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Brunnermeier & Koby The “Reversal Interest Rate” An effective Lower Bound on Monetary Policy Markus K. Brunnermeier & Yann Koby Princeton University Philadelphia Macro Workshop Philadelphia, April 7 th , 2017

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Page 1: The “Reversal Interest Rate” - Princeton · The “Reversal Interest Rate” ... Determinants of ... Zero/negative interest rates are not special! Interest rate cut

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The “Reversal Interest Rate” An effective Lower Bound on Monetary Policy

Markus K. Brunnermeier & Yann Koby

Princeton University

Philadelphia Macro Workshop Philadelphia, April 7th, 2017

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Motivation

Transmission of Monetary Policy• Central Banks Financial Institutions (Banks) Loan, Deposits

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Motivation

Transmission of Monetary Policy• Central Banks Financial Institutions (Banks) Loan, Deposits

depends on• Pass through

• Profits of financial sector1. Reevaluation effect

2. Net Interest Margins (NIMs) effect

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Motivation

Transmission of Monetary Policy• Central Banks Financial Institutions (Banks) Loan, Deposits

depends on• Pass through

• Profits of financial sector1. Reevaluation effect

2. Net Interest Margins (NIMs) effect

Reversal Interest Rate• Rate at which accommodative policy becomes contractionary

Contrast with ZLB or concept of liquidity trap: rate at which MoPo is “ineffective” as opposed to “contractionary”

Determinants of 𝑅𝑅𝑅 and interaction with financial regulation𝑅𝑅𝑅𝑅 = 1 + 𝑟

Further interest rate cut iscontractionary accommodative

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Motivation

What determines the Reversal Rate?

How does it interact with financial regulation?• Acceleration + brakes = reversal

What are the lessons for

• QE

• Forward Guidance

• Long-lasting low interest rate environment?(“creeping up effect”)

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Literature

Theory• Oligopoly: Business margin: Monti-Klein model (𝐵 = 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),

• Risk-taking: Heider, Saidi & Schepens (2016)

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

• Delay: DeBondt (2005)

• … many missing

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Negative Central bank deposit (not borrowing) rates

Lower rates seem to damage• Net interest margin (FRB, 2016) - Banks’ profitability

• Bank lending, due to lower profitability

Effects are delayed

Stylized Facts

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Negative Central bank deposit (not borrowing) rates

Lower rates seem to damage• Net interest margin (FRB, 2016) - Banks’ profitability

• Bank lending, due to lower profitability

Effects are delayed

Stylized Facts

EnvironmentLow RateHigh Rate

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Negative Central bank deposit (not borrowing) rates

Lower rates seem to damage• Net interest margin (FRB, 2016) - Banks’ profitability

• Bank lending, due to lower profitability

Effects are delayed

Stylized Facts

EnvironmentLow RateHigh Rate

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Roadmap

Summary of stylized facts

1 period model• Monopolistic/monopsonic bank

Determinants of Reversal Rate

Interaction with financial regulation constrained

• Multiple banks in multiple banks & interbank market

• Multiple competing banks

• semi-elasticities

Multi-period model• Maturity structure of fixed interest assets

• Optimal length of interest cut (forward guidance) “creeping up effect”

• Interaction with QE – optimal sequencing

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Model: Banks’ balance sheet

Equity

Deposits 𝐷𝑡@𝑅𝐷

A L

Reserve𝑀𝑡@𝑅𝑀 𝐸0

Bonds 𝐵𝑡 @𝑅𝐵

Loans 𝐿𝑡 @𝑅𝐿

𝑀 + 𝑝𝐵𝐵 + 𝐿 = 𝐷 +𝑀0 + 𝑝𝐵𝐵0=𝐸0

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Model: Banks’ balance sheet

Equity

Deposits 𝐷𝑡@𝑅𝐷

A L

Reserve𝑀𝑡@𝑅𝑀 𝐸0

Bonds 𝐵𝑡 @𝑅𝐵

Loans 𝐿𝑡 @𝑅𝐿

𝑀 + 𝑝𝐵𝐵 + 𝐿 = 𝐷 +𝑀0 + 𝑝𝐵𝐵0=𝐸0

Endowment𝑀0, 𝐵0

𝑡 = 0 𝑡 = 1Surprise interest rate move 𝑅𝑀

(at 𝑡 = 0+)

Interest paymentsEquity 𝐸1

Choose𝑀,𝐵

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Model

Loan demand 𝑳 𝑅𝐿 elasticity 𝜀𝐿 𝑅𝐿

Deposit supply 𝑫 𝑅𝐷

• Deposits offer liquidity service 𝐷𝑖 𝑅𝐷 = argmax 𝑈(𝑊, ℒ 𝑀,𝐷 )

• Cash is imperfect substitutes elasticity 𝜀𝐷 𝑅𝐷

𝑅𝐷 can be negative changes esp. close 0

Monopoly bank

s.t. 𝑀 + 𝑝𝐵𝐵𝑠𝑎𝑓𝑒 𝑎𝑠𝑠𝑒𝑡𝑠

+ 𝐿 = 𝐷 +𝑀0 + 𝑝𝐵𝐵0=𝐸0

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Model

Loan demand 𝑳 𝑅𝐿 elasticity 𝜀𝐿 𝑅𝐿

Deposit supply 𝑫 𝑅𝐷

• Deposits offer liquidity service 𝐷𝑖 𝑅𝐷 = argmax 𝑈(𝑊, ℒ 𝑀,𝐷 )

