International Coordination of Macro-Prudential andpubdocs.worldbank.org/.../ABCDE-presentation-Kharroubi.pdf · I Frictions to cross-border capital ⁄ows How do policies interact

International Coordination of Macro-Prudential andMonetary policies1

Enisse KharroubiMonetary and Economic DepartmentBank for International Settlements

Annual Bank Conference on Development EconomicsMultilateralism: Past, Present, and Future.

June 17-18, 2019

1Views expressed here are not necessarily the views of the BIS.Kharroubi () MP and MaP Coordination June 17-18, 2019 1 / 16

Introduction

When is international policy coordination desirable?

Literature starting from Obsfeld and Rogo¤ (1992) �nds little gainsto international coordination on monetary policy (MP).

I Negligible welfare losses to domestically oriented monetary policies

But what about macro-prudential policy (MaP) ?

I Does a similar kind of result hold ?

I What drives cooperation gains ?

I How the conduct of other policies (MP) a¤ects these gains?

Kharroubi () MP and MaP Coordination June 17-18, 2019 2 / 16

An overview of the main resultsMain results

Does a similar kind of result hold?I Both MaP and MP coordination yields welfare gains. But unlike MP,MaP coordination is a Pareto improvement.

I MP takes place ex post, after shock are realized and uncertainty hasunraveled, i.e. once countries have become asymmetric

I MaP takes place ex ante (risk sharing), under the veil of ignorance andhas positive GE spill-overs.

What drives gains to policy cooperation ?I Frictions to cross-border capital �ows

How do policies interact with each other ?I Welfare gains to MaP cooperation larger under Nash MP.























IntroductionSome papers in the literature.

Policy coordination:I extensive literature on MP coordination (cross-border, cross-policy).Engel (2016) provides a nice survey.

I Much less on MaP coordination. Jeanne (2014), Bengui (2015) andEngel (2015)

MP and MaP in open economy:I Objectives: Benigno (2009), Corsetti et. al. (2011), Faia and Monacelli(2008), Bengui (2014), Senay and Sutherland (2018).

I E¤ectiveness: Rey (dilemma vs. trilemma), Mendoza (2016) andAizenmann et al. (2018).

I Leakages: Aiyar (2012) for the UK, Barroso et al. (2016) for Brazil

Liquidity managment/provisionI Under-insurance and pecuniary externalities (Gromb and Vayanos 2002,Lorenzoni 2008 or Stein 2012), particularly in open economy context(Caballero and Krishnamurthy 2003 or Jeanne and Korinek 2010,Brunnermeier and Sannikov (2014)).Kharroubi () MP and MaP Coordination June 17-18, 2019 4 / 16

The modelFramework and technologies.

A 3-period economy à la Holmstrom-Tirole (1998) with 2 regions andrisk neutral banks maximizing �nal pro�ts.

At date 0, banks hold unit endowment and invest in risky assets.I At date 1, risky asset returns 1 in one region and 0 in the otherI Regions are symmetric and there is no aggregate uncertainty.

At date 1, once uncertainty is resolved:I If risky assets pay-o¤: banks can save for a return r (< 1)I If risky assets do not pay-o¤: banks can reinvest with unit return 1.












The model

MarketsI Ex ante risk sharing: At date 0, banks can issue claims on their riskyassets and buy claims on the other region�s risky assets.

I Ex post market for liquidity: At date 1, once uncertainty is resolved,banks can exchange liquidity.

PoliciesI Monetary policy sets the return r to savings between date 1 and date2 (deposit facility).

I Macro-prudential policy sets the max limit on banks�borrowing atdate 0 (leverage ratio or CFM).


The model

MarketsI Ex ante risk sharing: At date 0, banks can issue claims on their riskyassets and buy claims on the other region�s risky assets.

I Ex post market for liquidity: At date 1, once uncertainty is resolved,banks can exchange liquidity.

PoliciesI Monetary policy sets the return r to savings between date 1 and date2 (deposit facility).

I Macro-prudential policy sets the max limit on banks�borrowing atdate 0 (leverage ratio or CFM).


The decentralized equilibrium

The portfolio choice for banks:

maxL;L�;D

[1+ L� L� � R1L]R�2 + [βR�1L� +D � R2D ]

s.t. D � 1� λ and L � m (1+ L� L�)

Assuming max (r ; r �) � (R2;R�2 ) � 1, the equillibrium on market expost funding:

1+ L� � L| {z }Funding Supply

= βR�1L� +D| {z }

Funding Demand




maxL;L�;D

[1+ L� L� � R1L]R�2 + [βR�1L� +D � R2D ]

s.t. D � 1� λ and L � m (1+ L� L�)



= βR�1L� +D| {z }

Funding Demand




maxL;L�;D

[1+ L� L� � R1L]R�2 + [βR�1L� +D � R2D ]

s.t. D � 1� λ and L � m (1+ L� L�)



= βR�1L� +D| {z }

Funding Demand



At the equilibrium, borrowing and issuance constraints bind:

D = 1� λD� = 1� λ�

andL = m (1+ L� L�)L� = m� (1+ L� � L)

Negative spill-over: Higher issuance by one region implies lowerissuance by the other region.

At the equilibrium, ex post funding is in excess supply:

(R2;R�2 ) = max (r ; r�) and

L � λ+ (1�max (r ; r �)) L�L� � λ� + (1�max (r ; r �)) L

Positive spill-over: Higher issuance by one region allows for largerissuance by the other region.



At the equilibrium, borrowing and issuance constraints bind:

D = 1� λD� = 1� λ�

andL = m (1+ L� L�)L� = m� (1+ L� � L)

Negative spill-over: Higher issuance by one region implies lowerissuance by the other region.

