Working Paper Series Monetary policy and cross-border interbank market fragmentation : lessons from the crisis

We present a two-country model with an enhanced banking sector featuring risky lending and cross-border interbank market frictions. We find that (i) the strength of the financial accelerator, when applied to banks operating under uncertainty in an interbank market, will critically depend on the economic and financial structure of the economy; (ii) adverse shocks to the real economy can be the source of banking crisis, causing an increase in interbank funding costs, aggravating the initial shock; and (iii) central bank asset purchases and long-term refinancing operations can be effective substitutes for, or supplements to, conventional monetary policy. JEL: E44, E52, F32, F36


Non-technical summary
The interbank market plays a pivotal role in the euro area. It is an important source of short-term funding for banks and the first stage of transmission of the ECB's monetary policy to the real economy. Measurable deviations in interbank market funding costs from the ECB's intended policy stance, like in the aftermath of the great financial and euro area sovereign debt crisis, may therefore blur the signal of monetary policy and lead to impairments in the transmission.
This article develops, calibrates and simulates a structural model of the euro area economy that incorporates three major factors, or frictions, that may cause such deviations to emerge: asymmetric information between borrowers and lenders, monitoring costs and counterparty uncertainty. Specifically, we assume that there are two countries and two types of banks in each country: savings banks, which have excess liquidity that they are willing to trade across borders in the interbank market, and lending banks, which operate under a structural liquidity deficit and require funding that they can obtain from the unsecured area-wide interbank market. Lending banks, however, face idiosyncratic loan return shocks that are unobservable from the point of view of savings banks. These shocks mean that lending banks have a positive probability of default, which gives rise to a spread over the risk-free rate controlled by the central bank. In addition, lending banks face an additional risk premium when taking a position in the cross-border interbank market, where asymmetric information, counterparty risk and search and monitoring costs are particularly relevant.
Our key findings are that such frictions in the interbank market can play an important role in propagating and amplifying the effects of both idiosyncratic and common shocks in a currency union. For example, adverse shocks hitting both countries equally will cause lending banks to raise the risk premium they charge in the interbank market, thereby driving a wedge between banks' funding costs and the key policy rate controlled by the monetary authority. This wedge will be even wider for cross-border interbank trades, thereby hitting countries with a greater reliance on international wholesale funding more strongly.
While such interbank market frictions can therefore reduce the effectiveness of conventional monetary policy actions, our simulations also show that non-standard policy

