Reversal Interest Rate Slides.pdf - Princeton University

The “Reversal Interest Rate” Brunnermeier & Koby

An effective Lower Bound on Monetary Policy Markus K. Brunnermeier & Yann Koby Princeton University Philadelphia Macro Workshop

Philadelphia, April 7th, 2017

Motivation  Transmission of Monetary Policy

Brunnermeier & Koby

• Central Banks

Financial Institutions (Banks)

Loan, Deposits

Motivation  Transmission of Monetary Policy • Central Banks

Financial Institutions (Banks)

depends on • Pass through • Profits of financial sector

Brunnermeier & Koby

1. 2.

Reevaluation effect Net Interest Margins (NIMs) effect

Loan, Deposits

Motivation  Transmission of Monetary Policy • Central Banks

Financial Institutions (Banks)

Loan, Deposits

depends on • Pass through • Profits of financial sector 1. 2.

Reevaluation effect Net Interest Margins (NIMs) effect

 Reversal Interest Rate Brunnermeier & Koby

• 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 accommodative contractionary 𝑅𝑅𝑅

𝑅 =1+𝑟

 Determinants of 𝑅𝑅𝑅 and interaction with financial regulation

Motivation  What determines the Reversal Rate?  How does it interact with financial regulation? • Acceleration + brakes = reversal

Brunnermeier & Koby

 What are the lessons for • QE • Forward Guidance • Long-lasting low interest rate environment? (“creeping up effect”)

Literature  Theory • Oligopoly: • Competitive:

Business margin: Monti-Klein model (𝐵 = 0) Re-evaluation: BruSan “I theory of money”

 Interest rate sensitivity of banks’ • • • •

Stock price: Lending: Deposits: Risk-taking:

Flannery & James (1984), Begenau et al. (2015) Landier et al. (2015) Drechsler et al. (2015), Heider, Saidi & Schepens (2016)

Brunnermeier & Koby

 Deposit rate pass through • Competition: • Delay: • … many missing

Maudos & de Guevarra (2005) DeBondt (2005)

Stylized Facts  Negative Central bank deposit (not borrowing) rates  Lower rates seem to damage

Brunnermeier & Koby

• 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

Brunnermeier & Koby

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

Brunnermeier & Koby

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

Brunnermeier & Koby

 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 𝐿𝑡 @𝑅𝐿

Deposits 𝐷𝑡 @𝑅𝐷

Bonds 𝐵𝑡 @𝑅𝐵 Reserve𝑀𝑡 @𝑅𝑀

Equity

𝐸0

𝑀 + 𝑝𝐵 𝐵 + 𝐿 = 𝐷 + 𝑀0 + 𝑝𝐵 𝐵0

Brunnermeier & Koby

=𝐸0

Model: Banks’ balance sheet A

L

Loans 𝐿𝑡 @𝑅𝐿

Deposits 𝐷𝑡 @𝑅𝐷

Bonds 𝐵𝑡 @𝑅𝐵 Reserve𝑀𝑡 @𝑅𝑀

Equity

𝐸0

𝑀 + 𝑝𝐵 𝐵 + 𝐿 = 𝐷 + 𝑀0 + 𝑝𝐵 𝐵0

Brunnermeier & Koby

=𝐸0

Endowment 𝑀0 , 𝐵0

Choose 𝑀, 𝐵

𝑡 = 0 Surprise interest rate move 𝑅𝑀 (at 𝑡 = 0+ )

Interest payments Equity 𝐸1

𝑡=1

Model  Loan demand 𝑳 𝑅𝐿

elasticity 𝜀 𝐿 𝑅𝐿

 Deposit supply 𝑫 𝑅𝐷 • Deposits offer liquidity service

𝐷 𝑖 𝑅𝐷 = argmax 𝑈(𝑊, ℒ 𝑀, 𝐷 )

• Cash is imperfect substitutes  𝑅𝐷 can be negative

elasticity 𝜀 𝐷 𝑅𝐷 changes esp. close 0

Brunnermeier & Koby

 Monopoly bank s.t. 𝑀 + 𝑝𝐵 𝐵 + 𝐿 = 𝐷 + 𝑀0 + 𝑝𝐵 𝐵0 𝑠𝑎𝑓𝑒 𝑎𝑠𝑠𝑒𝑡𝑠

=𝐸0

Model  Loan demand 𝑳 𝑅𝐿

elasticity 𝜀 𝐿 𝑅𝐿

 Deposit supply 𝑫 𝑅𝐷 • Deposits offer liquidity service

𝐷 𝑖 𝑅𝐷 = argmax 𝑈(𝑊, ℒ 𝑀, 𝐷 )

