given Asset Price

In an optimal loan contract, a firm guarantees repayment up to the liquidation value of its asset in any future state of the world; conversely, a sovereign does not repay bondholders in the next period with probability ρi . Hence, in the benchmark model, profit maximization implies in a straightforward manner that banks underwrite risky sovereign debt only if its yield is greater than the lending rate, and sufficient to equalize the expected return on sovereign bonds to the one on firm loans, i.e. rgi =

ri +ρi 1−ρi .

By contrast, when the sovereign default shock is included, banks make present investment decisions anticipating that, if domestic sovereign default occurs in the next period, a share of them will be forced into bankruptcy. As discussed in the setup, this implies that, conditional on sovereign default occurring, a positive return realizing at time-1 increases banks’ expected profits to a minor extent than in the benchmark model. Consequently, the yield threshold at which the expected return on domestic sovereign bonds equals the expected return on firm loans is lower, and equal to rgi =

ri (1−ρi )+ρi (1−δ) . 1−ρi

Until the marginal buyer of sovereign debt is a foreign investor, its equilibrium yield will be: rgi =

ρi 1−ρi .

As discussed in more details below, this implies that, once the lending

rate reaches the threshold ri =

ρδ 1−ρδ ,

a bank in country i will not lend additional funds to

firms as long as domestic sovereign debt is available (Lemma 2). The introduction of a banking-sovereign nexus also affects firms’ profit maximization problem. Specifically, firms’ expected payoff from depositing their wealth reduces given that banks, if bankrupt, would only repay an amount α (1 + ri ) (I − B) at time-2 rather than (1 + ri ) (I − B) at time-1. As in the benchmark model, the firms’ problem can be simplified taking into account that: (i) if the firm undertakes the project, borrowing an amount different than B cannot be optimal (i.e. it must be either b = B or b = 0); (ii) as P ≤ Y , the whole time-1 wealth is invested in asset purchases (y = 0). Given a lending rate rf and a deposit rate rid , a country i’s firm with borrowing requirement B will prefer to undertake the project rather than depositing its wealth in the banks if the following condition holds:   


Y 0 f f γ X1 + P − 1 + r B + (1 − γ) X2 + X1 − 1 + r B + X2 ≥ P 

 γ (1 − δρi ) 1 + rid (I − B) + δρi α 1 + rid (I − B) + P +  

0 Y d d (1 − γ) (1 − δρi ) 1 + ri (I − B) + δρi α 1 + ri (I − B) + X2 . P

(17)

Equation (17) represents the firms’ IPC in the ‘sovereign default shock’ scenario. If the lending rate and the deposit rate are equal (a condition that is satisfied in equilibrium), the right hand side of equation (17) increases with B, while its left hand side decreases with B. In other words, the IPC becomes tighter as firms’ borrowing needs increase. It is 21

convenient to represent the value that equation (17) assumes when B = I: Y Y + X2 (1 − γ) ≥ I (1 + ri ) γ + (1 − γ) . γ + (1 − γ) P P



X1







(18)

This condition defines an interest rate ri such that a firm with maximal borrowing requirement is indifferent between the two choices. As equation (17) tightens in B, if ri ≤ ri , then the IPC is satisfied for all firms. Hence, all firms with borrowing requirement lower than or equal to the discounted value of collateral demand funds to invest in the project, while the others deposit their wealth in the banks. This makes possible to determine the total demand and the total supply of funds in a similar manner as in Section 3.1 (see the proof of Lemma 2 for more details). The following lemma characterizes the equilibrium emerging in the full model for an exogenous asset liquidation value P , and a liquidity injection L. Lemma 2 Assume δ > 0. Moreover, assume ρR > ρS ≥ 0, and

δρR 1−δρR

< ri . Given an

exogenous asset value P , in equilibrium: ˆ such that, for any L ≥ L, ˆ the firm’s investment participation (i) There is a threshold L constraint (17) is not biding, ∀B. Firms with borrowing requirement satisfying B ≤ P 1+ri

borrow and undertake the project, the others deposit their wealth.

ˆ such that, for any L ≤ L, in equilibrium rS = rR , and a (ii) There is a threshold L > L higher L reduces the interest rate. h

i

h

i

(iii) There is a non-empty interval L, L such that: (a) for any L ∈ L, L , country R’s lending rate rR is constant in L and equal to

δρR 1−δρR ;

h

i

(b) at least for some L ∈ L, L ,

country S’ lending rate rS is reducing in L. Then, for any L > L, in equilibrium rS < rR unless rR = 0. (iv) The value of L reduces both in the sovereign risk ρR and in the share of domestic banks exposed to sovereign risk δ. Moreover, if c is sufficiently large, L − L equals GR , the amount of risky country’s sovereign debt issued. Proof See Appendix A. As long as the marginal buyer of risky sovereign debt is a foreign investor, the yield is determined by the default risk: assuming

δρR 1−δρR

< ri simply rules out the trivial case in

which sovereign yields are so high that there is no real investment in equilibrium. The intuition behind the results summarized in Lemma 2 is as follows. The bankingsovereign nexus leads banks to overestimate the expected return on domestic sovereign debt relative to firm loans. This feature has no effect with sufficiently low liquidity, and the monetary transmission mechanism works as in the benchmark model. Nevertheless, once the lending rate equals

δρi 1−δρi ,

domestic banks perceive equal expected return on

sovereign bonds and firm loans. As long as the marginal buyer of risky sovereign debt 22

is a foreign investor, the yield is determined by the default risk and cannot reduce. As further liquidity is injected, the availability of sovereign bonds granting high yields prevents domestic banks from reducing lending rates. The collateral constraint does not relax and prevents corporate lending from increasing; the whole liquidity injected is used by banks to underwrite domestic sovereign debt. This ‘credit trap’ ends only once the marginal buyer of sovereign debt becomes a domestic bank. Beyond this level, liquidity injections simultaneously reduce sovereign yield and lending rates, regaining effectiveness. The mechanism just described implies that, as long as sovereign default risks are different, monetary policy produces diverging lending responses across the monetary union countries. Indeed, the higher the sovereign risk, the smaller the initial range of liquidity in which monetary policy is effective. Figure 3 analyzes the case in which the monetary union is composed of a risky country and a safe one. In the safe country, the lending rate continuously decreases as liquidity is injected by the central bank, with monetary policy successfully boosting lending. By contrast, beyond the threshold L, the lending rate in country R does not reduce, given that banks can underwrite domestic sovereign debt – which they perceive as granting the same expected return as collateralized firm loans. As long as sovereign debt is available, the lending rate does not reduce, debt capacity of firms does not expand, and banks invest the whole liquidity injected in sovereign bonds. Monetary policy will further stimulate lending in country R only if the liquidity injection is so forceful to switch the marginal buyer of sovereign debt to a domestic bank. Further noticeable implications include the following. First, a higher sovereign risk increases the threshold

