The Role of Interbank The Role of Interbank Markets in Monetary Markets in Monetary Policy:Policy:A Model with RationingA Model with Rationing

Xavier FreixasXavier FreixasUniversitat Pompeu Fabra and CEPRUniversitat Pompeu Fabra and CEPR

José JorgeJosé JorgeCEMPRE, Faculdade Economia, Universidade PortoCEMPRE, Faculdade Economia, Universidade Porto

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MotivationMotivation

Starting point:Starting point: Paradox in the way we model Paradox in the way we model the microfoundations of monetary policy.the microfoundations of monetary policy.

1.1. The role of banks is justified by the The role of banks is justified by the existence of asymmetric information.existence of asymmetric information.

2.2. Yet, when it comes to monetary policy Yet, when it comes to monetary policy transmission mechanisms, the Interbank transmission mechanisms, the Interbank Market is assumed to be a perfect market Market is assumed to be a perfect market that plays a neutral role in the allocation of that plays a neutral role in the allocation of resources. resources.

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Empirical evidence on Empirical evidence on liquidity and the interbank liquidity and the interbank marketmarket

Micro data: Kashyap and Stein (2000) found Micro data: Kashyap and Stein (2000) found that the impact of monetary policy is more that the impact of monetary policy is more pronounced for banks with less liquid pronounced for banks with less liquid balance sheets.balance sheets.Ashcraft (2006) on bank holding companiesAshcraft (2006) on bank holding companiesHence 1) liquidity matters and 2) interbank Hence 1) liquidity matters and 2) interbank markets cannot be perfect.markets cannot be perfect.

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Related literatureRelated literature

1.1. Money view vs. Broad Credit ChannelMoney view vs. Broad Credit Channel2.2. Stein 1998 spread augmented interest Stein 1998 spread augmented interest

rate channelrate channel3.3. Interbank market modelsInterbank market models

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MethodologyMethodology

1.1. We introduce asymmetric information We introduce asymmetric information in the interbank market.in the interbank market.

2.2. Derive the contracts available in the Derive the contracts available in the interbank market.interbank market.

3.3. Derive the individual net demands.Derive the individual net demands.4.4. Derive the equilibrium in the interbank Derive the equilibrium in the interbank

market.market.

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Main ResultsMain Results

Under perfect information, the money Under perfect information, the money view holds.view holds.Under asymmetric information, there Under asymmetric information, there is rationing in the interbank market.is rationing in the interbank market.Our model is consistent with the main Our model is consistent with the main empirical results.empirical results.

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ConclusionMotivation Model AsymmetricInformation

Perfect Markets

The ModelThe ModelFirms invest one unit at date 0.Firms invest one unit at date 0.Firms face a liquidity shock (cost Firms face a liquidity shock (cost overrun) overrun) νν at date 1.at date 1.Firms either borrow funds and Firms either borrow funds and continue or are liquidated.continue or are liquidated.If firms are not liquidated, they If firms are not liquidated, they produce Y with certainty.produce Y with certainty.

ProjectProject

We focus on We focus on date 1.

00 11 22

I = 1I = 1 Y (or 0)[ ]ννν ,∈ Y (or 0)

date 1.

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ConclusionMotivation Model AsymmetricInformation

Perfect Markets

The supply of bank retail deposits is The supply of bank retail deposits is inelastic in the short runinelastic in the short runRelationship banking is assumed. Relationship banking is assumed. The amount of equity is fixed The amount of equity is fixed ––zerozero--in the in the short run.short run.Simplification: each bank lends only to a Simplification: each bank lends only to a single firm (portfolios are not perfectly single firm (portfolios are not perfectly diversified and banks suffer different diversified and banks suffer different shocks).shocks).

