the reversal rate - banquedefrance

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The Reversal Interest Rate An effective Lower Bound on Monetary Policy

Markus K. Brunnermeier & Yann Koby

Safe Assets & Valentin Haddad

Princeton University

Banque de France Paris, Sept. 20th, 2016

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Motivating Questions

New Keynesian models: ZLB = Liquidity trap

Is zero special? Are negative rates special? No Ignoring headline risk

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Lower bound Rate at which accommodative policy becomes contractionary

(possibly due to financial instability) Does strict financial regulation reduce effectiveness MoPo?

Acceleration + brakes = reversal

What factors determines the Reversal Rate? Market structure & funding structure Banks equity Interaction with prudential regulation Interaction with QE

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What c determines the Reversal Rate? Market structue & funding structure Banks equity Interaction with prudential regulation Interaction with QE

Further interest rate cut iscontractionary accommodative

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What factors determines the Reversal Rate? Market structure & funding structure Banks equity Interaction with prudential regulation (reversal) Expected length of interest rate cut/forward guidance Interaction with QE (current MoPo affects future MoPo and )

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Motivation

Interest rate cut Substitution effect: safe asset risky loans

Wealth effect: negative rate = tax Not in representative agent analysis

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Motivation


Wealth effect: negative rate = tax

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Banks balance sheet

policy rate

predetermined

, depends on competition & elasticities

depends on investors

Equity

Deposits @

A L

Reserves @

0

Bonds @

Loans @

WholeSale@

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Model

Loan market (aggregate) semi-elasticities

= 01 log

Deposit market (aggregate)

= 01 | log

|

= argmax (, , ) Bank competition

banks

Bertrand competition

but house bank advantage Liquidity service

Cash is imperfect substitute

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Model


= 01 log


= 01 | log

|

= argmax (, , )

Example:

= 1 (Cobb-Douglas)

= 1 + 1 (1)

(CES, elasticity of subst.) for = perfect substitutes ZLB

for = 0 perfect complements Bank

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Model


= 01 log


= 01 | log

|

= argmax (, , )

Example:

= 1

= 1 + 1 (1)

For varying

Bank

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Model


= 01 log


= 01 | log

|

= argmax (, , )

Bank competition banks


but house bank advantage

Liquidity service

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Model


= 01 log


= 01 | log

|

= argmax (, , ) ,

log ;

Bank competition banks


but house bank advantage

Liquidity service

+

Mark-up

Mark-down

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Roadmap

1 period model Impact of rate cut on profit/equity

Competition structure unconstrained

Interaction with financial regulation constrained

Impact of rate cut on lending

Determinants of Reversal Ratesemi-elasticities

Multi-period model Maturity structure of legacy holdings vs. NIM-business

Optimal length of interest cut

Optimal dividends for lending

Interaction with QE optimal sequencing

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Roadmap

1 period model Impact or rate cat on profit/equity

Perfect competition perfect pass through

Local monopolist/monopsonist imperfect pass throughmark-up depends on semi-elasticities

1 =max,

+ ()

+

+(1 + )0

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Perfect competition pass through

= = perfect pass through

1. Profit from NIM-business, = 0

2. Zero pass through on , d = Funding of bonds that yield is now lower by

Interest rate cut = stealth recapitalization

Equity

Deposits @

A L

Reserves @

0

Bonds @

Loans @

WholeSale@

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Monopoly

Loan problem is separate from deposit problem Why? Reserve holdings is in between

Loan rate after mark-up

= + (), 1()

Deposit rate after mark-down

= + (), 1()

Next period equity has four parts:

1 = + + + (1 + )0

Implicit assumption: Price stickiness

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Response to interest rate change

Monopoly/monopsony1 =

+

1

+ + (1 + )0

1

=

By envelop theorem, NIM are changed

by cost of funding (deposit minus loans) are changed

Prop. 1:

1

=

Net interest margin+ 0

rolledover equity

reevaluation

=

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Constraint

Economic or regulatory constraint

0 10

1

0

Decline in equity decline in lending

If constraint binds: interest rate cut cant lead to a substitution from to

Loan mark-up even larger than in monopoly case

Deposit margin is not affected Since constraint only binds Loan and deposit decisions are separable

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Impact on LENDING

Constraint 0

1

0

10

= 1

1

1

Sum up: Interest rate cut can lead to more or less lending

(depending how large is)

Need data on banks interest rate sensitivity (Sraer et al. 2015, Piazzesi et al. 2015)

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Reversal Rate determinants

Prop 2: For sufficiently large 0,1, there exists a reversal rate

such that an interest rate cut beyond

is contractionary (reduces lending)

is generically not zero

Prop 3,4,5: (comparative statics) decreases in , increases in 0 and 1 weakly decreases in and weakly increases in

weakly decreases in and weakly increases in

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Numerical example: 1 period model

Constant & , = = , for different

Policy ratePolicy rate Policy rate

Policy rate

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Restriction on dividend policy

Prop 9:Banks dividend policy does not optimize lending after an interest rate cut.