δρR 1−δρR

and lowers L; this implies a smaller initial range of liquidity

in which monetary policy is effective, and a credit trap equilibrium with lower aggregate lending. The flat section of the curve representing country R’s lending rate in Figure 3 shifts towards the top left. Intuitively, a riskier sovereign debt is traded at a higher yield on the international market, but domestic banks perceive it as granting a higher return. Second, the greater the amount of risky sovereign debt issued, the greater the liquidity range in which monetary policy is not effective, L − L. This is due to the fact that the marginal buyer switches to a domestic banks at a higher liquidity level L. In Figure 3, the flat section of the curve representing country R’s lending rate expands. Third, let us consider the effect of variations in δ, the share of banks exposed to the sovereign default shock. The greater the δ, the less banks internalize the default risk of their sovereign; hence, the greater

δρR 1−δρR

and the smaller L. The flat section of the

curve representing country R’s lending rate in Figure 3 shifts towards the top left. The implications are the same as those resulting from an increase in sovereign risk: a smaller initial range of liquidity in which monetary policy is effective, and a credit trap equilibrium with lower aggregate lending. The results summarized in Lemma 2 already explain why the banking-sovereign nexus penalizes domestic lending and produces diverging responses across countries. Nevertheless, a complete characterization of the monetary transmission mechanism cannot abstract 23

Market for loans

r, lending

lendingS

lendingR

f rR

δρR 1−δρR

0

r

ρR 1−ρR

rSf L

L

L

Market for government bonds

marginal buyer is foreign

marginal buyer is domestic

r gR

(1−δ)ρR 1−ρR

0

r gS L

L

L

Figure 3: Equilibrium Responses to Liquidity Injections The figure describes the equilibria on the markets for loans and government bonds as function of the total liquidity injected by the central bank. The price of collateral is considered exogenous; the probability of sovereign default is null in country S (ρS = 0) and positive in country R (ρR > 0).

from collateral price dynamics. In the rest of this section, I show how the collateral channel, first, affects the results described in Lemma 2; and second, leads sovereign risk not only to penalize domestic lending, but also to generate negative cross-border effects.

4.2

Equilibrium with Endogenous Asset Price: Asymmetric Lending Responses

As underlined in the benchmark model, liquidity injections do not only affect lending through a reduction in the interest rate. As the project grants higher returns than bank deposits, a higher aggregate investment boosts the total wealth available to firms demanding assets in the next period. This, in turn, can boost its liquidation price. At time-0, banks upgrade their expectations of the collateral value, acknowledge a higher debt capacity of firms, and hence grant more loans. This affects the results in Lemma 2: although liquidity is in the region where country R’s lending rate is flat, debt capacity of firms can benefit from an increase in collateral

24

prices. Constant the denominator of the collateral constraint, a higher expected price of asset, possibly produced by an higher lending in country S, would increase its numerator. These collateral price dynamics possibly reduce the extent to which lending remains constrained in the risky country, but have second-order effects only, without preventing asymmetric responses across countries. Results are described in the following proposition. Proposition 2 Assume δ > 0. If sovereign default risks differ, ρR > ρS ≥ 0, corporate lending responds differently to liquidity injections across theh monetary union countries. In h 0 00 i i 0 00 particular, there is an interval L , L such that, for L ∈ L , L : (i) Country S’ lending rate reduces in L and domestic banks lend the whole liquidity injected to domestic firms; (ii) Country R’s lending rate is constant at the level

δρR 1−δρR

and domestic banks – mainly

– use the liquidity injected to underwrite domestic sovereign debt; (iii) Country R’s corporate lending increases only to the extent that the higher country S’ lending boosts the expected price of firms’ collateral; 0

(iv) The greater theh δ and/or the ρR , the lower the threshold L . Moreover, the length i 0

00

of the interval L , L

is non decreasing in country R’s sovereign debt supply, and

strictly increasing if c is sufficiently large. Proof See Appendix A. The interpretation of the results summarized in Proposition 2 closely follow Lemma 2. In the safe country, an increase in the aggregate liquidity produces both a reduction in the lending rate and possibly an increase in the expected value of collateral. Debt capacity of firms expands and banks lend the whole liquidity injected by the central bank to domestic firms, until the lending rate reaches the lower bound.13 In the risky country, instead, the transmission of monetary policy to corporate lending is impaired. As exposed to the sovereign default shock, banks underestimate the return on firm loans relative to the one on domestic sovereign bonds. The lending rate does not respond to monetary policy, as long as banks have the opportunity to underwrite additional sovereign debt. Given the presence of a collateral constraint, this feature implies that the debt capacity of domestic firms will not react to liquidity injections, unless a higher lending in country S is able to raise the expected price of collateral. Proposition 2 underlines that a greater share of banks exposed to the sovereign default shock and/or a higher sovereign risk reduce the initial range of liquidity in which monetary policy is fully effective, as well as implying a credit trap equilibrium with lower aggregate lending. Furthermore, a greater supply of risky sovereign debt enlarges the range of liquidity within which this credit trap realizes. Consequently, a higher level in each of 13

This lower bound is zero if ρS = 0 and larger than zero otherwise, but strictly lower than

25

δρR . 1−δρR

these dimensions will imply an exacerbated asymmetry in lending responses to monetary policy across countries. Section 5 argues that these results can shed light on the poor lending response to the ECB’s non-standard measures that EA’s stressed countries displayed during the euro sovereign debt crisis.

4.3

Equilibrium with Endogenous Asset Price: Spillover Effects of Sovereign Risk

In this section I show that, when banks are exposed to the sovereign default shock, sovereign risk in one country can generate negative spillover effects on lending in the other country, although not directly subject to sovereign risk, through the collateral channel. The demand for and the supply of liquidated assets are determined in a similar manner as in Section 3.1.2. However, differently than in the benchmark model, the total time1 wealth available to firms demanding liquidated assets depends on the realization of sovereign default. Conditional on sovereign default not realizing, the expected time-1 wealth of firms demanding asset equals: "ˆ Q(B, r) =

X i

(1 − γi )

Ei (P ) 1+ri

ˆ (X1 − B(1 + ri )) dF (B) +

0

I Ei (P ) 1+ri

# (I − B)(1 + ri )dF (B) ,

where terms can be interpreted similarly as in Section 3.1.2.14 By contrast, if at time-1 sovereign default occurs in country i, this would force a share δ of domestic banks into bankruptcy. These banks would only repay to creditor firms an amount α (1 + ri ) (I − B) at time-2 instead of (1 + ri ) (I − B) at time-1. These firms are potential buyers of the asset liquidated at time-1. Hence, conditional on sovereign default realizing in country i, the expected time-1 wealth available to the domestic demand for liquidated assets reduces by an amount equal to: ˆ δ

I Ei (P ) 1+ri

(I − B)(1 + ri )dF (B).

