Global banking and the conduct of macroprudential policy in a monetary union

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Global banking and the conduct of macroprudential policy in a monetary union

Jean-Christophe Poutineau, Gauthier Vermandel

To cite this version:

Jean-Christophe Poutineau, Gauthier Vermandel. Global banking and the conduct of macropruden- tial policy in a monetary union. Journal of Macroeconomics, Elsevier, 2018, 54 (B), pp.306-331.

�10.1016/j.jmacro.2017.04.010�. �halshs-01525396�

H ighlights

• W e estim ate a tw o-country m odelw ith internationalbanking for the Euro A rea

• W e exam ine the role ofcross-border lending on the reaction ofcapitalbu ers

• Targeting a nationalcredit-to-G D P ratio should be favored to federalaverages

• A federaltargeting is desirable for a share ofcross-border banking reaching 45%

• Even w ith perfect banking integration,a nationaltargeting rem ains optim al

Global Banking and the Conduct of Macroprudential Policy in a Monetary Union

Jean-C hristophe Poutineau

^a

,G authier Verm andel

^b,c,∗

a

CREM, UMR CNRS 6211, Universit´e de Rennes I, 7 Place Hoche, 35065 Rennes Cedex, France.

b

Paris-Dauphine University & PSL Research University, Place du Mar´echal de Lattre de Tassigny, 75016 Paris, France.

c

France Strat´egie, 18 Rue de Martignac, 75007 Paris.

A bstract

T his paper questions the role ofcross-border lending in the definition ofnationalm acro- prudentialpoliciesin the European M onetary U nion. W e build and estim ate a two-country D SG E m odelw ith corporate and interbank cross-border loans,C ore-Periphery diverging financialcycles and a nationalim plem entation of coordinated m acroprudentialm easures based on C ountercyclicalC apitalB u ers. W e get three m ain results. First, targeting a national credit-to-G D P ratio should be favored to federal averages as this rule induces better stabilizing perform ances in front ofim portant divergences in credit cycles between core and peripheralcountries. Second,policies reacting to the evolution ofnationalcredit supply should be favored as the transm ission channelof m acroprudentialpolicy directly im pacts the m arginalcost ofloan production and,by so,financialinterm ediaries. T hird, the interestoflifting up m acroprudentialpolicym aking to the supra-nationallevelrem ains questionable for adm issible value ofinternationallending between Eurozone countries. In- deed,nationalcapitalbu ersreacting to the union-w ide loan-to-G D P ratio only lead to the sam e stabilization resultsthan the one obtained underthe nationalreaction ifcross-border lending reaches 45% . H owever,even ifcross-border linkages are high enough to justify the im plem entation ofa federaladjusted solution,the reaction to nationallending conditions rem ains rem arkably optim al.

∗

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

Keywords: M acroprudentialPolicy,G lobalB anking,InternationalB usiness C ycles,Euro A rea

JEL classification: F42,F45,E58,F34

1. Introduction

T he disruption offinancialrelationsthatfollow ed the 2007 subprim e crisissetthe basis for the adoption of m acroprudential policies in m ost countries.

¹

In the Euro A rea, the im plem entation ofsuch m easuresrem ainsfragm ented along nationallinesw hile the coordi- nation and internalization ofcross-borderspilloversare achieved through the actionsofthe European System ic R isk B oard (ESR B ,henceforth). T hisfederalorganization accountsfor two conflicting features ofthe Eurozone that can be approached by contrasting core and peripheralcountries.

²

Panel(a) ofFigure 1 show s that financialcycles (as m easured by the credit to G D P ratio in percentage deviation from H P trend) rem ain clearly national, w hich m ilitates for a decentralized definition and im plem entation ofm acroprudentialm ea- sures. H owever,asreported in panel(b)ofFigure 1,these two regionsare closely linked by cross-border banking activities (as m easured by the share ofloans lent to a foreign agent residing in another Euro A rea country) and the internationalspillovers ofnationalm acro- prudentialpolicies m ay be harm fulfor the m onetary union. T he rem aining uncertainties on undesirable side-e ects of self oriented m acroprudentialpolicies have thus put global banks at a centralstage in the on-going debate related to the conduct ofm acroprudential policies.

³

T his paper questions how sizable cross-border lending flow s should be treated in the definition of national m acroprudential policies in the Euro A rea. W e m ore particularly assess w hether cross-border bank lending should explicitly be considered in the setting of coordinated nationalm acroprudentialm easuresorw hethernationalregulatorsshould only focus on the sole national financial stance to contribute to the financial stability of the Eurozone.

1

In a nutshell, macroprudential policy aims at completing monetary policy to enhance t he resilience of

t he

financial system and contain the procyclicality offinancial factors on activity.

2

In the

first group we aggregate data for countries with a current account surplus and low govern-

ment 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, It aly and Portugal).

3

For 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, Sta

ff

Working Paper).

2000 2003 2006 2008 2011

−5 % 0 % 5 %

Credit-to-GDP

% deviation from H P Trend

2003 2004 2006 2007 2008 2010 2011 2012 6 %

8 % 10 % 12 % 14 %

Share of Cross-Border Loans in Banks’ Balance Sheet

Core count ries Peripheral count ries

Not e: Cross-border lending refers t o anyfinancing arrangement t hat crosses nat ional borders between a domest ic bank and a foreign borrower. T he share of cross-border loans is comput ed here as t he rat io between loans t o euro area excluding t he domest ic area and t he loans t o euro area (i.e. cross-border loans between core count ries are included in t he calculat ion of t he share of int ernat ional loans). Sources: ESRB and ECB st at ist ics.

Figure 1: Stylized facts characterizing the Eurosystem banking system: credit cycles remain clearly national while cross-border lending experienced an important growth

W e build and estim ate a two-country D SG E m odel that accounts for two m ajor as- pects to address the question at hands. First, we extend the setup of Poutineau and Verm andel( 2015) - featuring cross-border banking on the corporate and interbank loan m arkets

⁴

-to account for bank capitalregulation and thus to contrast the e ectiveness of m acroprudentialpolicy from banking autarky to perfect integration. Second,in line w ith the actualorganization ofm acroprudentialpolicy,

⁵

we focus on the joint-optim ization of m acroprudentialpolicy rulesin each country using the countercyclicalcapitalbu er(C C B , henceforth) rate as an instrum ent. T his solution has becom e one ofthe leading facets of prudentialregulation since the adoption ofB aselIIIaccords ( 2010) by building up a bank capitalbu erduring periodsofexcessive creditgrow th thatcan be released w hen system ic risks abate. T he internationaldim ension ofbanks o ered by our setting allow s us to con- trast di erent C C B rules based on: ( i ) the federalor the nationalcredit-to-gdp targeting,

4

In this paper, we omit the mortgage market and concentrate on corporate and interbank loans. Given t he 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.

5

We 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.

( ii ) the loan dem and (from firm s) or supply (from banks) to G D P targeting,and ( iii ) the loan inflow s-to-G D P ratio targeting as envisaged by R ey ( 2015).

T he m ethodology em ployed in this paper com prises three steps. First, w e build and estim ate a two-country D SG E m odelforthe Euro A rea w ith only m onetary policy (asthere are no observations for an estim ation of a m acroprudential rule). Second, we com pute the optim alpolicy rules (both m onetary and m acroprudentialpolicy) given the estim ated param eters assum ing a two-stage gam e w here m onetary policy is the leader.