Introduction
In the years following the global financial and the euro area sovereign debt crisis, the process of financial integration in the euro area moved into reverse as firms and households in the southern European periphery started to face much higher borrowing costs than their counterparts in the northern core. One of the key channels at the heart of this financial fragmentation was the interbank market where the costs of cross-border lending rose sharply, and volumes fell dramatically, in particular in peripheral economies, thereby likely having contributed to reinforcing the macroeconomic fallout from the sharp collapse in aggregate demand. Although market segregation gradually receded over the past few years, probably also thanks to the actions taken by the European Central Bank (ECB), normal market functioning has not yet been fully restored. At face value, these facts contradict the predictions of standard open-economy models in which complete financial markets can be expected to facilitate, rather than to impede, effective risk-sharing and thereby help temper the adverse effects of asymmetric shocks.
Against this background, and with a view to improving our understanding of recent events, this article analyses the role of frictions in the interbank market of a currency union and examines how unconventional monetary policy measures may mitigate, or offset, the effects such frictions may have on financial conditions and, ultimately, on output and inflation. To this aim, we develop, calibrate and simulate a two-country dynamic stochastic general equilibrium (DSGE) model in which lending banks obtain funds from both domestic and foreign savings banks to refinance loans to the private sector, but where interbank lending is subject to both borrower and country-specific idiosyncratic risk. Using this framework, we show that (i) the strength of the financial accelerator, when applied to banks operating under uncertainty in an interbank market, will critically depend on the economic and financial structure of the economy; (ii) adverse shocks to the real economy can be the source of banking crises, causing an increase in the interbank fundig costs, aggravating the initial shock; and (iii) central bank asset purchase policies and long-term refinancing operations can both be an effective substitute for, or complement to, changes in the conventional monetary policy instrument.
The interbank market plays a pivotal role in the euro area. Its smooth functioning is central for banks to cope efficiently with idiosyncratic liquidity shocks and to ensure a uniform transmission of the common monetary policy. Frictions in the interbank ECB Working Paper Series No 2139 / April 2018 market may blur the signal coming from monetary policy and ultimately hamper its transmission. One reason why interbank markets may not operate efficiently has to do with transaction costs: owing to the unsecured lending nature of the market, and its overthe-counter (OTC) structure 1 , trading relationships are often plagued by asymmetric information, counterparty risk and search and monitoring costs (see e.g. Afonso et al. 2011, Flannery 1996. As a result, banks' wholesale market funding costs may differ across the currency union, and some banks may face hard borrowing constraints, which could affect both credit supply and the ultimate borrowing conditions of the non-financial sector. These frictions are particularly relevant in cross-border transactions, where differences in banking supervision up until the introduction of the Single Supervisory Mechanism (SSM) in 2014, 2 the state of the business cycle, insolvency laws or accounting standards may obfuscate the evaluation of the creditworthiness of foreign banks and expose lenders to uncertain counterparty risk. Freixas and Holthausen (2005) show that such market imperfections may cause liquidity shortages or the payment of interest rate premia that reflect the adverse selection of borrowers across countries. In crisis times, these effects may become even more visible. Using bank-to-bank loan level data from TARGET2 3 , Abbassi et al. (2014) find that for the same borrower on the same trading day, and after controlling for lender and borrower fixed effects, cross-border loans were up to 25 basis points more expensive than domestic loans in the first three months following the collapse of the former investment bank Lehman Brothers in 2008. De Andoain et al.
(2014) estimate that the premium charged to banks in more stressed economies spiked even more dramatically, reaching over 63 basis points. The presence of a risk premia unrelated to the specific borrower suggests that information asymmetry constraints are important and that factors other than direct counterparty risks may also drive pricing behavior in interbank markets.
Cross-border interbank lending has been and continues to be an important element of the financial structure in the euro area. Prior to the outbreak of the global financial crisis, more than half of the average daily turnover in the unsecured market was with non-domestic euro area counterparts (ECB 2009a). Strong credit growth in parts of the euro area, buoyant financial innovation and lax financial regulation all contributed to an increasing reliance on confidence-sensitive wholesale funding, with banks in current account surplus countries providing funding to banks in current account deficit countries (see van Rixtel and Gasperini 2013). After the outbreak of the crisis, the share of crossborder interbank lending fell dramatically to just over 25% in 2013 before recovering again to reach levels around 40% in 2014 (ECB 2015).
These sharp variations in the funding structure of banks -broadly speaking the mix between wholesale and deposit funding -may have had severe repercussions on their operations and their willingness and ability to extend credit to the non-financial sector.
Several empirical studies document that banks whose liabilities are mainly sticky household deposits, which are often protected by generous government insurance schemes, continued to lend in the aftermath of the crisis whereas banks that relied predominantly on debt funding fared worse (Cornett et al. 2011, Ivashina and Scharfstein 2010, Demirgüç-Kunt and Huizinga 2010. In other words, wholesale funding, and cross-border funding in particular, makes banks more vulnerable to changes in market financing conditions with possibly strong repercussion on bank lending. These studies therefore tend to suggest that real shocks may be amplified, and financial shocks accelerated, by banks' structural recourse to wholesale financing. Despite its empirical relevance, however, few efforts have been undertaken to study the main mechanisms and propagation channels of the interbank market in a structural model of the macroeconomy. Indeed, financing frictions were long absent in a general equilibrium context. The dominance of the Modigliani-Miller theorem (1958) that the financing structure of a firm is irrelevant for its value confined the analysis to real and nominal frictions in the wider economy (Christiano et al. 2005, Smets andWouters 2007). The seminal work by Bernanke et al. (1999) and the subsequent contributions by Christiano et al. (2004Christiano et al. ( , 2010Christiano et al. ( , 2014 and Iacoviello (2005) made financial factors acceptable, and even desirable, in workhorse general equilibrium models. Their studies showed that asymmetric information, agency problems and borrowing constraints are important factors in driving and amplifying business cycles.
Yet, less progress has been made in understanding the impact of the financing structure ECB Working Paper Series No 2139 / April 2018 of banks on lending conditions of the private sector and, hence, on aggregate output and inflation. In the pioneering work of Bernanke et al. (1999) and Christiano et al. (2004), and in subsequent work that followed (cf. Goodfriend and Mccallum 2007, De Graeve 2008, Christensen and Dib 2008, banks were either relegated to act as simple intermediaries between savers and borrowers or were operating under perfect competition. It was only more recently that a more prominent role was given to banks in general equilibrium models. Gerali et al. (2010) andDarracq Paries et al. (2011) illustrate the effects of imperfect competition in the banking industry on credit spreads and show that changes in banks' leverage ratio can impact loan supply conditions. However, in these models, banks can obtain funding in a frictionless interbank market at the rate set by the central bank. Others have made attempts to model the interbank market more explicitly. Gertler and Kiyotaki (2010), building on Kiyotaki and Moore (1997), introduce a borrowing constraint in the interbank market by assuming that banks may divert borrowed assets for personal gain, causing a spread between lending and deposit rates. In the face of an adverse shock, this spread widens, which raises the cost of credit of firms, affecting real activity. Dib (2010) andde Walque et al. (2010) include an interbank market in which, due to an implicit enforceability problem, borrowing banks can choose an optimal level of default, 4 and where banks must hold a regulatory level of capital. Calibrated for the US economy, both papers show that bank capital attenuates, rather than amplifies, the real effects of shocks in this framework. Hilberg and Hollmayr (2011) incorporate a secured interbank market into an otherwise standard DSGE model and study the impact of central bank collateral policy on interbank lending rates. They show that a change in the haircut applied to central bank refinancing operations can be effective in steering interbank rates, but that the presence of an interbank market also attenuates the effects of conventional monetary policy. Similarly, Carrera and Vega (2012) model the interactions between banks' reserve requirements and interbank lending activity, which they assume is costly due to monitoring costs. They find that an increase in required reserves increases demand in the competitive interbank market and pushes up the interest rate charged on these operations as lending banks will have to pay higher monitoring costs. Funding conditions in the interbank market then trickle down to lending and deposit rates, affecting real 4 That is, default is not related to banks' own idiosyncratic risks but a choice variable subject to an exogenous cost of default.
ECB Working Paper Series No 2139 / April 2018 activity. In the framework of Carrera and Vega (2012), changes in reserve requirements are therefore qualitatively similar to traditional changes in policy rates.
Cross-border interbank lending, by contrast, has been largely ignored so far in the literature. In 't Veld and van Lelyveld (2014) examine the role of international capital flows in the boom-bust cycle in Spain by allowing borrowing-constrained households to borrow directly from foreign lenders. Using an estimated three-country model, they find that the convergence of interest rates in Spain to the levels prevailing in other euro area Member States, a loosening of collateral constraints as well as falling risk premia on Spanish housing and capital has fuelled the Spanish housing boom. Poutineau and Vermandel (2015) model the banking sector explicitly in a two-country DSGE model. Contrary to Quint and Rabanal (2014), who study the optimal design of macro-prudential policies in the euro area in a two-country DSGE model, they allow for cross-border lending to firms and banks. They find that cross-border loans amplify the propagation of countryspecific shocks. Dräger and Proaño (2015) also allow for cross-border banking where an international wholesale branch is collecting deposits from across the currency union and distributes them to retail banks in the two countries. Although their model gives not rise to interbank flows, similar to Poutineau and Vermandel (2015), they find that cross-border banking amplifies the effects of exogenous shocks in a currency union.
In this article, we try to bring the various strands of the literature together by incorporating credit risk in the interbank market of a currency union in a New Keynesian two-country, two-sector model with sticky prices, habits in consumption and investment adjustment costs. There are two types of banks in each country: savings banks, which have excess liquidity that they are willing to trade across borders in the interbank market, and lending banks, which operate under a structural liquidity deficit and require funding that they can obtain from the unsecured area-wide interbank market. Following the costly state verification framework of Bernanke et al. (1999), lending banks face idiosyncratic loan return shocks that are unobservable from the point of view of savings banks. A positive probability of default gives rise to an external finance premium that depends on the leverage of the borrower.
In addition, lending banks face a risk premium when taking a position in the crossborder interbank market. This second friction is in the same spirit as the external financial intermediation premium in Christoffel et al. (2008), but tailored to the features Regarding the first question, we find that our model exhibits the financial accelerator effect (see Bernanke et al. 1999) in the face of a common monetary policy shock but that, compared to previous findings in the literature, there are noticeable differences in the way our model can give rise to changes in the transmission of monetary policy. In particular, compared to a situation where the financial accelerator operates directly at the balance sheet of firms, the strength, and at times also the direction of propagation, crucially depends on the share of saver households in the economy, the asset composition of lending banks' balance sheets and the degree of competition in the lending market.
Regarding the second question, our model is able to replicate some of the key features of the financial crisis that resulted in a segmented interbank market. 5 We show that capital flows resulting from international financial integration can be highly procyclical, fluctuating in response to business cycles, thereby raising financial and economic fragility even before a crisis emerges, mainly by fostering credit growth. This means that in the wake of an adverse shock to the value of assets in one country, the rate charged by foreign lenders in the common interbank market will rise as banks' balance sheets deteriorate (area-wide) economy by lowering the policy rate in response to the initial shock. That is, compared to a model without cross-border interbank lending, and contrary to unionwide shocks, monetary policy will be less effective. Moreover, as foreign funding becomes more expensive, the economy that draws the shock is forced to improve its trade balance more sharply relative to the case without financial frictions.
Finally, we study the effectiveness of two of the ECB's recent non-standard measures.
We find that providing long-term refinancing operations (LTROs) to banks increases the effectiveness of monetary policy per unit of stimulus -that is, LTROs empower conventional monetary policy. The second policy focuses on the ECB's asset-backed securities purchase programme (ABSPP) that is particularly well suited to study in our model economy. Although securitization is more complex in practice, the ultimate effects of the ABSPP can be well approximated by assuming that the central banks purchases directly risky loans from banks, thereby freeing up bank balance sheet capacity and reducing their funding costs in the interbank market. We find that asset purchases in the form of loans, either directly or through purchases of ABS, can be an effective substitute for, or complement to, reductions in the key policy rate.
The rest of the paper is organized as follows. Section 2 lays out the model setup. Section 3 discusses model calibration and section 4 presents numerical simulations, illustrating the role of the interbank market in driving the dynamics of the model. Section 5 analyses the effects of the ECB's policy measures, while section 6 offers some concluding remarks.

