The I Theory of Money - PDF Free Download

The I Theory of Money Markus K. Brunnermeier & Yuliy Sannikov Princeton University CSEF-IGIER Symposium Capri, June 24 th, 2015

Motivation Framework to study monetary and financial stability Interaction between monetary and macroprudential policy Connect theory of value and theory of money Intermediation (credit) Excessive leverage and liquidity mismatch Inside money as store of value Demand for money rises with endogenous volatility In downturns, intermediaries create less inside money Endogenous money multiplier = f(capitalization of critical sector) Value of money goes up Disinflation spiral a la Fisher (1933) Fire-sales of assets iquidity spiral Flight to safety Time-varying risk premium and endogenous volatility dynamics

Some literature Macro-friction models without money Kiyotaki & Moore, BruSan2014, He & Krishnamurthy, DSS2015 Money models without intermediaries Money pays no dividend and is a bubble store of value With intermediaries/inside money Money view (Friedman & Schwartz) vs. Credit view (Tobin) New Keynesian Models: BGG, Christian et al., money in utility function

With intermediaries/inside money Money view (Friedman & Schwartz) vs. Credit view (Tobin) New Keynesian Models: BGG, Christian et al., money in utility function Some literature Macro-friction models without money Kiyotaki & Moore, BruSan2014, He & Krishnamurthy, DSS2015 Money models without intermediaries Store of value: Money pays no dividend and is a bubble

Some literature Macro-friction models without money Kiyotaki & Moore, BruSan2014, He & Krishnamurthy, DSS2015 Money models without intermediaries Store of value: Money pays no dividend and is a bubble Friction OG deterministic endowment risk borrowing constraint Only money Samuelson With capital Diamond With intermediaries/inside money Money view (Friedman & Schwartz) vs. Credit view (Tobin) New Keynesian Models: BGG, Christian et al., money in utility function

Some literature Macro-friction models without money Kiyotaki & Moore, BruSan2014, He & Krishnamurthy, DSS2015 Money models without intermediaries Store of value: Money pays no dividend and is a bubble Friction OG Incomplete Markets + idiosyncratic risk Risk deterministic endowment risk borrowing constraint Only money Samuelson Bewley With capital Diamond yagari, Krusell-Smith With intermediaries/inside money Money view (Friedman & Schwartz) vs. Credit view (Tobin) New Keynesian Models: BGG, Christian et al., money in utility function

Some literature Macro-friction models without money Kiyotaki & Moore, BruSan2014, He & Krishnamurthy, DSS2015 Money models without intermediaries Store of value: Money pays no dividend and is a bubble Friction OG Incomplete Markets + idiosyncratic risk Risk deterministic endowment risk borrowing constraint investment risk Only money Samuelson Bewley With capital Diamond yagari, Krusell-Smith Basic I Theory With intermediaries/inside money Money view (Friedman & Schwartz) vs. Credit view (Tobin) New Keynesian Models: BGG, Christian et al., money in utility function

Roadmap Model absent monetary policy Toy model: one sector with outside money Two sector model dding intermediary sector and inside money Model with monetary policy Model with macro-prudential policy

One sector basic model Technologies a 1 Each households can only operate one firm Physical capital dk t = (Φ ι k t δ)dt + σ a dz a a t + σd Z t t Output y t = k t Demand for money sector idiosyncratic risk

Net worth dding outside money q t K t value of physical capital Postulate constant q t ι q dt + Φ(ι δ) dt + σb dz t b + σd Z t b p t K t value of outside money Postulate value of money changes proportional to K t Outside Money Technologies a Money 1 Each households can only operate one firm Physical capital dk t = (Φ ι k t δ)dt + σ a dz a a t + σd Z t t Output y t = k t Demand for money sector idiosyncratic risk

Net worth dding outside money qk t value of physical capital dr a = ι dt + Φ(ι δ) dt + q σa dz a a t + σd Z t pk t value of outside money dr M = Φ(ι δ) dt + σ a a dz t Outside Money Technologies a g Money 1 Each households can only operate one firm Physical capital dk t = (Φ ι k t δ)dt + σ a dz a a t + σd Z t t Output y t = k t Demand for money sector idiosyncratic risk