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ConclusionMotivation Model AsymmetricInformation

Perfect Markets

Bank’sBank’s liquidityliquidity shocksshocks

Firms’Firms’ liquidityliquidity shocksshocks νν (positive (positive orornegativenegative))DepositDeposit shocksshocks DD (positive (positive orornegativenegative))BuffersBuffers againstagainst liquidityliquidity shocksshocks::–– TT--BillsBills–– InterbankInterbank loansloans

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TheThe defaultingdefaulting thresholdthreshold for for thethe firmfirmdependsdepends onon thethe contractcontract establishedestablishedbetweenbetween thethe firmfirm andand thethe bankbank

(Y(Y-- Repayment of Initial Loan)/(1+rRepayment of Initial Loan)/(1+rLL))

TheThe continuationcontinuation of of thethe projectproject dependsdependsonon thethe banksbanks onlyonly andand, , inin particular, particular, onon thethe interbank interbank marketmarket::

νν > Y/(1+r> Y/(1+rLL))

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ConclusionMotivation Model AsymmetricInformation

Perfect Markets

Benchmark : Perfect Information CaseBenchmark : Perfect Information Case

The liquidity shock The liquidity shock νν is public knowledge.is public knowledge.Banks obtain funding in the interbank Banks obtain funding in the interbank market.market.Only projects with high cost overrun are Only projects with high cost overrun are liquidated.liquidated.Equilibrium entails no rationing.Equilibrium entails no rationing.

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Asymmetric InformationAsymmetric Information

The information about The information about νν is private to the relationship is private to the relationship firmfirm--bank.bank.

Moral Hazard / Gambling for resurrectionMoral Hazard / Gambling for resurrection–– Bankers have access to an alternative Bankers have access to an alternative private private

benefits projectbenefits project which yields pledgeable return which yields pledgeable return KKand private benefits.and private benefits.

–– The choice of this project is not observable.The choice of this project is not observable.Private benefits are proportional to Private benefits are proportional to LL => Bad borrowers => Bad borrowers

want the want the largest loanlargest loan available in the interbank available in the interbank market.market.

Interbank market Interbank market contractscontracts

Contracts are defined by Contracts are defined by (L, r(L, rLL))..Interbank market contracts: Banks Interbank market contracts: Banks obtain a loan at the risk free rate up to obtain a loan at the risk free rate up to the size of . the size of .

( )LrrDKL

+−

=1

1

L

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Result: Pooling EquilibriumResult: Pooling Equilibrium::

bad/ insolvent prefer to borrow the bad/ insolvent prefer to borrow the maximum amount.maximum amount.borrowers pool at the level of the fully borrowers pool at the level of the fully collateralized loan. No risk spread in collateralized loan. No risk spread in the interbank market.the interbank market.

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Intuition:Intuition:

If there was a larger risky loan, lenders could If there was a larger risky loan, lenders could separate good from bad borrowers by offering a separate good from bad borrowers by offering a loan of a slightly smaller size at a slightly lower loan of a slightly smaller size at a slightly lower interest rate.interest rate.

Such a contract would attract only good borrowers, Such a contract would attract only good borrowers, as bad ones always apply for the largest loan.as bad ones always apply for the largest loan.

But then the contract with bad borrowers is not But then the contract with bad borrowers is not profitable. Hence there is no profitable. Hence there is no separating separating equilibrium. equilibrium.

0

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ImplicationsImplications

Banks are rationed in the interbank market.Banks are rationed in the interbank market.

Banks face limited available liquidityBanks face limited available liquidity……

…… that depends on monetary policy!that depends on monetary policy!1.1. Bank depositsBank deposits2.2. Balance sheet channel.Balance sheet channel.

Projects are liquidated ifProjects are liquidated if1.1. Excessive cost overrun (as in perfect information case)Excessive cost overrun (as in perfect information case)2.2. Bank itself is rationedBank itself is rationed

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Comparative Comparative staticsstatics

The relevance of imperfections in the The relevance of imperfections in the interbank market for monetary policy interbank market for monetary policy depends on:depends on:1.1.TheThe dependencedependence ofof firmsfirms onon bankbank

financefinance..2.2.TheThe extentextent ofof relationshiprelationship bankingbanking..3.3.HeterogeneityHeterogeneity onon banks’banks’ liquidityliquidity

positionspositions..

