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Global Banking and the Conduct of Macroprudential
Policy in a Monetary Union
Jean-Christophe Poutineaua, Gauthier Vermandelb,c,∗
aCREM, UMR CNRS 6211, Universit´e de Rennes I,
7 Place Hoche, 35065 Rennes Cedex, France.
bParis-Dauphine University & PSL Research University,
Place du Mar´echal de Lattre de Tassigny, 75016 Paris, France.
cFrance Strat´egie, 18 Rue de Martignac, 75007 Paris.
Abstract
This paper questions the role of cross-border lending in the definition of national macroprudential
policies in the European Monetary Union. We build and estimate a two-country DSGE model
with corporate and interbank cross-border loans, Core-Periphery diverging financial cycles and
a national implementation of coordinated macroprudential measures based on Countercyclical
Capital Buffers. We get three main results. First, targeting a national credit-to-GDP ratio
should be favored to federal averages as this rule induces better stabilizing performances in front
of important divergences in credit cycles between core and peripheral countries. Second, policies
reacting to the evolution of national credit supply should be favored as the transmission channel
of macroprudential policy directly impacts the marginal cost of loan production and, by so,
financial intermediaries. Third, the interest of lifting up macroprudential policymaking to the
supra-national level remains questionable for admissible value of international lending between
Eurozone countries. Indeed, national capital buffers reacting to the union-wide loan-to-GDP
ratio only lead to the same stabilization results than the one obtained under the national reaction
if cross-border lending reaches 45%. However, even if cross-border linkages are high enough
to justify the implementation of a federal adjusted solution, the reaction to national lending
conditions remains remarkably optimal.
Keywords: Macroprudential Policy, Global Banking, International Business Cycles, Euro Area
JEL classification: F42, F45, E58, F34
∗Corresponding author
Email addresses: jean-christophe.poutineau@univ-rennes1.fr (Jean-Christophe Poutineau),
gauthier@vermandel.fr (Gauthier Vermandel)
Preprint submitted to Elsevier April 27, 2017
1. Introduction
The disruption of financial relations that followed the 2007 subprime crisis set the basis for the
adoption of macroprudential policies in most countries.1In the Euro Area, the implementation of
such measures remains fragmented along national lines while the coordination and internalization
of cross-border spillovers are achieved through the actions of the European Systemic Risk Board
(ESRB, henceforth). This federal organization accounts for two conflicting features of the Euro-
zone that can be approached by contrasting core and peripheral countries.2Panel (a) of Figure 1
shows that financial cycles (as measured by the credit to GDP ratio in percentage deviation from
HP trend) remain clearly national, which militates for a decentralized definition and implementa-
tion of macroprudential measures. However, as reported in panel (b) of Figure 1, these two regions
are closely linked by cross-border banking activities (as measured by the share of loans lent to a
foreign agent residing in another Euro Area country) and the international spillovers of national
macroprudential policies may be harmful for the monetary union. The remaining uncertainties
on undesirable side-effects of self oriented macroprudential policies have thus put global banks at
a central stage in the on-going debate related to the conduct of macroprudential policies.3
2000 2003 2006 2008 2011
−5 %
0 %
5 %
Credit-to-GDP
% deviation from HP Trend
2003 2004 2006 2007 2008 2010 2011 2012
6 %
8 %
10 %
12 %
14 %
Share of Cross-Border Loans
in Banks’ Balance Sheet
Core countries Peripheral countries
Note: Cross-border lending refers to any financing arrangement that crosses national borders between a domestic bank and
a foreign borrower. The share of cross-border loans is computed here as the ratio between loans to euro area excluding the
domestic area and the loans to euro area (i.e. cross-border loans between core countries are included in the calculation of the
share of international loans). Sources: ESRB and ECB statistics.
Figure 1: Stylized facts characterizing the Eurosystem banking system: credit cycles remain clearly national while
cross-border lending experienced an important growth
This paper questions how sizable cross-border lending flows should be treated in the definition
of national macroprudential policies in the Euro Area. We more particularly assess whether
cross-border bank lending should explicitly be considered in the setting of coordinated national
1In a nutshell, macroprudential policy aims at completing monetary policy to enhance the resilience of the
financial system and contain the procyclicality of financial factors on activity.
2In the first group we aggregate data for countries with a current account surplus and low government bond
yields over the sample period (Austria, Belgium, Germany, Finland, France, Luxembourg and Netherlands), while
in the second group, we aggregate data for countries with a current account deficit and high government bond yields
over the sample period (Spain, Greece, Ireland, Italy and Portugal).
3For example, regarding issues related to macroprudential policy with global banking, we refer to the IMF (2013,
key issues, p31), the ESRB handbook (2014), ECB (2015, Financial Stability Review, May), Bank of England (2015,
Staff Working Paper).
2
macroprudential measures or whether national regulators should only focus on the sole national
financial stance to contribute to the financial stability of the Eurozone.
We build and estimate a two-country DSGE model that accounts for two major aspects to
address the question at hands. First, we extend the setup of Poutineau and Vermandel (2015) -
featuring cross-border banking on the corporate and interbank loan markets4- to account for bank
capital regulation and thus to contrast the effectiveness of macroprudential policy from banking
autarky to perfect integration. Second, in line with the actual organization of macroprudential
policy,5we focus on the joint-optimization of macroprudential policy rules in each country using
the countercyclical capital buffer (CCB, henceforth) rate as an instrument. This solution has
become one of the leading facets of prudential regulation since the adoption of Basel III accords
(2010) by building up a bank capital buffer during periods of excessive credit growth that can be
released when systemic risks abate. The international dimension of banks offered by our setting
allows us to contrast different CCB rules based on: (i) the federal or the national credit-to-gdp
targeting, (ii) the loan demand (from firms) or supply (from banks) to GDP targeting, and (iii)
the loan inflows-to-GDP ratio targeting as envisaged by Rey (2015).
The methodology employed in this paper comprises three steps. First, we build and estimate
a two-country DSGE model for the Euro Area with only monetary policy (as there are no ob-
servations for an estimation of a macroprudential rule). Second, we compute the optimal policy
rules (both monetary and macroprudential policy) given the estimated parameters assuming a
two-stage game where monetary policy is the leader.6Third, we examine implications of cross-
border lending on the optimal design of macroprudential rules across country members of the
Eurosystem using the optimal monetary policy rule as a benchmark.
The main result of the paper suggests that self oriented macroprudential national policies re-
acting to the evolution of home country loan creation should be favored even with high amounts of
cross-border lending flows: First, targeting a national credit-to-gdp ratio should be favored to fe-
deral averages as this rule induces better stabilizing performances in front of important divergences
in credit cycles between core and peripheral countries. Second, policies reacting to the evolution
of national credit supply should be favored as the transmission channel of macroprudential policy
directly impacts the marginal cost of loan production and, by so, financial intermediaries. Third,
the interest of lifting up macroprudential policymaking to the supra-national level remains questi-
onable for admissible value of international lending between Eurozone countries. Indeed, national
capital buffers reacting to the union-wide loan-to-GDP ratio only lead to the same stabilization
results than the one obtained under the national reaction if cross-border lending reaches 45%.
However, even if cross-border linkages are high enough to justify the implementation of a federal
adjusted solution, the reaction to national lending conditions remains remarkably optimal.
Additionally, we outline some particularities regarding the conduct of macroprudential poli-
4In this paper, we omit the mortgage market and concentrate on corporate and interbank loans. Given the
insignificant size of cross-border housing loans in the portfolio of banks (the share of cross-border loans is below 1%
in the Euro Area according to ECB internal data), this omission does not seem to be important for the analysis
conducted here.
5We refer to Carboni et al. (2013) for a discussion regarding the macroprudential policy mandate in the Euro
Area shared between European Central Bank and the Single Supervisory Mechanism, national competent authorities
and coordinated by the European Systemic Risk Board.
6A important branch of the literature analyzed the interaction between monetary policy and financial stability,
a topic not covered in the paper as we concentrate here on interactions between national prudential authorities. We
refer to Woodford (2012) for a summary of policy challenges and results offered by the existing literature concerning
the role of monetary policy in providing financial stability.
3
cies for peripheral countries. We find that adjusting the macroprudential instrument to capital
inflows-to-GDP is a promising tool for these countries that have experienced a large amount of
loan inflows. Furthermore, disentangling the demand/supply of credit has implications for ma-
croprudential policymaking as it is preferable to target credit suppliers for core countries and
borrowers for peripheral economies.
Our approach is partly related to a set of papers examining macroprudential measures in the
Eurozone with a closed economy setup. Notably, Darracq-Pari`es et al. (2011) and Angelini et al.
(2014) build a DSGE model of the Eurozone close to Gerali et al. (2010) with both corporate
and housing credit markets and evaluate the optimal mix between monetary and macroprudential
policy using loss functions. As a key contribution to the literature, they suggest that time-
varying capital requirements can improve macroeconomic stability by supporting monetary policy
actions. Our analysis can thus be considered as an extension to these papers, by accounting for
the heterogeneity between Euro Area participants and the existence of national macroprudential
policies with cross-border spillovers.
Our paper also contributes to macroprudential policy analysis in open economies. As an
example, Quint and Rabanal (2014) account for financial asymmetries between participating
countries and focus on the interaction between financial and housing cycles without considering
cross-border flows between countries. By omitting cross-border lending, they naturally find that
there are no important spillover effects of regulation from one member state to another via an
estimated two-country DSGE model of the Eurozone. Additionally, Jeanne (2014) employs a
static open economy model to evaluate the effectiveness of macroprudential and capital control
measures. Contrary to Quint and Rabanal (2014), he finds that these prudential policies generate
important global spillovers even with international coordination.
The paper is organized as follows: Section 2 describes the financial sector of the model.
Section 3 takes the model to the data. Section 4 discusses the performance of macroprudential
policy. Section 5 provides a sensitivity analysis to assess the robustness of our results. Section 6
concludes.
2. The financial sector
The economy is composed of two countries of unequal size and populated by households, firms
and banks. This first section describes the banking component of the model while the rest of the
framework (standard to the literature) is presented in appendix.
2.1. The financial sector in a nutshell
Figure 2 provides a broad picture of the financial sector and summarizes its interaction with the
rest of the economy. Banks engage in interbank lending/borrowing relations and provide corporate
loans to entrepreneurs and deposit services to households. Authorities affect the decisions of the
banking sector through monetary and macroprudential policies.
To introduce an interbank market, we assume that banks are heterogenous in terms of liquidity.
This feature gives rise to an interbank market where liquid banks provide interbank loans to
both home and foreign banks. This feature is line with the current European banking system
characterized by banks relying on wholesale fundings as illustrated by Giannone et al. (2012).
In our setup, the distinction between liquid and illiquid banks lies in the direct access of liquid
banks to ECB fundings which allow intra-financial sector flows between financial intermediaries.7
7This assumption is empirically motivated: in the Eurosystem, only a fraction of the 2500 banks participates
4
Monetary
Policy
Macroprudential
Policy
Macroprudential
Policy
Bank
Bank
Production
Production
Household
Household
Cc,t
Cp,t
Ls
c,t
Ls
p,t
Investment
Flows
Consumption
Flows
Corporate
Credit Flows
Interbank
Credit Flows
Refinancing
Rate Rt
νc,t capital
buffers
νp,t capital
buffers
Deposits Dd
c,t
Deposits Dd
p,t
Figure 2: Macroprudential policy and cross-border banking in a New Keynesian Framework
Extending this assumption to an international perspective, illiquid banks can borrow from both
domestic and foreign liquid banks, which gives rise to cross-border interbank lending flows. The
decision of the banking system regarding the provision of deposit services to households and loans
to the corporate sector affects the rest of the economy through the setting of deposit and lending
interest rates.8In line with the EMU situation, we do not consider cross-border deposit nor
cross-border lending to households. The international flow of loans between economies is thus a
consequence of interbank liquidity provision and borrowing choices undertaken by entrepreneurs
(following a comparison between the relative interest rates of domestic and foreign corporate
loans).
This paper adopts a macroeconomic perspective to focus on the effect of cross-border lending
on the conduct of macroprudential policy in a heterogeneous monetary union. As a consequence,
the financial sector is combined with a standard two-country DSGE model accounting for short run
rigidities in goods prices and nominal wages. In what follows, we outline the main assumptions
regarding the functioning of the financial sector that are deemed necessary to improve both
the tractability of the analysis and the estimation of the many behavioral parameters of the
DSGE structure. Some modelling choices have been done in line with the DSGE literature that
contrast with a more standard description of the behavior of the banking sector as summarized
by Freixas and Rochet (2008) and VanHoose (2009). As in the initial contribution of Gerali et al.
