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
Motivation Transmission of Monetary Policy Central Banks Financial Institutions (Banks) Loan, Deposits
Motivation Transmission of Monetary Policy Central Banks Financial Institutions (Banks) Loan, Deposits depends on Pass through Profits of financial sector 1. Reevaluation effect 2. Net Interest Margins (NIMs) effect
Motivation Transmission of Monetary Policy Central Banks Financial Institutions (Banks) Loan, Deposits depends on Pass through Profits of financial sector 1. 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 Further interest rate cut is contractionary accommodative R = 1 + r Determinants of R RR and R RR interaction with financial regulation
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 )
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
Stylized Facts 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 Negative Central bank deposit (not borrowing) rates Lower rates seem to damage Net interest margin (FRB, 2016) - Banks profitability Environment Low Rate High Rate Bank lending, due to lower profitability Effects are delayed
Stylized Facts Negative Central bank deposit (not borrowing) rates Lower rates seem to damage Net interest margin (FRB, 2016) - Banks profitability Environment Low Rate High Rate Bank lending, due to lower profitability Effects are delayed
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
Model: Banks balance sheet A L Loans L t @R L Deposits D t @R D Bonds B t @R B Equity ReserveM t @R M E 0 M + p B B + L = D + M 0 + p B B 0 =E 0
t = 0 Surprise interest t = 1 rate move R M (at t = 0 + ) Model: Banks balance sheet A L Loans L t @R L Deposits D t @R D Bonds B t @R B Equity ReserveM t @R M E 0 M + p B B + L = D + M 0 + p B B 0 =E 0 Endowment M 0, B 0 Choose M, B Interest payments Equity E 1
Model Loan demand L R L elasticity ε L R L Deposit supply D R D Deposits offer liquidity service D i R D = argmax U(W, L M, D ) Cash is imperfect substitutes elasticity ε D R D R D can be negative changes esp. close 0 Monopoly bank s.t. M + p B B safe assets + L = D + M 0 + p B B 0 =E 0
Model Loan demand L R L elasticity ε L R L Deposit supply D R D Deposits offer liquidity service D i R D = argmax U(W, L M, D ) Cash is imperfect substitutes elasticity ε D R D R D can be negative changes esp. close 0 Monopoly bank s.t. M + p B B safe assets + L = D + M 0 + p B B 0 =E 0 M αd
Model Loan demand L R L elasticity ε L R L Deposit supply D R D Deposits offer liquidity service D i R D = argmax U(W, L M, D ) Cash is imperfect substitutes elasticity ε D R D R D can be negative changes close 0 Monopoly bank s.t. M + p B B safe assets + L = D + M 0 + p B B 0 =E 0 M αd
Net Interest Margin If M αd doesn t bind. R M Mark-up Mark-down
Surprise interest rate cut Impact on bank s profit/equity Proposition If B 0 is sufficiently small, then there exists a Reversal interest rate R RR such that Corollary R RR 1 0 generically
Determinants of Reversal Rate: B 0 & QE Lowering B 0 (holding E 0 fixed), e.g. via QE, prior to R M cut increases R RR
Policy rate Determinants of Reversal Rate: B 0 & QE Lowering B 0 (holding E 0 fixed), e.g. via QE, prior to R M -cut increases R RR
Determinants of Reversal Rate Lowering B 0 (holding E 0 fixed), e.g. via QE, prior to R M -cut increases R RR R RR increases in ε D (more elastic deposit supply) R RR and the regulatory constraint f L E ; γ E increases in γ (capital requirement)
Regional Heterogeneity 2 regions: North and South Segmented markets L S R L > L N (R L ) Monopoly bank in each region Regional differences Safe asset holdings are higher in North than South M N > M S Reversal Rate is higher in North than South Interbank market RR R N RR > R N S > R S RR N-bank lends to S-bank on interbank market RR R N,interbank > R RR N > R RR N S > R RR RR S > R S,interbank
Bank Heterogeneity multiple banks Without competition effects = simply comparative static of previous analysis With competition effects Differentiated loan products L i (R L i, R L i ) strictly decreasing in R L i and increasing in all R i Conjectured variation function h L i (R L i ; R L i ) captures competition Differentiated deposit products D i (R i D, R i D ) L
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
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
Multi-period model (sketch) Maturity of outstanding B-assets = 2 periods in I theory = 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 3 3 1 B NIM t ถdΠ t + dπ t + 1 + r f + dr f + π E t=1 >0 <0 t=1 1 1 + r f + dr f + π E t dπ t NIM <0
Multi-period: R RR & forward guidance Start with R F = R RR for B 0 = 0 Consider an interest rate cut beyond for next τ periods Cash flow Cash flow t = 1 t = 2 t = 3 t = 4 Π M Π B dπ M ( ) BdR M (+) dπ M ( ) BdR M (+) dπ M ( ) dπ M ( ) in I theory = If interest rate is expected to last too long it counterproductive Prop 8a: Ideal length of interest rate cut maturity of B r RR is lower initially and increases as bonds mature bond maturity length of lending-maximizing policy rates
Multi-period: R RR & forward guidance Start with R F = R RR for B 0 = 0 Consider an interest rate cut beyond for next τ periods Cash flow Cash flow t = 1 t = 2 t = 3 t = 4 Π M Π B dπ M ( ) BdR M (+) dπ M ( ) BdR M (+) dπ M ( ) dπ M ( ) in I theory = If interest rate is expected to last too long it counterproductive Prop: Ideal length of interest rate cut maturity of B r RR is lower initially and increases as bonds mature bond maturity length of lending-maximizing policy rates
Multi-period: Bonds with various maturity Start with R M = R RR for B 0 = 0 Average maturity is still 2, but split over two bonds Cash flow Cash flow t = 1 t = 2 t = 3 t = 4 Π M Π B dπ M ( ) B/2dR M (+) B/2dR M dπ M ( ) B/2dR M (+) dπ M ( ) B/2dR M (+) dπ M ( ) in I theory = Prop 7b: Not only average maturity of legacy bonds matter r RR increases over time as bond mature Effect of low interest rate environment dies out over time
Multi-period: Bonds with various maturity Start with R M = R RR for B 0 = 0 Average maturity is still 2, but split over two bonds Cash flow Cash flow t = 1 t = 2 t = 3 t = 4 Π M Π B dπ M ( ) B/2dR M (+) B/2dR M dπ M ( ) B/2dR M (+) dπ M ( ) B/2dR M (+) dπ M ( ) in I theory = Prop: Creeping-up Effect Not only average maturity of legacy bonds matter R RR increases over time as bond mature Effect of low interest rate environment dies out over time
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
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
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)
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)
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)