Princeton University Updates: http://www.princeton.edu/~markus/research/papers/i_theory_slides.pdf
Motivation Unified framework to study financial and monetary stability Combines intermediation (credit) and money - inside money Value of money endogenous - store of value, liquidity (Samuelson, Bewley, Kiyotaki-Moore…)
Fisher (1933) deflationary spiral after negative productivity
shock Negative shock hits asset side of intermediaries’ balance sheets Difference and is amplified through leverage and volatility dynamics to literature! Decline in inside money, leads to deflationary pressure that hits intermediaries’ balance sheet on the liability side
Brunnermeier & Sannikov 2011
Inside money and outside money “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 Difference to New Keynesian framework 2
Some Literature Medium of exchange Store of value & liquidity Samuelson’s OLG Bewley Scheinkman & Weiss Homstrom & Tirole Kiyotaki & Moore (2008)
(new) monetarists
Consumption smoothing Precaution savings for uninsurable endowment shocks to keep project running new investment opportunity + “resell constraint’’
Brunnermeier & Sannikov 2011
Financial stability & monetary policy Diamond & Rajan (2006) Stein (2010) Curdia & Woodford (2010)
New Keynesian framework
Economies with financial frictions Bernanke,Gertler & Gilchrist, Kiyotaki & Moore, Geanakoplos, He & Krishnamurthy, Brunnermeier & Sannikov 2010
3
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Outline of Modeling Ideas
heterogeneous agents net worth
productivity 4
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Efficient Allocation of Physical Capital
heterogeneous agents net worth
productivity 5
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Allocation with Extreme Financial Constraint
heterogeneous agents capital productivity 6
Switching Types and Money Money (gold) intrinsically worthless
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Agents willing to hold money if someone (productive agents becoming unproductive) will want to hold money later
money
capital productivity 7
Switching Types and Money Money (gold) intrinsically worthless
Agents willing to hold money if someone (productive agents becoming unproductive) will want to hold money later Inefficiencies Allocation (money does not generate any income) Brunnermeier & Sannikov 2011
Underinvestment (price of capital and hence investment is low)
money
capital productivity 8
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Two polar cases Economy
Assets
Value of fiat money
Frictions (severe)
No claims
high
Frictionless
Issue claims • Debt • Equity
low
9
Two polar cases introducing intermediaries Economy
Assets
Value of fiat money
Intermediaries’ capitalization
Frictions (severe)
No claims
high
defunct