To consider how this feature affects the transmission of monetary policy to corporate lending, it is convenient to compare the asset market equilibrium in the full model with the one that would emerge in the benchmark model. Suppose that the liquidity shock hitting firms has a magnitude γ < γˆ . From Proposition 1, we know that in the benchmark model economy sufficiently forceful liquidity injections will allow the asset price to reach its full value, Y , and corporate lending to ´Y reach its maximum level in both countries, 0 BdF (B). By contrast, in the full model the occurrence of sovereign default would reduce the time-1 liquidity available to firms demanding liquidated assets. In that future state of the 14

Note that outcomes realizing in the future state of the world where sovereign default occurs enter the expected profit of domestic banks to a degree 1 − δ < 1 only. This implies that, differently than in the benchmark model, if ρi 6= ρj then Ei (P ) 6= Ej (P ).

26

world, a similar reduction in liquidity can imply that the liquidation price of assets will be strictly lower than the full value, regardless of the monetary policy stance. Specifically, there are values of γ < γˆ such that, even if: 

P1 (B, r, sdefi = 0) = min

Q(B, r, sdefi = 0) ,Y γ1 + γ2



Q(B, r, sdefi = 1) ,Y γ1 + γ2



= Y,

at the same time: 

P1 (B, r, sdefi = 1) = min

< Y.

When banks make their investment decisions at time-0, they take into account that, with probability ρi , the liquidation price of collateral will be lower than Y , adjusting downward their expectations of the price of collateral and debt capacity of firms. Therefore, the collateral constraint becomes binding for a larger share of firms, and corporate lending reduces. Intuitively, a lower collateral price implies that firms’ capacity to repay loans in the next period is reduced; hence, banks reduce the maximum amount of funds that they are willing to grant in a loan contract. It is noteworthy that country i’s sovereign risk depresses banks’ expectation of the collateral value in country j to a greater extent than in country i. The reason is that the reduction in the asset liquidation price is realized in the future state of the world where country i’s sovereign is insolvent and a share of domestic banks are bankrupt; hence, at time-0, this potential reduction enter their expected profits to a degree 1 − δ < 1 only. Spillover effects of sovereign risk are characterized in the following proposition. Proposition 3

Assume δ > 0. If sovereign default risk ρi > 0 for some i, then:

(i) There is a threshold γˆδ > 0 such that, for γ ≥ γˆδ , for any L, the time-1 price of collateral is strictly smaller than Y with positive probability, and at time-0 country ´Y j’s corporate lending is constrained at a level strictly lower than 0 BdF (B). (ii) This threshold satisfies γˆδ < γˆ , i.e. the range of the liquidity shock values within which lending is sub-optimal, regardless of L, is greater than in the benchmark model. (iii) An increase in δ and/or ρi strengthens spillover effects of sovereign risk. Specifically, a greater δ reduces γˆδ ; a greater ρi reduces the level of lending in a credit trap equilibrium. Proof See Appendix A. Proposition 3 underlines a transmission channel able to explain weak credit dynamics throughout the monetary union and whose implications can be tested empirically (as discussed in more details in the next section). Specifically, the banking-sovereign nexus leads sovereign risk to generate negative cross-border effects on lending; these effects are realized through endogenous variations in collateral values, under the assumption that 27

asset markets are sufficiently integrated to let the price in country i being affected by a drop in the demand in country j. Due to a collateral-in-advance constraint produced by financial frictions, these effects will persist regardless of the strength of the central bank intervention under some circumstances – namely, if the impact of the crisis on corporate liquidity, captured by the parameter γ, is sufficiently severe. Intuitively, even in a country that does not suffer from sovereign risk, banks rationally anticipate that the possible occurrence of sovereign default in the other country is likely to cause, through disruptions in the banking system, liquidity problems for firms operating there, so reducing their demand for liquidated assets. With a sufficiently integrated asset market, a fall in demand from one country will depress the asset price in the other. But lower collateral values imply a lower ability to repay debt in the next period: hence, banks grant less funds in loan contracts. Consequently, aggregate lending reduces even in the country that is not directly affected by sovereign risk. Finally, Proposition 3 also shows that a greater share of banks exposed to the sovereign default shock, as well as a higher sovereign risk in country R, will exacerbate the risk of contagion across economies. It is worth underlying the crucial role that banks, as intermediaries in channeling liquidity from the central bank to borrowers, play for the emergence of credit trap equilibria. Interestingly, this implies that non-standard measures able to boost corporate liquidity and/or asset prices beyond the banking intermediation channel would overcome the limitations underlined above, mitigating both the impaired transmission of the monetary stimulus to the stressed country and the negative spillover effects of sovereign risk.

5

ECB’s Policy and Lending During the Crisis

This section compares the model results with descriptive evidence on the corporate lending response to the ECB’s policy during the euro sovereign debt crisis.15 In a first phase of the crisis, in 2008-09, sovereign debt across the EA was not affected, and the ECB focused on stemming the negative financial shock and the collapse in the interbank market that followed. As with the other major central banks, the ECB complemented the reduction in the policy interest rate with the adoption of several non-standard measures. In particular, it is worth mentioning the following: a fixed-rate full-allotment procedure guaranteeing unlimited access to the central bank liquidity, an extension of the maturity of liquidity provision, an extension of the list of eligible collateral accepted in refinancing operations, liquidity provisions in foreign currency, and purchases of covered bonds issued in the EA. Although there is evidence suggesting that such measures have been beneficial in stabilizing the financial system in this first phase (Fahr et al. 2011, Giannone et al. 2012) cross-border financial flows strongly decreased. European investors reduced their overseas 15

See ECB (2015) for a comprehensive review of more recent ECB’s measures, as e.g. the targeted longer-term refinancing operations (TLTROs) and the expanded asset purchase programme (APP), which is beyond the scope of this paper.