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ConsistencyConsistency

Two empirical puzzles (Bernanke and Gertler Two empirical puzzles (Bernanke and Gertler 1995): 1995):

Magnitude effect: The impact of monetary Magnitude effect: The impact of monetary policy is larger than we would expect from policy is larger than we would expect from firms’ individual decisions.firms’ individual decisions.

Composition effect: Monetary policy has most Composition effect: Monetary policy has most direct effects over short term interest rates, direct effects over short term interest rates, but it affects both short and long term but it affects both short and long term investment.investment.

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The model’s ResultsThe model’s Results

Magnitude effect: Magnitude effect: There are positive NPV projects that are not There are positive NPV projects that are not

undertaken because of rationing. Interest rates undertaken because of rationing. Interest rates differ from opportunity cost of capital.differ from opportunity cost of capital.

ResultsResults

Proposition 4 (Magnitude Effect) Proposition 4 (Magnitude Effect) The aggregate effect of an The aggregate effect of an interest rate shock is larger than the sum of the individual effinterest rate shock is larger than the sum of the individual effects ects of an increase in the user cost of capital.of an increase in the user cost of capital.

Proof: Proof: First, aggregate output equalsFirst, aggregate output equals

Second, sum of individual effects:Second, sum of individual effects:

y is the output from an individual firmy is the output from an individual firmrrFF is the interest rate on bank loansis the interest rate on bank loansThere is a number of firms for which an increase in There is a number of firms for which an increase in rrFF reduces reduces

output,output,BUT it has measure zero.BUT it has measure zero.■■

( )( ) ( ) 0110 >−=

−−=Υ ∫ ∫ Ydr

dYranddBYdBB r

B

B

Fεν

νν ν

)

( ) ∫ ∫ ===ν

ν νννε 011 F̂

FFFuc d

ydrdyd

ydrdyr

2222

ConclusionMotivation Model AsymmetricInformation

Perfect Markets

Composition PuzzleComposition PuzzleBanks ration their clients regardless of Banks ration their clients regardless of

the maturity of their investments.the maturity of their investments.

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The model’s ResultsThe model’s Results (2)(2)

Kashyap and Stein Liquidity Puzzle:Kashyap and Stein Liquidity Puzzle:1.1. The effect of interest rates occurs The effect of interest rates occurs

(mostly) through the rationing channel.(mostly) through the rationing channel.2.2. Banks with less liquidity, are more likely Banks with less liquidity, are more likely

to be rationed.to be rationed.3.3. Hence monetary policy has a larger effect Hence monetary policy has a larger effect

on banks with less liquidity.on banks with less liquidity.

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What empirical predictions?What empirical predictions?

0

0,5

1

1,5

2

2,5

3

0 1 2 3 4 5 6 7

Predicted Efectiveness of Monetary Policy

Cum

ulat

ive

Dev

iatio

n of

Out

put f

rom

Tre

nd

Data for the United Kingdom, Netherlands, France, Data for the United Kingdom, Netherlands, France, United States, Italy, Austria, Germany and Japan.United States, Italy, Austria, Germany and Japan.

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To concludeTo conclude

Asymmetric information may imply rationing in the Asymmetric information may imply rationing in the interbank market.interbank market.

Results are consistent with the findings by Kashyap Results are consistent with the findings by Kashyap and Stein.and Stein.

The model allows to understand better the magnitude The model allows to understand better the magnitude and the composition puzzles.and the composition puzzles.

The model predicts that monetary policy would be The model predicts that monetary policy would be more effective when interbank market more effective when interbank market imperfections are stronger.imperfections are stronger.