⁶

T hird,we exam ineim plicationsofcross-borderlending on theoptim aldesign ofm acroprudentialrules across country m em bers of the Eurosystem using the optim alm onetary policy rule as a benchm ark.

T he m ain result ofthe paper suggests that selforiented m acroprudentialnationalpoli- cies reacting to the evolution ofhom e country loan creation should be favored even w ith high am ounts ofcross-border lending flow s: First,targeting a nationalcredit-to-gdp ratio should be favored to federalaverages as this rule induces better stabilizing perform ances in front of im portant divergences in credit cycles between core and peripheralcountries.

Second,policiesreacting to the evolution ofnationalcreditsupply should be favored asthe transm ission channelofm acroprudentialpolicy directly im pacts the m arginalcost ofloan production and, by so, financial interm ediaries. T hird, the interest of lifting up m acro- prudential policym aking to the supra-national level rem ains questionable for adm issible value ofinternationallending betw een Eurozone countries. Indeed,nationalcapitalbu ers reacting to the union-w ide loan-to-G D P ratio only lead to the sam e stabilization results than the one obtained under the national reaction if cross-border lending reaches 45% . H owever,even ifcross-border linkages are high enough to justify the im plem entation ofa federaladjusted solution,the reaction to nationallending conditions rem ains rem arkably optim al.

A dditionally,we outline som e particularities regarding the conduct ofm acroprudential

6

A important branch of the literature analyzed t he interaction between monetary policy and

financial

stability, a t opic 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 off ered by the

existing lit erature concerning the role of monetary policy in providing

financial st ability.

policies for peripheralcountries. W e find that adjusting the m acroprudentialinstrum ent to capitalinflow s-to-G D P is a prom ising toolfor these countries that have experienced a large am ount ofloan inflow s. Furtherm ore,disentangling the dem and/supply ofcredit has im plications for m acroprudentialpolicym aking as it is preferable to target credit suppliers for core countries and borrowers for peripheraleconom ies.

O ur approach is partly related to a set ofpapers exam ining m acroprudentialm easures in the Eurozone w ith a closed econom y setup. N otably,D arracq-Pari` es et al.( 2011) and A ngelinietal.( 2014 )build a D SG E m odelofthe Eurozone close to G eralietal.( 2010)w ith both corporate and housing creditm arketsand evaluate the optim alm ix between m onetary and m acroprudentialpolicy using loss functions. A s a key contribution to the literature, they suggest that tim e-varying capitalrequirem ents can im prove m acroeconom ic stability by supporting m onetary policy actions.O uranalysiscan thusbeconsidered asan extension to these papers,by accounting for the heterogeneity between Euro A rea participants and the existence ofnationalm acroprudentialpolicies w ith cross-border spillovers.

O ur paper also contributes to m acroprudentialpolicy analysis in open econom ies. A s an exam ple,Q uint and R abanal( 2014) account for financialasym m etries between partici- pating countries and focuson the interaction between financialand housing cycles w ithout considering cross-border flow s betw een countries. B y om itting cross-border lending,they naturally find that there are no im portant spillover e ects ofregulation from one m em ber state to anothervia an estim ated two-country D SG E m odelofthe Eurozone. A dditionally, Jeanne( 2014 )em ploysa static open econom y m odelto evaluate the e ectivenessofm acro- prudentialand capitalcontrolm easures. C ontrary to Q uint and R abanal( 2014),he finds that these prudentialpolicies generate im portant globalspillovers even w ith international coordination.

T he paperis organized as follow s:Section 2 describes the financialsectorofthe m odel.

Section 3 takesthe m odelto the data.Section 4 discussesthe perform ance ofm acropruden- tialpolicy.Section 5 provides a sensitivity analysis to assess the robustness ofour results.

Section 6 concludes.

2. T he financial sector

T he econom y iscom posed oftw o countriesofunequalsize and populated by households, firm s and banks. T his first section describes the banking com ponent of the m odelw hile the rest ofthe fram ework (standard to the literature) is presented in appendix.

2.1. The financial sector in a nutshell

Figure 2 provides a broad picture ofthe financialsector and sum m arizes its interaction w ith the rest ofthe econom y. B anks engage in interbank lending/borrow ing relations and provide corporate loans to entrepreneurs and deposit services to households. A uthorities a ectthe decisionsofthe banking sectorthrough m onetary and m acroprudentialpolicies.

M onet ar y Policy M acr opr udent ial

Policy

M acr opr udent ial Policy

B ank

B ank

P r oduct ion

P r oduct ion

H ousehold

H ousehold

Cc,t

Cp,t

L^sc,t

L^sp,t

Invest ment Flows

Consumpt ion Flows Corporat e

Credit Flows Int erbank

Credit Flows Refinancing

Rat e Rt

νc,tcapit al buffers

νp,tcapit al buffers

Deposit s Dc,t^d

Deposit s Dp,t^d

Figure 2: Macroprudential policy and cross-border banking in a New K eynesian Framework

To introduce an interbank m arket,we assum e that banks are heterogenous in term s of liquidity. T his feature gives rise to an interbank m arket w here liquid banks provide inter- bank loansto both hom e and foreign banks.T hisfeature isline w ith the currentEuropean banking system characterized by banks relying on w holesale fundings as illustrated by G i- annone et al.( 2012). In our setup,the distinction betw een liquid and illiquid banks lies in the direct access ofliquid banks to EC B fundings w hich allow intra-financialsector flow s betw een financialinterm ediaries.

⁷

Extending this assum ption to an internationalperspec-

7

T his assumption is empirically motivated: in the Eurosystem, only a fraction of the 2500 banks par-

tive,illiquid banks can borrow from both dom estic and foreign liquid banks,w hich gives rise to cross-border interbank lending flow s. T he decision ofthe banking system regarding the provision of deposit services to households and loans to the corporate sector a ects the rest ofthe econom y through the setting ofdeposit and lending interest rates.

⁸

In line w ith the EM U situation,w e do not consider cross-border deposit nor cross-border lending to households. T he internationalflow ofloans between econom ies is thus a consequence of interbank liquidity provision and borrow ing choicesundertaken by entrepreneurs(follow ing a com parison between the relative interest rates ofdom estic and foreign corporate loans).

T his paper adopts a m acroeconom ic perspective to focus on the e ect ofcross-border lending on the conduct ofm acroprudentialpolicy in a heterogeneous m onetary union. A s a consequence,the financialsector is com bined w ith a standard two-country D SG E m odel accounting for short run rigidities in goods prices and nom inal wages. In w hat follow s, we outline the m ain assum ptions regarding the functioning ofthe financialsector that are deem ed necessary to im prove both the tractability ofthe analysisand the estim ation ofthe m any behavioralparam eters of the D SG E structure. Som e m odelling choices have been done in line w ith the D SG E literature thatcontrastw ith a m ore standard description ofthe behaviorofthe banking sectorassum m arized by Freixasand R ochet( 2008)and VanH oose ( 2009). A s in the initial contribution of G erali et al.( 2010 ), this m acro superstructure is augm ented w ith a highly sim plified banking m odel. A host of assum ptions should be invoked thate ectively splintera bank’sdecisionsinto independentchoicesaboutdi erent portions ofits balance sheet.

