Document 1952991

Princeton University
Updates: http://scholar.princeton.edu/markus/files/i_theory_slides.pdf
Motivation
 Unified framework to study financial and monetary stability
 I: Intermediation (credit) - Inside money
 Value of money endogenous - store of value, liquidity
Brunnermeier & Sannikov 2011
 In downturns, intermediaries create less inside money
 Value of outside (base) money goes up
 Fisher (1933) deflationary spiral hits borrowers on liability side
 Endogenous money multiplier = f(health of intermediary sector)
 Monetary policy (interest rates, open market operations)
 Fills in demand for money when money multiplier contracts
 Redistribution from/towards intermediary sector
2
Some Literature
 Role of money

Unit of account
 Medium of exchange
 Store of value (Samuelson, Bewley, Scheinkman-Weiss, Kiyotaki-Moore)
 Without intermediaries
 Inflation in downturns: less money needed since fewer transactions
 With intermediaries
Brunnermeier & Sannikov 2011
 Money view: (Friedman & Schwartz 1963)
 “Moneyness” of bank liabilities decrease in downturns of intermediation
 Credit view (demand/supply): (Tobin)
BGG, KM, He & Krishnamurthy, BruSan10, Goodfriend 05, Curdia & Woodford 10, …
 Financial stability + monetary policy
 Diamond & Rajan (2006), Stein (2012),
3
Brunnermeier & Sannikov 2011
Outline of Modeling Ideas
heterogeneous agents
net worth
productivity
4
Efficient Allocation of Physical Capital
Brunnermeier & Sannikov 2011
 “Bliss Regime”
heterogeneous agents
net worth
productivity
5
Allocation with Extreme Financial Constraint
Brunnermeier & Sannikov 2011
 “Autarky Regime”
heterogeneous agents
capital
productivity
6
Switching Types and Money
 “(Outside) Money Regime”
 Money intrinsically worthless, but …
 ∃ an equilibrium
(coordination)
 Agents store wealth in money while unproductive
Brunnermeier & Sannikov 2011
 Trade it for physical capital when become productive
money
capital
productivity7
Switching Types and Money
 “(Outside) Money Regime”
 Inefficiencies
 Allocation
(money has low return)
Brunnermeier & Sannikov 2011
 Underinvestment
(marginal buyer is less productive)
⇒ price of capital is low ⇒ capital production unattractive
money
capital
productivity8
Two Polar Regimes
Regime
“Bliss”
Brunnermeier & Sannikov 2011
“Money”
Frictions
Unproductive
agents hold
Value of
fiat
money
Price of
capital
small
claims on productive agents
low
high
severe
money
high
low
9
Two Polar Regimes with Intermediaries
Regime
“Bliss”
Brunnermeier & Sannikov 2011
“Money”
Frictions
Unproductive
agents hold
Value of
fiat
money
Price of
capital
Intermediaries’
capitalization
small
claims on productive agents
low
high
well
severe
money
high
low
poor
 Role of intermediaries
 Relax financing constraint by monitoring productive agents
 Have to take on productive agent’s equity risk (so that they
have incentive to monitor)
 Intermediation depends on their ability to absorb risk
net worth of intermediaries
10
Debt
underwriting
Intermediaries and Lending
 Intermediation is risky
depends on banks’
balance sheet
 Monitoring technology
Brunnermeier & Sannikov 2011
Diamond (1984)
Homstrom-Tirole (1997)
intermediaries
Assets
Liabilities
Risk-free piece
to entrepredeposits
neurs
Risky piece to
entrepreneur
(equity stake) net worth
heterogeneous agents
deposits
money
11
Negative Macro Shocks
intermediaries
Assets
Risk-free piece
to entreprens.
Liabilities
deposits
Risky stake
Brunnermeier & Sannikov 2011
net worth
deposits
money
14
Negative Macro Shocks
intermediaries
Assets
Risk-free piece
to entreprens.
Liabilities
deposits
Risky stake
Brunnermeier & Sannikov 2011
net worth
deposits
money
15
Shrinking Balance Sheets
Brunnermeier & Sannikov 2011




Intermediary net worth
Capital: fire sales, price q
Money:
 Lending + deposits
 value of money p
 Multiplier
Allocation efficiency

Externality among banks!