28

investments and started increasing their exposure to home markets. Sovereign debt markets in the EA remained relatively calm in this period, with the demand for sovereign bonds sustained by banks that regarded government bonds as highly rated collateral in obtaining short-term loans from the ECB (see Lane 2012). The crisis entered a new phase in May 2010, with the Greek sovereign debt breakdown and the risk of its possible impact on Ireland, Portugal, and even Spain and Italy thereafter. The ECB intervened in the secondary markets for sovereign bonds with its Securities Markets Programme (SMP), and some non-standard measures taken in the first phase of the crisis were reintroduced. The exacerbation, from mid-2011 onwards, of the euro area sovereign debt crisis induced further policy response. In particular, the ECB adopted two three-year Longer-Term Refinancing Operations (LTROs) to provide banks with sufficient medium-run liquidity (implemented in December 2011 and in February 2012, they counted up to 489 billion euros and 529.5 billion euros, respectively) and the Outright Monetary Transactions (OMT), a program designed for the sovereign bond secondary market subject to strict and effective conditionality.16 The measures briefly reviewed above were adopted to support an effective transmission of the policy interest rate to the euro area economy, under exceptional disruptions in the financial system which led to the collapse of the interbank market. The main target of the ECB’s non-standard measures consisted in providing the necessary liquidity to avoid credit restrictions to the private sector, particularly to NFCs. The SMP and the OMT programs were also tailored to avoid lending constraints due to fall in value of sovereign bonds held by banks. There is evidence that the ECB’s policy has been effective in providing stressed countries’ banks with sufficient liquidity. The largest part of the liquidity injected through the two three-year LTROs was borrowed by banks in Greece, Ireland, Italy, and Spain. Furthermore, TARGET2 balances (Figure 4) show that, within the EA, there has been a substantial flow of liquidity from the core to the periphery.17 Nevertheless, this liquidity inflow did not seem to benefit their real economies. As discussed in the introduction, there is evidence of a credit crunch in the EA’s periphery, particularly severe for firms relying on bank lending. Further evidence documents that in Ireland, Italy, Portugal, and Spain the volume of new loans to NFCs (up to EUR 1 mln) decreased by 82%, 21%, 45%, and 66%, respectively, from the pre-crisis peak to June 2013.18 Although a divergence in corporate lending between core and stressed countries could be also due to a stronger collapse in the demand for goods and services in the latter than in the former, there is evidence suggesting that credit factors have been crucial. For 16 Although no EA’s country has ever applied for this program, Altavilla et al. (2014) find that the OMT announcement significantly reduced the Italian and Spanish government bond yields. 17 See Fagan and McNelis (2014) for more details, including an analysis of the functioning of the TARGET system. 18 Institute of International Finance and Bain & Company (2013).

29

Figure 4: Target2 Balances The Trans-European Automated Real-time Gross Settlement Express Transfer System (TARGET) is a cross-border payment system that allows EA’s banks to access liquidity through the national central banks. Source: Euro Crisis Monitor, Institute of Empirical Economic Research, Osnabrück University.

instance, both the SAFE and the bank lending survey (BLS) show that small and mediumsized enterprises based in Italy, Spain, Greece, and Ireland faced the strongest financing obstacles when applying for a bank loan during the crisis (see ECB 2013). Furthermore, Acharya et al. (2015) show that firms with a higher exposure to banks based in stressed countries became financially constrained and reduced their business during the crisis. Figure 5 provides another important piece of evidence. Since mid-2010, the transmission of the reduction in the ECB’s policy rate to the real economy has been particularly poor in stressed countries. Although bank funding costs were massively reduced by the ECB’s provision of large liquidity at a low cost, in the periphery lending rates remained high and linked to the path of domestic sovereign yields, in contrast to developments in the core – from June 2010 to March 2015, the correlation between domestic sovereign yields and lending rates exceeds the one between the latter and the MRO by 43.7% in Italy and by 19.2% in Spain, while the MRO has been more strongly correlated with lending rates than domestic sovereign yields by 4.4% in France and by 9.8% in Germany. Since the second half of 2013, stressed countries’ sovereign yields have started reducing, and so also lending rates. In the model, banks make their present investment decisions anticipating that the occurrence of domestic sovereign default in the next period would generate a liquidity shock – e.g. a bank run – forcing a share of them into bankruptcy and, as protected by limited liabilities, leading to zero profit. High sovereign yields may imply low expected returns from a foreign investor’s point of view, if due to the perception of a high default risk; from the perspective of domestic banks that do not fully internalize the default risk of their sovereign, the same yields may be perceived as granting high expected returns instead. In the light of this hypothesis, an easier and cheaper access to the central bank liquidity does not necessary lead risky countries’ banks to reduce lending rates and grant more loans: as long as sovereign debt grants high yields, these banks are likely to use 30

NFC lending rates and ECB policy rate

10‐year sovereign bond yields

7

7

6

6

5

5 Germany

4

4

France Italy

3

3

Spain MRO

2

2

1

1

0

0

Figure 5: NFCs Lending Rates, ECB Policy Rate, and Sovereign Yields The left panel shows monthly variations in the lending rate to NFCs, 1-5 years maturity, up to 1 million euros, compared with the ECB main refinancing operations rate (MRO). Data on the other periphery countries are not shown as incomplete. Data source: ECB Statistical Data Warehouse. The right panel shows monthly variations in 10-year sovereign bond yield. Data source: OECD.

instead the funds provided by the central bank to increase their home sovereign exposure. The descriptive evidence reported in this section is in line with this prediction; it suggests that, while sovereign yield spreads remained high, a larger provision of liquidity to banks poorly affected the real economy in the periphery, exacerbating instead the segmentation in the sovereign debt markets and the home bias of bank sovereign portfolios. As soon as the ECB’s policy and forward guidance started to more effectively contrast sovereign market turmoil, lending rates in the periphery have started responding again to the monetary stimulus, and bank domestic sovereign holdings have ceased to increase. In addition to the mechanism impairing the effectiveness of monetary policy in stressed countries, the model highlights transmission channels producing negative effects on lending even in safe countries. Namely, sovereign risk in one country can depress debt capacity of firms throughout the monetary union, through collateral price dynamics. If the crisis is particularly severe – i.e. the share of firms forced to liquidate assets is sufficiently large – liquidity injections cannot successfully contrast such negative effects. This mechanism has testable implications. In industries with integrated collateral markets across the monetary union countries, asset prices and debt capacity of firms are more likely to respond to an expected reduction in the asset demand due to sovereign risk in another country. By contrast, industries with segmented collateral markets are more likely to be immune to this risk. Exploiting these implications, the following difference-in-differences strategy could allow the identification of this transmission channel. Consider a panel data set of secured debt tranches of an industrial sector in an EA’s core country at two different time periods, before and after the emergence of high sovereign yield spreads. Debt tranches whose underlying collateral markets exhibit larger degree of integration with the EA’s periphery (e.g. measured by the volume of cross-border trading) should display larger price

31

declines (or lower price increases) than tranches whose underlying collateral markets are less integrated. If the data support this hypothesis, contrasting sovereign market turmoil should be considered beneficial for the transmission of the ECB’s monetary policy even to economies that do not directly suffer from high sovereign risk. A similar methodology can also allow us to test a different, but closely related, model prediction. According to Proposition 2 (iii), a higher lending in core countries can raise the expected price of collateral, reducing the extent to which debt capacity of firms in stressed countries is constrained by high lending rates. Then, we should observe that in stressed countries, secured debt tranches whose underlying collateral markets exhibit larger degree of integration with core countries should display lower price declines (or larger price increase) than tranches whose underlying collateral markets are less integrated. Similar studies are beyond the scope of this paper and left for future research.