(2010), this macro superstructure is augmented with a highly simplified banking model. A host
of assumptions should be invoked that effectively splinter a bank’s decisions into independent
choices about different portions of its balance sheet.9
regularly to the bidding process in main refinancing operations of the ECB while the others rely on interbank
funding.
8For tractability reasons we assume that even if banks differ in their ability to raise funds from the central
bank, their loan and deposit supply decisions remain homogenous after aggregation. In a real life situation, illiquid
banks may face more difficulties in attracting households deposits requiring banks to set higher deposit rates to
compensate their default risk. Regarding corproate loans provision, the tighter funding constraint of illiquid may
diminish their loan supply compared to liquid banks.
9First, portfolio separation holds (Baltensperger (1980) and Santomero (1984)), which means (Sealey and Lindley
(1977) and Sealey (1985)) that a number of assumptions have been invoked. For instance, either shareholder
5
This paper extends Poutineau and Vermandel (2015) to account for deposit decisions and for
macroprudential consideration in the balance sheets of financial intermediaries. The stickiness in
both deposit and loan interest rates is a key ingredient of the framework. The setting of interest
rate mimics the way other sticky nominal variables such as prices and wages are set in the model
by adopting a Calvo-type mechanism. This device, shared by most DSGE models with a banking
sector, partly contrasts with the literature developed from the banking industry perspective.
Indeed, most of the banking literature has, following Flannery (1982) original work on deposits
as quasi-fixed factors, focused on intertemporal quantity adjustment costs. It is also worth noting
that the substantial banking literature on this topic has proposed alternative ways of approaching
this question, including Cosimano and Van Huyck (1989), Cosimano (1987,1988), and Elyasiani
et al. (1995) and Abo-Zaid (2015). Furthermore, sluggish and even asymmetric variations in bank
retail rates have been documented in the empirical literature as in Van Leuvensteijn et al. (2013)
through imperfect competition among banking systems, while Kopecky and Van Hoose (2012) rely
on intertemporal quantity adjustment costs together with imperfect competition to explain such
observations. The adoption of a Calvo mechanism combined with monopolistic competition has
been employed here in a macro-perspective for credit and deposit interest rates, as this solution
allows us to consider the sluggishness in the adjustment of all the nominal variables of the economy
(prices, wages and interest rates) through the estimation of a ”Calvo lottery parameter”.
As a second major noticeable difference from Poutineau and Vermandel (2015), we account
for endogenous leverage of financial intermediaries, thus reflecting the riskiness in the balance
sheet of banks. We use time-varying capital requirements as the macroprudential instrument.
As underlined by Angelini et al. (2014), capital buffers have taken a center stage in the ongoing
debate on regulatory reform and have become one of leading facet of macroprudential regulation.
Specifically in the European Union, a number of macro-prudential policy instruments including
countercyclical buffers are embedded in the legislative texts transposing the Basel III regulatory
standards into EU law.10 To account for this compulsory macroprudential instrument, we borrow
the modelling device of Darracq-Pari`es et al. (2011) and Angelini et al. (2014) by assuming that
each type of bank must pay a quadratic cost when its risk weighted assets ratio deviates from the
time-varying ratio fixed by the macroprudential authority in country iaccording to the systemic
risk arising within the financial system. The decision to penalize banks for keeping equity-capital
positions below the official benchmark is easy to understand, as undercapitalized banks make
the banking sector more fragile and in turn subject to bank runs (Diamond and Rajan (2001)).
Symmetrically, the decision to impose costs on banks for having equity-capital positions above
the required levels may be understood in a macroeconomic perspective: by keeping more equity
capital levels than required by the official regulation, the banking sector diverts resources and, in
turn, creates credit rationing for both entrepreneurs and illiquid banks. This may create lower
unanimity is assumed for all banks in the model, or risk neutrality has been assumed to render shareholder unanimity
a non-issue. In addition, it must be assumed that banks’ costs of real resources utilized in their operations are
separable from resource costs for others of the banks’ assets and liabilities at during each period and across periods
if interperiod adjustment costs are taken into account. Finally, banks must have access to a market in which they
can both borrow and lend at exactly the same interest rate. Only when all such assumptions are invoked, it is
legitimate for each bank to be able to make separable decisions about balance-sheet choices as assumed in this
model.
10Namely the new Capital Requirements Directive (CRD IV) and the Capital Requirements Regulation (CRR).
We refer to Carboni et al. (2013) for a discussion regarding the macroprudential policy mandate in the Euro Area
shared between ECB/SSM, national competent authorities and coordinated by the ESRB.
6
than desired banking activity, reduce investment in the economy and incur inefficiencies.11
2.2. Interbank relations
In each country the banking system consists of two distinct branches: a continuum of monopo-
listic banks and financial packers. Monopolistic banks provide different types of loans and deposit
services and set interest rates on a Calvo basis. The financial intermediary is a CES packer that
produces one homogenous loan and deposit service.12 A share λof banks is illiquid (i.e. credit
constrained), while the remaining share of banks 1-λis liquid and supplies interbank loans to
illiquid banks.
The representative share λof illiquid banks bin country ihas the following balance sheet,
Ls
i,t =IBH
i,t +BKill
i,t +Di,t +liabill
i,t,(1)
where Ls
i,t is the loan supply of borrowing banks, IBH
i,t is the interbank loans supplied by liquid
banks subject to external habits, BKill
i,t is the bank capital, Di,t are deposit services to households
and liabi,t are other liabilities in the balance sheet of the bank that are not considered in the
model.13 To close the model, we assume that the cost of these liabilities is set by the central
bank through its refinancing rate. We suppose that the demand for interbank funds are subject
to external habits at a degree hB
iwhere IBH
i,t =IBd
i,t −hB
i(IBd
i,t−1−IBd
i). These habits captu-
res the empirical autocorrelation of interbank funding. In addition, these habits are empirically
documented in the interbank network literature: Finger et al. (2014,2015) find at a bank level
that bilateral links between banks are persistent as banks heavily rely on well-established business
relations, thus exhibiting some habits in borrowing/lending decisions.
The one-period stream of profits of the b-th illiquid bank is given by:
Πill
i,t =1−µB(1 −Et{ηi,t+1})1 + RL
i,tLs
i,t −1 + RD
i,tDi,t −1 + PI B
i,t IBH
i,t (2)
−(1 + Rt)liabill
i,t −Frwaill
i,t −υitBKill
i,t ,
where µB∈[0,1] denotes the loss-given-default (i.e. the percentage of the amount owed on a
defaulted loan that the bank is not able to recover), 1−Et{ηi,t+1}is the expected average default
11Van den Heuvel (2008) finds using a general equilibrium model that increasing capital requirements induces
high welfare costs in terms of unconditional consumption, suggesting that capital requirements should be lower
than in the current adequacy framework. Clerc et al. (2015) highlight the presence of a tradeoff using a financial
accelerator model between too high and too low capital requirements.
12The financial packer acts as a loan and deposit bundler in a perfectly competitive market. Banks sup-
ply differentiated types bof deposits Di,t (b) and loans Ls
i,t (b) bundled by financial packers. Their packing
technology for deposit services and loans reads as, Dd
i,t = [(1/ni)1/DG(Di,t (b)(D−1)/D)]D/(D−1),and
Ld
i,t = [(1/ni)1/LG(Ls
i,t (b)(L−1)/L)]L/(L−1). It maximizes profits, RD
i,tDd
i,t +RL
i,tLd
i,t − G(RD
i,t (b)Di,t (b)) −
G(RL
i,t (b)Ls
i,t (b)), subject to their two technology curves. Here, Ld
i,t is the loans demand from home and fo-
reign entrepreneurs, Dd
i,t is the deposit services demand from domestic households and G(.) is the aggregator
function. Deposits and loans are imperfect substitute with elasticity of substitution D<−1 and L>1. The
corresponding demand functions associated from the previous problem are, Di,t (b) = (1/ni)(RD
i,t(b)/RD
i,t)−DDd
i,t
and Ls
i,t (b) = (1/ni)(RL
i,t(b)/RL
i,t)−LLd
i,t. The aggregate price index of all varieties in the economy is given by,
RD
i,t = [(1/ni)G(RD
i,t (b)1−D)]1/(1−D)and RL
i,t = [(1/ni)G(RL
i,t (b)1−L)]1/(1−L).
13We suppose that they follow an exogenous AR(1) shock process εB
i,t such that, liabi,t =eεB
i,t liabi,this shock
captures some aggregate movements in the funding constraint araising from the wholesale funding market, see for
instance P´erignon et al. (2017) for an analysis of liquidity runs on the French unsecured market of certificates of
deposits.
7
rate of the bank’s home and foreign customers,14 RD
i,t is deposit rate, PIB
i,t is the borrowing cost
on the interbank, Rtthe interest rate set by the central bank and Fi(·) denotes the capital
requirement cost function. This cost function is taken from Gerali et al. (2010) and is defined as
Fi(x)=0.5χkx2where χk≥0 is the cost of capital adequacy framework paid in term of bank
capital.15 This cost function is a shortcut that makes bank capital more costly than any source
of financing, and allows in turn to mimic the response of credit rates and credit to a capital
requirement tightening consistently with empirical evidence (see for instance Fraisse et al. (2013)
for an empirical measure of this elasticity). When the bank capital-to-risky-asset ratio rwaill
i,t is
below the policy target υit, the bank is penalized by regulatory rules that affect the borrowing
rates in the monetary union and in turn damage output. This penalization replicates the market
discipline imposed by investors on low capitalized banks, forcing the latter to boost their retained
earnings though higher credit rates. The risk is evaluated through fixed weights on assets, based
on the type of the borrowers (1 for corporate exposure and 0.20 for interbank exposure between
OECD banks as defined in Basel accords) as defined in Basel I accords. Since illiquid banks are
only exposed to corporate risk, the risk weighted assets ratio is given by rwaill
i,t =BKill
i,t /Ls
i,t. In
addition, the financial intermediary has access to domestic and foreign interbank loans to meet its
balance sheet. The modelling device to introduce international borrowing is analogous to trade
channels through a CES as in Poutineau and Vermandel (2015) and Brzoza-Brzezina et al. (2015).
The total amount borrowed by the representative bank reads as follows:
IBd
i,t =1−αIB
i1/ξ IBd
hi,t(ξ−1)/ξ +αI B
i1/ξ IBd
fi,t(ξ−1)/ξ ξ/(ξ−1)
,(3)
where parameter ξ > 0 is the elasticity of substitution between domestic and foreign interbank
funds, αIB
irepresents the percentage of cross-border interbank loan flows in the monetary union
and IBd
hi,t+1 (resp. IBd
fi,t+1) the amount of domestic (resp. foreign) loans demanded by borrowing
bank bin country i. This existence of an home bias on the interbank market is empirically
motivated, Fricke and Lux (2015) find, using Italian bank-level data, that Italian banks tend to
trade with each other rather than with foreign banks, in particular after the financial turmoil.
More broadly in the literature of finance, the home bias in portfolio was first documented by
French and Poterba (1991).
The total cost incurred by illiquid banks to finance interbank loans, 1 + PIB
i,t , is thus defined
according to the CES aggregator:
1 + PIB
i,t = (1−αIB
i(1 + RIB
h,t )1−ξ+αIB
i(1 + RIB
f,t )1−ξ)1/(1−ξ),(4)
where 1 + RIB
h,t (resp. 1 + RI B
f,t ) is the cost of loans obtained from home (resp. foreign) banks in
country i. Finally following Gerali et al. (2010), the bank capital accumulation process of illiquid
14To simplify both the steady state and the log-linear version of the model, the bank default expectation regarding
entrepreneurs’ projects is defined by a geometric average of home and foreign surviving rates of entrepreneurs,
ηi,t = (ηE
h,t)1−αL
h(ηE
f,t )αL
j¯ηαL
h−αL
jwhere ηE
i,t+1is the default rate of entrepreneurs operating in country i∈ {c, p}.
The expression ¯ηαL
h−αL
jensures the detesministic steady state remains symmetric between Core and Periphery
without affecting the dynamic of the model up to a first order approximation.
15The quadratic nature of this cost has been discussed in the previous subsection.
8
banks (BKill
i,t ) is determined by:
BKill
i,t =1−δill
iΠill
i,t−1,(5)
where δill
i∈[0,1] measures resources used in managing bank capital and conducting the overall
banking intermediation activity and is determined endogenously by the steady state of the model.