⁹

t icipates regularly to the bidding process in main re

financing operations of the ECB while the others rely

on interbank funding.

8

For tractability reasons we assume that even if banks diff er in their ability t o 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 di

ffi

culties 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.

9

First, 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 unanimity is assumed for all banks in t he model, or risk neutrality has been assumed t o 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 t he banks’ assets and liabilities at during each period and across periods if interperiod adjust ment 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

T his paper extends Poutineau and Verm andel( 2015) to account for deposit decisions and for m acroprudential consideration in the balance sheets of financial interm ediaries.

T he stickiness in both deposit and loan interest rates is a key ingredient of the fram e- work. T he setting ofinterest rate m im ics the way other sticky nom inalvariables such as prices and w ages are set in the m odelby adopting a C alvo-type m echanism . T his device, shared by m ost D SG E m odels w ith a banking sector,partly contrasts w ith the literature developed from the banking industry perspective. Indeed,m ost ofthe banking literature has, follow ing Flannery ( 1982) original w ork on deposits as quasi-fixed factors, focused on intertem poralquantity adjustm ent costs. It is also worth noting that the substantial banking literature on thistopic hasproposed alternative w aysofapproaching thisquestion, including C osim ano and Van H uyck ( 1989),C osim ano ( 1987 , 1988), and Elyasianiet al.

( 1995) and A bo-Zaid ( 2015). Furtherm ore, sluggish and even asym m etric variations in bank retailrates have been docum ented in the em piricalliterature as in Van Leuvensteijn et al.( 2013) through im perfect com petition am ong banking system s,w hile K opecky and Van H oose( 2012)rely on intertem poralquantity adjustm entcoststogetherw ith im perfect com petition to explain such observations. T he adoption ofa C alvo m echanism com bined w ith m onopolistic com petition has been em ployed here in a m acro-perspective for credit and deposit interest rates, as this solution allow s us to consider the sluggishness in the adjustm ent ofallthe nom inalvariables ofthe econom y (prices,w ages and interest rates) through the estim ation ofa ”C alvo lottery param eter”.

A s a second m ajor noticeable di erence from Poutineau and Verm andel( 2015),we ac-

countforendogenousleverage offinancialinterm ediaries,thusreflecting the riskinessin the

balance sheet ofbanks. W e use tim e-varying capitalrequirem ents as the m acroprudential

instrum ent.A sunderlined byA ngelinietal.( 2014),capitalbu ershavetaken a centerstage

in the ongoing debate on regulatory reform and have becom e one ofleading facetofm acro-

prudentialregulation. Specifically in the European U nion,a num ber ofm acro-prudential

policy instrum ents including countercyclicalbu ers are em bedded in the legislative texts

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.

transposing the B aselIIIregulatory standards into EU law .

¹⁰

To account for this com pul- sory m acroprudentialinstrum ent,we borrow the m odelling device ofD arracq-Pari` es et al.

( 2011)and A ngelinietal.( 2014)by assum ing thateach type ofbank m ustpay a quadratic cost w hen its risk weighted assets ratio deviates from the tim e-varying ratio fixed by the m acroprudentialauthority in country i according to the system ic risk arising w ithin the financialsystem . T he decision to penalize banks for keeping equity-capitalpositions below the o cialbenchm ark is easy to understand,as undercapitalized banks m ake the banking sector m ore fragile and in turn subject to bank runs ( D iam ond and R ajan ( 2001)). Sym - m etrically,the decision to im pose costs on banks for having equity-capitalpositions above the required levels m ay be understood in a m acroeconom ic perspective: by keeping m ore equity capital levels than required by the o cial regulation, the banking sector diverts resources and,in turn,creates credit rationing for both entrepreneurs and illiquid banks.

T his m ay create low er than desired banking activity, reduce investm ent in the econom y and incur ine ciencies.

¹¹

2.2. Interbank relations

In each country the banking system consists of two distinct branches: a continuum ofm onopolistic banks and financialpackers.M onopolistic banks provide di erent types of loansand depositservicesand setinterestrateson a C alvo basis.T hefinancialinterm ediary is a C ES packer that produces one hom ogenous loan and deposit service.

¹²

A share λ of

10

Namely 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.

11Van den Heuvel

(2008)

finds using a general equilibrium model that increasing capital requirements

induces high welfare costs in terms of uncondit ional consumption, suggesting that capital requirements should be lower than in the current adequacy framework.

Clerc et al.

(2015) highlight the presence of a t radeoff using a

financial accelerator model between t oo high and too low capital requirements.

12

T hefinancial packer acts as a loan and deposit bundler in a perfectly competitive market. Banks supply diff erentiated types b of deposits D

i ,t

(b) and loans L

^s_{i ,t}

(b) bundled by

financial packers. T heir packing tech-

nology for deposit services and loans reads as, D

^d_{i ,t}

= [(1/ n

i

)

^{1/ D}G(Di ,t

(b)

^(D−1)/D

)]

^{D/ (D−1)}

, and L

^d_{i ,t}

= [(1/ n

i

)

^{1/ L}G(L^s_{i ,t}

(b)

^{(L−1)/ L}

)]

^{L/ (L−1)}

. It maximizes profits, R

^D_{i ,t}

D

^d_{i ,t}

+ R

^L_{i ,t}

L

^d_{i ,t}− G(R^D_{i ,t}

(b) D

i ,t

(b))

− G(R^L_{i ,t}

(b) L

^s_{i ,t}

(b)), subject to their two technology curves. Here, L

^d_{i ,t}

is the loans demand from home and foreign entrepreneurs, D

_{i ,t}^d

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. T he corresponding demand functions associated from the previous prob-

lem are, D

i ,t

(b) = (1/ n

i

)(R

^D_{i ,t}

(b)/ R

^D_{i ,t}

)

^{− D}

D

^d_{i ,t}

and L

^s_{i ,t}

(b) = (1/ n

i

)(R

^L_{i ,t}

(b)/ R

^L_{i ,t}

)

^{− L}

L

^d_{i ,t}

. T he aggre-

banks is illiquid (i.e. credit constrained),w hile the rem aining share ofbanks 1- λ is liquid and supplies interbank loans to illiquid banks.

T he representative share λ of illiquid banks b in country i has the follow ing balance sheet,

L

^si ,t

= I B

i ,t^H

+ B K

i ,t^{i ll}

+ D

i ,t

+ liab

^{i ll}i ,t

, (1)

w here L

^s_{i ,t}

is the loan supply of borrow ing banks, I B

_{i ,t}^H

is the interbank loans supplied by liquid banks subject to external habits,B K

_{i ,t}^{i ll}

is the bank capital, D

i ,t

are deposit services to households and liab

i ,t

are other liabilities in the balance sheet of the bank that are not considered in the m odel.

¹³

To close the m odel, w e assum e that the cost of these liabilities is set by the central bank through its refinancing rate. W e suppose that the dem and for interbank funds are subject to externalhabits at a degree h

^Bi

w here I B

^Hi ,t

= I B

i ,t^d

− h

^Bi

( I B

^di ,t−1

− I B

^di

). T hese habits captures the em piricalautocorrelation of interbank funding.In addition,these habits are em pirically docum ented in the interbank network literature: Finger et al. ( 2014, 2015) find at a bank level that bilateral links betw een banks are persistent as banks heavily rely on well-established business relations, thus exhibiting som e habits in borrow ing/lending decisions.