6

Conclusion

This paper studies the limitations of non-standard monetary policy in stimulating lending in a monetary union suffering from disruptions in the financial system and a sovereign debt crisis. The framework includes the hypothesis that banks are exposed to a liquidity shock if their sovereign defaults, and studies how this feature affects the transmission of monetary policy to corporate lending. The model shows that a similar banking-sovereign nexus can crucially impair a proper monetary transmission mechanism. The theoretical mechanisms provide a clear interpretation of the heterogeneous transmission of the ECB’s policy measures to the economies of the EA; they also suggest that a large use of non-standard measures in times of high sovereign yields can lead banks in stressed countries to increase their domestic sovereign holdings, rather than channeling funds to the real economy. Furthermore, the model highlights a new transmission channel, with testable implications, through which sovereign risk in one country can constrain corporate lending throughout the monetary union. The policy implications of the model mechanisms are threefold. First, it can be beneficial to redesign the EA’s financial system with the aim of weakening the link between a country’s banking and the health of its public finances. A concrete example could be the ongoing reform of banking supervision in the EA; at the same time, the banking-sovereign nexus could be directly challenged by limiting the ability of sovereigns to entangle banks with non-collateralized debt (see e.g. Acharya 2012, and Korte and Steffen 2015). Mitigating the dependence of an economy on domestic banking by promoting cross-border lending would also have positive effects, to the extent that an easier access to foreign credit markets will provide firms with better credit opportunities than those offered by a domestic banking system entangled in a too high exposure to its sovereign. Second, it can be important to complement monetary policy with a timely intervention counteracting sovereign market turmoil – in line with the ECB’s OMT and the more recent

32

public sector purchase programme (PSPP). Indeed, a reduction in sovereign yield spreads would lessen banks’ search for sovereign yields in stressed countries, so allowing a more effective monetary stimulus to corporate lending. The model predicts that this would not only benefit stressed countries: given the possibility of cross-border effects of sovereign risk, even in core countries lending would benefit from a similar intervention. Third, the model can provide insights to design specific measures within quantitative easing programs like the recent ECB’s asset purchase program; beyond that, it suggests that intervening in different policy areas – as fiscal policy – might also be beneficial. Specifically, the model stresses that the role of banks, as intermediaries in channeling liquidity from the central bank to borrowers, is crucial for the emergence of credit traps. By contrast, measures able to directly improve corporate sector liquidity and/or boost asset prices circumventing the banking intermediation would possibly complement expansionary monetary policy and guarantee a more effective stimulus to real investment. A limit of the present analysis is that it abstracts from strategic default considerations. It can be interesting to augment the framework so as to model governments who maximize domestic welfare, and face preexisting sovereign debt that can be financed by taxing domestic firms, by issuing new sovereign debt, or can be defaulted. A similar extension would allow us to study how the monetary policy stance, set at the monetary union level, might affect the cost of raising sovereign debt, hence governments’ fiscal policy and strategic default decisions taken at the national level.

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Lane, Philip R. (2012), “The European Sovereign Debt Crisis,” Journal of Economic Perspectives, 26(3): 49-68. Livshits, Igor, and Koen Schoors (2009), “Sovereign Default and Banking,” BEROC Working Paper Series. Mishkin, Frederic (2011), “Monetary Policy Strategy: Lessons from the Crisis”, in Jarocinski et al. (2011), 67-118. Ortiz-Molina, Hernan, and Gordon M. Phillips (2014), “Real Asset Illiquidity and the Cost of Capital,” Journal of Financial and Quantitative Analysis, 49(1): 1-32. Shleifer, Andrei, and Robert W. Vishny (1992), “Liquidation Values and Debt Capacity: A Market Equilibrium Approach,” Journal of Finance, 47(4): 1343–66. (2011), “Fire Sales in Finance and Macroeconomics,” Journal of Economic Perspectives, 25(1): 29–48. Standard & Poor’s (2004), “Sovereign Risk for Financial Institutions,” RatingsDirect on the Global Credit Portal. (2011), “Banks: Rating Methodology and Assumptions,” RatingsDirect on the Global Credit Portal. Uhlig, Harald (2014), “Sovereign Default Risk and Banks in a Monetary Union,” German Economic Review, 15(1): 23-41.

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Appendix A. Proofs Proof of Lemma 1 (i) First, as international investors are willing to underwrite country i’s sovereign bonds govi at an interest rate rint =

ρi 1−ρi ,

their equilibrium interest rate rgi cannot exceed

∀i; at the same time, rgi cannot be lower than

ρi 1−ρi ,

ρi 1−ρi ,

∀i, otherwise underwriting sovereign

debt would lead to expected losses; then, in equilibrium it must be rgi =

ρi 1−ρi ,

∀i. Second,

all banks, regardless of the country where they are based, are indifferent between lending funds to firms at an interest rate rf and underwriting country i’s sovereign bonds, ∀i, if and only if the expected returns on the two investments are equal, 1 + rf = (1 − ρi ) (1 + rgi ) ⇔ r gi =

rf +ρi 19 1−ρi .

However, as rgi ≤

ρi 1−ρi ,

∀i, for any rf > 0, firm loans guarantee a

higher expected return than government bonds, and banks supply funds to firms only (provided that the collateral-in-advance constraint is satisfied in any loan contract). It results that, for any rf > 0, the overall supply of funds from banks and the overall effective demand from firms must equal. Only if rf = 0, government bonds from both countries, and firm loans grant the same (null) expected returns. In this case, banks are indifferent between the following choices: lending funds to firms at a zero interest rate, up to the limit fixed by the collateral-in-advance constraint in any loan contract; depositing funds in the central bank; underwriting country i’s sovereign debt that grants yield

ρi 1−ρi ;

or holding a

differentiated sovereign bonds portfolio with any weight ∈ [0, 1].  (ii.a) In the following, I prove that in equilibrium country i’s banks do not lend funds to country j’s firms, ∀i, j. From (i), we know that country i’s banks underwrite a positive amount sovereign debt only if ri = 0, ∀i. Then, for any aggregate liquidity L < Lmax – where Lmax is the level for which ri = 0 – the whole supply of funds is invested in firm loans only. Assume the aggregate liquidity is any L < Lmax , and the two markets for funds are in equilibrium for ri > rj . If rj is the country j’s equilibrium interest rate on domestic loans, the presence on a marginal cost on foreign lending and a no arbitrage condition imply that the equilibrium lending rate to foreign firms will be rj + c. Firstly, consider the case where ri > rj + c. Firms in country i with B ≤

P 1+rj +c ,

and whose IPC is satisfied,

apply for foreign loans; the others deposit wealth in domestic banks. But then, country ´I i’s aggregate supply of funds will be greater or equal to L + P/(1+ri ) (I − B) dF (B) > 0. As neither domestic nor foreign firms demand those funds, ri must move down. Then, in equilibrium it must be ri ≤ rj + c, at which no firm prefer to apply for foreign loans.20 Then, there is no equilibrium where ri > rj + c; this implies that banks never lend funds to firms abroad in equilibrium.  19

Note that, when P is exogenously given, in any optimal financial contract firm loans guarantee repayment in the next period up to P . 20 P then B > 1+rPj +c ; i.e. any firm that does not have Note that ri ≤ rj + c implies that, if B > 1+r i access to sufficient domestic funds to undertake the project, cannot have access to sufficient foreign funds to undertake the project.

