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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.
Kharroubi () MP and MaP Coordination June 17-18, 2019 3 / 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.
Kharroubi () MP and MaP Coordination June 17-18, 2019 3 / 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.
Kharroubi () MP and MaP Coordination June 17-18, 2019 3 / 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.
Kharroubi () MP and MaP Coordination June 17-18, 2019 3 / 16
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.
Kharroubi () MP and MaP Coordination June 17-18, 2019 5 / 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.
Kharroubi () MP and MaP Coordination June 17-18, 2019 5 / 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.
Kharroubi () MP and MaP Coordination June 17-18, 2019 5 / 16
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).
Kharroubi () MP and MaP Coordination June 17-18, 2019 6 / 16
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).
Kharroubi () MP and MaP Coordination June 17-18, 2019 6 / 16
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
Kharroubi () MP and MaP Coordination June 17-18, 2019 7 / 16
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
Kharroubi () MP and MaP Coordination June 17-18, 2019 7 / 16
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
Kharroubi () MP and MaP Coordination June 17-18, 2019 7 / 16
The decentralized equilibrium
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.
Kharroubi () MP and MaP Coordination June 17-18, 2019 8 / 16
The decentralized equilibrium
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.
Kharroubi () MP and MaP Coordination June 17-18, 2019 8 / 16
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.
Kharroubi () MP and MaP Coordination June 17-18, 2019 9 / 16
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.
Kharroubi () MP and MaP Coordination June 17-18, 2019 9 / 16
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)
Kharroubi () MP and MaP Coordination June 17-18, 2019 10 / 16
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)
Kharroubi () MP and MaP Coordination June 17-18, 2019 10 / 16
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)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
Kharroubi () MP and MaP Coordination June 17-18, 2019 11 / 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
Kharroubi () MP and MaP Coordination June 17-18, 2019 11 / 16
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
Kharroubi () MP and MaP Coordination June 17-18, 2019 12 / 16
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
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Quantifying welfare gains
Splitting welfare gains by region, by policy
Kharroubi () MP and MaP Coordination June 17-18, 2019 14 / 16
Quantifying welfare gains
Which region bene�ts from coordinating what policies?
Kharroubi () MP and MaP Coordination June 17-18, 2019 15 / 16
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.
Kharroubi () MP and MaP Coordination June 17-18, 2019 16 / 16