• Cash is imperfect substitutes elasticity 𝜀𝐷 𝑅𝐷

𝑅𝐷 can be negative changes esp. close 0

Monopoly bank

s.t. 𝑀 + 𝑝𝐵𝐵safe assets

+ 𝐿 = 𝐷 +𝑀0 + 𝑝𝐵𝐵0=𝐸0

𝑀 ≥ 𝛼𝐷

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Model

Loan demand 𝑳 𝑅𝐿 elasticity 𝜀𝐿 𝑅𝐿

Deposit supply 𝑫 𝑅𝐷

• Deposits offer liquidity service 𝐷𝑖 𝑅𝐷 = argmax 𝑈(𝑊, ℒ 𝑀,𝐷 )

• Cash is imperfect substitutes elasticity 𝜀𝐷 𝑅𝐷

𝑅𝐷 can be negative changes close 0

Monopoly bank

s.t. 𝑀 + 𝑝𝐵𝐵safe assets

+ 𝐿 = 𝐷 +𝑀0 + 𝑝𝐵𝐵0=𝐸0

𝑀 ≥ 𝛼𝐷

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If 𝑀 ≥ 𝛼𝐷 doesn’t bind.

Net Interest Margin

𝑅𝑀Mark-up

Mark-down

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Surprise interest rate cut

Impact on bank’s profit/equity

PropositionIf 𝐵0 is sufficiently small, then there exists a “Reversal interest rate” 𝑅𝑅𝑅 such that

Corollary 𝑅𝑅𝑅 − 1 ≠ 0 generically

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Determinants of Reversal Rate: 𝐵0 & QE

Lowering 𝐵0 (holding 𝐸0 fixed), e.g. via QE, prior to 𝑅𝑀 cutincreases 𝑅𝑅𝑅

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Policy rate

Determinants of Reversal Rate: 𝐵0 & QE

Lowering 𝐵0 (holding 𝐸0 fixed), e.g. via QE, prior to 𝑅𝑀-cutincreases 𝑅𝑅𝑅

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Determinants of Reversal Rate

Lowering 𝐵0 (holding 𝐸0 fixed), e.g. via QE, prior to 𝑅𝑀-cutincreases 𝑅𝑅𝑅

𝑅𝑅𝑅 increases • in 𝜀𝐷 (more elastic deposit supply)

𝑅𝑅𝑅 and the regulatory constraint 𝑓 𝐿

𝐸; 𝛾 𝐸

• increases in 𝛾 (capital requirement)

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Regional Heterogeneity

2 regions: North and South• Segmented markets 𝐿𝑆 𝑅

𝐿 > 𝐿𝑁(𝑅𝐿)

• Monopoly bank in each region

Regional differences• Safe asset holdings are higher in North than South

𝑀𝑁∗ > 𝑀𝑆

• Reversal Rate is higher in North than South

𝑅𝑁𝑅𝑅 > 𝑅𝑁∪𝑆

𝑅𝑅 > 𝑅𝑆𝑅𝑅

Interbank market• N-bank lends to S-bank on interbank market

𝑅𝑁,𝑖𝑛𝑡𝑒𝑟𝑏𝑎𝑛𝑘𝑅𝑅 > 𝑅𝑁

𝑅𝑅 > 𝑅𝑁∪𝑆𝑅𝑅 > 𝑅𝑆

𝑅𝑅 > 𝑅𝑆,𝑖𝑛𝑡𝑒𝑟𝑏𝑎𝑛𝑘𝑅𝑅

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Bank Heterogeneity – multiple banks

Without competition effects• = simply comparative static of previous analysis

With competition effects• Differentiated loan products

𝐿𝑖(𝑅𝑖𝐿, 𝑹𝑖

𝐿) strictly decreasing in 𝑅𝑖𝐿 and increasing in all 𝑹−𝑖

𝐿

Conjectured variation function 𝒉−𝑖𝐿 (𝑅𝑖

𝐿; 𝑹−𝑖𝐿 ) captures competition

• Differentiated deposit products 𝐷𝑖(𝑅𝑖

𝐷, 𝑹𝑖𝐷)

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Multiple banks & Interbank market

Pass-through, following Amiti, Itskhoki, Konings (2016)

𝜶 are mark-ups elasticities of prices/rates• positive on diagonal and negative off-diagonal

𝜷 are weight of opportunity costs of lending and cost of leverage

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Roadmap

Summary of stylized facts

1 period model• Monopolistic bank

Determinants of Reversal Rate

Interaction with financial regulation constrained

• Multiple banks in multiple banks & interbank market

• Multiple competing banks

• semi-elasticities

Multi-period model• Maturity structure of fixed interest assets

• Optimal length of interest cut (forward guidance)

• Interaction with QE – optimal sequencing

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Multi-period model (sketch)