The Model
The model is made up of two economies that share a single currency and monetary policy.
In each economy there are two types of households, savers and borrowers, monopolistic competitive firms, savings and lending banks as well as a fiscal authority. The two economies, of size n and (1 − n), trade in both non-durable consumption goods and financial services in the form of interbank credit. In the following, we describe the decision-making problems of the economic agents resident in the home economy. Unless otherwise stated, analogous conditions hold for the foreign economy. The time notation refers to the period in which the value is determined.
ECB Working Paper Series No 2139 / April 2018

Households
The household sector is made up of a mass λ ∈ [0, 1] of patient households with discount factor β and (1 − λ) of impatient households with discount factor β B < β. The patient households are referred to as the savers and the impatient households as the borrowers.

Savers
The saver household h ∈ [0, λ] chooses the level of consumption of non-durable goods C h,t , hours worked L h,t , the housing stock D h,t , and bank deposit savings S h,t to maximize its lifetime utility subject to the nominal budget constraint where determines the relative weight of non-durable consumption in the saver's utility and κ the degree of external habit formation in consumption. The parameter φ refers to the inverse of the Frisch labour supply elasticity. P C t and P D t are the price indices for consumption and housing goods respectively (see derivation below). δ D ∈ (0, 1) denotes the depreciation rate of housing. The saver can deposit his savings in domestic banks which pay the risk-free nominal interest rate R S t . Finally, the saver provides labour at the flexible nominal wage rate W t and owns the stock of net wealth of the economy, except for housing that is in part also owned by the borrower household, therefore receiving profits π t from the banking and corporate sector and paying lump sum taxes T t .
Because saver households have the same preferences over consumption, housing, labour, savings and investment, and are assumed to have the same initial wealth, we focus on a representative saver from now onwards and drop the h subscript. The saver household chooses the optimal inter-temporal plan subject to the budget constraint, resulting in a ECB Working Paper Series No 2139 / April 2018 set of familiar first-order conditions that will hold in equilibrium: where λ C t and λ D t are the marginal utilities of consumption and housing respectively, and is the real stochastic discount factor over the interval [t, t + 1]. Equations (2.1) and (2.2) are the Euler equations implied by the demand for domestic deposits and the demand for housing respectively. The relative price of housing is given by The real wage rate is given by w t = W t /P C t , which is equal to the marginal rate of substitution between labour and consumption in equilibrium (2.3).

Borrowers
Preferences of the borrowers are the same as those of the saver except for the difference , subject to the nominal budget constraint The notations are identical to the saver household and where the superscript B characterizes variables specific to borrowers. As in Moore (1997) andIacoviello (2005), borrowers finance their consumption of housing with credit CR HH h,t obtained from lending banks at the mortgage rate R M h,t . Banks impose collateral constraints of the form That is, banks will only lend out a fraction m of the housing value with a view to ensuring that households will not default the following period. For numerical simplicity, we assume that the borrowing constraint is always binding. While this will certainly be ECB Working Paper Series No 2139 / April 2018 true in the deterministic steady state, under uncertainty the borrowers could self-insure in some states of the world by borrowing below the limit to protect against the effects of adverse shocks. We therefore follow Iacoviello (2005) and choose the parameter m to minimize the probability of this occurring.
The decision-making problems of the representative borrower household lead to a labour supply condition analogous to that of the saver household. The housing investment decision leads to an Euler equation of the form

Firms
We introduce nominal rigidities in the price of consumption goods following Calvo (1983).
To this end, we assume there are two types of firms in the model economy: intermediate goods firms that are price takers in perfect competition, and final goods firms that operate under monopolistic competition. There is 'price-stickiness' introduced in the latter sector as only a fixed proportion of firms is able to update prices each period.

Intermediate goods firms
Each intermediate goods producer hires capital services K D t and labour L D t to produce a homogeneous output Y w,t subject to a Cobb-Douglas production function where the superscript D indicates factor demand, and A t and Z t are, respectively, stationary union-wide and country-specific total factor productivity shocks. Both are modelled as AR(1) processes: There is an equivalent process for z t ≡ ln Z t . Taking both the aggregate real wage index w t and real rental price of capital r k t as given, the profit maximization implies labour and capital demand given by where P w,t is the price at which the output is sold to all final goods firms. This implies that P w,t /P C t = mc t is the real marginal cost in the final good sector.