Frictionless
Issue claims • Debt • Equity
low
perfect
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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 Monitoring technology
Diamond (1984) Homstrom-Tirole (1997)
intermediaries Assets loans to entrepreneurs
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entrepreneur equity
Liabilities
deposits
net worth
heterogeneous agents deposits money 11
Intermediaries and lending Monitoring technology
Diamond (1984) Homstrom-Tirole (1997)
intermediaries Assets
Liabilities
Brunnermeier & Sannikov 2011
entrepreneur equity
deposits net worth
deposits loans to entrepreneurs money 12
Intermediaries and lending Monitoring technology
Diamond (1984) Homstrom-Tirole (1997)
intermediaries Assets loans to entrepreneurs
Brunnermeier & Sannikov 2011
entrepreneur equity
Liabilities
deposits
net worth
deposits money 13
Negative Macro Shocks intermediaries Assets loans to entrepreneurs
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entrepreneur equity
Liabilities
deposits
net worth
deposits money 14
Negative Macro Shocks intermediaries Assets loans to entrepreneurs
Liabilities
deposits
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entrepreneur equity net worth
deposits money 15
Shrinking Balance Sheets
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Intermediary net worth Lending to entrepreneurs Value of capital q Deposit/inside money Value of outside money p Multiplier
intermediaries Assets loans to entrepreneurs entrepreneur equity
Liabilities
deposits net worth
deposits money 16
Overview Passive monetary policy: “Gold standard” Quantity of outside money fixed Interest rate zero When a negative macro shock hits intermediaries quantity of inside money shrinks value of outside money increases - deflationary spiral intermediaries are hit on the liability side
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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
Comparison to New Keynesian and Monetarism 17
The Model: Technology consumption rate
Output:
y𝑡𝜔 = 𝑎𝜔𝑘𝑡𝜔 = 𝑐𝑡𝜔 + 𝑖𝑡𝜔 𝑘𝑡𝜔 investment rate
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Capital:
𝑑𝑘𝑡𝜔 = Φ 𝑖𝑡𝜔 − 𝛿 ω 𝑘𝑡 𝑑𝑡 + 𝑑𝜀𝑡ω Φ 0 = 0, Φ′ > 0, Φ′′ < 0 𝐶𝑜𝑣,𝜀𝑡ω , 𝜀𝑡ω ′-
heterogeneous agents
Outside money (gold) is in fixed supply
ω 18
Notation: Three distributions intermediaries Assets
loans to entrepreneurs
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entrepreneur equity
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) 19
Scale Invariance Allocation of capital
𝜁𝑡 𝜔 𝑑𝜔 +
𝜉𝑡 𝜔 𝑑𝜔 = 1
All capital in the economy = 𝐾𝑡 Capital value (in output) = 𝑞𝑡 𝐾𝑡
Outside money supply = 1 Value of money (in output) =
intermediaries Assets
loans to entrepreneurs
entrepreneur equity
Liabilities
deposits
net worth