Given the functional form of Fi(·), the first order condition on loans which determines the marginal
cost of supplying an additional unit of loans to home and foreign entrepreneurs is:
1 + MCill
i,t =
1 + PIB
i,t +χkυit −rwaill
i,trwaill
i,t2
1−µB(1 −Et{ηi,t+1}).(6)
From this equation, we observe that an increase (reduction) in the CCB rate υi,t (risk weighted
assets ratio rwaill
i,t) imposes on banks to accumulate more equity via retained earnings through a
rise in credit rates. Parameter χkdetermines the elasticity of interest rates to capital regulation
change.16 During phases of expansion, banks have incentives to increase their leverage away from
the target in order to boost their profits. This risk taking by banks is addressed in our model
though the cost function that forces banks to control their capital structure.
The fraction 1 −λof remaining liquid banks has the following balance sheet:
Ls
i,t +IBs
i,t =LEC B
i,t +BKliq
i,t +Di,t +liabliq
i,t ,(7)
where Ls
i,t is the lending supply to entrepreneurs, IBs
i,t is the supply of funds on the interbank
market, LECB
i,t is the amount of refinancing operations obtained by the liquid bank, BKliq
i,t is
the amount of bank capital, Di,t are deposits collected from domestic households and liabi,t are
exogenous liabilities as explained previously. The one-period profit of the bank Πliq
i,t is defined as:
Πliq
i,t =1−µB(1 −Et{ηi,t+1})1 + RL
i,tLs
i,t +1 + RIB
i,t IBs
i,t −1 + RD
i,tDi,t (8)
−(1 + Rt)liabliq
i,t −(1 + Rt)LEC B
i,t −F(rwaliq
i,t −υit)BKliq
i,t .
Here, RIB
i,t is the interest rate set by liquid banks to home and foreign illiquid banks, Rtis the
refinancing rate of the central bank and Fi(·) denotes the same Basel cost function as for illiquid
banks: Fi(x)=0.5χkx2. Interbank claims affect the amount of equity held by banks and are
given a risk weight at 20%. The risk weighted asset ratio for liquid bank incorporating corporate
and bank exposures is given by rwaliq
i,t =BKliq
i,t /(Ls
i,t + 0.2IBs
i,t).According to the illiquid bank,
bank capital of liquid banks evolves according to
BKliq
i,t = (1 −τliq
i)Πliq
i,t−1,(9)
where δliq
i∈[0,1] is similar to the illiquid bank and measures the fraction of capital used during
the intermediation process that cannot be re-invested next period. The first order condition on
16Empirically, Fraisse et al. (2013) find at a bank level that one percentage increase in capital requirements leads
to a reduction in lending by approximately 10%.
9
loans determining the marginal cost of loans of the liquid bank bis:
1 + MCliq
i,t =
1 + Rt+χkυit −rwaliq
i,t rwaliq
i,t 2
1−µB(1 −Et{ηi,t+1}),(10)
and the second first order condition on interbank loans determines the interbank rate set by banks
operating in country i:
RIB
i,t =Rt+ 0.2χk(υit −rwaliq
i,t )(rwaliq
i,t )2.(11)
Here again, an increase in bank capital requirements raises the bank’s cost of lending, and in
turn increases both interbank and corporate interest rates. This result is consistent with standard
business cycle models and is referred to the bank capital channel as in Van den Heuvel (2008),
Meh and Moran (2010), Darracq-Pari`es et al. (2011) and Angelini et al. (2014).
2.3. Interest rate setting
We assume that interest rates on deposits and corporate credit loans are sticky. In particular,
sluggish and even asymmetric variations in bank retail rates have been documented in the empi-
rical literature as in Kopecky and Van Hoose (2012) and Van Leuvensteijn et al. (2013) through
imperfect competition among banking systems. The setting of interest rate mimics the way other
sticky nominal variables such as prices and wages are set in the model. As in Darracq-Pari`es et al.
(2011), we introduce a Calvo model for credit rates to firms and deposit rates while the interbank
rate is left flexible as banks operate under perfect competition on the interbank market. Banks
must solve a two-stage problem. In the first stage, banks minimize the cost of managing their
funds on a competitive input markets by computing the marginal cost of supplying an additional
loan to borrowers and a deposit service to households. The computation of these marginal costs
has already been performed in the previous subsection. In a second stage, they operate under
monopolistic competition by applying a markup (markdown) on their commercial loan (depo-
sit) rate, and set the interest rate on a staggered basis. Using a Calvo nominal rigidity device,
each period a random fraction θL
i(θD
i) of banks is unable to update its lending (deposit) rate,
RL
i,t =RL
i,t−1(RD
i,t =RD
i,t−1), creating an imperfect transmission of monetary policy decisions to
borrowers and savers living in the monetary union. The bank that it is able to modify its loan
interest rate (with a constant probability 1 −θL
i) chooses RL∗
i,t to maximize its expected stream
of profits adjusted by the risk of default:
EtX∞
s=0 θL
iτΛi,t+s1−µB(1 −ηi,t+1+τ)RL∗
i,t −exp(εL
i,t+s)MCL
i,t+sLs
i,t+s,(12)
where εL
i,t is an ad-hoc markup AR(1) shock to the credit rate equation, θL
i∈[0,1) is the Calvo
lottery coefficient determining the degree of nominal rigidity and MCL
i,t is the aggregate marginal
cost combining outputs from liquid and illiquid banks of country i. We aggregate loans from liquid
and illiquid banks and their respective marginal costs before applying the markup for tractability
purposes: this device is useful to compute a single Phillips curve as well as an unique credit
rate for both liquid and illiquid banks. We borrow this shortcut procedure from Gerali et al.
(2010) adapted in a different context, i.e. all banks belonging to a national banking system share
the same marginal cost of production, reflecting the average liquidity degree of national banks:
1 + MCL
i,t = (1 + M Cill
i,t )λ(1 + MCliq
i,t )(1−λ). In addition, the banking spread reflecting the level of
financial distress is given by SL
i,t = (1 + RL
i,t)/(1 + Rt).
10
In a similar fashion for deposit rates, assuming that it is able to modify its interest rate with a
constant probability 1−θD
i, the representative bank chooses RD∗
i,t to maximize its expected stream
of profits, by applying a markdown on the refinancing rate of the central bank Rt:
EtX∞
τ=0 θD
iτΛi,t+sRt+sexp(εD
i,t+s)−RD∗
i,t Di,t+s,(13)
where εD
i,t is an ad-hoc time-varying AR(1) markdown shock to the deposit rate equation and
θD
i∈[0,1) is the Calvo lottery parameter.
2.4. Macroprudential policy
Macroprudential policy affects the general equilibrium of the economy through the policy
instrument vi,t that contributes to the marginal cost of commercial banks’ loans. As a consequence,
a macroprudential policy tightening is associated with higher lending rates, and lower bank credit
growth and asset prices. We assume that the macroprudential authority sets the time-varying
capital requirement νi,t according to:
vi,t = (1 −ρv
i) ¯ν+ρv
iνi,t−1+φi(Ti,t −¯
Ti),(14)
where ρv
i∈[0,1) is the smoothing coefficient of the rule, Ti,t is the macroprudential target, φi≥0
is the macroprudential weight to the target in country iand ¯
Tiis the steady state of the target.
In our specification, capital requirements are expected to increase when the target deviates from
its steady state. The choice of the target Ti,t is a key aspect of the paper that will be discussed
below.
The ESRB has developed a buffer guide to choose the CCB rate based on the credit-to-gdp
gap.17 However, the global nature of the European banking system introduces many possibilities
for the definition of the credit-to-gdp ratio taken into account by national authorities. Indeed,
the CCB rate may be adjusted to the credit supply (of banks) or the credit demand (of entrepre-
neurs),18 either on a national or on a federal basis. Our framework with international bank flows
allows us to distinguish between five operational targets as listed in Table 1.
The first set of credit targeting rules is oriented towards the supply of credit using either
a federal (1.a) or a country-specific aggregate (1.b). A macroprudential policy based on credit
supply aims at stabilizing lenders by focusing more on the stabilization of financial shocks hitting
lenders rather than demand and supply shocks hitting borrowers. Given the scale of cross-border
loans in the Eurozone, the decisions of the national supervisor has side effects on countries where
a national bank has a subsidiary or branches or where this bank lends to may favor a federal
definition of the ratio. Thus to handle these pecuniary externalities, we evaluate the possibility of
an union-wide targeting system (1.a) against a national targeting system (1.b), the latter being
expected to create more externalities (positive or negative) as it affects the foreign banking system
without taking into account its financial developments.19
17Other indicators (such as early warning variables) are included in the CCB guide which are not implementable
in our model.
18In an open economy context where banks can lend across borders, banks supply credit to both home and foreign,
which creates a gap between the domestic supply and the domestic demand for loans. This distinction between
demand and supply is easy to see on the market clearing conditions of interbank (Equation B.23) and corporate
markets (B.22).
19For further discussions of these cross-border issues, we refer to Beck et al. (2016).
11
Table 1
Various Macroprudential Policy Schemes in terms of Target (average in the monetary union, national supply or
national target) and in terms of policy stance (common or national-adjusted)
Schemes Target
Loan Supply Targeting
1.a Union-wide loan supply Tt= (Ls
t+ (1 −λ)IB s
t)/Yt
1.b National loan supply Ti,t = (Ls
i,t +λIB d
i,t)/Yi,t for i∈ {c, p}
Loan Demand Targeting
2.a Union-wide loan demand Tt= (Ld
t+λIB d
t)/Yt
2.b National loan demand Ti,t = (Ld
i,t +λIB d
i,t)/Yi,t for i∈ {c, p}
Capital Inflows Targeting
3 Capital Inflows Ti,t = (Ld
i,t −Ls
i,t +λIB d
i,t −(1 −λ)IB s
i,t)/Yi,t for i∈ {c, p}
Note: variables without country subscript such as xtdenote union-wide averages computed as a weighted sum of each country
xt=nxc,t + (1 −n)xp,t.
The second set of credit targeting rules concentrates on the demand of credit emanating from
entrepreneurs.20 The interest of a CCB rate tailored to borrowers is that it may provide more
stabilization following real and nominal shocks hitting households and firms at the expense of fi-
nancial shocks affecting banks. This solution seeks at internalizing the social cost of entrepreneurs’
over-borrowing that may arise given their biased expectations. As this policy regime inefficiently
affects foreign borrowers through cross-border lending, spillovers effects may be dampened by a
federal targeting (2.a) rather than a national one (2.b).
We also evaluate the interest of adopting provisional measures to affect cross border lending
directly, through targeting capital inflows in the CCB. This solution, as envisaged by Jeanne
and Korinek (2010), Brunnermeier et al. (2012) and Rey (2015), is relatively similar to a capital
control measure. The main insight behind this scheme would rely on the fact that persistent
capital account imbalances induce financial stability risks and may have implications for the
sustainability of net external asset positions. In particular since the creation in the Eurozone,
global banking has experienced an explosive growth helping to fuel unsustainable credit booms in
peripheral economies such as in Spain and in Ireland, followed by a sudden stop in capital inflows
compensated by unconventional measures. Macroprudential policies can play a key role to contain
this problem by imposing targeted regulations on banks engaged in cross-border activities. When
borrowing to other European banks is increasing faster with respect to the GDP, a national
authority can rise the CCB rate to affect banks’ balance sheet management and reduce their
exposure to international borrowing. In addition when system risks abate in one economy, leading
to capital flow reversals, national authorities may release the buffer thus loosening the banks’
funding constraint to address the procyclicality of capital flows.
20A loan demand targeting is feasible in a real life situation, the ECB already disentangles the credit demand
and supply by collecting the domestic and cross-border positions of Euro area monetary financial institutions since
1999 for each participant of the monetary union. Regarding the demand side of credit markets, the bank lending
survey published by the ECB on a quarterly basis provides an analysis of the driving forces of the demand of credit
in the Euro Area. For the supply side, both the ECB and the BIS collect domestic and cross-border positions of
euro area monetary financial institutions.
12
3. Estimation strategy
We fit the previous two country DSGE to Eurozone data over the sample time period 1999Q1-
2013Q4 using Bayesian techniques. We estimate structural parameters and the sequence of shocks
by following the seminal contributions of Smets and Wouters (2003,2007) and Christiano et al.
(2005). For a detailed description, we refer to the original papers.