Final Good Producers
Each final good producer firm j purchases output from the intermediate good sector at price P w,t and converts it into a differentiated good sold at price P P t (j) to households, durable good producers and the fiscal authority. Summing the demand schedules from each buyer (see Section 2.2.3) implies a total demand for good j given by where σ denotes the elasticity of substitution between the different varieties, assumed to be identical across the currency union. Every period, each firm faces a fixed probability 1 − ξ that it will be able to update its price. Denoting the optimal price at time t for good j as P * t (j), the firms allowed to re-optimize prices maximize expected discounted profits by solving The solution to the price setting problem yields a price P * t which is independent of the firm's history of prices and therefore optimal for all price setters. With real marginal cost given by mc t = Pw,t P C t and producer price inflation denoted by Π P t ≡ , we can write this as Using the aggregate producer price index P P t and the fact that all resetting firms will choose the same price, by the law of large numbers we can find the evolution of the price index as given by Whilst the distribution of prices is not required to track the evolution of the aggregate price index, it implies a loss of output due to dispersion in prices. Final output is given ECB Working Paper Series No 2139 / April 2018 where price dispersion is given by for non-optimizing firms j = 1, ..., J. As a proportion (1 − ξ) of firms will optimize prices in period t and knowing that the distribution of non-optimized prices will be the same as the overall distribution, price dispersion can be written as a law of motion (2.8)

Consumption Good Producers
Households purchase differentiated final goods and combine bundles of domestically produced goods and aggregate imports to produce the final consumption bundle according where τ C can be interpreted as the degree of home bias in household consumption expenditures, and θ C is the CES between domestic and foreign produced goods (see Armington 1969). H t and IM t are bundles of differentiated domestic and foreign produced goods which households combine into baskets of goods using where the asterisk indicates variables of the foreign country. The households purchase good H t (j) from producer j ∈ (0, 1) at price P P t (j) to maximize (2.9) subject to total expenditure P P t H t = 1 0 P P t (j)H t (j)dj, with an equivalent problem for imports IM t (j * ). This leads to Dixit and Stiglitz (1977) demand schedules (2.12)

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Equivalent conditions for the domestic demand of the investment good and government consumption good hold. We assume no pricing to market, which implies that P IM t = P P * t . The final good firms take input prices as given and maximize their profits Profit maximization yields the following demand schedules for the domestic bundle and aggregate imports This leads to the consumer price index P C t given by

Housing Producers
The price of durable housing goods can differ from that of consumption goods due to the presence of adjustment costs. To ensure that savers and borrowers observe the same house price, we let housing good producers augment the existing stock D T t according to the following law of motion where the function S(·) is a positive function of changes to investment, as applied to capital formation in Christiano et al. (2005), and is given by (2.17) The housing goods producers solve where P P t is the domestic producer price. This leads to the first-order condition

Financial Intermediation
There are two types of banks: savings banks that take deposits from domestic households and lend in the currency union-wide interbank market and lending banks that provide loans to both domestic firms and households and finance these using interbank borrowing and their own net worth. A financial friction emerges due to idiosyncratic loan return shocks faced by lending banks. Costly state verification leads to an external finance premium as in Bernanke et al. (1999). In addition, in light of the empirical evidence that borrower banks often have to pay a premium that reflects not borrower but countryspecific risks when accessing the international interbank market (cf. Section 1), we add a further friction whereby cross-border interbank credit faces additional monitoring costs that depend on the exposure of the borrowing country to foreign debt and to the prevailing risk in the lending market.
Savings banks operate under perfect competition with free entry, but aggregate shocks can lead to unexpected profits or losses. The banks are owned by the patient households who are paid all bank profits, or recapitalize banks if and when necessary. Lending banks face idiosyncratic shocks when extending credit to the real economy that are costly for creditors to observe. Limited liability implies that these banks earn profits in equilibrium. Lending banks are treated slightly differently to savings banks in that they pay a fixed dividend rate to ensure they cannot become fully self-funded, equivalent to the assumption of an exogenous exit rate or higher banker discounting (see e.g. Bernanke et al. 1999, Gertler andKiyotaki 2010). The friction implies that equity is always more valuable than debt, without which banks would not pay dividends in equilibrium.
Another difference is that savings banks can access central bank credit whereas lending banks cannot. This is in part motivated by the risk exposure and specialization of lending banks; savings banks are well diversified and the central bank requires a proportion of ECB Working Paper Series No 2139 / April 2018 safe assets as collateral.

Lending Banks
There are many lending banks of unit mass indexed b ∈ [0, 1]. They extend credit CR t to the non-financial sector, which they finance with domestic IB H t and cross-border IB F t interbank borrowing and net worth N t : where IB H t and IB F t are chosen to maximize a CES Armington aggregator (see Armington 1969) of domestic and foreign interbank borrowing where τ IB can be interpreted as a home bias in interbank borrowing and θ IB is the elasticity of substitution between domestic and foreign borrowing. A non-zero θ IB implies that domestic and foreign interbank borrowing are not perfect substitutes, rendering differences in lending rates. Maximization yields the following familiar demand schedules ( 2.22) When granting loans to the non-financial private sector, we assume that lending banks cannot diversify risk in their loan portfolio and that they experience idiosyncratic loan return shocks ω t (b) that affect the value of the asset side of their balance sheets. 6 The shocks are log-normally distributed, log(ω t (b)) ∼ N −(σ 2 ω,t /2), σ 2 ω,t , with mean 6 Thus allowing us to study imperfect diversification in a tractable way.
After aggregate and idiosyncratic shocks hit the economy, net worth of lending banks evolves according to where R CR t is the ex post return on banks' loan portfolio CR t . Limited liability implies that if the realization of the shock is below a threshold valueω t , then the lending bank will default on its interbank borrowing as they would otherwise be insolvent. This threshold value is found when setting N t (b) = 0: The lending banks will pay the saver households a fixed dividend rate, investing all remaining profits in their own net worth. It is assumed that a defaulting bank will exit but that for every exiting bank, a new one enters and is given a The loan portfolio is comprised of mortgage loans to households CR HH t and lending to firms CR F t . The former are treated as nominal one period bonds, whereas, for the latter, it is convenient to consider the banks owning the physical capital directly and renting it out to firms. 7 Capital investment is subject to costs analogous to those in housing investment and, to ensure the leverage of a bank is independent of its net worth, we introduce a representative capital producer that sells capital to the banks at relative price Q K t . This leads to a first order condition equivalent to equation (2.18) that determines Q K t . Gross nominal return on capital is given by The lending banks specify a contract for interbank funds subject to participation constraints given in the following section. After detailing the solution to the savings banks' 7 As in Gertler and Kiyotaki (2010). This is equivalent to the firms using state-contingent debt to purchase the capital themselves. It is natural to assume that debt contracts are state-contingent due to costless monitoring and enforcement, and the risk neutrality of the lender.
ECB Working Paper Series No 2139 / April 2018 problem, we discuss the contract that determines the demand for interbank credit, and the supply of credit to the non-financial private sector.