36

(ii.b) In the following, I prove that ri = rj , ∀L. From (ii.a) we know that, in equilibrium, it is not possible that ri > rj + c; it is left to consider the case in which rj < ri ≤ rj + c. From (iii) below,21 we know that in any equilibrium the IPC is satisfied; from (ii.a) above, we know that in any equilibrium there is no lending abroad. Therefore, in each country market clearing implies that the equilibrium interest rate moves so as to equal the domestic supply of funds to the domestic demand for funds. Suppose that both economies are in equilibrium and ri > rj . As P and L are equal, the supply of funds in county i equals ´I S(L, ri ) = L+ P/(1+ri ) (I − B) dF (B) and must be strictly larger than the supply of funds ´I in country j, S(L, rj ) = L + P/(1+rj ) (I − B) dF (B). At the same time, the demand for ´ P/(1+ri ) funds in county i equals D(L, ri ) = 0 BdF (B) and must be strictly smaller than ´ P/(1+rj ) the demand for funds in country j, D(L, rj ) = 0 BdF (B). But then, if the market for funds is in equilibrium in country j, it cannot be in equilibrium for country i, and vice versa: which is a contradiction. Therefore, in any equilibrium we must have that ri = rj .  (iii) From (ii.a), we know that in any equilibrium firms do not borrow from foreign banks. This condition, together with the assumption that banks are perfectly competitive, implies that the equilibrium lending rate must be equal to the equilibrium deposit rate. This allows us to simplify the IPC as follows: 

X1 γ + (1 − γ)

Y Y + X2 (1 − γ) ≥ I (1 + ri ) γ + (1 − γ) . P P 





This condition defines a threshold ri in the interest rate on deposits above which firms do not find profitable to undertake the project. Notice that ri is independent of B: either the IPC is satisfied for all firms, or it is satisfied for no firm. Suppose that r > ri : all firms deposit their initial wealth in the domestic banks. Even if the central bank liquidity injection is at minimum level, L = 0, the total supply of funds is strictly positive and ´I equal to 0 (I − B) dF (B) > 0. However, the private demand for funds is null and, as r > 0, also governments’ effective demand for funds is null. But then the market for funds does not clear, and the interest rate must move down. Suppose instead that L > 0: this increases further the supply of funds, which still faces a null demand, hence the same argument applies. Then, it must be that in any equilibrium r ≤ ri , which implies that the IPC is always satisfied.  (iv) Suppose that the claim is incorrect. Then, there must be L1 > L0 such that r (L1 ) = ´ P/(1+ˆr) r (L0 ) = rˆ > 0. Equal interest rate implies that D (L0 ) = D (L1 ) = 0 BdF (B). In any equilibrium the market for funds clears. Then, both ˆ

ˆ

I

(I − B)dF (B) =

S (L0 ) = L0 + P/(1+ˆ r)

P/(1+ˆ r)

BdF (B), 0

21

It is possible to use the proof of Lemma 1 (iii) here, given that it does not rely on any statement proved in Lemma 1 (ii.b).

37

and

ˆ

ˆ

I

P/(1+ˆ r)

(I − B)dF (B) =

S (L1 ) = L1 + P/(1+ˆ r)

BdF (B), 0

must be satisfied in equilibrium. But this is not possible, given that L1 > L0 implies that: ˆ

ˆ

I

I

(I − B)dF (B).

(I − B)dF (B) > L0 +

L1 +

P/(1+ˆ r)

P/(1+ˆ r)

Then, either in the first case (in which the liquidity injected is L1 ) there is excess supply, which leads to a reduction in the interest rate at a level r < rˆ; or in the second case (in which the liquidity injected is L0 ) there is excess demand, which leads to an increase in the interest rate at a level r > rˆ. Then, for any L1 > L0 , we must have that r (L1 ) < r (L0 ) unless r = 0. This also implies that there must be an Lmax such that r(Lmax ) = 0. 

Proof of Proposition 1 (i-ii) Holding the results stated in Lemma 1, the benchmark model economy (i.e. when δ = 0) corresponds to a multi-country version of the closed economy described in Benmelech and Bergman (2012). Benmelech and Bergman (2012) show that the asset pricing function, evaluated at a zero lending rate, determines whether the economy will be in a ’credit trap’ equilibrium or not. In the multi-country framework described in Section 2, the asset pricing function (evaluated at a zero lending rate) is given by: Q(B, 0) P (B, 0) = min ,Y γR + γS 



.

The argument provided in Benmelech and Bergman (2012), pp. 3026 ss., implies the existence of a threshold in

Q(B,0) γR +γS ,

below which P ∗ will be always constrained at levels

strictly lower than Y , regardless of L. This equilibrium is defined as a ‘credit trap’ equilibrium.22 Otherwise, sufficiently forceful injections of liquidity will enable a full liquidation price of assets, P ∗ = Y , and lending reaches the maximal level. Define γ ≡

γR +γS . 2

Given that: "ˆ

Q(B, 0) =

X

(1 − γi )

it is straightforward to prove that must be a γˆ such that

I

(X1 − B)dF (B) + Q(B,0) γR +γS

#

(I − B)dF (B) , B

0

i

P∗

ˆ

B

is strictly decreasing in γ, for any B. Then, there

is strictly lower than Y , regardless of L, and the economy is in

a credit trap. Note that the equilibrium price of assets is crucial to determine whether the economy is in a ‘credit trap’ or not. As in the setup described in Section 2 the market for firms’ 22

Note that the ‘credit trap’ equilibrium described here and in Proposition 3 is of a different nature than the one in Proposition 2; in the latter, moreover, above a certain threshold, liquidity injections regain effectiveness in boosting lending.

38

assets is unique across the monetary union countries, differently than in Benmelech and Bergman (2012), the sum γR + γS (or, equivalently, their average) determines whether both economies are in a ‘credit trap’ equilibrium or not; moreover, monetary policy equally affects lending in both countries. This is shown in the following.  (iii) As there is one market for firms’ assets in the monetary union, the law of one price trivially implies that, for any L, P is equal in both countries. Hence, in any country i, ´ P/(1+ri ) total lending in equilibrium will be equal to 0 BdF (B). From Lemma 1 (ii), we have that, regardless of differences in sovereign default risk ρi , for any aggregate liquidity level L the equilibrium interest rate is equal in both countries, ri = rj = r. Then, for any ´ P/(1+r) L, the amount of total lending in each country is equal and given by 0 BdF (B). From Lemma 1 (iv), we have that an increase in L constantly reduces the interest rate up to the zero bound. Then, it is possible to conclude that a liquidity injection always produces equal effects in both countries. 

Proof of Lemma 2 (i) Market clearing implies that, in each country, there are at least some firms for which the IPC is satisfied (see Lemma 1). If r ≤ ri , we know that the IPC is satisfied for all firms. If r > ri , it is possible that the IPC is satisfied for those firms with borrowing requirement ˜ and it is not for all the others. Suppose smaller than or equal to a certain threshold, B, that r > ri and there are some firms for which the IPC is not satisfied. In thiscase, the ˜ . Hence, marginal borrowing firm must have a borrowing requirement B = min P , B 1+r

the total supply of funds is equal to: ˆ

I

(I − B) dF (B).