3.1. Data
We split the Eurozone in two groups adopting the core-periphery dichotomy as in Quint and
Rabanal (2014) and Poutineau and Vermandel (2015). Core countries gather Austria, Belgium,
Germany, Finland, France, Luxembourg and Netherlands while peripheral countries include Spain,
Greece, Ireland, Italy and Portugal. The model is estimated with Bayesian methods on Eurozone
quarterly data over the sample period 1999Q1 to 2013Q4, which makes 60 observations for each
observable variable. Concerning the transformation of series, the point is to map non-stationary
data to a stationary model. Data which are known to have a trend (namely GDP, consumption,
investment, corporate loan and interbank supply) or unit root are made stationary in two steps.
First, we divide the sample by the population. Second, data are taken in logs and we use a
first difference filtering to obtain growth rates. In addition, real variables are deflated by the
HICP price index and we remove the seasonal component in the data using a multiplicative
decomposition. Furthermore, we demean the data as we do not use the information contained in
the observable mean. Interest rates are set on a quarterly basis by dividing them by 4. Since hours
worked are not observable for the Euro Area, we adopt the same modelling strategy as Smets
and Wouters (2003) to identify TFP shocks using employment as a proxy for hours worked.
Employment is divided by the working population index, taken in logs and demeaned. To map
employment to hours worked in our model, we introduce an auxiliary equation for each country
which states that only a share θE
i∈[0,1) of firms is allowed to adjust its level of employment ˆei,t
to its optimal labor demand Hd
i,t:
ˆei,t =βˆei,t+1 +1−βθE
i1−θE
i/θE
ilog Hd
i,t/¯
Hd−ˆei,t.(15)
The vector of observable variables reads as:
Yt= 100[∆ˆyi,t,ˆei,t,∆ˆci,t ,∆ˆıi,t,ˆπC
i,t,∆ ˆwi,t,ˆrD
i,t,∆ˆ
ls
i,t,∆b
ibs
i,t,ˆrt] for i={c, p}.
3.2. Calibration, priors and model assumptions
We fix a small number of parameters commonly used in the literature of real business cycles
models which are weakly identified. The discount factor βis set at 0.99, the depreciation rate δ
at 0.025, the capital share αat 0.38, the share of steady state hours worked ¯
Hat 1, the spending
to GDP ratio gat 24%.21 Concerning Pand W(the substitutability between final goods and
labor), we consider the calibration at 10 as in Smets and Wouters (2007). Regarding financial
parameters, we fix ¯
N/ ¯
K(the net worth to capital) ratio to 0.40 to be consistent with the observed
debt-to-financial assets ratio of non-financial corporations which fluctuates between 50% and 65%
since 1999. The steady state value of spreads and the bank balance sheet are calibrated on their
averages observed over the sample period in the Euro Area: ¯
R-¯
RD=1.66/400, ¯
RL-¯
RD=3.67/400,
21This calibration offers a consumption-to-output ratio of 55.45% (vs 57.31% in the data) and investment-to-
output ratio of 20.55% (vs 20.70% in the data).
13
¯
D/ ¯
Ls=0.46, rwa=¯v=0.10 and IBd/¯
Ls=0.20. The capital regulation cost χkis set at 11 as in
Gerali et al. (2010) to replicate the response of credit and interest rate to a capital requirement
rise.
For substitution parameters for corporate and interbank loans υand ξas well as for the fraction
of illiquid banks λ, to our knowledge there are no empirical analysis using bank level data that
provides an estimation of these parameters. We rely on the previous fit exercise of Poutineau and
Vermandel (2015) by calibrating λat 0.38 and υ,ξat 1.1. The latter calibration for substitution
parameters is rather conservative by allowing very low substitution effects between home and
foreign loans.22 The quarterly share of defaulting firms’ projects 1 −¯ηEis fixed at 0.025/4,23 and
the auditing cost µBat 0.10,24 those values are very similar to Bernanke et al. (1999). We compute
the parameter governing the relative size of the core area nat 0.58 as in Kolasa (2009), which
is the share implied by nominal GDP levels averaged over the period 1999-2013. We calibrate
symmetrically the adjustment cost on deposits χD
iat 0.0007 as in Schmitt-Groh´e and Uribe
(2003) to remove an unit root component generated by the two-country set-up. Finally, the lower
bound ωmin and the shape κof the Pareto distribution are endogenously determined by the model
equations assuming a risk-free economy with no spread and default, we obtain: ωmin=1- ¯
N/ ¯
Kand
κ=¯
K/ ¯
N. Our calibration delivers for the main endogenous variables the following steady state:
¯ωC=0.6015, εD=-2.41, εL=4.37, ¯rL=0.0192 and ¯rK=0.0166.
Our priors are listed in Table B.7. Overall, they are either relatively uninformative or consis-
tent with earlier contributions to Bayesian estimations. For a majority of new Keynesian models’
parameters, i.e. σL
i,hC
i,θP
i,ξP
i,θW
i,ξW
i,θE
i,χI
i,ψi,φπ,φ∆yand shock processes parameters, we
use the prior distributions close to Smets and Wouters (2003,2007). Calvo probabilities for rates
have the same uninformative priors as for prices/wages while loans habits are given a prior mean
0.5 with standard deviation 0.2. Our priors for openness parameters are based on their observed
average over the sample period. Substitutabilities between home/foreign credit and final goods
are set to 2 with standard deviations of 0.50. We set the prior for the elasticity of the external
finance premium κito a beta distribution with prior mean equal to 0.05 and standard deviation
0.02 consistent with prior information of Gilchrist et al. (2009). Finally, in order to catch up
the correlation and co-movements between countries’ aggregates, we estimate the cross-country
correlation between structural shocks, associated priors are inspired by in Jondeau et al. (2006)
and Kolasa (2009), we set the mean of the prior distribution for shock correlations between core
countries and peripheral countries at 0.2 with a standard deviation at 0.2.
Finally, regarding bank capital regulation for the fit exercise, we disable the macroprudential
instrument by fixing the CCB rate to its deterministic steady state value:
νi,t = ¯v. (16)
22In contrast, Brzoza-Brzezina et al. (2015) assign a value of 6 to their substitution parameter, which is rather
high with respect to the literature of trade. In general, substitution parameters for goods market are rather low
and usually remain between 1 and 2 as in Quint and Rabanal (2014) or Poutineau and Vermandel (2015).
23This is consistent with corporate default statistics from Moody’s, the rating agency, which show an average
default rate on (non-US) non-financial corporate bonds of 0.75% for the period 1989-2009, as shown by Darracq-
Pari`es et al. (2011). The other rating agency Standards & Poor’s evaluates the rate of default for the period
1991-2014 to 0.58%. We consider a default rate of 0.63% which is in the ballpark of the numbers found by rating
agencies.
24The auditing cost cannot be observed as few data on loan losses are publicly available for reasons of confidenti-
ality. Dermine and De Carvalho (2006) find using bank level data that these costs critically depends on the size of
the loans: recovery costs on smaller loans are substantially higher than on large loans, 4.1% vs. 0.9%. In addition,
once the contentious department has to rely on external lawyers, the recovery costs rise to 10.4%.
14
This assumption is reasonable for two main reasons. First over the sample period, capital regula-
tion has been mainly dominated by the Basel I Accords characterized by fixed capital requirement
ratios. Second, even through the adoption of the Basel III Accords allows Euro Area countries to
employ the countercyclical capital buffer as a shield against the build up of financial imbalances,
it has not been yet employed by a participant of the monetary union.25
3.3. Estimation results
The methodology employed is standard to the Bayesian estimations of DSGE models.26 Ta-
ble B.7 reports estimation results which summarizes the means and the 5th and 95th percentiles
of the posterior distributions while the latter are drawn in Figure B.6. According to this figure,
prior and posterior distributions are relatively different showing that the data were fairly infor-
mative. Several parameters are well identified for one country but weakly for the other economy,
we decide to keep these parameters in the fit exercise after checking that their weak identification
does not affect our estimations (i.e. calibrating these parameters and re-estimating the model
provides very similar results). While our estimates of the standard parameters are in line with
the literature (see for instance Smets and Wouters (2003) and Quint and Rabanal (2014)), several
observations are worth making by commenting the mean of the posterior distribution of structural
parameters.
First regarding asymmetries in business and credit cycles between the core and the periphery,
they are mainly driven by the standard deviation of shocks which are larger in peripheral econo-
mies. In particular, inefficiency shocks for wages and prices are more volatile in periphery which
may constitute an issue in the implementation of a single monetary policy. In the same vein for
macroprudential regulation, the presence of heterogenous financial shocks in terms of volatility
questions the perspective of a single federal macroprudential authority.
Second turning to structural parameters, we find an important difference between countries
regarding parameter θE
ithat determines the adjustment of employment to the demand of hours
worked: core countries observe a sluggish response of employment to the cycle while the mirror
image is seen for periphery. Still regarding the labor market, wage rigidity and indexation para-
meters are also higher in core countries suggesting that core countries are farther from the optimal
allocation characterized by flexible wages and prices. However this interpretation is nuanced by
Gal´ı (2013) showing that wage rigidities can, in some particular situations, play a stabilizing role
for the economy. One of these particular situations exposed by Gal´ı (2013) is a monetary policy
weakly oriented toward inflation which can be observed when monetary policy has hit its lower
bound. In the light of this new reinterpretation that meets the current situation of the Euro Area,
wages and employment rigidities of core countries may have been stabilizing frictions since the
financial crisis episode in 2009.
25The ESRB offers on its website an interactive map of the Euro Area on countercyclical capital buffers. To this
date, only Sweden and Norway have activated the CCB rate in the European Union but both of these countries are
not Euro Area participants.
26The posterior distribution combines the likelihood function with prior information. To calculate the posterior
distribution to evaluate the marginal likelihood of the model, the Metropolis-Hastings algorithm is employed. We
compute the posterior moments of the parameters using a sufficiently large number of draws, having made sure
that the MCMC algorithm converged. To do this, a sample of 250,000 draws was generated for four chains through
parallelization, neglecting the first 50,000. The scale factor was set in order to deliver acceptance rates of between
20 and 30 percent for each chain. Convergence was assessed by means of the multivariate convergence statistics
taken from Brooks and Gelman (1998). We estimate the model using the dynare package of Adjemian et al. (2011).
We provide in the online appendix the bayesian IRF of the model which are all fairly consistent with VAR-type
models evidence.
15
Third, the results related to market integration are in line with the standard empirical evi-
dence. In particular, peripheral economies are more open and dependent to the core area than
the opposite, except for interbank facilities. This latter result is hard to reconcile with the empi-
rical evidence as, before the financial crisis, peripheral economies where net recipient of interbank
loans that fueled the property boom. This could be a limitation of the analysis conducted here,
however by summing both the net entry of corporate and interbank loans, our model predicts
that peripheral economies were net recipient of loans consistently with the historical experience
of the Euro Area.
4. The performance of Macroprudential Policy
4.1. The suboptimality of the federal solution
The countercyclical capital buffer (CCB, henceforth), as defined in the Basel III accords (2010)
and ESRB handbook (2014), is an instrument designed to contain the procyclicality of the financial
sector. It is aimed at building up a capital buffer when threats to resilience are high or during
periods of excessive credit growth and can be released when systemic risks abate. The ESRB has
selected the credit-to-gdp gap as a leading indicator to signal upcoming crises that the CCB is
meant to mitigate. A natural translation of the CCB’s objective in our setup corresponds to the
minimization of the variance of the credit-to-gdp ratio in the monetary union:27
L=σ2
L/Y +λYσ2
Y+λνσ2
ν,(17)
where σ2
L/Y ,σ2
Yand σ2
νdenote respectively the unconditional variance of the credit-to-gdp ratio,
output and policy tool νi,t while parameters λYand λνare weights on output and CCB. This
ad-hoc loss function Lborrowed from Angelini et al. (2014) is obtained as a weighted average of
national loss functions for each area. It is defined as, L=nLc+ (1 −n)Lp, where for each country
the national loss is given by, Li=σ2
i,L/Y +λYσ2
i,Y +λνσ2
i,ν . Noticeably, as our model features
an interbank market, the credit-to-gdp ratio is given by the aggregate credit supply divided by
output: ctgi,t=(Ls
i,t + (1 −λ)IBs
i,t)/Yi,t. As Angelini et al. (2014), we assume that λν=0.10 and
λY=0, however in a robustness section we investigate whether our results are sensitive to this
calibration.