intermediaries
Assets
Risk-free piece
to entreprens.
Risky stake
Liabilities
deposits
net worth
deposits
money
16
Overview
 Passive monetary policy: “Gold standard”
 Quantity of outside money fixed
 Interest rate zero
 A negative macro shock hits intermediaries
 Asset side:
liquidity spiral
(“skin in the game”)
 Liability side:
deflationary spiral
Brunnermeier & Sannikov 2011
 Active Monetary Policy
 Introduce long-term bond
 Short-term interest rate policy
 Value of long-term bonds rises in downturns – substitute for reduction of
inside money
 Asset purchase and OMO
 Redistributional effects
17
Formal Model: Key Frictions
 HH can borrow from other HH, cannot issue equity
 Inefficient: risky projects cannot sustain high leverage
 … but HH can issue equity to intermediaries
 Intermediaries
 Assets: diversified asset across households
 Liabilities: inside money
Brunnermeier & Sannikov 2011
diversification
debt, not equity
intermediary
less productive HH
debt and equity
productive HH
debt, not equity
18
The Model: Technology
consumption goods (rate)
Output:
y𝑡𝜔 = 𝑎𝜔𝑘𝑡𝜔 = 𝑐𝑡𝜔 + 𝑖𝑡𝜔 𝑘𝑡𝜔
Investment goods
Brunnermeier & Sannikov 2011
Capital:
𝑑𝑘𝑡𝜔 = Φ 𝑖𝑡𝜔 − 𝛿 ω 𝑘𝑡 𝑑𝑡 + 𝑘𝑡 𝑑𝜀𝑡ω
Φ 0 = 0, Φ′ > 0, Φ′′ < 0
𝐶𝑜𝑣[𝜀𝑡ω , 𝜀𝑡ω ′]
• heterogeneous agents
ω
• Outside money (gold) is in fixed supply
• Contracting friction: contract on 𝑞𝑡 𝑘𝑡 but not on 𝑘𝑡 19
Agents’ Portfolios
 HH type 𝜔:
 Capital employed in technology 𝜔
 Money (long and short)
 Intermediaries
 Capital diversified portfolio across
Brunnermeier & Sannikov 2011
different technologies 𝜔
 Money (short)
heterogeneous agents
deposits
money
20
Notation: Three distributions
intermediaries
Assets
Risk-free piece
Brunnermeier & Sannikov 2011
Risky stake in
entrepreneurs
Liabilities
deposits
net worth
heterogeneous agents
Interm’s
portfolio
𝜁𝑡 (𝜔)
HH’s
holdings
𝜉𝑡 (𝜔)
deposits
money
ω
HH’s net worth distribution
𝜃(𝜔)
21
Scale Invariance
 Allocation of capital
 All capital in the economy = 𝐾𝑡

𝜁𝑡 𝜔 𝑑𝜔 +
𝜉𝑡 𝜔 𝑑𝜔 = 1
intermediaries
Assets
Risk-free piece
 Capital value (in output) = 𝑞𝑡 𝐾𝑡
 Outside money supply = 1
 Value of money (in output) =
= 𝑃𝑡 = 𝑝𝑡 𝐾𝑡
Brunnermeier & Sannikov 2011
 Nominal risk free rate = 0
heterogeneous agents
deposits
money
Risky stake in
entrepreneurs
Liabilities
deposits
net worth
𝑁𝑡 = 𝜂𝑡 𝐾𝑡
Interm’s
portfolio
𝜁𝑡 (𝜔)
HH’s
holdings
𝜉𝑡 (𝜔)
ω
𝜃(𝜔)
22
The Model: Preferences
 All agents have logarithmic utility with discount rate
∞
𝐸
0
𝑒 −𝜌𝑡 log 𝑐𝑡 𝑑𝑡
 Retirement: intermediary gets utility boost, when it
decides to become a household forever
 Implications of log utility:
= 𝜌 × 𝑛𝑒𝑡 𝑤𝑜𝑟𝑡ℎ
 Consumption is independent of investment opportunity
 Required return = 𝐶𝑜𝑣 𝑎𝑠𝑠𝑒𝑡 𝑟𝑖𝑠𝑘, 𝑛𝑒𝑡 𝑤𝑜𝑟𝑡ℎ 𝑟𝑖𝑠𝑘
 Asset demands are myopic
(no Mertonian hedging demand, no precautionary motive)
Brunnermeier & Sannikov 2011
 Consumption
23
Solution steps
1. Equilibrium conditions
𝑞
𝑝
𝑝
 Postulate : 𝑑𝑞𝑡 = 𝜇𝑡 𝑞𝑡 𝑑𝑡 + 𝑞𝑡 𝑑𝜀 𝑞 and 𝑑𝑝𝑡 = 𝜇𝑡 𝑝𝑡 𝑑𝑡 + 𝑝𝑡 𝑑𝜀𝑡
 Agents’ optimization
Brunnermeier & Sannikov 2011