S(L, r) = L + P ˜) min( 1+r ,B

As by assumption ri >

δρR 1−δρR ,

and r > ri , then r >

δρR 1−δρR .

This implies that firm loans

grant a higher expected return than sovereign debt; then banks do not lend funds to governments. Thus, the total demand for funds is equal to: ˆ D(L, r) =

P ˜) min( 1+r ,B

BdF (B).

0

As the right hand side of condition (17) is increasing in the interest rate, the level of ˜ must decrease as the interest rate reduces. As the aggregate borrowing requirement B liquidity increases, the supply of funds raises and the interest rate moves down. At a ˆ the interest rate eventually reaches ri , for which the IPC is satisfied certain liquidity level L for all firms. As L is defined as the aggregate liquidity level at which the interest rate ˆ < L.  reaches δρR , and by assumption ri > δρR , then it must be that L 1−δρR

1−δρR

39

(ii) From (i) we know that L is the threshold at which rR = have that rR >

δρR 1−δρR .

δρR 1−δρR ,

and for L < L we

Then, for any L ≤ L, as firm loans grant a higher expected return

than sovereign bonds, banks do not lend funds to government. Thus, Lemma 1 (ii) still applies, and an increase in L up to L reduces the equilibrium interest rate, which must be equal in both countries.  (iii)

From (i) and (ii), as L reaches the threshold L, the lending rate in both countries

equals

δρR 1−δρR .

At this level, country R’s banks obtain the same expected return lending to

firm and underwriting domestic sovereign bonds, which pay a nominal yield rgR =

ρR 1−ρR .

Indeed, when δ > 0, the banks’ profit maximization problem implies that country R’s banks prefer to lend to firms only if the following condition is satisfied: fD rR >

(1 − ρR )rgR − ρR (1 − δ) . 1 − δρR

Despite increases in L, as long as the marginal buyer of sovereign debt is an international investor, the yield paid by country R’s sovereign bonds remains constant at the level r gR =

ρR 1−ρR ;

hence, no arbitrage implies that the lending rate does not reduce and remain

fD constant in L at rR =

δρR 1−δρR

(as shown in Figure 3 above). Constant the lending rate,

the collateral constraint does not relax. This implies that country R’s banks invest any additional fund injected beyond L into purchases of domestic sovereign bonds. As the total liquidity level reaches a certain threshold L, the whole supply of sovereign debt is purchased by domestic banks. Beyond L, a further increase in the supply of funds faces an unchanged demand for funds, given that banks cannot purchase more units of domestic sovereign debt from international investors. Hence, if L > L, market clearing implies that liquidity injections regain effectiveness in country R, reducing both the sovereign yield and the lending rate, relaxing the collateral constraint and allowing further increases in corporate lending. If ρS = 0, this mechanism generating a flat region in the lending rate does not apply in country S; it straightforward to verify that it does apply otherwise, in a similar manner as the one described for country R. Nevertheless, as long as the sovereign default risks are cross-country different, the flat region and the following credit trap will emerge for different liquidity levels in the two countries;23 hence, even in this case lending responses will remain asymmetric across countries, and the claim in (iii) still holds.  (iv)

The claim concerning the effectshof increases in δ and/or ρ is trivially implied by i

the arguments provided in (i-iii) above. L, L is exactly equal to the amount of sovereign

debt supplied GR only if the marginal cost on foreign lending c is sufficiently large; it is smaller than GR otherwise. Indeed, the possibility of cross-border lending implies that, in equilibrium, cross-country differences in the lending rate must lie in the interval [−c, c]. Suppose they do not, and specifically that rR > rS + c. But then, there will be no demand 23

Specifically, the credit trap region begins for a lower liquidity level in the country suffering from a higher risk of sovereign default.

40

for those funds supplied by country R’s banks, and by market clearing interest rates adjust such that rR = rS + c.  Robustness: Allowing Firms not to Deposit Initial Wealth In the full model, the risk of bank bankruptcy may rise the firm’s incentive not to deposit funds in the bank, so as to have them available to purchase liquidated asset at time-1. For simplicity, the setup described in Section 2 does only allow firms to choose between undertaking the project and depositing their wealth in the banks. Suppose instead that, in an otherwise unaltered setup, those firms which do not undertake the project can freely choose how much of their initial wealth to deposit, a ∈ [0, A]. The linearity of the maximization problem implies a corner solution, then it must be either a∗ = A or a∗ = 0.24 The time-0 expected payoff from choosing a = A is given by the right hand side of equation (17), while the one from h i 0

choosing a = 0 equals γR (I − B + P ) + (1 − γR ) (I − B) YP + X2 . Rearranging terms, a∗ = A ⇔ "

αδρR rR ≥ 1 − δρR + γR + (1 − γR ) YP

#−1

− 1.

This condition fixes a possibly greater than zero lower bound for the interest rate in country R. Indeed, suppose that there is an equilibrium with the interest rate below this bound: private deposits dry up and, by market clearing, the interest rate increases until this bound is reached. However, the maximum possible value of this lower bound, which is reached for P → 0, is bounded from above by

δρR 1−δρR .

This implies that, even in this

modified setup, all the results described in Lemma 2 apply unchanged; the only difference consists in the fact that, beyond L, country R’s interest rate does not converge to zero as L increases (as shown in Figure 3); it converges instead to a value possibly greater than zero, but still smaller than

δρR 1−δρR .



Proof of Proposition 2 In the following, I provide the complete proof for the case in which ρR > ρS = 0. Provided the validity of the statements proved in the proof of Lemma (ii), the arguments extend in a straightforward manner to the more general case in which ρR > ρS ≥ 0. (i) From Lemma 2 we know that, in country S, injections of liquidity continuously reduce the lending rate up to the zero-bound. First, they expand lending by increasing the discounted price of collateral through reductions in the denominator of

ES (P ) 1+rS .

Moreover,

as described in Proposition 1, since the project is more profitable than deposits, a higher amount of lending at time-0 will increase Q(BS , rS ) at time-1, boosting the expected liquidation price of collateral – unless it is already at its upper-bound Y . This will expand lending further at time-0 because the collateral constraint relaxes even more, through increases in the numerator of 24

ES (P ) 1+rS .

As liquidity is injected, corporate lending can reach

If the corner solutions lead to the same expected payoff, then a∗ ∈ [0, A].