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= 𝑃𝑡 = 𝑝𝑡 𝐾𝑡
heterogeneous agents
𝜁𝑡 (𝜔)
HH’s holdings 𝜉𝑡 (𝜔)
deposits money 𝜃 𝜔 𝑞𝑡 𝐾𝑡 + 𝑃𝑡 − 𝑁𝑡 HH’s net worth distr.
Interm’s portfolio
ω 𝜃 𝜔 𝑑𝜔 = 1
𝜃(𝜔) 20
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 𝑤𝑜𝑟𝑡 Required return = 𝐶𝑜𝑣 𝑎𝑠𝑠𝑒𝑡 𝑟𝑖𝑠𝑘, 𝑛𝑒𝑡 𝑤𝑜𝑟𝑡 𝑟𝑖𝑠𝑘 Consumption is independent of investment opportunity Asset demands are myopic (no Mertonian hedging demand, no precautionary motive)
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Consumption
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Equilibrium Definition For each history of shocks * 𝑑𝜀𝑠𝜔
𝜔, 𝑠
∈ 0, 𝑡 +
𝑞𝑡 the price of physical capital 𝑃𝑡 = 𝑝𝑡 𝐾𝑡 the value of money 𝜁𝑡 𝜔 , 𝜉𝑡 (𝜔) the allocation of capital
𝑖𝑡𝜔 the rate of entrepreneurs investment rates of consumption of all agents
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Retirement rate of intermediaries
such that Given prices all agents choose portfolios & consumption to
maximize utility, intermediaries choose optimally when to retire Markets for capital, money and consumption goods clear
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Derivation - Roadmap Individual choices 𝑐𝑡 = 𝜌 ∗ net worth 𝑖𝑡𝜔
Required excess return = Cov [asset risk, net worth risk] 𝑞
𝑝
𝑝
Postulate: 𝑑𝑞𝑡 = 𝜇𝑡 𝑑𝑡 + 𝑑𝜀 𝑞 and 𝑑𝑝𝑡 = 𝜇𝑡 𝑑𝑡 + 𝑑𝜀𝑡
Market clearing 𝑞
𝑞
𝑝
𝑞
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Endogenously determines 𝜇𝑡 , 𝑑𝜀𝑡 , 𝜇𝑡 , 𝑑𝜀𝑡
𝑞 𝑞 𝑝 𝑞 Derive 𝜇𝑡 , 𝑑𝜀𝑡 , 𝜇𝑡 , 𝑑𝜀𝑡
as functions of 𝜂 Need low of motion of 𝜂
Depends on postulated price processes 𝑞𝑡 and 𝑝𝑡 (fixed point) 23
Internal investment decision 𝑑𝑘𝑡𝜔 = Φ 𝑖𝑡𝜔 − 𝛿 𝜔 𝑑𝑡 + 𝑑𝜀𝑡𝜔 Given the price of capital 𝑞𝑡 , the optimal investment solves max Φ 𝑖 𝑞𝑡 − 𝑖 ⇒ 𝑖 ∗ 𝑞𝑡 𝑖
Determines for each HH ω
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𝑐 𝜔 𝑞𝑡 = 𝑎𝜔 − 𝑖 ∗ 𝑞𝑡 𝑔𝜔 𝑞𝑡 = Φ 𝑖 ∗ 𝑞𝑡
− 𝛿𝜔
24
Return on physical capital 𝑞
𝑞
If 𝑑𝑞𝑡 = 𝜇𝑡 𝑞𝑡 𝑑𝑡 + 𝑞𝑡 𝑑𝜀𝑡 endogenous 𝜔 𝑞 𝑐 𝑡 𝑞 𝑞 𝑑𝑟𝑡𝜔 = + 𝑔𝜔 𝑞𝑡 + 𝜇𝑡 + 𝐶𝑜𝑣 𝑑𝜀𝑡𝜔 , 𝑑𝜀𝑡 𝑞𝑡
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dividend yield
capital gains rate
𝑞
𝑑𝑡 + (𝑑𝜀𝑡𝜔 + 𝑑𝜀𝑡 ) risk (endogenous + exogenous)
25
Return on Money In the “long-run” 𝑑𝐾𝑡 = 𝐾𝑡
(𝜁 𝜔 + 𝜉 𝜔 )𝑔𝜔 𝑞𝑡 𝑑𝜔 +
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𝑝 𝜇𝑡 𝑝𝑡 𝑑𝑡
𝜇𝑡𝐾
𝑝 𝑝𝑡 𝑑𝜀𝑡
𝜁 𝜔 + 𝜉 𝜔 𝑑𝜀𝑡𝜔 𝑑𝜀𝑡𝐾
If 𝑑𝑝𝑡 = + endogenous then a dollar invested in money earns return 𝑝 𝑝 𝑝 𝑑𝑟𝑡𝑀 = (𝜇𝑡𝐾 +𝜇𝑡 + 𝐶𝑜𝑣,𝑑𝜀𝑡𝐾 , 𝑑𝜀𝑡 -)𝑑𝑡 + 𝑑𝜀𝑡𝐾 + 𝑑𝜀𝑡 𝑑𝜀𝑡𝑀
26
Intermediaries’ “Risk Balance Sheet” Assets 𝑞𝑡 𝐾𝑡
Liabilities 𝑞
𝜁𝑡 𝜔 𝑑𝜀𝑡 + 𝑑𝜀𝑡𝜔 𝑑𝜔
𝑞𝑡 𝐾𝑡
𝜁𝑡 𝜔 𝑑𝜔 − 𝑁𝑡 𝑑𝜀𝑡𝑀
𝑁𝑡 𝑑𝜀𝑡𝑁
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𝑑𝑁𝑡 = −𝜌𝑁𝑡 𝑑𝑡 + 𝑁𝑡 𝑑𝑟𝑡𝑀 𝑞 𝑑𝜀𝑡
+ 𝑑𝜀𝑡𝜔 − 𝑑𝜀𝑡𝑀 , 𝑑𝜀𝑡𝑁 𝑑𝜔 𝑑𝑡
+ 𝑞𝑡 𝐾𝑡
𝜁𝑡 𝜔 𝐶𝑜𝑣
+ 𝑞𝑡 𝐾𝑡
𝜁𝑡 𝜔 𝑑𝜀𝑡 + 𝑑𝜀𝑡𝜔 − 𝑑𝜀𝑡𝑀 𝑑𝜔
𝑑𝜂𝑡 = 𝑑 𝑁𝑡 /𝐾𝑡 = ⋯
𝑞
Equilibrium Conditions 1. Market clearing for capital goods and bonds
𝜁𝑡 𝜔 𝑑𝜔 +