Savings Banks
A representative savings bank has access to the central bank's liquidity providing operations CB t , raises deposits S t from patient households and extends both domestic IB H t and cross-border IB F * t interbank loans: Maximizing the expected profits leads to the zero-arbitrage condition whereR IB t is the ex post return on interbank lending, and the condition R S t = R t under standard one-period central bank finance, where R t is the policy rate. The savings bank can only observe the loan return of the lending bank if it pays a proportional monitoring fee µ. As shown in Townsend (1979), the implication of this costly state verification is that the fee will only be paid in the event of default, with all other debtors paying the same interest rate. Interbank lending is subject to a participation constraint that accounts for the distribution of idiosyncratic shocks drawn by lending banks and the aggregate state of the economy.
For the domestic market, the savings banks require the expected real return from granting each interbank loan to be equal to their expected real funding rate, using the household Euler equation. This can be written as f ω; −σ 2 2 , σ 2 dω is the cumulative density function up tō ω (b), with probability density function f ω; −σ 2 2 , σ 2 . Note that this implies that the value F (ω t+1 (b) , σ ω,t+1 ) is the probability of default. Because all banks will choose the same leverage ratio, individual bank net worth does not effect the interest rate paid on ECB Working Paper Series No 2139 / April 2018 credit and equation (2.27) will therefore also hold if the index b is dropped, with the variables treated as the aggregate averages. 8 When taking positions in the cross-border interbank market, we assume that savings banks incur additional monitoring costs Γ IB,t that are increasing in the exposure of the destination country to cross-border debt, and to risk within the economy. Such costs reflect factors such as asymmetric information, counterparty risk as well as differences in cross-border macroeconomic conditions. Specifically, it is given by where the second element in the fraction highlights the additional increase to the monitoring costs following a shock to the variance of the idiosyncratic loan return shock. That is, country-specific risk shocks will cause an increase in the finance premium of borrowing banks in the cross-border interbank market. Therefore, the participation constraint for international interbank loans can be expressed as

. Equation (2.29) implies a spread in the cross-border interbank market
that is a function of the monitoring cost Γ IB,t , which itself is an increasing function of total cross-border exposure. In other words, the higher the volume of cross-border loans, the higher the spread required to compensate savings banks for the increase in credit risk. In a similar vein, aggregate shocks that lead to a decline in nominal domestic GDP will cause the ratio of net foreign assets to output to increase, thereby leading to a rise in the spread.
Also, the spread is increasing in the standard deviation of the loan return shock: a higher σ ω,t will increase the risks of default by making lower realization of ω t (b) more likely.

Interbank Credit Market
To model the over-the-counter structure of the interbank market, we follow Bernanke et al. (1999) in our treatment of the lending contract. The lending banks choose credit to the non-financial private sector CR t , the volume of interbank lending IB H t and IB F t , and interest rates R IB,H t and R IB,F t to maximize their expected real net worth. The banks pay a fraction (1 − γ) of their profits as a dividend, with the remaining surplus retained as internal equity finance. Substituting in the expression forω t+1 the problem is written as The solution to the contract problem yields a condition that determines the wedge between the nominal risk-free rate R S t , and the expected return from credit to the nonfinancial sector R CR t+1 . We can express this as with key arguments given, although the nominal stochastic discount factors of both countries are also arguments of function s. In this solution, which is given in full in the online appendix, the expected real return to lending is equated with the real marginal cost of external finance. Because the solution is a function of the leverage rather than the bank size, the contract interest rates will be independent of the bank's own history of shocks. As leverage increases, the capital-asset ratio Nt CRt falls, the probability of default increases, and the marginal cost of borrowing rises. This is the financial accelerator mechanism; if, for instance, an adverse shock reduces the net worth of the banking sector, bank leverage will increase, and so will the credit wedge s, causing a further deepening of the downturn.

Firm and Household Credit
As discussed previously, firm loans are treated as equivalent to equity, and so the return on firm credit is simply the gross return on capital, R K t , defined in equation (2.25). The repayment rate on household credit is the contracted nominal rate R M t−1 . The optimality condition implies the zero-arbitrage condition which must hold in equilibrium.

Monetary Policy
The monetary authority sets the nominal short-term interest rate in response to deviations of the consumer price inflation rate from the union-wide inflation targetΠ EM U and off-trend output growth with weights ϕ π and ϕ y attached to inflation and output growth respectively. There is inertia in the rule governed by ϕ r . The union-wide variables Π EM U t and Y EM U t are weighted averages of the home and foreign country variables: With a single policy rate, the economy as presented to this point features a unit root stemming from a single savings rate across both economies. As savers in both countries face the same return on assets, long-run effects from transitory shocks would prevail. For instance, if one of the economies were to draw a positive supply shock, its net foreign asset position would improve and the economy will have a current account surplus that would persist in the long run, with a permanent increase in the wealth of savers. To restore the stationary property of the model, we assume, consistent with past modelling practise in open-economy models, that the central bank applies a small premium on the refinancing rate that depends on the net foreign asset position N F A t of the home country. 9 The rates paid on central bank credit CB t are determined by where ϑ t is a stationary, mean one shock to the premium, and κ the premium elasticity.
R P t = R P t * is the central policy rate, and R t and R * t the rates paid on central bank credit.
Central bank funds are in zero net supply so if savings banks in the home country borrow from the central bank, it follows that foreign country savings banks are depositors, and R t > R t * . The risk premium will cause the net foreign asset position of banks in each country to adjust until N F A t = N F A * t = 0 and R t = R * t . The structure of the premium implies that there will be small positive profits in equilibrium which are transferred equally to savers in the union. In the numerical simulations we choose κ sufficiently low to allow the rates to be very close, generating persistent effects of shocks whilst ensuring that the model is stationary.