• Cash is imperfect substitutes  𝑅𝐷 can be negative

elasticity 𝜀 𝐷 𝑅𝐷 changes esp. close 0

Brunnermeier & Koby

 Monopoly bank s.t. 𝑀 + 𝑝𝐵 𝐵 + 𝐿 = 𝐷 + 𝑀0 + 𝑝𝐵 𝐵0 safe assets

=𝐸0

𝑀 ≥ 𝛼𝐷

Model  Loan demand 𝑳 𝑅𝐿

elasticity 𝜀 𝐿 𝑅𝐿

 Deposit supply 𝑫 𝑅𝐷 • Deposits offer liquidity service

𝐷 𝑖 𝑅𝐷 = argmax 𝑈(𝑊, ℒ 𝑀, 𝐷 )

• Cash is imperfect substitutes  𝑅𝐷 can be negative

elasticity 𝜀 𝐷 𝑅𝐷 changes close 0

Brunnermeier & Koby

 Monopoly bank s.t. 𝑀 + 𝑝𝐵 𝐵 + 𝐿 = 𝐷 + 𝑀0 + 𝑝𝐵 𝐵0 safe assets

=𝐸0

𝑀 ≥ 𝛼𝐷

Net Interest Margin  If 𝑀 ≥ 𝛼𝐷 doesn’t bind.

Mark-up 𝑅𝑀

Brunnermeier & Koby

Mark-down

Surprise interest rate cut  Impact on bank’s profit/equity

Brunnermeier & Koby

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

 Corollary

𝑅𝑅𝑅 − 1 ≠ 0 generically

Determinants of Reversal Rate: 𝐵0 & QE

Brunnermeier & Koby

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

Determinants of Reversal Rate: 𝐵0 & QE

Brunnermeier & Koby

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

Policy rate

Determinants of Reversal Rate  Lowering 𝐵0 (holding 𝐸0 fixed), e.g. via QE, prior to 𝑅𝑀 -cut increases 𝑅𝑅𝑅  𝑅𝑅𝑅 increases • in 𝜀 𝐷 (more elastic deposit supply)

 𝑅𝑅𝑅 and the regulatory constraint 𝑓 𝐸𝐿 ; 𝛾 𝐸 Brunnermeier & Koby

• increases in 𝛾 (capital requirement)

Regional Heterogeneity  2 regions: North and South • Segmented markets 𝐿𝑆 𝑅𝐿 > 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 𝑅𝑅 𝑅𝑅 𝑅𝑁 > 𝑅𝑁∪𝑆 > 𝑅𝑆𝑅𝑅

Brunnermeier & Koby

 Interbank market • N-bank lends to S-bank on interbank market 𝑅𝑅 𝑅𝑅 𝑅𝑅 𝑅𝑅 𝑅𝑁,𝑖𝑛𝑡𝑒𝑟𝑏𝑎𝑛𝑘 > 𝑅𝑁 > 𝑅𝑁∪𝑆 > 𝑅𝑆𝑅𝑅 > 𝑅𝑆,𝑖𝑛𝑡𝑒𝑟𝑏𝑎𝑛𝑘

Bank Heterogeneity – multiple banks  Without competition effects • = simply comparative static of previous analysis

 With competition effects • Differentiated loan products  𝐿𝑖 (𝑅𝑖𝐿 , 𝑹𝐿𝑖 ) strictly decreasing in 𝑅𝑖𝐿 and increasing in all 𝑹𝐿−𝑖  Conjectured variation function 𝒉𝐿−𝑖 (𝑅𝑖𝐿 ; 𝑹𝐿−𝑖 ) captures competition

• Differentiated deposit products

Brunnermeier & Koby

 𝐷𝑖 (𝑅𝑖𝐷 , 𝑹𝐷 𝑖 )

Multiple banks & Interbank market

Brunnermeier & Koby

 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

Brunnermeier & Koby

 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 Brunnermeier & Koby

 Present Value impact on equity valuation 3

෍ 𝑡=1

1

1 + 𝑟𝑓 + 𝑑𝑟𝑓 +

𝐵 𝑑 Π ถ 𝑡 𝑡 𝜋𝐸 >0

+

𝑑Π𝑡𝑁𝐼𝑀