𝜉𝑡 𝜔 𝑑𝜔 = 1
2. Market clearing for output:
𝜁𝑡 𝜔 + 𝜉 𝜔 𝑐 𝜔 𝑞𝑡 𝑑𝜔 = 𝜌 𝑞𝑡 + 𝑝𝑡
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3. Valuation of capital -- return = Cov(risk, net worth risk) Intermediaries 𝐸 𝑑𝑟𝑡𝜔 − 𝑑𝑟𝑡𝑀 HH 𝜔 𝐸 𝑑𝑟𝑡𝜔 − 𝑑𝑟𝑡𝑀
𝑞
≤ 𝐶𝑜𝑣 𝑑𝜀𝑡 + 𝑑𝜀𝑡𝑀 , 𝑑𝜀𝑡𝑁
= 𝑖𝑓 𝜁𝑡 𝜔 > 0
𝑞
≤ 𝐶𝑜𝑣 𝑑𝜀𝑡 + 𝑑𝜀𝑡𝑀 , 𝑑𝜀𝑡𝐻𝐻−𝑁 (= 𝑖𝑓 𝜉𝑡 𝜔 > 0) 28
Simplified Example Three household types 𝜔 only Low: Medium:
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High:
very bad technology, hold money risk-free technology, prefer to hold capital over money risky production – low net worth
Intermediaries choose to invest only in the most productive technology (due to high monitoring cost)
29
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Example
allocation to the most productive technology
some intermediaries retire
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
301/2
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32
Observations As 𝜂 goes down: Intermediaries take on less risk, competition decreases Price of capital q and investment, i(q), decrease Capital is allocated less efficiently
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Unproductive households hold less inside money (loans to
intermediaries/entrepreneurs) and more outside fiat money Price of outside money goes up (deflation) Additional source of amplification in economy with money: value of assets fall value of liabilities increase (due to deflation)
33
Monetary Policy So far, Gold Standard outside money fixed, pays no interest no central bank
• Introduce consul (perpetual) bond – pays interest rate in ST (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)
34
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 transacting)
Endogenous market reaction
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Price of long-term bond (in money, per unit coupon rate) 𝑑𝐵𝑡 = 𝜇𝑡𝐵 𝐵𝑡 𝑑𝑡 + 𝐵𝑡 𝑑𝜀𝑡𝐵 𝑞𝑡 = price of capital Assets 𝑝𝑡 𝐾𝑡 = value of money
intermediaries
Liabilities
long-term bonds 𝑏𝑡 𝐾𝑡
deposits
entrepr._equity 𝑞𝑡 𝐾𝑡 𝜁𝑡 𝜔 𝑑𝜔
net worth 35
Disentangling Money and Bonds Return on money:
𝑑𝑟𝑡𝑀 = 𝜇𝑡𝑀 𝑑𝑡 + 𝑑𝜀𝑡𝑀
Price of bond:
𝑑𝐵𝑡 𝐵𝑡
1 𝐵𝑡
= 𝜇𝑡𝐵 𝑑𝑡 + 𝑑𝜀𝑡𝐵 ( is current yield)
Return on bonds:
1 𝐵𝑡
𝑑𝑟𝑡𝐵 = 𝑑𝑟𝑡𝑀 + ( − 𝑟𝑡 + 𝜇𝑡𝐵 + 𝐶𝑜𝑣 𝜀𝑡𝐵 , 𝜀𝑡𝑀 )𝑑𝑡 + 𝑑𝜀𝑡𝐵
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𝑑 𝑝𝑡 +𝑏𝑡 𝐾𝑡 𝑏𝑡 𝑀 All monetary instruments: = 𝑑𝑟𝑡 + 𝑑𝑟𝑡𝐵 − 𝑑𝑟𝑡𝑀 (𝑝𝑡 +𝑏𝑡 )𝐾𝑡 𝑝𝑡 +𝑏𝑡 𝑝 𝑝 𝑝 = 𝜇𝑡 + 𝜇𝑡𝑏 + 𝜇𝑡𝐾 + 𝐶𝑜𝑣 𝜀𝑡 + 𝜀𝑡𝑏 , 𝜀𝑡𝐾 𝑑𝑡 + 𝑑𝜀𝑡 + 𝑑𝜀𝑡𝑏 + 𝜀𝑡𝐾
Collecting shocks: 𝑑𝜀𝑡𝑀
+
𝑏𝑡 𝑑𝜀𝑡𝐵 𝑝𝑡 +𝑏𝑡
𝑝
= 𝑑𝜀𝑡 + 𝑑𝜀𝑡𝑏 + 𝜀𝑡𝐾 36
Equilibrium Conditions 1. Market clearing for capital goods and bonds