Net worth Demand with E 0 e ρt log c t dt qk t value of physical capital dr a = ι dt + Φ(ι δ) dt + q σa dz a a t + σd Z t pk t value of outside money dr M = Φ(ι δ) dt + σ a a dz t g Outside Money Technologies a Consumption demand: ρ p + q K t = ι K t sset (share) demand x a : E dr a dr M /dt = Cov[dr a dr M, x a = E dra dr M /dt σ 2 dn t a Money a ] = n t dr M +x a dr a dr M = ( ι)/q σ 2 = q q+p Investment rate: (Tobin s q) Φ ι = 1/q For Φ ι = 1 κ log(κι + 1) ι = q 1 κ 1 xa σ2

Net worth Demand with log-utility qk t value of physical capital dr a = ι dt + Φ(ι δ) dt + q σa dz a a t + σd Z t pk t value of outside money dr M = Φ(ι δ) dt + σ a a dz t g Outside Money Technologies a Consumption demand: ρ p + q K t = ι K t sset (share) demand x a : E dr a dr M /dt = Cov[dr a dr M, x a = E dra dr M /dt σ 2 dn t a Money a ] = n t dr M +x a dr a dr M = ( ι)/q σ 2 = q q+p Investment rate: (Tobin s q) Φ ι = 1/q For Φ ι = 1 κ log(κι + 1) ι = q 1 κ 1 xa σ2

Net worth Demand with log-utility qk t value of physical capital dr a = ι dt + Φ(ι δ) dt + q σa dz a a t + σd Z t pk t value of outside money dr M = Φ(ι δ) dt + σ a a dz t g Outside Money Technologies a Consumption demand: ρ p + q K t = ι K t sset (share) demand x a : E dr a dr M /dt = Cov[dr a dr M, dn t a Money a ] = n t dr M +x a dr a dr M x a = E dra dr M /dt = ( ι)/q = q σ 2 σ 2 q+p Investment rate: (Tobin s q) Φ ι = 1/q For Φ ι = 1 κ log(κι + 1) ι = q 1 κ 1 xa σ2

Net worth Market clearing qk t value of physical capital dr a = ι dt + Φ(ι δ) dt + q σa dz a a t + σd Z t pk t value of outside money dr M = Φ(ι δ) dt + σ a a dz t g Outside Money Technologies a Consumption demand: ρ p + q K t = ι K t sset (share) demand x a : E dr a dr M /dt = Cov[dr a dr M, dn t a Money a ] = n t dr M +x a dr a dr M x a = E dra dr M /dt = ( ι)/q = q σ 2 σ 2 q+p Investment rate: (Tobin s q) Φ ι = 1/q For Φ ι = 1 κ log(κι + 1) ι = q 1 κ 1 xa σ2

Equilibrium Moneyless equilibrium p 0 = 0 Money equilibrium p = σ ρ ρ q q 0 = κ+1 κρ+1 > q = κ+1 κ ρ σ+1 q 0 p q 0 ρ σ

Welfare analysis Moneyless equilibrium p 0 = 0 Money equilibrium p = σ ρ ρ q q 0 = κ+1 κρ+1 > q = κ+1 g 0 welfare 0 > < κ ρ σ+1 g welfare

Welfare analysis Moneyless equilibrium p 0 = 0 Money equilibrium p = σ ρ ρ q q 0 = κ+1 κρ+1 q = κ+1 κ ρ σ+1 welfare 0 < welfare What ratio nominal to total wealth p q+p Force agents to hold less k & more money Raise p q+p if and only if σ(1 κρ) 2 ρ maximizes welfare? owers q higher E[dr a dr M ] = ι dt pecuniary externality q Create q-risk to make precautionary money savings more attractive

Roadmap Model absent monetary policy Toy model: one sector with outside money Two sector model with outside money dding intermediary sector and inside money Model with monetary policy Model with macro-prudential policy

Outline of two sector model Technologies b Technologies a 1 B 1 1 1 Households have to Switch Switch technology Specialize in one subsector Demand for money sector specific + idiosyncratic risk for one period dk t = dt + σ b dz b b dk t k t + σd Z t = dt + σ a dz a a t + σd Z t t k t