Idea Interest rate cut can recapitalize banks

Part of the capital gains is wasted due to dividend payouts

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Multi-period model (sketch)

Maturity of legacy assets = 3 periods

Interest rate cut is expected to last for 5 periods

Cash flow

If interest rate is expected to last too long it counterproductive

Ideal length of interest rate cate maturity of

Present Value impact on equity valuation

=1

31

1 + + +

>0

+

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Multi-period model (sketch)

Maturity of legacy assets = 3 periods

Interest rate cut is expected to last for 5 periods

Cash flow

If interest rate is expected to last too long it counterproductive

Prop 7: Ideal length of interest rate cut maturity of

Prop 8: Increase in bond duration implies increase in duration of lending-maximizing

policy rates

Present Value

Cash flow = = = = =

Legacy asset

(+)

(+)

(+)

NIM-business

()

()

()

()

()

in I theory =

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RR & forward guidance

Forward guidance = duration of interest rate cut shrinks over time

Effect of the interest rate cut dies out and -effect dominates

Length of forward guidance should depend on maturity of positions

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RR & QE: Optimal sequencing

1. Induce banks to hold more long-run assets

2. Interest rate cut stealth recapitalization

3. QE: banks sell now highly priced long-run assets to CB

4. Further interest rate cut is less effective/contractionary

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RR & QE: Optimal sequencing

1. Induce banks to hold more long-run assets

2. Interest rate cut stealth recapitalization

3. QE: banks sell now highly priced long-run assets to CB

4. Further interest rate cut is less effective/contractionary

Reloading strategy

1. if banks suffer losses (e.g. delinquencies) & RR rises >

2. Raise policy rate (to increase banks interest margin)

3. Reverse QE or another LTRO

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Heterogeneity

Across banks Banks with large legacy assets benefit

Banks with low equity and large NIM-business (going forward) suffer

Across countries (pass through) whole sale funding in Sweden

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GE perspective: credit demand perspective

So far, Strong focus on banks & credit supply

Redistribute wealth towards banks to stimulate credit supply

Low pass through of lending rate/deposit rate affects redistribution credit demand aspects Households benefit less from smaller reduction in

suffer less from smaller reduction in High MPC or low MPC households

Firms Balance sheet constrained or not

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Literature

Theory Oligopoly: Business margin: Monti-Klein model ( = 0)

Competitive: Re-evaluation: BruSan I theory of money

Interest rate sensitivity of banks Stock price: Flannery & James (1984), Begenau et al. (2015)

Lending: Landier et al. (2015)

Deposits: Drechsler et al. (2015),

Deposit rate pass through Competition: Maudos & de Guevarra(2005)

Delay: DeBondt (2005)

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Conclusion

Zero/negative interest rates are not special!


Wealth effect: tax + prudential regulation

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Conclusion: Reversal Interest Rate

Zero/negative interest rates are not special!

Interest rate cut Substitution effect: safe asset risky loans Wealth effect: tax

+ prudential regulation Reverses substitution effect + amplification

What determines the Reversal Rate? Market structure and pass through of rates Interaction with prudential regulation Banks equity capitalization countercyclical regulation Duration risk of banks (long-dated assets) Length of rate cut (forward guidance) & maturity legacy assets Timing of dividends Interaction with QE (correct sequencing)

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Safe Assets & Valentin Haddad

Princeton University

Federal Reserve Board Washington, Aug. 2nd, 2016

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Definitions of Safe Asset

1. Safe = risk-free for a particular horizon E.g. holders are infinitely risk aversion Caballero & Farhi but inflation risk

2. Safe = informationally insensitive No decline in value due to asymmetric info

3. Safe = Good friend analogy Safe for random horizon Appreciates in times of crisis

Safe = Safe Asset Tautology Safe because perceived to be safe

(multiple equilibria)

Bubble

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Bubble

Holmstrom& Gordon

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Bubble

Brunnermeier & Haddad

Holmstrom& Gordon

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Safe asset & money - close cousins

Store of value store of value

Held in addition to risky assets

Held in order to produce (private) safe assets (by banks!)

Reference/benchmark asset unit of account

Good collateral: stable margins transaction role Facilitates financial trade

Pool ofrisky high yield assets

Safe asset Deposits

Equity

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Safety versus Risk

US Treasury downgraded by S&P (due to default risk) but yield declines

German CDS spread versus yield during Euro crisis

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Model ingredients

Risky investment is subject to liquidity shocks A la Holmstrom & Tirole 1998

Liquidity shocks can be dealt with Safe assets

Market liquidity (or risky asset)

Market liquidity is endogenous To economic activity

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The Curse of Safety

Investment equilibrium

High real investment

High market liquidity of risky assets Less safe asset holdings

necessary

Pool ofrisky high yield assets

Safe asset

Equity Risky assets

Safe asset

Equity

Safety equilibrium

Low real investment

Low market liquidity of risky assets High safe asset holdings

necessary

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Model setup

Continuum of investors Take prices and market liquidity as given

Maximize final wealth max[]

Three periods = 0: Allocate initial resources to risky and safe asset

= +

= 1: Liquidity shocks

= 2: Output is realized

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Opportunity set

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Dealing with liquidity shock

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Dealing with liquidity shock

Remarks: Liquidity demand: marginal return from safe assets is larger

when insufficient cover for liquidity shock Market liquidity is only relevant when used

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Individual demand for safety

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Role of market liquidity (of risky asset)

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Equilibrium

Aggregate supply of safe asset Elastic supply fixed

Aggregate market liquidity Risky investment fosters liquidity > 0

Better substitutability in secondary market Micro-foundation: Search market externality (see paper)

cv

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Aggregate demand for safety

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Equilibria

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The Curse of Safety Investment equilibrium

High real investment

High market liquidity of risky assets Less safe asset holdings

necessary

Riskyassets

Equity Risky assets

Safe asset

Equity

Safety equilibrium

Low real investment

Low market liquidity of risky assets High safe asset holdings

necessary

Private demand for safety crowds out market safety Invest in safe asset rather than risky -> low market liquidity

-> more need for safe assets

cvc

v

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Conclusion The Curse of Safety

Scarcity of safe asset because in wrong equilibrium Secular stagnation

(too little risky real investment)

Fight fire with fire Reduce supply of safe asset

(in order to jump to good equilibrium)

In international context: Capital controls

the reversal rate - banquedefrance

Economy & Finance