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𝜁𝑡 𝜔 𝑑𝜔 + 𝜉𝑡 𝜔 𝑑𝜔 = 1, 𝜁𝑡𝐵 + 𝜉𝑡𝐵 𝜔 𝑑𝜔 = 1 2. Market clearing for output: 𝜁𝑡 𝜔 + 𝜉 𝜔 𝑐 𝜔 𝑞𝑡 𝑑𝜔 = 𝜌 𝑞𝑡 + 𝑝𝑡 + 𝑏𝑡 3. Valuation of capital -- return = Cov(risk, net worth risk) 𝑞 𝜔 𝑀 𝐸 𝑑𝑟𝑡 − 𝑑𝑟𝑡 ≤ 𝐶𝑜𝑣 𝑑𝜀𝑡 + 𝑑𝜀𝑡𝑀 , 𝑑𝜀𝑡𝑁 = 𝑖𝑓 𝜁𝑡 𝜔 > 0 𝑞 𝐸 𝑑𝑟𝑡𝜔 − 𝑑𝑟𝑡𝑀 ≤ 𝐶𝑜𝑣 𝑑𝜀𝑡 + 𝑑𝜀𝑡𝑀 , 𝑑𝜀𝑡𝐻𝐻−𝑁 (= 𝑖𝑓 𝜉𝑡 𝜔 > 0) 4. Valuation of bonds 𝐸 𝑑𝑟𝑡𝐵 − 𝑑𝑟𝑡𝑀 = 𝐶𝑜𝑣 𝑑𝜀𝑡𝐵 , 𝑑𝜀𝑡𝑁 𝐸 𝑑𝑟𝑡𝐵 − 𝑑𝑟𝑡𝑀 ≤ 𝐶𝑜𝑣 𝑑𝜀𝑡𝐵 , 𝑑𝜀𝑡𝐻𝐻−𝑁
(assuming 𝜁𝑡𝐵 > 0) (= if 𝜉𝑡𝐵 𝜔 > 0) 37
Short-term interest rate 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
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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 38
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
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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 39
New Keynesian
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Risk build-up phase
I-Theory Endogenous due to accommodating monetary policy
Net worth dynamics
zero profit
no dynamics dynamic
State variables
Many exogenous shocks Intermediation/friction shock
Monetary policy rule
Taylor rule Depends on signal quality (is approximately optimal and timeliness of various only if difference in u’ is well observables proxied by output gap) • spreads • credit aggregates (?)
Policy instrument
Short-term interest rate + expectations
Short-term interest rate + long-term bond + expectations
Role of money
In utility function (no deflation spiral)
Storage Precautionary savings
Endogenous intermediation shock
40
Monetarism
I-Theory
Focus
Price stability
Price and Financial stability
Theory
Quantity theory of money P*Y = v*M
Distribution of wealth (liquidity, balance sheet)
Transaction role of money
endogenous money multiplier
M0 (Brunner, Meltzer)
Outside money is only imperfect substitute for inside money (intermediation)
Monetary aggregates
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M1-2(Friedman,Schwartz) Inside and outside money are perfect substitutes
Bank underwriting (credit lines) is substitute to bank deposits (difficult to measure M1-3 in a meaningful way) Monetary policy
Constant growth of M2 (Friedman)
Recapitalize banks through monetary policy Switch off deflationary 41 pressure
Conclusion Unified macromodel to analyze both Financial stability Monetary stability Liquidity spirals Fisher deflation spiral
GDP drops are associated with deflation (not inflation)
absent monetary policy
Capitalization of banking sector is key state variable Price stickiness plays no role (unlike in New Keynesian models)
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Monetary policy rule Redistributional feature Time inconsistency problem – “Greenspan put”
Further research “Minsky cycle” 42
Intermediaries and lending Monitoring technology
Diamond (1984) Homstrom-Tirole (1997)
intermediaries Assets
Liabilities
Brunnermeier & Sannikov 2011
entrepreneur equity
heterogeneous agents
deposits net worth
deposits
loans to entrepreneurs money 43