Market clearing conditions
In each economy, the labour market is in equilibrium when total supply by households equals the demand from intermediate good producers (2.34) The corresponding domestic capital market equilibrium condition is given by Total demand for domestically produced goods include the demand from domestic households H T with g t following a stationary stochastic process. The net foreign asset position evolves according to the following nominal law of motion where the trade balance is defined as The bilateral terms of trade are given by: and, as discussed previously, the central bank funds are in zero net supply worldwide, (2.40) are assumed to be 10% per annum. Adjustment costs ζ K in capital investment are fixed at 5.2 (following estimations in Christoffel et al. 2008), while those in housing investment (ζ D ) are set at 1.7 as estimated in Quint and Rabanal (2014). The elasticity of substitution across the final goods σ is chosen so as to ensure a steady state mark-up of 1.35 and the Calvo parameter ξ is set to be 0.9, both in line with estimates obtained by Christoffel et al. (2008).

Calibration and Parametrization
On the banking side, savings banks' monitoring costs, µ, are assumed to be 0.2 as in Quint and Rabanal (2014) and Carlstrom and Fuerst (1997). For the borrowers' loan-tovalue ratio, we use the estimated value of m = 0.55 from Iacoviello (2005). reported by Colangelo and Lenza (2013). The elasticity of substitution between domestic and foreign interbank funding θ IB is fixed at 2, implying that these sources of funding are not perfect substitutes.
On the policy side, we fix the share of government spending in GDP at 20%. Together with the other parametrization of our model, this ensures that we are able to get close matches of the relative spending shares of consumption (59%), investment (21%) and housing investment (4.5%) in GDP with their empirical first moments for the euro area as a whole. Regarding monetary policy, we follow Christoffel et al. (2008) and set the central bank response to inflation ϕ π to 1.9 and to output growth ϕ y to 0.15. Policy inertia is set at 0.87.
Finally, the standard deviations and persistence coefficients of the shock processes are largely taken from Christoffel et al. (2008), with the exception of the risk shock, which is taken from Quint and Rabanal (2014), and the government spending shock, which has been calibrated on the basis of estimates obtained by Smets and Wouters (2003

Numerical Results and Analysis
To evaluate the model dynamics, we compute a second order Taylor approximation of the decision and transition functions and simulate impulse response functions. In a first step, we look at the implication of our interbank market setup for the transmission of monetary policy by considering a standard monetary policy shock. In a second step, we analyze how frictions in the cross-border interbank market may affect the dynamics of the economy in the face of country-specific idiosyncratic shocks. Figure 1 shows the impulse responses of a number of variables to a reduction in the union-wide policy rate and compares these to a modified version of our model in which the interbank frictions are shut off, that is, the model collapses to one of complete financial markets where the spread between bank lending rates and the policy rate is fixed to its steady state value.

The interbank market and the transmission of monetary policy
In both instances, the interest rate controlled by the monetary authority drops by about the same amount initially. In our baseline model, however, the unanticipated reduction in interest rates leads to an increase in the value of collateral held by lending banks. This, in turn, lowers their funding costs in the interbank market as the perceived risk of default falls. Lending banks operating under perfect competition will pass-through the relief in funding costs to their final customers, causing mortgage rates and financing costs faced by non-financial firms to drop by more than the initial reduction in the key policy rate.
It is this additional fall in the borrowing conditions of households and firms that then leads to more investment, more housing demand and, ultimately, higher domestic demand and inflation in the currency union. In other words, like in Bernanke et al. (1999), the transmission of a conventional change in monetary policy is more powerful in affecting broader macroeconomic conditions. However, unlike in Bernanke et al. (1999), the amplification in transmission comes directly from banks operating in an interbank market characterized by uncertainty on part of savings banks when extending short-term credit to counterparties in need of liquidity.

ECB Working Paper Series No 2139 / April 2018
This implies that there are major differences to a situation where the financial accelerator operates directly at the balance sheet of firms. The impact on aggregate demand, as well as the strength of the pass-through of interbank conditions to final borrowing conditions, will ultimately depend on three factors: the relative share of saver and borrower households in the economy, the structure of lending banks' balance sheets and the degree of competition in the lending market. Starting with the latter, the less concentrated the lending market is, the stronger is the pass-through and the more pronounced are the effects on the real economy. That is, modifications of our model along the lines of Gerali et al. (2010), introducing monopolistic competition in the banking sector, can be expected to dampen the accelerator effect as banks would pass-on lower interbank funding costs at a pace slower than under our baseline model. Similarly, the larger the share of bank lending to households, the larger the impact on output, given the role played by private consumption in aggregate demand. And, finally, although the friction lowers borrowing costs for firms and impatient households, figure 1 also shows that the policymaker keeps the interest rate higher relative to the fixed spread economy due to increased output and inflation. Saver households hence face a higher savings rate, causing them to consume less non-durable and durable goods in response. This effect offsets, to some extent, the increase in housing investment coming from borrowers.
We illustrate this last point in 1: the red dashed line shows our baseline model, assuming, however, a smaller share of savers λ=0.5. As expected, because the financial friction reduces borrowing costs beyond the initial change in the policy rate, the more borrowers there are, the larger the accelerator effect. Fewer savers, in turn, imply that the offset from a higher policy, and hence savings rate, will also be smaller.
Overall, therefore, our simulations tend to suggest that, contrary to previous findings in the literature (e.g. Hilberg and Hollmayr 2011), the presence of an interbank market can, and in many circumstances is very likely to, amplify changes in the key policy rate.
And although the mechanism is similar to the well-known financial accelerator, there are noticeable differences in the way our model setup can give rise to changes in the transmission of monetary policy.
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Asymmetric shocks and cross-country spillovers
A key result of the previous section is that union-wide shocks will propagate differently through the economy once financial frictions are allowed for and that it matters whether these frictions are operating on the banking or the firm side. In this section we will focus on the implications of our interbank market setup for the propagation and impact of idiosyncratic country-specific shocks. Specifically, we look at how a positive shock to the variance of the idiosyncratic loan return shock ω(b) will affect the behavior of banks in the cross-border interbank market and analyze the footprint this will ultimately leave on aggregate demand.
Recall that savings banks incur additional monitoring costs when taking positions in the cross-border interbank market. These costs are a function of an economy's net foreign exposure and the prevailing level of "economic" risk (cf. equation 2.28). Therefore, a shock that raises the skewness of the distribution of ω(b) in one country but not in the other, and hence increases the relative risk of bank default, will cause savings banks to raise the risk premium they charge to borrowers resident in the economy hit by the shock, even though the average loan return remains unchanged.
This can be seen in figure 2: in our baseline model the funding rate in the cross-border interbank market, R IB,F t , increases by significantly more than compared to a model in which banks are insensitive to both macroeconomic and counterparty risks. As a result, banks with a liquidity deficit will partly substitute more expensive foreign borrowing with domestic borrowing, forcing consumers to dial back more vigorously their imports in response. Naturally, this effect will be stronger the more heavily the economy's banking sector relies on cross-border interbank market funding, 1 − τ IB , or, similarly, the more difficult it is to switch foreign with domestic funding (θ IB ). This also means that, should countries differ in their financial structure, symmetric shocks too can cause differences in banks' funding costs across the currency union. For example, an economy which predominantly finances loans to firms and households using funds from abroad, will see its overall funding costs increase more sharply in the face of an adverse shock, thereby causing a steeper economic contraction than compared to an economy that mainly relies on domestic funding. This stylized finding has been one of the key aspects of the crisis in peripheral euro area economies: because many banks funded large parts of their liquidity needs abroad, the sudden market freeze meant that aggregate imports What is more, with lending to the real economy having become riskier in the wake of the shock, domestic savings banks too will ration their supply of interbank funds, and will increase the rate they charge on the remaining funds, causing a contraction in credit supply to the real economy. The consequences are well-known: with credit less abundant and more expensive, both households and firms reduce their investment and housing activities, amplifying the contraction in aggregate demand that would have prevailed in the absence of frictions in the interbank market.
The consequence is that interbank markets characterized by risky lending and costly state

