the “reversal interest rate” - princeton · the “reversal interest rate” ... determinants...
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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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& K
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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
Bru
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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)
Bru
nn
erm
eier
& K
ob
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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)
Bru
nn
erm
eier
& K
ob
y
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)