Net worth Net worth dd outside money Technologies b Outside Money Technologies a Money Money B 1 1 Switch Switch technology Households have to Specialize in one subsector for one period Demand for money

Net worth Net worth dd intermediaries Technologies b Outside Money Technologies a Net worth Money Money B 1 1 Risk can be partially sold off to intermediaries Risk is not contractable (Plagued with moral hazard problems)

Net worth Net worth dd intermediaries Technologies b Outside Money Technologies a Net worth Money Money B 1 1 Intermediaries Can hold outside equity & diversify within sector b Monitoring

Inside equity Net worth dd intermediaries Technologies b Outside Money Technologies a Money Money B 1 Net worth 1 Intermediaries Can hold outside equity & diversify within sector b Monitoring

Inside equity HH Net worth dd intermediaries Technologies b Outside Money Pass through Outside Money Technologies a Money Inside Money (deposits) B 1 Net worth Money 1 Intermediaries Can hold outside equity & diversify within sector b Monitoring Create inside money Maturity/liquidity transformation

Inside equity HH Net worth Shock impairs assets: 1 st of 4 steps Technologies b Outside Money Pass through Technologies a Money Inside Money (deposits) B 1 Net worth osses Money 1

Inside equity HH Net worth Shrink balance sheet: 2 nd of 4 steps Technologies b Money Deleveraging Deleveraging Outside Money Pass through Inside Money Inside Money (deposits) (deposits) Technologies a B 1 1 Net worth osses Money 1 Switch

Inside equity HH Net worth iquidity spiral: asset price drop: 3 rd of 4 Technologies b Money Deleveraging Outside Money Deleveraging Pass through Inside Money Inside Money (deposits) (deposits) Technologies a B 1 1 Net worth osses Money 1 Switch

Inside equity HH Net worth Disinflationary spiral: 4 th of 4 steps Technologies b Money Deleveraging Deleveraging Outside Money Pass through Inside Money Inside Money (deposits) (deposits) Technologies a B 1 1 Net worth osses Money 1

Formal model: capital & output Technologies b a Physical capital K t - Capital share ψ t 1 ψ t Output goods Y b b t = k t Y a a substitutes t = k t ggregate good (CES) - Consumed or invested - numeraire Price of goods Y t = P t b = 1 2 1 2 Y t b (s 1)/s + 1 s/(s 1) 2 Y a (s 1)/s t Y t Y t b 1/s Imperfect P t a = 1 2 Y t Y t a 1/s Model setup in paper is more general: Y t = ψ t K t

Formal model: risk When k t is employed in sector a by agent j dk t = Φ ι t δ k t dt + σ a k t dz t a + σ j k t d Z t a Investment rate (per unit of k t ) sectorial idiosyncratic independent Brownian motions (fundamental cash flow risk) Φ ι t is increasing and concave, e.g. log[ κι t + 1 /κ] ll dz are independent of each other Intermediaries can diversify within sector b Face no idiosyncratic risk Households cannot become intermediaries or vice versa

sset returns on money Money: fixed supply in baseline model, total value p t K t Return = capital gains (no dividend/interest in baseline model) If dp t /p t = μ p p t dt + σ t dzt, dk t /K t = Φ ι t δ dt + 1 ψ t σ a dz a t + ψ t σ b b dz t (σ t K ) T dz t dr t M = Φ ι t δ + μ t p + σ t p T σt K dt + σ t p + σt K dz t π t = p t q t +p t fraction of wealth in form of money

Inside equity HH Net worth Capital/risk shares Technologies b Outside Money Pass through Technologies a Fraction α t of HH Money Inside Money (deposits) 1 χ t ψ t q t K t Money Net worth N t ψ t q t K t χ t 1 χ t (1 ψ t )q t K t If χ t > χ, inside and outside equity earn same returns (as portfolio of b-technology and money). If the equity constraint χ t = χ binds, inside equity earns a premium λ

llocation Equilibrium is a map Histories of shocks prices q t, p t, λ t, allocation Z τ, 0 τ t α t, χ t & portfolio weights (x t, x t a, x t b ) wealth distribution η t = N t (p t +q t )K t 0,1 intermediaries wealth share ll agents maximize utility Choose: portfolio, consumption, technology ll markets clear Consumption, capital, money, outside equity of b