T he one-period stream ofprofits ofthe b-th illiquid bank is given by:

i lli ,t

= 1 − µ

^B

(1 − E

t

{η

i ,t+ 1

}) 1 + R

^L_{i ,t}

L

^s_{i ,t}

− 1 + R

^D_{i ,t}

D

i ,t

− 1 + P

_{i ,t}^{I B}

I B

^H_{i ,t}

(2)

− (1 + R

t

)liab

^{i ll}_{i ,t}

− F r wa

^{i ll}_{i ,t}

− υ

i t

B K

^{i ll}_{i ,t}

,

w here µ

^B

[0, 1]denotes the loss-given-default ( i.e. the percentage ofthe am ount owed on a defaulted loan that the bank is not able to recover),1 − E

t

{η

i ,t+ 1

} is the expected gate price index of all varieties in the economy is given by, R

^D_{i ,t}

= [(1/ n

i

)G(R

_{i ,t}^D

(b)

^{1− D}

)]

^{1/ (1− D)}

and R

^L_{i ,t}

= [(1/ n

i

)G(R

_{i ,t}^L

(b)

^{1− L}

)]

^{1/ (1− L)}

.

13

We suppose that they follow an exogenous AR(1) shock process

ε^B_{i ,t}

such that, li ab

_{i ,t}

= e

^{εBi , t}

li ab

_i

, t his

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.

average default rate ofthe bank’s hom e and foreign custom ers,

¹⁴

R

^Di ,t

is deposit rate,P

i ,t^{I B}

is the borrow ing cost on the interbank,R

t

the interest rate set by the centralbank and F

i

(·)denotesthe capitalrequirem entcostfunction. T hiscostfunction istaken from G erali etal.( 2010)and isdefined asF

i

( x)= 0 .5χ

^k

x

²

w hereχ

^k

0 isthe costofcapitaladequacy fram ework paid in term ofbank capital.

¹⁵

T hiscostfunction isa shortcutthatm akesbank capitalm ore costly than any source offinancing,and allow s in turn to m im ic the response of credit rates and credit to a capitalrequirem ent tightening consistently w ith em pirical evidence (see for instance Fraisse et al.( 2013) for an em piricalm easure ofthis elasticity).

W hen the bank capital-to-risky-assetratio r wa

^{i ll}i ,t

is below the policy target υ

i t

,the bank is penalized by regulatory rules that a ect the borrow ing rates in the m onetary union and in turn dam ageoutput.T hispenalization replicatesthem arketdisciplineim posed by investors on low capitalized banks,forcing the latter to boost their retained earnings though higher creditrates. T he risk isevaluated through fixed weightson assets,based on the type ofthe borrowers(1 forcorporate exposure and 0.20 forinterbank exposure between O EC D banks as defined in B asel accords) as defined in B asel I accords. Since illiquid banks are only exposed to corporate risk, the risk weighted assets ratio is given by r wa

^{i ll}i ,t

= B K

i ,t^{i ll}

/ L

^si ,t

. In addition,the financialinterm ediary has access to dom estic and foreign interbank loans to m eet its balance sheet. T he m odelling device to introduce internationalborrow ing is analogous to trade channels through a C ES as in Poutineau and Verm andel ( 2015) and B rzoza-B rzezina et al.( 2015). T he total am ount borrow ed by the representative bank reads as follow s:

I B

^d_{i ,t}

= 1 − α

^{I B}_i ^1/ξ

I B

^d_{hi ,t} ^(ξ−1)/ξ

+ α

^{I B}_i ^1/ξ

I B

_{f i ,t}^{d (ξ−1)/ξ ξ/ (ξ−1)}

, (3)

w here param eter ξ > 0 is the elasticity of substitution between dom estic and foreign in-

14

To 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,

η_{i ,t}

= (η

^E_{h ,t}

)

^{1− αLh}

(η

^E_{f ,t}

)

^αLjη

¯

^{αLh− αLj}

where

η^E_{i ,t + 1}

is t he default rate of entrepreneurs operating in country i

{c, p}. The expression ¯η^{αLh− αLj}

ensures the detesministic steady state remains symmetric between Core and Periphery without aff ecting the dynamic of the model up to a

first order approximation.

15

T he quadratic nature of this cost has been discussed in the previous subsection.

terbank funds,α

^{I B}i

represents the percentage of cross-border interbank loan flow s in the m onetary union and I B

^d_{hi ,t+ 1}

(resp.I B

^d_{f i ,t+ 1}

) the am ount ofdom estic (resp. foreign) loans dem anded by borrow ing bank b in country i. T his existence ofan hom e bias on the inter- bank m arket is em pirically m otivated,Fricke and Lux ( 2015) find,using Italian bank-level data,that Italian banks tend to trade w ith each other rather than w ith foreign banks,in particular after the financialturm oil. M ore broadly in the literature offinance,the hom e bias in portfolio w as first docum ented by French and Poterba ( 1991).

T he totalcost incurred by illiquid banks to finance interbank loans,1 + P

i ,t^{I B}

,is thus defined according to the C ES aggregator:

1 + P

_{i ,t}^{I B}

= ( 1 − α

^{I B}_i

(1 + R

^{I B}_h,t

)

^{1− ξ}

+ α

^{I B}_i

(1 + R

^{I B}_{f ,t}

)

^{1− ξ}

)

^{1/ (1− ξ)}

, (4) w here 1+ R

^{I B}_h,t

(resp. 1+ R

^{I B}_{f ,t}

)isthe costofloansobtained from hom e (resp. foreign)banks in country i . Finally follow ing G eraliet al.( 2010),the bank capitalaccum ulation process ofilliquid banks ( B K

_{i ,t}^{i ll}

) is determ ined by:

B K

_{i ,t}^{i ll}

= 1 − δ

^{i ll}_i ^{i ll}_{i ,t−1}

, (5)

w here δ

_i^{i ll}

[0 , 1]m easures resources used in m anaging bank capitaland conducting the overallbanking interm ediation activity and isdeterm ined endogenously by the steady state ofthe m odel. G iven the functionalform ofF

i

(·),the first order condition on loans w hich determ ines the m arginalcost ofsupplying an additionalunit ofloans to hom e and foreign entrepreneurs is:

1 + M C

^{i ll}i ,t

= 1 + P

_{i ,t}^{I B}

+ χ

^k

υ

i t

− r wa

^{i ll}_{i ,t}

r wa

^{i ll}_{i ,t} ²

1 − µ

^B

(1 − E

t

{η

i ,t+ 1

}) . (6)

From this equation, w e observe that an increase (reduction) in the C C B rate υ

i ,t

(risk

weighted assets ratio r wa

^{i ll}_{i ,t}

) im poses on banks to accum ulate m ore equity via retained

earnings through a rise in credit rates.Param eter χ

^k

determ ines the elasticity ofinterest

rates to capitalregulation change.

¹⁶

D uring phases ofexpansion,banks have incentives to increase theirleverage away from the targetin orderto boosttheirprofits. T hisrisk taking by banks is addressed in our m odelthough the cost function that forces banks to control their capitalstructure.