Internal investment
Return from holding capital
Return from holding/issuing money
Agents’ and intermediaries optimal choice
 Portfolio
 Consumption
 Market clearing conditions
2. Law of motion of state variable (wealth distribution)
3. Express in ODEs of state variable
25
Internal Investment Decision
𝑑𝑘𝑡𝜔 = Φ 𝜄𝑡𝜔 − 𝛿 𝜔 𝑑𝑡 + 𝑘𝑡𝜔 𝑑𝜀𝑡𝜔
 Given the price of capital 𝑞𝑡 , the optimal investment
solves
max Φ 𝜄 𝑞𝑡 − 𝜄 ⇒ 𝜄∗ 𝑞𝑡
𝑖
 Determines for each HH ω
Brunnermeier & Sannikov 2011
 𝑐 𝜔 𝑞𝑡 = 𝑎𝜔 − 𝜄∗ 𝑞𝑡
 𝑔𝜔 𝑞𝑡 = Φ 𝜄∗ 𝑞𝑡
output rate net investment
− 𝛿𝜔
26
Equilibrium Conditions
1. Market clearing for capital
𝜁𝑡 𝜔 𝑑𝜔 +
𝜉𝑡 𝜔 𝑑𝜔 = 1
2. Market clearing for net output:
𝜁𝑡 𝜔 + 𝜉 𝜔 𝑎𝜔 𝑞𝑡 𝑑𝜔 − 𝜄𝑡 = 𝜌 𝑞𝑡 + 𝑝𝑡
Brunnermeier & Sannikov 2011
3. Valuation of capital  -- return = Cov(risk, net worth risk)
 Intermediaries
𝐸 𝑑𝑅𝑡𝜔 − 𝑑𝑅𝑡𝑀
 HH 𝜔
𝐸 𝑑𝑅𝑡𝜔 − 𝑑𝑅𝑡𝑀
𝑞
≤ 𝐶𝑜𝑣 𝑑𝜀𝑡 + 𝑑𝜀𝑡𝑀 , 𝑑𝜀𝑡𝑁
𝑞
𝑁(𝜔)
≤ 𝐶𝑜𝑣 𝑑𝜀𝑡 + 𝑑𝜀𝑡𝑀 , 𝑑𝜀𝑡
𝑁(𝜔)
net worth risk of HH 𝜔, 𝑑𝜀𝑡
= 𝑖𝑓 𝜁𝑡 𝜔 > 0
(= 𝑖𝑓 𝜉𝑡 𝜔 > 0)
, depends on 𝜉𝑡 𝜔 and its net worth
30
Dynamics with One State Variable 𝜂
 𝑁𝑡 denotes aggregate net worth of intermediaries
 Depends on portfolio 𝜁𝑡 𝜔 , returns and retirement
 𝑞𝑡 𝐾𝑡 + 𝑃𝑡 − 𝑁𝑡 is the aggregate net worth of HH
 Allocation depends on returns, switching types
 Assume HH types switch very fast, so distribution over
types 𝜃(𝜔) is invariant
Brunnermeier & Sannikov 2011
 + scale invariance in 𝐾𝑡
 Wealth distribution is characterized by a single state
variable 𝜂𝑡 = 𝑁𝑡 /𝐾𝑡
31
Example
 Three household types 𝜔 only
 Low:
 Medium:
Brunnermeier & Sannikov 2011
 High:
very bad technology, hold money
own 65% of HH wealth
risk-free technology,
prefer to hold capital over money
own 35% of HH worth
risky production – low net worth
no net worth
 Intermediaries choose to invest only in high 𝜔
due to monitoring cost
32
Example
Brunnermeier & Sannikov 2011
some
intermediaries
retire
allocation to
the most
productive
technology
𝑎 = 1, 𝑟 = 5%, 𝛿 𝐻 = 0, 𝛿 𝑀 = 3%, 𝜎 = 25%, 𝜃 𝐿 = .65, 𝜃 𝑀 = 35%, 𝜃 𝐻 = 0%, Φ 𝑖 = 0.02𝑖
331/2
Brunnermeier & Sannikov 2011
34
Brunnermeier & Sannikov 2011
35
After a negative shock






Brunnermeier & Sannikov 2011


Intermediary net worth
Balance sheets
Competition among banks
Capital: fire sales, price q
Money:
 Lending + deposits
 value of money p
 Multiplier
Banks are hit on both sides
of their balance sheet
Allocation efficiency
Externality among banks!