At the equilibrium, ex post funding is in excess supply:

(R2;R�2 ) = max (r ; r�) and

L � λ+ (1�max (r ; r �)) L�L� � λ� + (1�max (r ; r �)) L

Positive spill-over: Higher issuance by one region allows for largerissuance by the other region.


Optimal monetary policyThe non-cooperative equilibrium

Optimal monetary policy:

maxr

π =h1+

�1� 1

βR2�LiR�2 + (1� R2) (1� λ)

s.t. R2 = R�2 = max (r ; r�)

Optimal interest rates in Nash equilibrium:

r = r � = rn (L; L�) �β

2

�1+max

�λ

L;

λ�

L�

��Equilibrium interest rate main properties:

I optimal for one region (core), too high for the other (periphery)I decreases in domestic banks leverage.


Optimal monetary policyThe non-cooperative equilibrium

Optimal monetary policy:

maxr

π =h1+

�1� 1

βR2�LiR�2 + (1� R2) (1� λ)

s.t. R2 = R�2 = max (r ; r�)

Optimal interest rates in Nash equilibrium:

r = r � = rn (L; L�) �β

2

�1+max

�λ

L;

λ�

L�

��Equilibrium interest rate main properties:

I optimal for one region (core), too high for the other (periphery)I decreases in domestic banks leverage.


Optimal macro-prudential policyThe non-cooperative equilibrium: Core vs. Periphery

Macro-prudential policy in the core region:

maxm

π =hλ+

�1� 1

β rn (L)�Lirn (L)

s.t. L = m (1+ L� L�) and L � λ+ (1� rn (L)) L�

No trade-o¤ for MaP: higher m ) higher L ) higher pro�ts π

Macro-prudential policy in the periphery region:

maxm�

π� =hλ� +

�1� 1

β rn (L)�L�irn (L)

s.t.L� = m� (1+ L� � L)L = m (1+ L� L�) and L� � λ� + (1� rn (L)) L

Trade-o¤ for MaP: higher m� ) higher L� but higher rn (L)

Optimal macro-prudential policy in Nash equilibrium:

L = λ+ (1� rn (L)) L� and L� = Ln (L)




maxm

π =hλ+

�1� 1





maxm�

π� =hλ� +

�1� 1





L = λ+ (1� rn (L)) L� and L� = Ln (L)




maxm

π =hλ+

�1� 1





maxm�

π� =hλ� +

�1� 1





L = λ+ (1� rn (L)) L� and L� = Ln (L)Kharroubi () MP and MaP Coordination June 17-18, 2019 10 / 16

Optimal macro-prudential policyThe cooperative equilibrium

Cooperative macro-prudential policy:

maxm;m�

π + π� =hλ+ λ� +

�1� 1

β rn (L)�(L+ L�)

irn (L)

s.t.

(L = m (1+ L� L�) and L� = m� (1+ L� � L)

L � λ+ (1� rn (L)) L� and L� � λ� + (1� rn (L)) L

No trade-o¤ for core: higher m ) larger global leverage L+ L� )larger global pro�ts π + π�

L = λ+ (1� rn (L)) L�

No trade-o¤ for periphery: higher m� ) larger L� and hencelarger L (positive GE spill-over):

L� = λ� + (1� rn (L)) L


Optimal macro-prudential policyThe cooperative equilibrium

Cooperative macro-prudential policy:

maxm;m�

π + π� =hλ+ λ� +

�1� 1

β rn (L)�(L+ L�)

irn (L)

s.t.

(L = m (1+ L� L�) and L� = m� (1+ L� � L)

L � λ+ (1� rn (L)) L� and L� � λ� + (1� rn (L)) L

No trade-o¤ for core: higher m ) larger global leverage L+ L� )larger global pro�ts π + π�

L = λ+ (1� rn (L)) L�

No trade-o¤ for periphery: higher m� ) larger L� and hencelarger L (positive GE spill-over):

L� = λ� + (1� rn (L)) L


Optimal macro-prudential policyComparing Nash and cooperation

In Nash, periphery limits bank leverage to steer FC set in the core.

In Coop, periphery internalizes the positive spill-over in bank leverage.I Gross cross border positions (L; L�) are largerI Global funding cost rn (L) is lower


Quantifying welfare gainsWe consider three parameters of the model

I Cost on cross-border capital �ows ( β from 55% to 95%)I Gross foreign liabilities in Core (λ from 40% to 80%)I Gross foreign liabilities in Periphery (λ� 0% to 40%)

Global welfare gains distribution (cooperative vs. Nash MP & MaP)0

.2.4

.6.8

0 1 2 3 4 5Note: Welfare gains computed as the ratio of global welfare under cooperative monetary and macroprudential policies to global welfare under Nash monetary and macroprudential policies.

in percentDistribution of global welfare gains


Quantifying welfare gains

Splitting welfare gains by region, by policy


Quantifying welfare gains

Which region bene�ts from coordinating what policies?


Conclusions

We have developed a model of monetary and macro-prudential policycross-border coordination where

I macro-prudential policy determines bank ex ante leverage.I monetary policy determines the cost of ex post borrowing

Global interest rate under Nash MP is optimal for one region and toohigh for the other. This creates incentives for periphery to use MaPto a¤ect funding conditions.

Trade-o¤: allowing more borrowing vs. correcting ine¢ cient fundingconditions. Main issue: misses the cross-border leverage externality.

Numerically, coordination gains can be sizeable, particurlarly for theperiphery. Asymmetry matters.


Documents

International Coordination of Macro-Prudential andpubdocs.worldbank.org/.../ABCDE-presentation-Kharroubi.pdf · I Frictions to cross-border capital ⁄ows How do policies interact