T he fraction 1 − λ ofrem aining liquid banks has the follow ing balance sheet:

L

^si ,t

+ I B

^si ,t

= L

^{E CB}i ,t

+ B K

i ,t^{li q}

+ D

i ,t

+ liab

^{li q}i ,t

, (7) w hereL

^s_{i ,t}

is the lending supply to entrepreneurs,I B

_{i ,t}^s

is the supply offunds on the inter- bank m arket,L

^{E CB}_{i ,t}

is the am ount ofrefinancing operations obtained by the liquid bank, B K

_{i ,t}^{li q}

is the am ount ofbank capital,D

i ,t

are deposits collected from dom estic households and liab

i ,t

are exogenous liabilities as explained previously. T he one-period profit of the bank

^{li q}_{i ,t}

is defined as:

li q

i ,t

= 1 − µ

^B

(1 − E

t

{η

i ,t+ 1

}) 1 + R

^L_{i ,t}

L

^s_{i ,t}

+ 1 + R

^{I B}_{i ,t}

I B

^s_{i ,t}

− 1 + R

^D_{i ,t}

D

i ,t

(8)

− (1 + R

t

)liab

^{li q}_{i ,t}

− (1 + R

t

)L

^{E CB}_{i ,t}

− F ( r wa

^{li q}_{i ,t}

− υ

i t

) B K

_{i ,t}^{li q}

.

H ere,R

^{I B}i ,t

is the interest rate set by liquid banks to hom e and foreign illiquid banks,R

t

is the refinancing rate ofthe centralbank and F

i

(·) denotes the sam e B aselcost function as for illiquid banks:F

i

( x) = 0 .5χ

^k

x

²

. Interbank claim s a ect the am ount ofequity held by banks and are given a risk weight at 20% .T he risk weighted asset ratio for liquid bank incorporating corporate and bank exposures is given by r wa

^{li q}_{i ,t}

= B K

_{i ,t}^{li q}

/ ( L

^s_{i ,t}

+ 0.2I B

_{i ,t}^s

) . A ccording to the illiquid bank,bank capitalofliquid banks evolves according to

B K

_{i ,t}^{li q}

= (1 − τ

_i^{li q}

)

^{li q}_{i ,t}

, (9)

w hereδ

^{li q}_i

[0, 1]is sim ilar to the illiquid bank and m easures the fraction ofcapitalused during the interm ediation process that cannot be re-invested next period. T he first order

16

Empirically,

Fraisseet al.

(2013)

find at a bank level that onepercentageincreasein capital requirements

leads to a reduction in lending by approximately 10%.

condition on loans determ ining the m arginalcost ofloans ofthe liquid bank b is:

1 + M C

^{i ll}_{i ,t}

= 1 + P

_{i ,t}^{I B}

+ χ

^k

υ

i t

− r wa

^{i ll}_{i ,t}

r wa

^{i ll}_{i ,t} ²

1 − µ

^b

(1 − E

t

{η

i ,t+ 1

}) , (10)

and the second first order condition on interbank loans determ ines the interbank rate set by banks operating in country i:

R

^{I B}_{i ,t}

= R

t

+ 0.2χ

^k

( υ

i t

− r wa

^{li q}_{i ,t}

)( r wa

^{li q}_{i ,t}

)

²

. (11)

H ere again,an increase in bank capitalrequirem ents raises the bank’s cost oflending,and in turn increasesboth interbank and corporate interestrates.T hisresultisconsistentw ith standard business cycle m odels and is referred to the bank capitalchannelas in Van den H euvel( 2008),M eh and M oran ( 2010), D arracq-Pari` es et al.( 2011) and A ngelini et al.

( 2014).

2.3. Interest rate setting

W e assum e thatinterestrateson depositsand corporate creditloansare sticky. In par- ticular,sluggish and even asym m etric variationsin bank retailrateshave been docum ented in the em piricalliterature asin K opecky and Van H oose( 2012)and Van Leuvensteijn etal.

( 2013)through im perfectcom petition am ong banking system s. T he setting ofinterestrate

m im ics the w ay other sticky nom inal variables such as prices and w ages are set in the

m odel. A s in D arracq-Pari` es et al.( 2011), w e introduce a C alvo m odel for credit rates

to firm s and deposit rates w hile the interbank rate is left flexible as banks operate under

perfect com petition on the interbank m arket. B anks m ust solve a two-stage problem . In

the first stage, banks m inim ize the cost of m anaging their funds on a com petitive input

m arkets by com puting the m arginalcost ofsupplying an additionalloan to borrowers and

a depositservice to households. T he com putation ofthese m arginalcostshas already been

perform ed in the previous subsection. In a second stage,they operate under m onopolistic

com petition by applying a m arkup (m arkdow n) on their com m ercialloan (deposit) rate,

and set the interest rate on a staggered basis.U sing a C alvo nom inalrigidity device,each

period a random fraction θ

^L_i

( θ

^D_i

) ofbanks is unable to update its lending (deposit) rate,

R

^Li ,t

= R

^Li ,t−1

( R

^Di ,t

= R

^Di ,t−1

),creating an im perfect transm ission of m onetary policy deci- sions to borrowers and savers living in the m onetary union. T he bank that it is able to m odify its loan interest rate (w ith a constant probability 1− θ

^L_i

) choosesR

^L∗_{i ,t}

to m axim ize its expected stream ofprofits adjusted by the risk ofdefault:

E

t

X

∞ s= 0

θ

^Li

τ

i ,t+ s

1 − µ

^B

(1 − η

i ,t+ 1+τ

) R

^L∗i ,t

− exp( ε

^Li ,t+ s

) M C

i ,t+ s^L

L

^si ,t+ s

, (12) w here ε

^L_{i ,t}

is an ad-hoc m arkup A R (1) shock to the credit rate equation, θ

^L_i

[0, 1) is the C alvo lottery coe cient determ ining the degree of nom inalrigidity and M C

_{i ,t}^L

is the aggregate m arginalcostcom bining outputsfrom liquid and illiquid banksofcountry i. W e aggregate loans from liquid and illiquid banks and their respective m arginalcosts before applying the m arkup for tractability purposes: this device is useful to com pute a single Phillips curve as well as an unique credit rate for both liquid and illiquid banks. W e borrow this shortcut procedure from G erali et al.( 2010) adapted in a di erent context, i.e. all banks belonging to a national banking system share the sam e m arginal cost of production, reflecting the average liquidity degree of national banks: 1 + M C

_{i ,t}^L

= (1 + M C

_{i ,t}^{i ll}

)

^λ

(1 + M C

_{i ,t}^{li q}

)

^{(1− λ)}

. In addition,the banking spread reflecting the leveloffinancial distress is given by S

_{i ,t}^L

= (1 + R

^L_{i ,t}

) / (1 + R

t

) .

In a sim ilarfashion fordepositrates,assum ing thatitisable to m odify itsinterestrate w ith a constant probability 1 − θ

^Di

,the representative bank chooses R

^D∗i ,t

to m axim ize its expected stream ofprofits,by applying a m arkdow n on the refinancing rate ofthe central bank R

t

:

E

t

X

∞

τ= 0

θ

_i^{D τ} i ,t+ s

R

t+ s

exp( ε

^D_{i ,t+ s}

)− R

^D∗_{i ,t}

D

i ,t+ s

, (13)

w here ε

^Di ,t

is an ad-hoc tim e-varying A R (1) m arkdow n shock to the deposit rate equation and θ

_i^D

[0, 1) is the C alvo lottery param eter.