intermediaries
Assets
Risk-free piece
to entreprens.
Risky stake
Liabilities
deposits
net worth

deposits
money
36
Monetary Policy
 So far, “Gold Standard”
 outside money supply is fixed
 pays no interest
 no central bank
• Introduce consul (perpetual) bond
• pays interest rate in short-term (outside) money
Brunnermeier & Sannikov 2011
 Monetary Policies
 Short-term interest rate policy
 Central bank accepts deposits
& pays interest rate (by printing money)
 E.g. short-term interest rate is lowered when η becomes small
 Budget neutral policies (at any point in time)
 Asset purchase program
 Bond – open market operations (OMO/QE)
38
Money and Long-term Bond
 Policy instruments (functions of 𝜂𝑡 )
 Central bank pays interest 𝑟𝑡 ≥ 0 on money (by printing)
 Sets total outstanding value 𝑏𝑡 𝐾𝑡 of perpetual bond
 By changing interest 𝑟𝑡
 Additional Quantitative Easing/Open market operations – to get around ZLB
 Endogenous market reaction
Brunnermeier & Sannikov 2011
 Price of long-term bond (in money, per unit coupon rate)
 𝑑𝐵𝑡 = 𝜇𝑡𝐵 𝐵𝑡 𝑑𝑡 + 𝐵𝑡 𝑑𝜀𝑡𝐵
 𝑞𝑡 = price of capital
 𝑝𝑡 𝐾𝑡 = value of money
Assets
intermediaries
long-term
bonds 𝑏𝑡 𝐾𝑡
entrepr._equity
𝑞𝑡 𝐾𝑡 𝜁𝑡 𝜔 𝑑𝜔
Liabilities
deposits
net worth 39
Short-term interest rate policy
 Without long-maturity assets changes in short-term interest
rate have no effect
 Interest rate change equals instantaneous inflation change
 With bonds: of all monetary instruments, fraction pt/(pt+bt) is
cash and bt/(pt+bt) are bonds
Brunnermeier & Sannikov 2011
 deflationary spiral is less pronounced because as η goes down,
growing demand for money is absorbed by increase in value of longterm bonds
 also, intermediaries hedge risks better by holding long-term bonds
 however, intermediaries also have greater incentives to increase
leverage/risk-taking ex-ante
 Effectiveness of monetary policy depend on maturity
structure (duration) of government debt
43
New Keynesian
I-Theory
Key friction
Price stickiness & ZLB
Financial friction
Driver
Demand driven
Misallocation of funds
as firms are obliged to meet increases incentive
demand at sticky price
problems and restrains
firms/banks from exploiting
their potential
Brunnermeier & Sannikov 2011
Monetary policy
• First order effects
Affect HH’s intertemporal
trade-off
Nominal interest rate
impact real interest rate due
to price stickiness
• Second order effects
Redistributional between
firms which could (not)
adjust price
Time consistency
Wage stickiness
Price stickiness +
monopolistic competition
Ex-post: redistributional
effects between financial
and non-financial sector
Ex-ante: insurance effect
leading to moral hazard in
risk taking (bubbles)
- Greenspan put -
Moral hazard
44
New Keynesian
Risk build-up phase
I-Theory
Endogenous due to
expected accommodating
monetary policy
Net worth dynamics
zero profit
no dynamics dynamic
State variables
Many exogenous shocks
Intermediation/friction
shock
Endogenous intermediation
shock
Brunnermeier & Sannikov 2011
Curdia & Woodford
Net worth dynamics
No – free entry zero profit yes
Monetary policy rule
Taylor rule (approximately
optimal only if difference in
u’ is well proxied by output
gap)
• spreads
• credit aggregates (?)
Depends on signal quality
and timeliness of various
observables
Policy instrument
Short-term interest rate
+ expectations
Short-term interest rate
+ long-term bond
+ expectations
45
Monetarism
I-Theory
Focus
Price stability
Price and
Financial stability
Theory
Quantity theory of money
P*Y = v*M
Transaction role of money
Exogenous M
Distribution of wealth
(liquidity, balance sheet)
Store of value
endogenous money
multiplier
Monetary aggregates
M0
Outside money is only
imperfect substitute for
inside money
(intermediation)
Brunnermeier & Sannikov 2011
M1-2(Friedman,Schwartz)
Inside and outside money
are perfect substitutes
Intermediation
(Brunner, Meltzer)
Monetary policy
Constant growth of M2
(Friedman)
Bank underwriting (credit
lines) is substitute to bank
deposits
(difficult to measure M1-3 in
a meaningful way)
Recapitalize banks through
monetary policy
Switch off deflationary
46
pressure
Conclusion
 Unified macro model to analyze both
 Financial stability
 Monetary stability
 Liquidity spirals
 Fisher deflation spiral
 Capitalization of banking sector is key state variable
 Price stickiness plays no role (unlike in New Keynesian models)
Brunnermeier & Sannikov 2011
 Monetary policy rule
 Affects money supply
 Redistributional feature
 Time inconsistency problem – “Greenspan put”
47