Maturity of outstanding 𝐵-assets = 2 periods

Interest rate cut is expected to last for 4 periods Cash flow

• If interest rate is expected to last “too long” it counterproductive

• Ideal length of interest rate cate ≤ maturity of 𝐵

Present Value impact on equity valuation

𝑡=1

31

1 + 𝑟𝑓 + 𝑑𝑟𝑓 + 𝜋𝐸𝑡 ถ𝑑Π𝑡

𝐵

>0

+ 𝑑Π𝑡𝑁𝐼𝑀

<0

+

𝑡=1

31

1 + 𝑟𝑓 + 𝑑𝑟𝑓 + 𝜋𝐸𝑡 𝑑Π𝑡

𝑁𝐼𝑀

<0

in “I theory” = ∞

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Multi-period: 𝑅𝑅𝑅 & forward guidance

Start with 𝑅𝐹 = 𝑅𝑅𝑅 for 𝐵0 = 0

Consider an interest rate cut beyond for next 𝜏 periods

Cash flow

• If interest rate is expected to last “too long” it counterproductive

Prop 8a: • Ideal length of interest rate cut ≤ maturity of 𝐵• 𝑟𝑅𝑅 is lower initially and increases as bonds mature• bond maturity length of lending-maximizing policy rates

in“I theory” = ∞

Cash flow 𝒕 = 𝟏 𝒕 = 𝟐 𝒕 = 𝟑 𝒕 = 𝟒

Π𝑀 𝑑Π𝑀

(−)𝑑Π𝑀

(−)𝑑Π𝑀

(−)𝑑Π𝑀

(−)

Π𝐵 −𝐵𝑑𝑅𝑀

(+)−𝐵𝑑𝑅𝑀

(+)

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Multi-period: 𝑅𝑅𝑅 & forward guidance

Start with 𝑅𝐹 = 𝑅𝑅𝑅 for 𝐵0 = 0

Consider an interest rate cut beyond for next 𝜏 periods

Cash flow

• If interest rate is expected to last “too long” it counterproductive

Prop: • Ideal length of interest rate cut ≤ maturity of 𝐵• 𝑟𝑅𝑅 is lower initially and increases as bonds mature• bond maturity length of lending-maximizing policy rates

in“I theory” = ∞

Cash flow 𝒕 = 𝟏 𝒕 = 𝟐 𝒕 = 𝟑 𝒕 = 𝟒

Π𝑀 𝑑Π𝑀

(−)𝑑Π𝑀

(−)𝑑Π𝑀

(−)𝑑Π𝑀

(−)

Π𝐵 −𝐵𝑑𝑅𝑀

(+)−𝐵𝑑𝑅𝑀

(+)

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Multi-period: Bonds with various maturity

Start with 𝑅𝑀 = 𝑅𝑅𝑅 for 𝐵0 = 0

Average maturity is still 2, but split over two bonds

Cash flow

Prop 7b: • Not only average maturity of legacy bonds matter• 𝑟𝑅𝑅 increases over time as bond mature• Effect of low interest rate environment dies out over time

Cash flow 𝒕 = 𝟏 𝒕 = 𝟐 𝒕 = 𝟑 𝒕 = 𝟒

Π𝑀 𝑑Π𝑀

(−)𝑑Π𝑀

(−)𝑑Π𝑀

(−)𝑑Π𝑀

(−)

Π𝐵 −𝐵/2𝑑𝑅𝑀

(+)−𝐵/2𝑑𝑅𝑀

(+)−𝐵/2𝑑𝑅𝑀

(+)

−𝐵/2𝑑𝑅𝑀

in“I theory” = ∞

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Multi-period: Bonds with various maturity

Start with 𝑅𝑀 = 𝑅𝑅𝑅 for 𝐵0 = 0

Average maturity is still 2, but split over two bonds

Cash flow

Prop: “Creeping-up Effect”• Not only average maturity of legacy bonds matter• 𝑅𝑅𝑅 increases over time as bond mature• Effect of low interest rate environment dies out over time

Cash flow 𝒕 = 𝟏 𝒕 = 𝟐 𝒕 = 𝟑 𝒕 = 𝟒

Π𝑀 𝑑Π𝑀

(−)𝑑Π𝑀

(−)𝑑Π𝑀

(−)𝑑Π𝑀

(−)

Π𝐵 −𝐵/2𝑑𝑅𝑀

(+)−𝐵/2𝑑𝑅𝑀

(+)−𝐵/2𝑑𝑅𝑀

(+)

−𝐵/2𝑑𝑅𝑀

in“I theory” = ∞

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RR & QE: Optimal sequencing

1. Induce banks to hold more long-run assets 𝐵• VLTRO

2. Surprise interest rate cut “stealth recapitalization”

3. QE: banks sell now highly priced long-run assets to CB• At market price

• Lowers banks 𝐵-holdings

4. Further interest rate cut is less effective and may even contractionary

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GE perspective

In GE have to take more things into account:• Modeling of nominal vs. real

• Endogenous default probabilities

• Banks’ hedging against Central Bank expected policy

• Redistribution of wealth in the economy

Still work in progress

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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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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

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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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

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)