2.4. Macroprudential policy

M acroprudential policy a ects the general equilibrium of the econom y through the

policy instrum ent v

i ,t

that contributes to the m arginal cost of com m ercial banks’ loans.

A s a consequence, a m acroprudentialpolicy tightening is associated w ith higher lending rates,and lowerbank creditgrow th and assetprices. W e assum e thatthe m acroprudential authority sets the tim e-varying capitalrequirem entν

i ,t

according to:

v

i ,t

= (1 − ρ

^v_i

)¯ ν + ρ

^v_i

ν

i ,t−1

+ φ

i

(T

i ,t

− ¯ T

i

) , (14)

w hereρ

^v_i

[0 , 1) is the sm oothing coe cient ofthe rule,T

i ,t

is the m acroprudentialtarget, φ

i

0 is the m acroprudentialw eight to the target in country i and ¯ T

i

is the steady state ofthe target. In our specification,capitalrequirem ents are expected to increase w hen the target deviates from its steady state. T he choice ofthe target T

i ,t

is a key aspect ofthe paper that w illbe discussed below .

T he ESR B hasdeveloped a bu erguide to choose the C C B rate based on the credit-to- gdp gap.

¹⁷

H owever,the globalnature ofthe European banking system introduces m any possibilities for the definition of the credit-to-gdp ratio taken into account by national authorities. Indeed, the C C B rate m ay be adjusted to the credit supply (of banks) or the credit dem and (of entrepreneurs),

¹⁸

either on a national or on a federal basis. O ur fram ework w ith internationalbank flow s allow s us to distinguish between five operational targets as listed in Table 1.

T he firstsetofcredittargeting rulesisoriented tow ardsthe supply ofcreditusing either a federal(1.a) or a country-specific aggregate (1.b). A m acroprudentialpolicy based on credit supply aim s at stabilizing lenders by focusing m ore on the stabilization offinancial shockshitting lendersratherthan dem and and supply shockshitting borrowers. G iven the scale of cross-border loans in the Eurozone, the decisions of the national supervisor has side e ects on countries w here a nationalbank has a subsidiary or branches or w here this bank lends to m ay favor a federaldefinition ofthe ratio. T hus to handle these pecuniary

17

Other indicators (such as early warning variables) are included in the CCB guide which are not imple- mentable in our model.

18

In 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 domest ic demand for loans. T his

distinction between demand and supply is easy to see on the market clearing condit ions of interbank

(Equation B.23) and corporate markets (B.22).

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 st ance (common or national-adjusted)

Schemes Target

L oan Suppl y Tar get ing

1.a Union-wide loan supply

T_t

= (L

^s_t

+ (1−

λ)I B_t^s

)/ Y

_t

1.b National loan supply

Ti ,t

= (L

^s_{i ,t}

+

λI B^d_{i ,t}

)/ Y

i ,t

for i

{c, p}

L oan Demand Tar get ing

2.a Union-wide loan demand

Tt

= (L

^d_t

+

λI B_t^d

)/ Y

t

2.b National loan demand

Ti ,t

= (L

^d_{i ,t}

+

λI B^d_{i ,t}

)/ Y

i ,t

for i

{c, p}

Capit al I nf l ows Tar get ing

3 Capital Inflows

T_{i ,t}

= (L

^d_{i ,t}−

L

^s_{i ,t}

+

λI B_{i ,t}^d −

(1

−λ)I B^s_{i ,t}

)/ Y

_{i ,t}

for i

{c, p}

Note: variables wit hout count ry subscript such as xtdenot e union-wide averages comput ed as a weight ed sum of each count ry xt= nxc,t+ (1−n)xp,t.

externalities, we evaluate the possibility of an union-w ide targeting system (1.a) against a national targeting system (1.b), the latter being expected to create m ore externalities (positive or negative) as it a ects the foreign banking system w ithout taking into account its financialdevelopm ents.

¹⁹

T he second setofcredittargeting rulesconcentrateson the dem and ofcreditem anating from entrepreneurs.

²⁰

T he interest of a C C B rate tailored to borrowers is that it m ay provide m ore stabilization follow ing realand nom inalshocks hitting households and firm s at the expense offinancialshocks a ecting banks. T his solution seeks at internalizing the socialcostofentrepreneurs’over-borrow ing thatm ay arise given theirbiased expectations.

A s this policy regim e ine ciently a ects foreign borrowers through cross-border lending, spillovers e ects m ay be dam pened by a federaltargeting (2.a) rather than a nationalone (2.b).

W e also evaluate the interest of adopting provisionalm easures to a ect cross border lending directly,through targeting capitalinflow s in the C C B .T his solution,as envisaged

19

For further discussions of these cross-border issues, we refer to

Beck et al.

(2016).

20

A loan demand targeting is feasible in a real life situation, the ECB already disentangles the credit

demand and supply by collecting the domest ic 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

market s, 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 t he Euro Area. For the supply side, both the ECB and the BIS

collect domestic and cross-border positions of euro area monetary

financial inst itutions.

by Jeanne and K orinek ( 2010), B runnerm eier et al.( 2012) and R ey ( 2015), is relatively sim ilar to a capitalcontrolm easure. T he m ain insight behind this schem e would rely on the fact that persistent capitalaccount im balances induce financialstability risks and m ay have im plications for the sustainability ofnet externalasset positions. In particular since the creation in the Eurozone,globalbanking has experienced an explosive grow th helping to fuelunsustainable creditboom sin peripheraleconom iessuch asin Spain and in Ireland, follow ed by a sudden stop in capital inflow s com pensated by unconventional m easures.

M acroprudentialpolicies can play a key role to contain this problem by im posing targeted regulationson banksengaged in cross-borderactivities.W hen borrow ing to otherEuropean banks is increasing faster w ith respect to the G D P,a nationalauthority can rise the C C B rate to a ect banks’balance sheet m anagem ent and reduce their exposure to international borrow ing. In addition w hen system risks abate in one econom y, leading to capital flow reversals, national authorities m ay release the bu er thus loosening the banks’ funding constraint to address the procyclicality ofcapitalflow s.

3. E stim ation strategy

W e fit the previous tw o country D SG E to Eurozone data over the sam ple tim e period 1999Q 1-2013Q 4 using B ayesian techniques. W e estim ate structural param eters and the sequence of shocks by follow ing the sem inal contributions ofSm ets and W outers ( 2003, 2007 ) and C hristiano et al. ( 2005). For a detailed description, we refer to the original papers.