41

the maximum possible level, or it can results being constrained at a sub-optimal level if γ ≥ γˆδ (see Proposition 3). In both cases, however, any central bank liquidity injection has always a positive effect on lending through at least the interest rate channel above described, up to the liquidity level leading to a zero interest rate. Furthermore, banks in country S, being exposed to a zero sovereign default probability, correctly internalize sovereign risks; hence, they do not underwrite sovereign debt as long as the lending rate is greater than zero,25 which implies that the whole liquidity injected by the central bank is lent out to domestic firms. Only beyond the zero bound, positive purchases of sovereign debt from country S’ banks are possible in equilibrium.  (ii) Lemma 2 and the collateral price dynamics explained in (i) imply that there is an h i 0

initial liquidity range, 0, L , in which also in country R liquidity injections reduce lending 0

rate and boost lendingh as in icountry S. However, beyond the liquidity threshold L and 0 00 for the whole interval L , L – whose length is a non-decreasing function of the amount of country R’s sovereign debt issued26 – the lending rate is constant in L and equal to δρR 1−δρR

(see Lemma 2). This implies that the denominator of

ER (P ) 1+rR

remains constant, i.e.

the collateral constraint does not relax, at least through the interest rate channel. The liquidity injected by the central bank is mainly used by country R’s banks to underwrite sovereign bonds, which domestic banks perceive as granting the same expected return as firm loans. Liquidity injections further relax the collateral constraint through the 00

interest rate channel only beyond L , threshold at which the marginal buyer of country R’s sovereign debt becomes a domestic bank (see Lemma 2).  h

0

00

i

(iii) In the interval L , L , corporate lending in country R can display some positive response if a higher lending in country S, by increasing Q(BS , rS ), boosts the expected liquidation price of collateral. In this case the collateral constraint, constant its denominator, can still relax thanks to an increase in the numerator of its right hand side,

ER (P ) 1+rR .

This implies that a part of the liquidity injected will be used by banks to increase lending even in country R. Nevertheless, the responses to monetary policy remain asymmetric, for the following two reasons: (i) this positive spillover from the safe country is only potential; (ii) even if it applies, in country R only part of the liquidity injected is lent to firms, while in country S the whole liquidity injected is lent to firms.  (iv) The claim is trivially implied by (i-iii) and Lemma 2. 

25 26

h

0

If ρS > 0, this lower-bound will be actually larger than 0: see Lemma 2. Asicross-country differences in the lending rate must lie in the interval [−c, c], the length of the interval

L ,L

00

displays one to one increases with GR if c is sufficiently large; otherwise, there is a level above

which an increase in GR produces no further increases in its length: see Lemma 2.

42

Proof of Proposition 3 (i-ii) From Proposition 1 we know that the asset pricing function, evaluated at a zero lending rate, determines whether the economy will be in a ‘credit trap’ equilibrium or not. Specifically, we know that there is a threshold in

Q(B,0) γR +γS

below which P ∗ will be always

constrained at levels strictly lower than Y , regardless of L; while this is not true above such threshold. Let us analyze the market for liquidated assets, conditional on sovereign default occurring at time-1. With respect to the benchmark, we have that the liquidity available to firms purchasing assets, Q(B, 0), for any B is lower and equal to: ˆ

I

Q(B, 0)δ>0 = Q(B, 0)δ=0 − δ

(I − B)dF (B). B

Moreover, as by assumption Y < I, we have that, for any B: ˆ

I

(I − B)dF (B) > 0,

δ B

hence we can conclude that Q(B, 0)δ>0 is strictly smaller than Q(B, 0)δ=0 for any B. But this implies that, conditional on sovereign default occurring at time-1, for a given γ, we have that δ > 0 implies a lower value in

Q(B,0) γR +γS

than δ = 0. In other words, given the

mechanism described in the proof of Proposition 1 above, we can conclude that there is a non empty set Γ such that, for γ ∈ Γ, conditional on sovereign default occurring in country i at time-1, in the ‘sovereign default sock’ scenario: ∗

P (B, r) = min

˜ Q(B, r) ,Y γ

!

=

˜ Q(B, r) < Y, ∀L, γ

while this does not hold in the benchmark economy. Country j’s banks, and a share equal to 1 − δ of country i’s banks, are not bankrupt in the time-1 state of the world in which sovereign default occurs in country i. Suppose that the time-0 liquidity injection assumes an arbitrarily large value (at least as large as to have, in the benchmark model, that lending is maximum), and that at time-0 these banks satisfied any loan demand up to b = Y . As the liquidation price of assets in this state of the world is P ∗ < Y , the time-0 expected price of assets must be also be strictly lower than Y . But then such banks’ choices27 do not fulfill the collateral-in-advance constraint (16), which must be satisfied in any optimal financial contract; this is a contradiction. This implies that, independently of further increases in liquidity injections at time-0, country j’s banks willingness to lend funds cannot exceed the threshold: Ej (P ) = (1 − ρi ) Y + ρi P ∗ < Y. 27

Besides leading to expected losses: to allow maximum lending, indeed, the equilibrium lending rate must be zero at time-0, hence banks do not make profits; moreover, all firms with borrowing requirement B ∈ (P ∗ , Y ] would obtain loans for values b > P ∗ but would only repay P ∗ with positive probability.

43

Therefore, at time-0 country j’s lending cannot be maximal, ∀L, and we can conclude that in the ‘sovereign default shock’ scenario the range of values in γ under which a credit trap equilibrium realizes is larger than in the benchmark model.  (iii) An increase in δ implies a lower value of Q(B, 0); this, given the argument provided in (ii) above, enlarges the range within which a credit trap equilibrium occurs. On the other side, an increase in ρi reduces Ej (P ), by increasing the probability that P ∗ < Y is going to emerge as equilibrium price of asset in the next period (see (ii) above). 

44

Appendix B. Supplementary Figures bln €

Total credit to NFC 8,000

5,000

7,500

4,500

7,000

4,000

6,500

3,500

6,000

3,000 2,500

5,500 Core

5,000

Periphery (right axis)

2,000

4,500

1,500

4,000

1,000

Figure 6: Total Credit to NFCs in the Euro Area This figure shows quarterly data on the outstanding amounts of credit, from all lending sectors, to NFCs based in the EA’s core and periphery countries. Data source: BIS. Periphery 200

1,000

900

180

200

900

800

180

160

800

160

700

140

700

140

600

120

600

120

500

100

500

100

80

400

400

France Germany

bln €

bln €

Core 1,000

80 Italy

300

Netherlands

60

300

Spain

60

200

Austria (right axis)

40

200

Greece (right axis)

40

20

100

Belgium (right axis) 100 0

Finland (right axis)

Ireland (right axis) Portugal (right axis)

0

0

20 0

Figure 7: Bank Loans to Domestic NFCs across Countries in the Euro Area The panels of this figure show monthly data on the outstanding amounts of bank loans to domestic NFCs across EA’s countries. Data source: ECB Statistical Data Warehouse.

Figure 8: SAFE: Change in Collateral Requirements The vertical axis value indicates the percentage difference between the entrepreneurs reporting increase in collateral requirements for bank loans in the past 6 months and those reporting decrease. In the shaded area the percentage of those reporting increase exceeds the percentage of those reporting decrease. Data source: SAFE, ECB.

45