Using the criterion (17), we are able to perform a similar exercise as Angelini et al. (2014)
by ranking macroprudential policies selecting CCB rule’s coefficients [ρυ
c,ρυ
p,φc,φp] that deliver
the smallest loss. We search over a four-dimensional grid over parameters ranges [0,1) for ρυ
i
and [0,5] for φi. As a benchmark for comparing our scenarios for CCB implementation, we
consider the optimal monetary policy situation characterized by the optimized Taylor rule that
maximizes the welfare of households living in the monetary union. Put differently, the interaction
between monetary and macroprudential policy follows a Stackelberg game where monetary policy
is leader by removing nominal inefficiencies in the Euro area through the refinancing rate, followed
afterward by macroprudential policy which dampens financial cycles. Optimal monetary policy is
27We are aware that the minimization of a loss function rather than a micro-founded welfare criterion is a
limitation of our analysis. However, it is also well-known that the usual welfare criterion weakly portrays the trade-
off faced by macroprudential authorities between macroeconomic and financial stabilization. A macroprudential
policy maximizing the welfare index reduces inflation to the detriment of the financial system which experiences
higher volatilities for credit supply and spreads. In response, Woodford (2012) employs an ad hoc loss function that
fairly portrays the objective of macroprudential policy. Most of the literature follows Woodford’s approach, such as
Darracq-Pari`es et al. (2011) and Angelini et al. (2014).
16
based on a second order approximation to equilibrium conditions of the model as in Schmitt-Groh´e
and Uribe (2007) using estimated parameters of Table B.7.28 Optimal weights in the Taylor rule
are respectively ρ=0.99, φπ=4.38, φ∆y=0.5.
Finally, the minimization of the variance of the credit-to-GDP gap can be re-interpreted
through an allocation problem for authorities. Entrepreneurs’ distorted beliefs generate over-
borrowing decisions which inefficiently amplify the cycle. By so, entrepreneurs do not internalize
their contribution to the financial amplification. Authorities thus implement a capital requirement
policy which can be seen as a Pigouvian tax on banks aiming at internalizing the increase of the
social cost through higher lending rates to entrepreneurs.29 Thus the financial amplification is
measured here through the variance of the credit-to-GDP ratio.
We evaluate the stabilization performance of each macroprudential policy scheme by minimi-
zing the second order loss function defined in Equation 17 subject to linear equilibrium conditions
of the estimated model.
Table 2
Loss-based ranking of different macroprudential policy implementation schemes
Optimal Stances Loss
Scheme ρυ
cφcρυ
pφpL LcLp
Loan Supply Targeting
1.a Union-wide loan supply 0.59 5.2 0.28 4.6 5.4076 3.9097 7.4761
1.b National loan supply 0.96 2.2 0.91 1.97 0.0071 0.0078 0.0062
Loan Demand Targeting
2.a Union-wide loan demand 0.46 2.64 0.49 1.25 5.4787 3.9577 7.5791
2.b National loan demand 0.16 2.55 0.96 2.79 0.67336 0.46427 0.9621
Capital Inflows Targeting
3. Capital Inflows 0.53 2.36 0.15 0.57 19.7407 13.5852 28.241
Table 2 reports the policy stance and the stabilizing performances for each implementation
scheme. The optimal stabilization of the financial system critically depends on the target selected
by macroprudential authorities. Unsurprisingly, we observe a clear ranking favoring operational
instruments reacting to national loan developments (schemes 1.b and 2.b) that outperforms solu-
tions based on federal loan developments (schemes 1.a and 2.a).
A natural question is thus to determine the degree of mutual financial cross-border lending
flows that should be observed to affect this main conclusion. Indeed, as underlined by Cecchetti
and Tucker (2016) and Beck et al. (2016) a higher banking integration should require a common
prudential standard (here, the targeting rule) applied appropriately to all parts of the financial
system. As a consequence, the efficiency of federal targeting rules (i.e. schemes 1.a and 2.a) is
expected to increase with the share of cross-border loans while national adjusted should be less
efficient. To investigate this question, Figure 3 reports minimized loss functions for different levels
28In the quantitative simulation, we first search for weights attached to inflation φπ, GDP growth φ∆yand the
smoothing degree ρin the Taylor rule that gives the highest unconditional welfare of households from Equation B.1.
Based on the grid search by 0.01 unit, we limit our attention to policy coefficients in the interval (1,5] for φπ, [0,0.5]
for φ∆y(Schmitt-Groh´e and Uribe,2007), and in the interval [0,0.99] for ρto speed up optimization routines. We
take into account the zero-lower bound by adding a penalty term in the welfare index associated to the variance of
the nominal interest rate following the calibration of Woodford (2003).
29We refer to Jeanne and Korinek (2013) for the implementation of macroprudential measures through a social
planner problem.
17
00.1 0.2 0.3 0.4 0.5
0
0.5
1
1.5
2
2.5
banking openness αL
i=αIB
i
loss function L
00.1 0.2 0.3 0.4 0.5
0
0.5
1
1.5
2
2.5
corporate credit only αL
i
loss function L
1a - union-wide loan supply 1b - national loan supply
2a - union-wide loan demand 2b - national loan demand
00.1 0.2 0.3 0.4 0.5
0
0.5
1
1.5
2
2.5
interbank credit only αIB
i
loss function L
Note: for each value of the share of foreign loans in the portfolio of entrepreneurs (denoted αL
i) and banks (denoted αIB
i),
we compute the optimal macroprudential policy for four different schemes. The loss function is an average between core
and periphery detailed in Equation 17. Capital inflows-adjusted policy is not reported as its loss is too high compared to
alternative schemes.
Figure 3: The role of cross-border banking in the scheme ranking.
of cross-border loans. Three component are presented related to an increase in total (namely the
sum of corporate and interbank) cross-border loans in the left panel, in corporate loans only in
the center panel and in interbank loans only in the right panel.
We can draw three main conclusions from Figure 3. First, the interest of conducting federal
based definition of the credit-to-gdp ratio unsurprisingly increases with the size of cross-border
flows. As reported in the first panel, the relative interest of implementing a national adjusted
rule (such as 1.b and 2.b) is magnified with respect to the federal adjusted rule for lower values
of αL
iand αIB
i. However for values of these parameters higher than 25%, the gap in the loss
function values tends to decrease significantly. Nevertheless, macroprudential rules based on a
federal definition of the credit to GDP ratio becomes only interesting for a mutual cross-border
lending openness lying around 45%. This figure is rather high with respect to the current value
of cross-border lending, which makes this solution not optimal for the moment.
Second, this policy outcome regarding the reduction in the loss function under a federal
definition of the credit-to-gdp ratio is mainly driven by the mutual openness of the corporate
credit markets. As reported in the center and right panels, interbank cross-border lending credit
has no noticeable impact on the relative ranking of policy solutions, while the integration of the
corporate loan segment determines the slope of the decrease in the loss function under the federal
solution.
Third, even if banking integration clearly enhances the stabilization performances of federal-
adjusted schemes, a macroprudential solution targeting the national credit supply remains re-
markably efficient with a global banking system. For the all spectrum of values of αL
iand αIB
i
displayed in panels of Figure 3, CCB reaction to a national definition of the credit-to-gdp ratio
determines the lowest value for the loss function. Thus, our experiments suggest that even if
cross-border linkages are high enough to justify the implementation of a federal adjusted solution,
the reaction to national lending conditions remains optimal.
18
4.2. Contrasting national solutions
As underlined in Table 2 our numerical results suggest that the best outcome for the loss
function value is obtained when macroprudential policy targets the national supply of loans
instead of the national demand for loans (i.e., accounts for the national and foreign nature of
loans contracted in the economy). The interest of targeting loan supply is easily understandable,
as the transmission channel of macroprudential policy directly impacts the marginal cost of loan
production and, by so, financial intermediaries. If macroprudential policy targets loan demand,
this direct channel is dampened, which leads to a lower reduction of the loss function. National
macroprudential policies reacting to federal averages do not target the origin of financial imba-
lances as regional divergences in credit cycles are too important to have a single federal target.
The solution focusing on cross-border lending developments (3), is clearly dominated by all the
other implementation schemes: in this case, the loss function reaches its highest value, revealing
that targeting external imbalances is not appropriate as it does not take into account the financial
roots of the problem.
To understand these results we simulate the dynamic responses to a negative productivity
shock in core countries and a negative net wealth shock in peripheral economies.30 We concentrate
on these two shocks as they are leading drivers of the loan-to-gdp ratio that authorities aim at
stabilizing through capital buffer measures.
First, Figure 4 reports the IRFs after a negative productivity shock for each CCB rule with
respect to the optimal monetary policy situation. Under the benchmark of an optimal monetary
policy (dashed lines), a negative home productivity shock depresses investment and activity and
implies inefficient fluctuations in the credit-to-gdp ratio. This shock translates to the peripheral
region through trade channels, cross-border lending, monetary policy reaction and shock corre-
lation. The introduction of national macroprudential measures has a clear stabilizing effect for
business cycles of the monetary union. The release of the buffer eases the bank capital constraint
which in turn lowers credit spreads and investment fluctuations. However, the targeting regime
determining the CCB rate critically affects the outcome the economy that does not experience
the shock and explains the effectiveness of national credit targeting regimes over federal ones. In
a federal targeting regime (1.a and 2.a), both countries react to a common average credit-to-gdp
ratio which leads the foreign country to react procyclically to foreign shocks. In addition, we
do not find clear differences between targeting national credit demand or supply. Finally CCB
rates adjusted to capital inflows fail at providing macroeconomic stability in particular for the
peripheral country. The shock in the core country generates a re-allocation of credit from core
to peripheral economies and authorities in peripheral economies procyclically tighten the capital
constraint which inefficiently amplifies the crisis.
Second, Figure 5 depicts the IRFs after a negative stock market shock in peripheral econo-
mies. Under the optimal monetary policy benchmark (dashed lines), this shock deteriorates the
borrowing conditions of entrepreneurs, thus incurring a large decline in output and investment
through the external finance premium channel. Consequently, the credit-to-gdp gap experiences
a large decline inefficiently driven by the biased expectations of entrepreneurs. Our main results
regarding the implementation of macroprudential measures are similar to the productivity shock.
National credit targeting is preferred to a federal one as the latter exacerbates fluctuations for
the country that does not experience the shock, creating a spillover effect. The same procyclical
mechanism is observed for the capital inflows targeting scheme. Finally, targeting the demand or
30As underlined by Angelini et al. (2014), supply shocks may dominate in normal times, while financial shocks
are important in exceptional times.
19
0 5 10 15
−0.6
−0.4
−0.2
0
core
output ˆyc,t
0 5 10 15
−1.5
−1
−0.5
0
credit-to-gdp ratio ˆ
ctgc,t
0 5 10 15
−1.5
−1
−0.5
0
investment ˆ
ic,t
0 5 10 15
0
1
2
3
·10−2
spread ˆrL
c,t −ˆrt
0 5 10 15
−6
−4
−2
0
capital buffers ˆνc,t
0 5 10 15
−0.1
−0.05
0
periphery
output ˆyp,t
0 5 10 15
−0.5
0
credit-to-gdp ratio ˆ
ctgp,t
0 5 10 15
−0.1
0
0.1
investment ˆ
ip,t
Optimal MoPo
Optimal MoPo + MAP (supply union)
Optimal MoPo + MAP (supply national)
0 5 10 15
−1
−0.5
0·10−2
spread ˆrL
p,t −ˆrt
0 5 10 15
−2
−1
0
capital buffers ˆνp,t
0 5 10 15
−0.6
−0.4
−0.2
0
core
output ˆyc,t
0 5 10 15
−1.5
−1
−0.5
0
credit-to-gdp ratio ˆ
ctgc,t
0 5 10 15
−1.5
−1
−0.5
0
investment ˆ
ic,t
0 5 10 15
0
1
2
3
·10−2
spread ˆrL
c,t −ˆrt
0 5 10 15
−6
−4
−2
0
capital buffers ˆνc,t
0 5 10 15
−0.1
−0.05
0
periphery
output ˆyp,t
0 5 10 15
−0.5
0
credit-to-gdp ratio ˆ
ctgp,t
0 5 10 15
−0.1
0
0.1
investment ˆ
ip,t
Optimal MoPo
Optimal MoPo + MaPru (demand union)
Optimal MoPo + MaPru (demand national)
0 5 10 15
−1
−0.5
0·10−2
spread ˆrL
p,t −ˆrt
0 5 10 15
−3
−2
−1
0
capital buffers ˆνp,t
0 5 10 15
−0.6
−0.4
−0.2
0
core
output ˆyc,t
0 5 10 15
−1.5
−1
−0.5
0
credit-to-gdp ratio ˆ
ctgc,t
0 5 10 15
−1.5
−1
−0.5
0
investment ˆ
ic,t
0 5 10 15
0
1
2
3
·10−2
spread ˆrL
c,t −ˆrt
0 5 10 15
−2
−1
0
capital buffers ˆνc,t
0 5 10 15
−0.1
−0.05
0
periphery
output ˆyp,t
0 5 10 15
−0.6
−0.4
−0.2
0
credit-to-gdp ratio ˆ
ctgp,t
0 5 10 15
−0.1
−0.05
0
investment ˆ
ip,t
Optimal MoPo
Optimal MoPo + MaPru (capital inflows)
0 5 10 15
−4
−2
0
·10−3
spread ˆrL
p,t −ˆrt
0 5 10 15
−0.2
0
0.2
0.4
capital buffers ˆνp,t
Figure 4: System response to an estimated negative productivity shock in core countries ηA
c,t measured in per-
centage deviations from steady state under different macroprudential policy rules (domestic or union-wide sup-
ply/demand/inflows targeting).