3.1. Data

W e splitthe Eurozone in two groupsadopting the core-periphery dichotom y asin Q uint

and R abanal( 2014) and Poutineau and Verm andel( 2015). C ore countries gather A ustria,

B elgium ,G erm any,Finland,France,Luxem bourg and N etherlands w hile peripheralcoun-

tries include Spain, G reece, Ireland, Italy and Portugal. T he m odel is estim ated w ith

B ayesian m ethods on Eurozone quarterly data over the sam ple period 1999Q 1 to 2013Q 4,

w hich m akes 60 observations for each observable variable. C oncerning the transform ation

ofseries,the point is to m ap non-stationary data to a stationary m odel. D ata w hich are

know n to have a trend (nam ely G D P,consum ption,investm ent,corporate loan and inter- bank supply) or unit root are m ade stationary in two steps. First,we divide the sam ple by the population. Second, data are taken in logs and we use a first di erence filtering to obtain grow th rates. In addition,realvariables are deflated by the H IC P price index and we rem ove the seasonalcom ponent in the data using a m ultiplicative decom position.

Furtherm ore,we dem ean the data as we do not use the inform ation contained in the ob- servable m ean. Interest rates are set on a quarterly basis by dividing them by 4. Since hours worked are not observable for the Euro A rea,we adopt the sam e m odelling strategy as Sm ets and W outers ( 2003) to identify T FP shocks using em ploym ent as a proxy for hours w orked. Em ploym ent is divided by the working population index,taken in logs and dem eaned. To m ap em ploym ent to hours worked in our m odel,we introduce an auxiliary equation for each country w hich states that only a share θ

_i^E

[0 , 1) offirm s is allow ed to adjust its levelofem ploym ent ˆ e

i ,t

to its optim allabor dem and H

_{i ,t}^d

:

e ˆ

i ,t

= βˆ e

i ,t+ 1

+ 1 − βθ

i^E

1 − θ

^Ei

/ θ

i^E

log H

i ,t^d

/ H ¯

^d

− ˆ e

i ,t

. (15) T he vector ofobservable variables reads as:

Y

t

= 100[ ˆ y

i ,t

, ˆ e

i ,t

, c ˆ

i ,t

, ˆ ı

i ,t

, π ˆ

^Ci ,t

, w ˆ

i ,t

, r ˆ

i ,t^D

, ˆ l

i ,t^s

, b ib

^si ,t

, r ˆ

t

] for i = {c, p}.

3.2. Calibration, priors and model assumptions

W e fix a sm allnum ber ofparam eters com m only used in the literature ofrealbusiness cycles m odels w hich are weakly identified. T he discount factorβ is set at 0.99,the depre- ciation rateδ at 0.025,the capitalshare α at 0.38,the share ofsteady state hours w orked H ¯ at1,the spending to G D P ratio g at24% .

²¹

C oncerning

P

and

W

(the substitutability betw een finalgoods and labor),we consider the calibration at 10 as in Sm ets and W outers ( 2007). R egarding financialparam eters, w e fix ¯ N / K ¯ (the net worth to capital) ratio to 0 .40 to be consistent w ith the observed debt-to-financialassets ratio ofnon-financialcor-

21

T his calibration off ers a consumption-to-output ratio of 55.45% (vs 57.31% in the data) and investment-

t o-output ratio of 20.55% (vs 20.70% in the data).

porations w hich fluctuates between 50% and 65% since 1999. T he steady state value of spreadsand the bank balance sheetare calibrated on theiraveragesobserved overthe sam - ple period in the Euro A rea: ¯ R-¯ R

^D

= 1.66/400, ¯ R

^L

-¯ R

^D

= 3.67/400, ¯ D / L ¯

^s

= 0.46,r wa= ¯ v= 0.10 and I B

^d

/ L ¯

^s

= 0.20. T he capitalregulation cost χ

^k

is set at 11 as in G eraliet al.( 2010) to replicate the response ofcredit and interest rate to a capitalrequirem ent rise.

Forsubstitution param etersforcorporate and interbank loansυ and ξ aswellasforthe fraction ofilliquid banks λ,to our know ledge there are no em piricalanalysis using bank level data that provides an estim ation of these param eters. W e rely on the previous fit exercise ofPoutineau and Verm andel( 2015) by calibrating λ at 0.38 and υ,ξ at 1.1.T he latter calibration for substitution param eters is rather conservative by allow ing very low substitution e ects betw een hom e and foreign loans.

²²

T he quarterly share of defaulting firm s’ projects 1 − ¯ η

^E

is fixed at 0.025/4,

²³

and the auditing cost µ

^B

at 0.10,

²⁴

those values are very sim ilar to B ernanke et al.( 1999). W e com pute the param eter governing the relative size ofthe core area n at 0.58 as in K olasa ( 2009),w hich is the share im plied by nom inalG D P levels averaged over the period 1999-2013. W e calibrate sym m etrically the adjustm ent cost on deposits χ

^Di

at 0.0007 as in Schm itt-G roh´ e and U ribe ( 2003) to rem ove an unit root com ponent generated by the two-country set-up. Finally,the lower bound ω

min

and the shape κ of the Pareto distribution are endogenously determ ined by the m odelequations assum ing a risk-free econom y w ith no spread and default,w e obtain:

ω

min

= 1-¯ N / K ¯ and κ= ¯ K / N. O urcalibration deliversforthe m ain endogenousvariablesthe ¯ follow ing steady state: ¯ ω

^C

= 0.6015,ε

^D

= -2.41,ε

^L

= 4.37,¯ r

^L

= 0.0192 and ¯ r

^K

= 0.0166.

22

In 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).

23

T his is consistent with corporate default statistics from Moody’s, the rating agency, which show an average default rat e on (non-US) non-financial corporate bonds of 0.75% for the period 1989-2009, as shown by

Darracq-Pari`es et al.

(2011). T he other rating agency Standards & Poor’s evaluates the rate of default for the period 1991-2014 t o 0.58%. We consider a default rate of 0.63% which is in the ballpark of the numbers found by rating agencies.

24

T he auditing cost cannot be observed as few data on loan losses are publicly available for reasons

of confidentiality.

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%.

O ur priors are listed in Table B .7. O verall, they are either relatively uninform ative or consistent w ith earlier contributions to B ayesian estim ations. For a m ajority of new K eynesian m odels’param eters,i.e. σ

_i^L

,h

^C_i

,θ

^P_i

,ξ

_i^P

,θ

^W_i

,ξ

_i^W

,θ

^E_i

,χ

^I_i

,ψ

i

,φ

^π

,φ

^∆y

and shock processes param eters, w e use the prior distributions close to Sm ets and W outers ( 2003, 2007 ). C alvo probabilitiesforrateshave the sam e uninform ative priors as forprices/w ages w hile loans habits are given a prior m ean 0.5 w ith standard deviation 0.2. O ur priors for openness param eters are based on their observed average over the sam ple period. Substi- tutabilities between hom e/foreign credit and finalgoods are set to 2 w ith standard devi- ations of0 .50. W e set the prior for the elasticity ofthe externalfinance prem ium κ

i

to a beta distribution w ith priorm ean equalto 0 .05 and standard deviation 0.02 consistentw ith prior inform ation ofG ilchrist et al.( 2009). Finally, in order to catch up the correlation and co-m ovem entsbetween countries’aggregates,we estim ate the cross-country correlation betw een structuralshocks,associated priors are inspired by in Jondeau et al.( 2006) and K olasa( 2009),we setthe m ean ofthe priordistribution forshock correlationsbetween core countries and peripheralcountries at 0 .2 w ith a standard deviation at 0.2.