The effects of unconventional monetary policy
In this final section we ask as to whether or not recent non-standard monetary policy measures have been able to overcome, or mitigate, frictions in the interbank market.
The two policies we discuss are long-term central bank refinancing operations and asset purchases.

Long-term refinancing operations
In our model economy, savings banks have access to funding from the central bank (cf. Section 2.3.2). In addition to standard one-period loans to banks, in this policy exercise, the operations of the central bank may take the form of multi-period loan contracts, similar to the ECB's LTROs. 10 To prevent corner solutions whereby savings banks will choose only short-term, or only long-term funding, the central bank sets a single target policy rate on multi-period bonds, and allows the short-term rate to be set via the zeroarbitrage condition. As discussed in section 2.3.2, the short-term central bank funds will be in zero net supply union-wide. This is also the case with long-term funds. Indeed, in equilibrium, we will find that savings banks will not hold long-term bonds at all; the availability of these loans is sufficient to introduce a wedge between the policy rate on long-term refinance operations and the household saving rate.
To maintain tractability and keep the number of state variables manageable, we follow Rudebusch and Swanson (2012) 11 and introduce multi-period loan contracts using geometrically decaying repayments over an infinite horizon. This setup reflects the aggregation of a large number of loans at different points of repayment and of different maturities. As well as introducing just one new state variable rather than potentially very many with long maturities, the appeal is that using infinitely long loans with geometrically declining repayments allows us to control the average maturity ψ ∈ [0, 1) with just one parameter, nesting the possibility of ψ = 0, in which case it collapses to a standard one-period loan contract.
Every period t, a savings bank can take out a new loan CB t and agree to repay an infinite number of declining payments such that the total amount due at period t is given by: When ψ > 0, R LT t is no longer equivalent to an interest rate. To analyze the role of the LTRO policy, we assume that the central bank chooses R LT t so that the average interest 10 See e.g. https://www.ecb.europa.eu/press/pr/date/2011/html/pr111208 1.en.html for information on this policy. 11 Described in detail to analyse term premia on bonds in a working paper version of the article (see Rudebusch and Swanson 2008). Used to introduce multi-period loan contracts in Benes and Lees (2010).
ECB Working Paper Series No 2139 / April 2018 rate on long-term borrowing equals the policy rate R t . As we are using perpetual loan repayments, we measure the average duration using Macaulay's duration of a stream of payments. It is then straightforward to calculate the equivalent average nominal interest rate on the amount borrowed from the total amount repaid. We find this leads to the following relationship between the rate R LT t and the policy rate R t : with average loan duration d = R/(R − ψ), where R is the steady-state policy rate. 12 We can then express equation (5.1) in recursive form as The important thing to note is that even if the bank does not borrow from the central bank in equilibrium, as will be the case with purely symmetric shocks, the availability of these loans is sufficient to have an important impact on the household saving rate, a point we will return to later. Using equation 5.3 as a constraint in the profit maximization problem of the savings bank leads to the following first-order conditions This, with equation (5.2), gives the spread between the policy rate R t and the deposit rate R S t . φ t is the real present value of the Lagrange multiplier on the law of motion of repayments due, and is a nominal pricing kernel for central bank credit. When d = 1 and ψ = 0, then R LT t = R t = R S t as in the standard model, and φ t is just the nominal stochastic discount factor. As the loan duration increases so ψ > 1, the implied future stream of payments increase and ψ t > Λ t,t+1 Π t,t+1 . 13 Figure 3 shows the LTROs at work, comparing the impulse response functions to the 12 For perpetual loan repayments, the average loan duration is measured using Macaulay's duration of a stream of payments, given by dt = ∞ t=1 tP Vt/ ∞ t=1 P Vt where P Vt is the present value of the cash flow (see e.g. Marrison 2002). Applying this to our example, we find in simulations that dt experiences only tiny fluctuations around its steady state value, and so we use the steady state value as a close approximation. This can be simplified to d = R R − ψ . It is then straightforward to calculate the average interest rate given that borrowing is a convergent series. 13 One difficulty with our approach is that introducing the policy, or changing the average duration, 2014. The policy has two major effects. First, in the face of an adverse shock, fewer cuts in policy rates are required to achieve the equivalent stimulus in a multi-period loan economy. The reason is that the reduction in policy rates lowers the average rates for longer and, hence, reduces by more the effective present funding costs of forward-looking banks. That is, long-term refinancing operations with fixed interest rates, such as the latest series of targeted LTROs, ensure planning certainty for banks and thereby, in practice, provide major help with respect to maturity transformation between longerterm lending and often short-term refinancing. And with banks passing on immediately the additional funding cost relief to the ultimate borrowing conditions of households and firms, policymakers are able to frontload required accommodation and thereby to mitigate the economic downturn.
The second interesting feature of LTROs is their asymmetric distributional effects when economies are hit by idiosyncratic shocks. As we argued before, once d > 1 (φ t > 0), the deposit rate in each country will no longer be fixed to the policy rate by the zero arbitrage condition. As equations (5.2) and (5.5) highlight, the spread between the policy rate and the deposit rate depends on the Lagrange multiplier, itself a function of the household stochastic discount factor. Specifically, using equations (5.2) and (5.5) we can give the spread as So, asymmetric shocks will affect the spread differently in each country as a first-order effect. From equations (5.4) and (5.5), a first order approximation suggests that: In other words, if the expected path of the nominal stochastic discount factor is greater in the domestic economy than in the foreign, then it follows that This can be seen in figure 3. Because consumers in the foreign economy, following the shock, expect a lower future marginal utility of consumption relative to the domestic country, LTROs, by easing financial conditions abroad by more, are able to fully offset