20
0 5 10 15
−0.1
0
0.1
0.2
core
output ˆyc,t
0 5 10 15
−1
0
1
credit-to-gdp ratio ˆ
ctgc,t
0 5 10 15
0
0.5
1
investment ˆ
ic,t
0 5 10 15
−6
−4
−2
0
·10−2
spread ˆrL
c,t −ˆrt
0 5 10 15
−15
−10
−5
0
capital buffers ˆνc,t
0 5 10 15
−0.4
−0.2
0
periphery
output ˆyp,t
0 5 10 15
−4
−2
0
credit-to-gdp ratio ˆ
ctgp,t
0 5 10 15
−3
−2
−1
0
investment ˆ
ip,t
Optimal MoPo
Optimal MoPo + MAP (supply union)
Optimal MoPo + MAP (supply national)
0 5 10 15
−0.1
−0.05
0
0.05
spread ˆrL
p,t −ˆrt
0 5 10 15
−30
−20
−10
0
capital buffers ˆνp,t
0 5 10 15
−0.1
0
0.1
0.2
core
output ˆyc,t
0 5 10 15
−1
0
1
credit-to-gdp ratio ˆ
ctgc,t
0 5 10 15
0
0.5
1
investment ˆ
ic,t
0 5 10 15
−4
−2
0·10−2
spread ˆrL
c,t −ˆrt
0 5 10 15
−15
−10
−5
0
capital buffers ˆνc,t
0 5 10 15
−0.4
−0.2
0
periphery
output ˆyp,t
0 5 10 15
−4
−2
0
credit-to-gdp ratio ˆ
ctgp,t
0 5 10 15
−3
−2
−1
0
investment ˆ
ip,t
Optimal MoPo
Optimal MoPo + MaPru (demand union)
Optimal MoPo + MaPru (demand national)
0 5 10 15
−0.1
−0.05
0
0.05
spread ˆrL
p,t −ˆrt
0 5 10 15
−30
−20
−10
0
capital buffers ˆνp,t
0 5 10 15
−0.3
−0.2
−0.1
0
core
output ˆyc,t
0 5 10 15
−3
−2
−1
0
credit-to-gdp ratio ˆ
ctgc,t
0 5 10 15
−1.5
−1
−0.5
0
investment ˆ
ic,t
0 5 10 15
0
2
4
6
·10−2
spread ˆrL
c,t −ˆrt
0 5 10 15
0
5
10
capital buffers ˆνc,t
0 5 10 15
−0.4
−0.2
0
periphery
output ˆyp,t
0 5 10 15
−4
−2
0
credit-to-gdp ratio ˆ
ctgp,t
0 5 10 15
−3
−2
−1
0
investment ˆ
ip,t
Optimal MoPo
Optimal MoPo + MaPru (capital inflows)
0 5 10 15
−2
0
2
4
·10−2
spread ˆrL
p,t −ˆrt
0 5 10 15
−6
−4
−2
0
capital buffers ˆνp,t
Figure 5: System response to an estimated negative firms net wealth shock in peripheral countries ηN
p,t measu-
red in percentage deviations from steady state under different CCB regulation schemes (domestic or union-wide
supply/demand/inflows targeting).
21
supply of credit provides very similar responses.
Table 3
Macroeconomic performances of different implementation schemes in comparison to the optimal policy benchmark
Standard deviations (%) Correlation
Core Periphery
Scheme ˆyc,t ˆ
ls
c,t iˆ
bc,t ˆsL
c,t ˆyp,t ˆ
ls
p,t iˆ
bp,t ˆsL
c,t corr(ˆyc,t,ˆyp,t)
Monetary Policy Only
Benchmark 100 100 100 100 100 100 100 100 0.15
Loan Supply Targeting
1.a Union-wide loan supply 91.57 91.95 75.11 127.47 103.88 113.45 73.86 105.96 0.15
1.b National loan supply 79.67 76.60 74.48 130.46 95.06 86.19 73.93 120.19 0.46
Loan Demand Targeting
2.a Union-wide loan demand 91.58 92.06 75.1 127.29 103.79 112.92 73.96 105.58 0.16
2.b National loan demand 82.89 92.94 71.73 137.08 76.24 63.42 76.19 116.41 0.44
Capital Inflows Targeting
3 Capital Inflows 93.42 138.3 73.27 156.67 96.33 79.92 88.94 90.46 0.37
Accounting for all shocks of the model, Table 3 reports the standard deviation of activity,
corporate and interbank loans and interest rate spread under alternative policy schemes. We
contrast our results with respect to the optimal monetary policy (without prudential regulation)
to measure how the conduct of macroprudential measures have decreased/increased the standard
deviation of endogenous variables for each country. This exercise measures how the stabilizing
gains are distributed between countries. We also report business cycle synchronization statistics,
as measured by the correlation of output between economies, to evaluate whether the scheme is
able to smooth the heterogeneity between Euro Area participants.
Overall, the highest gains can be obtained by adopting macroprudential policy measures re-
acting to national developments in the credit-to-gdp ratio. The reaction of the macroprudential
instrument to other measures of the credit-to-gdp ratio (based on either loan demand or federal
averages) leads to less reduction in the standard deviation of these aggregates. However, the im-
plementation of macroprudential policy is not a free lunch since the building up of a capital buffer
mechanically increases the volatility of the spread when stabilizing the debt-to-GDP ratio.31
In addition, we observe a natural link between loan-to-GDP stabilization and business cycle
synchronization, showing that the implementation of national-adjusted macroprudential policies
smooths the heterogeneity across regions. Such a result is interesting for monetary policy makers,
as the effectiveness of a single monetary policy critically depends on business cycle synchronization
between monetary union participants. Thus the enhanced cycle synchronization partially solves
the Euro Area’s problem of a “one-size-fits-all” monetary policy.
Contrasting the national demand and national supply targeting solutions, we find that their
effectiveness are clearly different according to the country considered. As an example, the supply
side oriented policy fits the situation of core economies, while the one oriented towards the demand
of credit meets the situation of peripheral economies in terms of macroeconomic stabilization. Core
31The variability of the lending spread is a leading indicator of financial distress, Woodford (2012) sets its
stabilization as an objective for monetary policy making with financial frictions.
22
countries should thus focus on the stabilization of its banks while peripheral economies should
stabilize its borrowers. Having asymmetric targets between regions of the Eurozone could be an
interesting perspective to implement stabilization policies.
Finally the capital inflows targeting solution fits well peripheral economies that were net
recipient of foreign claims before the 2009 crisis. However, this policy is harmful for core countries,
affected by an increase in the volatility of loans and of the credit spread. Over the sample time
period, core countries were net exporter of loans by fueling property booms in peripheral economies
through interbank lending, this capital outflow involves an inefficient and durable reduction of
the CCB rate enhancing the volatility of credit domestically. While capital controls appears to
be a promising tool for Periphery, it is clearly unsuited to countries experiencing capital outflows.
5. Additional sensitivity analysis
This section assesses the robustness of our results with respect to some key parameters of the
model and to the nature of shocks encountered in the economy.
5.1. Loss function calibration
Table 4
Sensitivity analysis of scheme ranking to different calibrated parameters
Euro area loss L
1.a 1.b 2.a 2.b 3
Loss output stabilization λy= 0 5.4076 0.0071 5.4787 0.67336 19.7407
λy= 5 6.0138 0.4063 5.9196 1.0906 16.7659
λy= 10 6.5325 0.8036 6.5119 1.5042 20.8989
Loss policy instrument λν= 0 5.4063 0.0004 5.5147 0.66152 19.9706
λν= 5 5.7099 0.28443 5.7186 0.97562 20.1045
λν= 10 5.9328 0.53581 5.9252 1.1936 20.4273
Loan substitutability ν, ξ = 0 5.5082 0.0072 5.4190 0.67025 19.7962
ν, ξ = 5 5.5206 0.0068 5.5392 0.6914 20.2309
ν, ξ = 10 5.5372 0.0067 5.5298 0.7056 20.9558
Share of core countries n= 0.4 5.5641 0.0069 5.5485 0.0868 19.0729
n= 0.5 5.6804 0.0069 5.7378 0.3138 19.7849
n= 0.6 5.4134 0.0071 5.4053 0.78181 20.2335
Flexible interest rates θL
i= 0 5.9139 0.0058 5.8096 0.65304 17.8474
θD
i= 0 5.8987 0.0074 5.8685 0.66579 16.6966
θL
i=θD
i= 0 5.9067 0.0059 5.8446 0.66382 21.3504
Note:λyand λνdenote respectively weights on output and policy tool volatities in the macroprudential loss function, νis
the substitution degree between home and foreign credit varieties and ndenotes the share of core countries in terms of real
GDP in the euro area. Losses are evaluated using the average of core and peripheral countries volatilities.
First, Table 4 reports the sensitivity analysis of the main results to the calibrated value of
some underlying parameters. The first experiments focus on the weight parameters of the loss
function of macroprudential authorities. As reported, the ranking of policies remain unaffected
by the value of these parameters. An increase in the policymakers preferences for output (denoted
λy) or the penalization of the variance of capital requirements (denoted λν) increases the loss.
Turning to structural parameters (namely the degree of substitutability between different varieties
of loans νand nthe share of core countries in the monetary union) the sensitivity analysis does
not alter the ranking of macroprudential decisions. As observed, an increase in the size of the
core countries’ group has opposite results on the value of the loss, depending on the dimension of
23
the credit-to-gdp ratio that is taken into account in the reaction of macroprudential policy. The
loss decreases for schemes based on a reaction to national loan developments while it increases
when the macroprudential instrument reacts to the federal value of the ratio. However, the gap
between the loss values remain so high that the ranking between national and federal solutions
is left unaffected. Regarding the nominal rigidities on interest rates, thus reflecting the imperfect
pass-through of both monetary and macroprudential policies, disabling this nominal friction does
not affect the ranking too.
5.2. Nature of shocks
Table 5
Robustness check: optimal monetary and macroprudential Policies conditional on shocks
Monetary Macroprudential Loss
Policy Policy Union Core Periph
Scheme ρ φπφ∆yρυ
cφcρυ
pφpLuLcLp
Supply Shocks
1.a Union-wide loan supply 0.94 5 0.5 0.82 0.30 0.41 3.86 1.3139 0.95417 1.8107
1.b National loan supply 0.94 5 0.5 0.95 2.72 0.86 2.58 0.0027 0.0041 0.0007
2.a Union-wide loan demand 0.94 5 0.5 0.90 3.54 0.39 0.50 1.3189 0.95679 1.819
2.b National loan demand 0.94 5 0.5 0.46 2.49 0.48 2.46 0.065797 0.04746 0.091119
3 Capital Inflows 0.94 5 0.5 0.81 3.63 0.43 0.98 1.9538 1.5535 2.5065
Demand Shocks
1.a Union-wide loan supply 0.99 1 0.5 0.66 3.07 0.62 2.16 0.20432 0.14956 0.27993
1.b National loan supply 0.99 1 0.5 0.94 2.52 0.64 2.52 0.0035 0.0039 0.0029
2.a Union-wide loan demand 0.99 1 0.5 0.58 2.61 0.39 2.37 0.2051 0.1504 0.2806
2.b National loan demand 0.99 1 0.5 0.05 2.35 0.80 2.69 0.7980 0.5139 1.1903
3 Capital Inflows 0.99 1 0.5 0.76 3.68 0.08 0.41 12.7015 11.5068 14.3513
Financial Shocks
1.a Union-wide loan supply 0 1.48 0.5 0.15 1.60 0.24 3.35 0.5895 0.4308 0.8086
1.b National loan supply 0 1.48 0.5 0.92 2.21 0.94 1.66 0.0023 0.0014 0.0035
2.a Union-wide loan demand 0 1.48 0.5 0.06 1.94 0.26 3.58 0.5900 0.4301 0.8107
2.b National loan demand 0 1.48 0.5 0.98 1.72 0.85 1.37 0.0054 0.0038 0.0077
3 Capital Inflows 0 1.48 0.5 0.30 0.47 0.96 4.63 2.6168 2.1119 3.3141
Note: each group of shocks is composed of core and peripheral shocks and their associated cross-correlation. Supply shocks
group gathers productivity shocks ηA
i,t; Demand shocks group gathers spending ηG
i,t, preferences ηU
i,t and investment ηI
i,t;
Financial shocks gathers collateral crunch ηN
i,t, riskiness ηQ
i,t and deposit cost-push ηD
i,t innovations.