Finally,regarding bank capitalregulation for the fit exercise,we disable the m acropru- dentialinstrum ent by fixing the C C B rate to its determ inistic steady state value:

ν

i ,t

= ¯ v. (16)

T his assum ption is reasonable for two m ain reasons.First over the sam ple period,capital regulation hasbeen m ainly dom inated by the B aselIA ccordscharacterized by fixed capital requirem entratios.Second,even through the adoption ofthe B aselIIIA ccordsallow sEuro A rea countries to em ploy the countercyclicalcapitalbu er as a shield against the build up of financial im balances, it has not been yet em ployed by a participant of the m onetary union.

²⁵

25

T he ESRB off ers on its website an interactive map of the Euro Area on countercyclical capital buff ers.

To this date, only Sweden and Norway have activated the CCB rat e in the European Union but both of

t hese countries are not Euro Area participants.

3.3. Estimation results

T he m ethodology em ployed isstandard to the B ayesian estim ationsofD SG E m odels.

²⁶

Table B .7 reports estim ation results w hich sum m arizes the m eans and the 5th and 95th percentilesoftheposteriordistributionsw hilethelatteraredraw n in FigureB .6 .A ccording to this figure, prior and posterior distributions are relatively di erent show ing that the data were fairly inform ative. Several param eters are well identified for one country but weakly for the other econom y,w e decide to keep these param eters in the fit exercise after checking that their w eak identification does not a ect our estim ations (i.e. calibrating these param eters and re-estim ating the m odel provides very sim ilar results). W hile our estim ates ofthe standard param eters are in line w ith the literature (see forinstanceSm ets and W outers( 2003)and Q uintand R abanal( 2014)),severalobservationsare worth m aking by com m enting the m ean ofthe posterior distribution ofstructuralparam eters.

First regarding asym m etries in business and credit cycles between the core and the periphery, they are m ainly driven by the standard deviation of shocks w hich are larger in peripheraleconom ies.In particular, ine ciency shocks for wages and prices are m ore volatile in periphery w hich m ay constitute an issue in the im plem entation ofa single m one- tary policy. In the sam e vein for m acroprudentialregulation,the presence ofheterogenous financialshocks in term s ofvolatility questions the perspective ofa single federalm acro- prudentialauthority.

Second turning to structuralparam eters,w e find an im portantdi erence betw een coun- triesregarding param eterθ

_i^E

thatdeterm inesthe adjustm entofem ploym entto the dem and ofhoursw orked:corecountriesobservea sluggish responseofem ploym entto thecyclew hile the m irror im age is seen for periphery. Stillregarding the labor m arket,w age rigidity and

26

T he 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 suffi ciently large number of

draws, having made sure that the MCMC algorithm converged. To do t his, a sample of 250, 000 draws was

generated for four chains through parallelization, neglecting the

first 50, 000. The scale fact or 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.

indexation param eters are also higher in core countries suggesting that core countries are farther from the optim al allocation characterized by flexible wages and prices. H owever thisinterpretation isnuanced byG al ´ ı( 2013)show ing thatwage rigiditiescan,in som e par- ticularsituations,play a stabilizing role forthe econom y. O ne ofthese particularsituations exposed by G al ´ ı( 2013)isa m onetary policy w eakly oriented toward inflation w hich can be observed w hen m onetary policy hashititslowerbound. In the lightofthisnew reinterpre- tation that m eets the current situation ofthe Euro A rea,w ages and em ploym ent rigidities of core countries m ay have been stabilizing frictions since the financial crisis episode in 2009.

T hird,the results related to m arket integration are in line w ith the standard em pirical evidence. In particular, peripheral econom ies are m ore open and dependent to the core area than the opposite,exceptforinterbank facilities.T hislatterresultishard to reconcile w ith the em piricalevidence as,before the financialcrisis,peripheraleconom ies w here net recipient of interbank loans that fueled the property boom . T his could be a lim itation ofthe analysis conducted here,however by sum m ing both the net entry ofcorporate and interbank loans,our m odelpredicts that peripheraleconom ies were net recipient ofloans consistently w ith the historicalexperience ofthe Euro A rea.

4. T he perform ance of M acroprudential P olicy 4.1. The suboptimality of the federal solution

T he countercyclicalcapitalbu er(C C B ,henceforth),asdefined in the B aselIIIaccords

( 2010)and ESR B handbook ( 2014),isan instrum entdesigned to contain the procyclicality

ofthe financialsector. Itisaim ed atbuilding up a capitalbu erw hen threatsto resilience

are high or during periods ofexcessive credit grow th and can be released w hen system ic

risks abate. T he ESR B has selected the credit-to-gdp gap as a leading indicator to signal

upcom ing crises that the C C B is m eant to m itigate. A naturaltranslation ofthe C C B ’s

objective in our setup corresponds to the m inim ization ofthe variance ofthe credit-to-gdp

ratio in the m onetary union:

²⁷

L = σ

²_{L / Y}

+ λ

Y

σ

²_Y

+ λ

ν

σ

²_ν

, (17)

w hereσ

²_{L / Y}

,σ

²Y

and σ

²ν

denote respectively the unconditionalvariance ofthe credit-to-gdp ratio,output and policy toolν

i ,t

w hile param eters λ

Y

and λ

ν

are weights on output and C C B . T his ad-hoc loss function L borrowed from A ngelini et al. ( 2014) is obtained as a weighted average of nationalloss functions for each area. It is defined as, L = nL

c

+ (1 − n)L

p

,w hereforeach country thenationallossisgiven by,L

_i

= σ

²_{i ,L / Y}

+ λ

Y

σ

²_{i ,Y}

+ λ

ν

σ

_{i ,ν}²

. N oticeably, as our m odel features an interbank m arket, the credit-to-gdp ratio is given by the aggregate credit supply divided by output: ctg

i ,t

= ( L

^s_{i ,t}

+ (1 − λ)I B

^s_{i ,t}

) / Y

i ,t

. A s A ngeliniet al.( 2014),w e assum e thatλ

ν

= 0 .10 and λ

Y

= 0,howeverin a robustness section we investigate w hether our results are sensitive to this calibration.

U sing the criterion ( 17 ), we are able to perform a sim ilar exercise as A ngelini et al.

( 2014) by ranking m acroprudentialpolicies selecting C C B rule’s coe cients [ ρ

^υ_c

, ρ

^υ_p

, φ

c

, φ

p

] that deliver the sm allest loss. W e search over a four-dim ensional grid over param eters ranges [0,1) forρ

^υ_i

and [0,5]forφ

i

. A s a benchm ark for com paring our scenarios for C C B im plem entation, we consider the optim alm onetary policy situation characterized by the optim ized Taylor rule that m axim izes the welfare of households living in the m onetary union. Put di erently,the interaction between m onetary and m acroprudentialpolicy fol- low sa Stackelberg gam e w here m onetary policy isleaderby rem oving nom inaline ciencies in the Euro area through the refinancing rate,followed afterward by m acroprudentialpolicy w hich dam pens financialcycles. O ptim alm onetary policy is based on a second order ap- proxim ation to equilibrium conditions ofthe m odelas in Schm itt-G roh´ e and U ribe ( 2007 )

27

We 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

t he trade-o

ff

faced by macroprudential authorities between macroeconomic and

financial stabilization. A

macroprudential policy maximizing the welfare index reduces inflation to the det riment 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).