Asset Purchases
The second policy instrument we analyze are asset purchases by central banks, which have become an integral part of policymakers' toolkit after, and in some jurisdictions even before, the outbreak of the global financial crisis. Several attempts have been made in the literature to quantify the effects of such purchases. 16 On the theoretical front, Chen et al. (2012) and Gertler and Karadi (2013) have recently made useful progress in capturing the effects of asset purchases on the broader macroeconomy. In this paper, we want to focus on one element of the ECB's asset purchase programme that has received less attention in the literature and that is particularly suited to study within the context of our model setup: its ABSPP.
The aim of this programme, launched in November 2014, is to facilitate credit provision to the real economy by freeing up bank balance sheet capacity. Although the effects of securitization are more complex in practice, mainly related to regulation, the general idea behind this programme can be illustrated by assuming that the central bank purchases assets directly from banks. Indeed, one of the main reasons for banks to engage in securitization is balance sheet relief: securitization typically involves a true sale of the underlying asset to a special purpose vehicle (SPV), removing assets from the balance 15 We tried different parameter values in the Taylor rule and found the relative impact of the availability of LTROs was unchanged. 16 For the United States, see, for instance, Krishnamurthy andVissing-Jorgensen (2011) andGagnon et al. (2011); for the euro area, see, for instance, Blattner and Joyce (2016) and Altavilla et al. (2015).
ECB Working Paper Series No 2139 / April 2018 sheet and thereby reducing the amount of capital that a financial institution is required to hold. We therefore follow Gertler and Karadi (2011) and treat asset purchases as if the central bank lends directly to the private sector, which is a convenient shortcut to analyzing the effects of the ECB's ABSPP.
Specifically, the central bank issues one-period bonds at the market rate and uses the proceeds to purchase a certain share Θ t of loans from lending banks. Profits are distributed to the households via lump sum transfers. 17 The central bank budget constraint can be written as where T t are transfers to households and B CB t central bank issued bonds. The first constraint is that all funds raised are used to purchase assets and the second that all profits are transferred to households.
At the start of the period during which the asset purchase will take place, the policymaker announces the purchase decision. This implies the lending banks' first-order conditions are unchanged except for the volume of loans on banks' balance sheets that changes to With this in mind, we now examine how asset purchases can help stabilize the economy in the face of an adverse shock, using again, for reasons of comparability, a risk shock in the domestic economy. Figure 4 shows the general workings of a temporary asset purchase programme. In our calibration the central bank is assumed to purchase 2% of all available assets in the first period, in equal proportions across economies, and to hold them for four years. At this point, the assets are gradually resold to the private sector, causing the central bank's balance sheet to contract by 2.5% every quarter.
The message is unambiguous: asset purchases in the form of loans, either directly or through purchases of ABS, can be an effective substitute, or complement, to reductions in the key policy rate. By reducing banks' risk exposure to the real economy, policymakers are able to lower banks' market-based funding needs and to compress their external conventional policy instruments to the same transitory risk shock. To ensure broad comparability, both policies are calibrated to ensure the same target horizon of four years. The chart emphasizes that, while both policies can effectively mitigate the impact of adverse shocks on output and inflation, asset purchases, even in relatively small size, are likely to be more powerful, reflecting the direct risk transfer from private to public balance sheets. This means there is a trade-off for policymakers between policy effectiveness and risk exposure. While an analysis of the optimal policy use goes beyond the scope of this article, it may seem advisable to central banks to choose the optimal policy mix depending on the severity and persistence of the shock, also bearing in mind that very large adverse shocks may affect the supply-side of the economy through hysteresis effects. In these instances, policy may prefer to minimise the initial impact of the shock by choosing a policy that would re-establish quickly orderly trading conditions in interbank markets.

Conclusion
Growing levels of excess liquidity in the wake of the ECB's asset purchase programme, together with attractive conditions attached to the ECB's targeted longer-term refinancing operations, have reduced the need of banks to seek funds in the euro area interbank market. Although these measures have undoubtedly contributed to restore the transmission of monetary policy, and thereby to reinforce the economic expansion the euro area is enjoying since about mid-2013, they also mask the prevailing fragilities related to the trading of central bank reserves in a currency union characterized by structural differences across borders. Such differences may lead to persistent cross-border capital flows intermediated, in part, by banks that are likely to price interbank loans not only according to the credit quality of their counterparts, but taking also into account differences in macroeconomic risk across euro area jurisdictions.
This article showed that, at times, such frictions in the interbank market may constrain the ability of monetary policymakers to achieve their area-wide price stability objective using merely conventional policy instruments. In good times, credit frictions in the interbank market may amplify changes in the key policy rate and contribute to boost cross-border interbank loans. In bad times, pro-cyclicality in bank lending and pricing may offset efforts by the central bank to stimulate the economy.
The good news is that the crisis has proven that unconventional policy measures can be highly effective in overcoming frictions in the interbank market. The findings in this article confirm, by and large, this presumption. In particular, long-term refinancing operations as well as asset purchase programmes can complement, or substitute for, changes in the key policy rate and ease financial conditions at a time when access to interbank credit might be restricted or excessively expensive. Reducing the need of recourse to such instruments in future crises, however, requires a more forceful convergence in the growth capacities of euro area economies, a task that lies beyond central bank mandates.