Second, Table 5 reports the sensitivity analysis of the main results to the nature of shocks
encountered in the economy. We distinguish between supply (productivity shocks), demand (gat-
hering public spending shocks, preference shocks and investment shocks) and financial shocks
(gathering shocks on the collateral of corporate lending, on riskiness of investment projects and
cost push shocks on deposit). As underlined by Angelini et al. (2014), supply and demand shocks
may dominate in normal times, while financial shocks are important in exceptional times. For
each shock, we contrast the consequences of adopting one of the macroprudential scheme adopted
for the definition of the credit-to-gdp ratio (1a to 3). As observed, the relative ranking of the
policy scheme is not altered by the nature of shocks encountered in the economy, as the solution
based upon the reaction of authorities to the fluctuations in the national loan supply to GDP
dominates all the other possibilities. However, the value of the loss fluctuates and it is higher
for financial shocks. Furthermore, a closer look at the macroprudential parameters shows that
24
the nature of the shock affects the contemporaneous policy stance of regional authorities. As
observed, for real shocks, the contemporaneous reaction of core countries authorities tends to be
higher for supply shocks while peripheral countries are more reactive for demand shocks. This
latter feature is also observed for exceptional times.
5.3. Structural financial asymmetries
Table 6
Sensitivity analysis of scheme ranking to financial structural asymmetries
Euro area loss L
1.a 1.b 2.a 2.b 3
Benchmark 5.4076 0.0071 5.4787 0.67336 19.7407
Firms rate of default 1 −¯ηE
p= 0.0125 6.6312 0.0078 6.6535 0.58638 22.6661
Share of illiquid banks λp= 0.48 6.0702 0.0078 6.3512 1.9242 21.7665
Corporate net wealth-to-assets ratio ¯
Np/¯
Kp= 0.2 7.4030 0.0070 7.3528 0.55023 22.8376
Bank leverage ratio BKc/¯
Ac= 0.06 6.5421 0.0163 6.5513 0.64037 19.651
Third, we investigate whether structural asymmetries affect the ranking of the model, results
are reported in Table 6. In the benchmark setup developed in the paper, we assumed that most
of the endogenous variables in the deterministic steady state were symmetric between countries.
However this assumption is questionable, in particular regarding the asymmetries in the financial
sector which may be an important feature for macroprudential policymaking. As a first exercise,
we examine whether the symmetry assumption on the default rate of entrepreneurs matters for
the scheme ranking. Since we cannot observe the default rate of entrepreneurs, we use as a proxy
the share of non-performing loans in the balance sheet of banks in BankScope database. We find
that the share of non-performing loans is on average twice higher in Periphery and calibrate the
defaulting share of entrepreneurs accordingly. We find that this structural asymmetry does not
affect the ranking, however we observe a small reduction of the gap between the demand-adjusted
and the supply-adjusted macroprudential policy. We also investigate the implications of cross-
country heterogeneity in the share of illiquid banks operating in the interbank market. We proxy
this parameter through the number of banks borrowing on the unsecured money market provided
by Garcia-de Andoain et al. (2014). We find that on average the share of banks borrowing on
the interbank market is 25% higher in Periphery, we calibrate λPaccordingly in our model.
The new ranking obtained from the new set of simulations show no important difference, except
for the national demand solution which becomes less efficient in stabilizing the credit-to-gdp
ratio. We also investigate the implication of asymmetric steady state leverages of firms and of
banks between countries. Core countries observed a lower net-worth-to-asset ratio than Peripheral
economies for firms,32 we take this feature into account by calibrating ¯
Np/¯
Kpat 20% as in
Italy. For banks, we use the ECB’s Risk Assessment Indicators (RAI) and find that Core banks
are less capitalized on average, in particular because of Belgium, Germany and Netherlands’s
low equity to assets ratios. We calibrate the leverage ratio of core banks to 6% to incorporate
this structural asymmetry and run the simulations. We observe no clear ranking change under
these two asymmetries. Overall, these robustness exercises confirm that these structural aspects
32There is a clear asymmetry between Core and Peripheral countries in terms of debt-to-financial assets ratios.
For instance, France had a ratio of 40%, Germany 60% and Netherlands 60% while Italy had 80% and Spain 60%.
25
does not affect the ranking as second order statistics minimized in the loss function are rather
independent of structural asymmetries.
6. Conclusion
This paper shows that international lending flows have mixed effects on the optimal conduct of
macroprudential policy in the Eurozone. Contrasting alternative rules for countercyclical capital
buffers, our results suggest that targeting a national credit-to-gdp ratio should be favored to federal
averages as this rule induces better stabilizing performances in terms of output and loan volatility.
The important divergences in credit cycles between core and peripheral countries reported in
the data require a national orientation of macroprudential policy tailored to domestic financial
developments. Our results have also underlined the reduced interest of lifting up macroprudential
policymaking to the supra-national level. Indeed, national capital buffers reacting to the union-
wide loan-to-GDP ratio lead to the same stabilization results than the one obtained under the
national reaction when mutual cross-border lending reaches 45%. However, even if cross-border
linkages are high enough to justify the implementation of a federal adjusted solution, the reaction
to national lending conditions remarkably remains optimal. In addition, we find that adjusting
the macroprudential instrument to capital inflows is a promising tool for countries experiencing
loans inflows.
The analysis of cross-border lending on the conduct of macroprudential policy is a burgeoning
research area. In this paper we focused on countercyclical capital buffers, and an interesting
question for future research is to evaluate how this result favoring self-oriented macropruden-
tial measures may be affected by the choice of alternative macroprudential instruments. The
construction of an original welfare index, that features a trade-off between macroeconomic and
financial stability, could be a next step of research. Finally, the analysis of the CCB rate through
a Ramsey allocation problem could also be part of a future research agenda.
Acknowledgments
We are very grateful to the editors and three anonymous referees for their helpful comments
that helped us to improve significantly the paper. We thank Taryk Bennani, Ambrogio Cesa-
Bianchi, Jean-Bernard Chatelain, Laurent Clerc, Patrick F`eve, Julien Idier, Christoffer Kok,
John Lewis, Pier Lopez, Marco Ratto, Karl Walentin and Raf Wouters for their comments. We
are grateful to Johannes Pfeifer for providing codes for optimal policy rules with restrictions. We
thank Jean-Pierre Allegret, Manuel Mota Freitas Martins and Tovonony Razafindrabe for their
discussions as well as participants at the conference in International Macroeconomics in Paris,
the Conference in Computational Economics, the International Symposium in Money Credit and
Banking in Lyon, the French Economic Association annual meeting in Lyon and seminars at the
Bank of England and the Banque de France. This paper was written while Gauthier Vermandel
was working for European Central Bank, DG Macroprudential Policy and Financial Stability,
Macro-Financial Linkages Division. We remain responsible for any errors and omissions.
Appendix A. Data sources
Gross domestic product: millions of national currency, current prices, quarterly levels,
seasonally adjusted - sources Eurostat.Private final consumption expenditure: millions of
national currency, current prices, quarterly levels, seasonally adjusted - sources Eurostat.Gross
26
fixed capital formation: millions of national currency, current prices, quarterly levels, seaso-
nally adjusted - sources Eurostat.GDP deflator: Deseasonalized using a multiplicative decom-
position - sources Eurostat.Loans to Non-Financial corporations: Index of Notional Stocks,
Total maturity, Euro area (changing composition) counterpart, Deseasonalized using a multipli-
cative decomposition, monthly data (aggregated to get quarterly data) - sources ECB (internal
backcasted series).Loans to MFIs: Index of Notional Stocks, Total maturity, Euro area (chan-
ging composition) counterpart, Deseasonalized using a multiplicative decomposition, monthly
data (aggregated to get quarterly data) - sources ECB (internal backcasted series).Borrowing
cost: monthly (taken in average to get quarterly data), Credit and other institutions (MFI except
MMFs and central banks); Loans up to 1 year; BS counterpart sector: Non-Financial corporations
(S.11); Outstanding amount - sources ECB (internal backcasted series).Deposit rate: monthly
(taken in average to get quarterly data), Firms and Households; - sources ECB (internal backcas-
ted series). Money market rates: money market interest rates, one year maturity, quarterly
data - sources Eurostat.
Appendix B. The non-banking part of the model
We extend the model of Poutineau and Vermandel (2015) to account for the conduct of
macroprudential policy in an heterogenous monetary union such as the Euro Area. Our model
describes a monetary union made of two asymmetric countries i∈ {c, p}(where cis for core and p
for periphery). Each part iof the monetary union is of a relative size ni.33 As shown in Figure 2,
each country is populated by consumers, intermediate and final producers, entrepreneurs, capital
suppliers and a banking system. Regarding the conduct of macroeconomic policy, we assume na-
tional fiscal authorities and a common central bank. The implementation of the macroprudential
policy is left open, and will be discussed below in another section. Our model is confronted to
the data using Bayesian econometrics and it encompasses several sources of rigidities to enhance
its empirical relevance. The set of real rigidities accounts for consumption habits, investment
adjustment costs and loan demand habits. Regarding nominal rigidities, we account for stickiness
in final goods prices and loan interest rates.
Appendix B.1. Households and labor unions
The preferences of the jth household are given by:
EtX∞
s=0βτexp(εU
i,t+s)log Ci,t+s−hC
iCi,t−1+s−χi
(1 + σH
i)H1+σH
i
i,t+s,(B.1)
where Etdenotes the expectation operator, β∈(0,1) is the discount factor, parameter σH
i>0
shapes the utility function of the jth household associated to hours worked Hi,t. The consumption
index Ci,t is subject to external habits with degree hC
i∈[0; 1) with Ci,t−1the aggregate lagged
consumption, while χi>0 is a shift parameter allowing us to pin down the steady state amount
of hours worked. The discount factor is affected by a time-preference shock εU
i,t following an
AR(1) stochastic process that exogenously changes the household’s intertemporal allocation of
consumption over the cycle.
33Normalizing the size of the monetary union to unity, the relative size of the core are is nand the relative size
of the peripheral area is 1 −n.
27
Household jth period budget constraint is given by:
wh
i,tHi,t +Dd
i,t−11 + RD
i,t−1
(1 + πC
i,t)+ Πi,t =Ci,t +Dd
i,t +ti,t +pi,tACD
i,t.(B.2)
The income of the representative household is made of labor income with the desired real wage
wh
i,t,34 interest payments for deposit services Dd
i,t and real earnings Πi,t from shareholdings of firms
and unions. The interest rate is deflated by the consumer price inflation rate 1+πC
i,t =PC
i,t/P C
i,t−1.
The representative household spends this income on consumption, deposits and tax payments for
a real amount of ti,t. Finally, we assume that the household has to pay quadratic adjustment costs
to buy new deposits,35 these costs are paid in terms home goods with relative price pi,t =Pi,t/P C
i,t
where Pi,t is the production price index of home produced goods while PC
i,t is the consumption price
index. Households consume both home and foreign goods and their corresponding consumption
basket follows a standard CES function:
Ci,t =1−αC
i1/µ C(µ−1)/µ
hi,t +αC
i1/µ C(µ−1)/µ
fi,t µ/(µ−1) ,(B.3)
where parameter µ > 0 is the elasticity of substitution between domestic and foreign final goods
and αC
i∈[0,1/2] measures the fraction of goods bought abroad. The corresponding price index
is, PC
i,t = (1−αC
iP1−µ
h,t +αC
iP1−µ
f,t )1/(1−µ).
Households delegate the wage negotiation process to unions. Households provide differentiated
labor types, sold by labor unions to perfectly competitive labor packers who assemble them in
a CES aggregator and sell the homogenous labor to intermediate firms.36 Unions negotiate the
real margin between the real desired wage of households wh
i,t and the real marginal product of
labor Wi,t/P C
i,t. Using a Calvo wage nominal rigidity device, each period a random fraction θW
iof
unions is unable to re-negotiate a new wage. Assuming that the trade union is able to modify its
wage with a probability 1−θW
i, the jth union chooses the nominal optimal wage W∗
i,t to maximize
its expected sum of profits:
EtX∞
s=0 θW
isΛi,t+s"W∗
i,t
PC
i,t+τ
s
Q
k=1 1 + πC
i,t+k−1ξW
i−exp(εW
i,t+s)wh
i,t+s#Hi,t+s,(B.4)
where Λi,t+τis household’s stochastic discount factor, εW
i,t is an ad-hoc wage-push shock to the
real wage equation following an AR(1) process which captures exogenous fluctuations in the wage
margin negotiated by unions and affects in turn the productivity of the economy.
34As explained below, the desired wage is negotiated by a trade union.
35This cost is almost neutral on the dynamic of the model and is necessary to remove an unit root component which
is standardly induced by the international nature of our model. See Schmitt-Groh´e and Uribe (2003) for an extensive
discussion and solutions regarding this issue. The functional form we choose is: AC D
i,t (j) = 0.5χD(Dd
i,t (j)−
¯
Di)2/¯
Di, where ¯
Diis the steady state level of deposits and χD>0 is the cost parameter.
36Labor packers are perfectly competitive and maximize profits, Wi,t Hd
i,t −G(Wi,t (j)Hi,t (j)), under their packing
technology constraint, Hi,t = [(1/ni)1/WG(Hi,t (j)(W−1)/W)]W/(W−1). Here, Wi,t is the production price, Hd
i,t
is the labor demand and Wis a substitution parameter. The first order condition which determines the optimal
demand for the jth labor type is, Hi,t (j) = (1/ni)(Wi,t (j)/Wi,t)−WHd
i,t,∀j. Thus the aggregate wage index of all
labor types in the economy emerges from the zero-profit condition: Wi,t = [(1/ni)G(Wi,t (j)1−W)]1/(1−W).
28
Appendix B.2. Firms
Intermediate firms produce differentiated goods, decide on labor and capital inputs on a
perfectly competitive inputs market and set prices according to the Calvo model. The ith firm
has the following Cobb-Douglas technology:
Yi,t = exp(εA
i,t)Ku
i,tαHd
i,t1−α,(B.5)
where Yi,t is the standard production function that combines (utilized) physical capital Ku
i,t, labor
demand Hd
i,t to household and (exogenous) technology εA
i,t. Intermediate firms solve a two-stage
problem. In the first stage, taking the real input prices wi,t and zi,t as given, firms rent inputs
Hd
i,t and Ku
i,t in a perfectly competitive factor market in order to minimize costs subject to the
production constraint (B.5) to determine the real marginal cost mci,t.
In the second-stage, the intermediate firm isets prices according to a Calvo mechanism. Each
period firm iis not allowed to re-optimize its price with probability θP
ibut price increases by
ξP
i∈[0; 1) with respect to the previous period’s rate of price inflation, Pi,t = (1 + πi,t−1)ξP
iPi,t−1.
The ith firm allowed to modify its selling price with a probability 1−θP
ichooses P∗
i,t to maximize
its discounted sum of profits:
EtX∞
s=0 θP
isΛi,t+s"P∗
i,t
PC
i,t+s
s
Q
k=1
(1 + πi,t+k−1)ξP
i−exp(εP
i,t+s)mci,t+s#Yi,t+s,(B.6)
where εP
i,t is an ad-hoc cost-push shock to the inflation equation following an AR(1) process which
captures exogenous inflation pressures.
Once goods are produced and prices are set, final firms act as goods packers: they combine
differentiated goods to produce the homogenous final good sold mainly to households.37
Appendix B.3. Entrepreneurs
The capital required by the intermediate firm in the production process is financed by an
entrepreneur that belongs to the same business unit i. The balance sheet of the ith entrepreneur
is given by:
qi,tKi,t =LH
i,t +Ni,t.(B.7)
Defining Qi,tKi,t as the amount of capital to be financed by entrepreneur i,qi,t =Qi,t/P C
i,t is the
real shadow value of capital goods. This quantity qi,tKi,t is financed by the entrepreneur through
two means: its net wealth Ni,t and the real amount borrowed from the banking system, LH
i,t+1.
Formally, loan demands are subject to external habits as follows: LH
i,t =Ld
i,t −hL
i(Ld
i,t−1−¯
Ld
i)
with the habit degree hL
i∈[0,1), Ld
i,t−1the aggregate average level of loans of the previous
period and ¯
Ld
ithe steady state stock of loans.38 Empirically, firms and banks operating in the
37Goods packers are perfectly competitive and maximize profits, Pi,tYd
i,t − G(Pi,t (i)Yi,t (i)), under their packing
technology constraint, Yd
i,t = [(1/ni)1/PG(Yi,t (i)(P−1)/P)]P/(P−1). Here, Pi,t is the production price, Yd
i,t is the
aggregate demand (or the resource constraint) and Pis a substitution parameter. The first order condition which
determines the optimal demand for the ith good is, Yi,t (i) = (1/ni)(Pi,t (i)/Pi,t)−PYd
i,t,∀i. Thus the aggregate price
index of all varieties in the economy emerges from the zero-profit condition: Pi,t = [(1/ni)G(Pi,t (i)1−P)]1/(1−P).
38In the estimation exercise, we use the total stock of loans, they are of different maturities implying a strong
autocorrelation. Simply by introducing loan demand habits, taking into account the high autocorrelation of loans
29
Euro Area choose longer debt maturities than the standard one-period contract usually used in
real business cycle models. Then the term hL
iLd
i,t−1allows for slow adjustment over time of the
balance sheet constraint, to capture the idea that in practice borrowers do not readjust their
outstanding amount of loans every quarter. This approach of introducing slow adjustment of
credit is close to Iacoviello (2015), employed here in a context of a financial accelerator model.
During phases of recession characterized by asset price collapses of qi,t, this friction prevents the
total stock of loans to fall at the same rate as the price of financial assets, thus making credit less
procyclical consistently with empirical evidence. Since these habits don’t directly affect the first
order condition of the entrepreneur (as the overall problem of the entrepreneur can be expressed
in terms of physical capital directly), their implications on entrepreneurs’ profits is rather minor
but large for financial intermediary facing a persistent demand for loans.
To introduce corporate cross-border lending, we follow Poutineau and Vermandel (2015) and
Brzoza-Brzezina et al. (2015) by adopting a CES function that bundles domestic and foreign loans
offered by banks operating in the monetary union:39
Ld
i,t =1−αL
i1/υ Ld
hi,t(υ−1)/υ +αL
i1/υ Ld
fi,t(υ−1)/υ υ/(υ−1)
.(B.8)
Here, parameter υ≥0 is the elasticity of substitution between domestic and foreign interbank
funds, αL
i∈[0,1/2] represents the percentage of cross-border interbank loan flows in the monetary
union and Ld
hi,t (resp. Ld
fi,t) the amount of domestic (resp. foreign) loans demanded by borrowing
entrepreneurs living in country i. As a consequence, the borrowing cost is a CES aggregate of
home and foreign credit rates defined as: 1+PL
i,t = ((1−αL
i)(1+RL
h,t)1−υ+αL
i(1+RL
f,t)1−υ)1/(1−υ).
Regarding financial frictions, we reinterpret the financial accelerator `a la Bernanke et al.
(1999) from a banking perspective in order to have state-contingent lending rates needed to
introduce macroprudential measures.40 To do so, we follow the modelling device of Poutineau
and Vermandel (2015) that provides a micro-foundation for the financial accelerator mechanism
relying on biased expectations of entrepreneurs instead of a standard moral hazard problem. The
investment projects undertaken by the entrepreneur are risky and differ with respect to their
individual returns. To model individual riskiness, we borrow from Bernanke et al. (1999) and
assume that each project has an individual return equal to ω1 + Rk
i,t,i.e. that the aggregate
return of investment projects in the economy 1 + Rk
i,t is multiplied by a random value ω. The
representative entrepreneur conducts a mass ωof diversified investment projects and the profit of
the ωth investment project is given by:
ΠE
i,t (ω) = ωEtn1 + Rk
i,t+1oqi,t Ki,t (ω)−1 + PL
i,tLH
i,t (ω),(B.9)
becomes tractable easily and does not change the steady state of the model. For instance in 1999, loans with a
maturity above one year represented 64% of the outstanding stock of loans in the Eurosystem.
39Kollmann et al. (2011) provides a complementary way of introducing cross-border lending through global banks.
However, this approach assumes a perfect credit market intregration between Euro participants that is not consistent
with the data. Alternatively, Dedola and Lombardo (2012) introduce cross-border loans through a portfolio problem
that requires a second order approximation to the policy function, which poses an issue when putting the model to
the data.
40The pathbreaking contribution of Bernanke et al. (1999) focuses on the demand side of credit market through
a moral hazard problem but neglects its supply side and in turn the possibility to introduce macroprudential
measures that could affect the macroeconomic outcome. Their model is closed assuming that lending rates are
pre-determined.
30
In order to acquire a loan, entrepreneurs have to engage in a financial contract before the
realization of ω.41 After engaging in the financial contract, entrepreneurs recognize ex post the
value of ωC
i,t which separates the default space (ω < ωC
i,t) from the space of gains (ω≥ωC
i,t).
Thereby the ex post threshold separating the default space from the profitable space is computed
trough the zero profit condition on Equation B.9:
ωC
i,t 1 + Rk
i,tqi,t−1Ki,t−1=1 + PL
i,t−1LH
i,t−1.(B.10)
Following Helpman et al. (2004), we adapt the Pareto distribution to model the productivity
of firms in a financial context. Investment projects are drawn from a Pareto distribution ω∼ P(κ)
with support ω∈[ωmin,+∞) where κ > 1 is the shape parameter and ωmin >0 is the lower bound
of the distribution. Given the characteristics of the distribution, it is possible to compute the share
of profitable projects, denoted ηE
i,t = (ωmin/ωC
i,t)κ, and their aggregate value, ¯ωi,t =κ/(κ−1)ωC
i,t.42
When the entrepreneur is underwater with an investment project value below the cost of credit,
she endogenously defaults on her loan and abandons her investment project.
To introduce a financial accelerator mechanism, we assume that entrepreneurs have short term
distorted expectations regarding the aggregate profitability of their aggregate investment projects
¯ωi,t, thus creating a financial friction in the economy with dynamic properties close to Bernanke
et al. (1999). The perceived ex ante value of profitable projects ¯ωi,t+1 is defined by the CES
function:43
g(¯ωi,t+1) = ¯ω1/(1−κi)
i(¯ωi,t+1)κi/(κi−1) ,(B.11)
where κi∈[0,1) is the elasticity of the external finance premium and ¯ωiis the steady state of
¯ωi,t+1. During phases of expansion characterized by high aggregate returns above the the steady
state ¯ωi,t+1 >¯ωi, entrepreneurs’ forecasts regarding the aggregate profitability are optimistic
with g(¯ωi,t+1)>¯ωi,t+1 . In contrast for low expected realizations of ¯ωi,t+1 below its steady state,
entrepreneurs tend to hold pessimistic expectations about their returns with g( ¯ωi,t+1)<¯ωi,t+1.
Finally in steady state, there is no expectation bias, g( ¯ωi) = ¯ωi.44 Any shock driving financial
returns above or below the steady state will trigger an acceleration of the business cycles through
these biased expectations for κi>0.
Aggregating all profitable investment projects (i.e. above ωC
i,t) that the entrepreneur does not
abandon, it chooses a capital value of Ki,t that maximizes its profit (before the realization of ω)
41The individual return ωis also referred as an idiosyncratic shock in the financial accelerator literature. The
debt contract is conclude before the idiosyncratic shock is recognized which generates unexpected losses for the
entrepreneurs and lenders.
42Using the characteristics of the Pareto distribution F(ω), the distribution of stochastic investment projects ω
has a positive support, is independently distributed (across entrepreneurs and time) with unitary mean E[ω] = 1,
and density function f(ω). Investment projects above the cut-off value, ω > ωC
i,t, have positive profits ΠE
i,t (ω)≥0
which allows entrepreneurs to repay its loans to the bank. The share of profitable projects 1 −F(ω) is computed
as, ηE= Pr ω≥ωC=R∞
ωCf(ω)dω= (ωmin/ωC)κwhile the conditional expectation of ωwhen entrepreneur’s
project is gainful is, ηE¯ω=R∞
ωCωf (ω)dω with ¯ω=Eω|ω≥ωC=κ
κ−1ωC.
43There is a rich literature providing evidence that entrepreneurs are more optimistic compared to the general
population; for some recent studies see, e.g., Landier and Thesmar (2009), Puri and Robinson (2013), Dawson and
Henley (2013).