Numerical example: capital shares ρ = 5%, =.5, σ a = σ b =.4, σ j =.9, σ a =.6, σ a = 1.2, s =.8, log κι + 1 Φ ι =, κ = 2, χ =.001 κ intermediaries 1 technology a HH technology b HH χψ

Numerical example: prices Disinflation spiral p q iquidity spiral

Numerical example: prices Disinflation spiral p π = p p+q q iquidity spiral

Numerical example: dynamics of η fundamental volatility η x t (σ b 1 b σ K t ) σ t = 1 ψ t(1 χ t ) η η leverage π η π/η elasticity amplification Steady state

Overview No monetary economics Fixed outside money supply mplification/endogenous risk through iquidity spiral Disinflationary spiral asset side of intermediaries balance sheet liability side Monetary policy side: Money vs. Credit view (via helicopter drop) Wealth shifts by affecting relative price between ong-term bond Short-term money Risk transfers reduce endogenous aggregate risk Macroprudential policy

Outside Money Pass through Bonds b t K t 1 χ t ψ t q t K t Inside Money (deposits) Net worth N t dverse shock value of risky claims drops Monetary policy response: cut short-term interest rate Value of long-term bonds rises - stealth recapitalization iquidity & Deflationary Spirals are mitigated

Effects of policy Effect on the value of money (liquid assets) helps agents hedge idiosyncratic risks, but distorts investment We saw this in the toy model with one sector Redistribution of aggregate risk, mitigates risk that an essential sector can become undercapitalized ffects earnings distribution, rents that different sectors get in equilibrium

Monetary policy and endogenous risk Intermediaries risk (borrow to scale up) η x t (σ b 1 b σ K t ) σ t = 1 ψ η η π η π/η amplification fundamental risk + ψ(1 χ) η η + π η 1 ψ b t p t B η B(η)/η mitigation Example: b t B η p t B η = α t π η π(1 π) α(η) Intuition: with right monetary policy bond price B(η) rises as η drops stealth recapitalization Can reduce liquidity and disinflationary spiral

Numerical example with monetary policy llocations Prices Higher intermediaries capital share (1 χ)ψ p less disinflation q is more stable ψ a ess production of good a

Numerical example with monetary policy ess volatile Steady state Recall b t B η p t B η = α t π η π(1 π) η x t (σ b 1 b σ K t ) σ t = 1 ψ η η π η π/η + ψ η η + π η 1 ψ b t p t B η B η /η

Numerical example with monetary policy Welfare: HH and Intermediaries Sum

Monetary policy in the limit full risk sharing of all aggregate risk σ t η = 1 ψ η η π η π η + x t ψ 1 χ η + π η η 1 ψ b t pt B η B(η)/η (σ b 1 b σ t K ) η is deterministic and converges over time towards 0

Monetary policy in the limit full risk sharing of all aggregate risk ggregate risk sharing makes q determinisitic ike in benchmark toy model Excessive k-investment Too high q (pecuniary externality) ower capital return Endogenous risk corrects pecuniary externality

Overview No monetary economics Fixed outside money supply mplification/endogenous risk through iquidity spiral Disinflationary spiral asset side of intermediaries balance sheet liability side Monetary policy Wealth shifts by affecting relative price between ong-term bond Short-term money Risk transfers reduce endogenous aggregate risk Macroprudential policy Directly affect portfolio positions

MacroPru policy Regulator can control cannot control Portfolio choice ψs, xs investment decision ι q consumption decision c of intermediaries and households

MacroPru policy Regulator can control cannot control Portfolio choice ψs, xs investment decision ι q consumption decision c of intermediaries and households De-facto controls q and p within some range De-factor controls wealth share η Force agents to hold certain assets and generate capital gains distorts In sum, regulator maximizes sum of agents value function Choosing ψ b, q, η

MacroPru policy: Welfare frontier Stabilize intermediaries net worth and earnings Control the value of money to allow HH insure idiosyncratic risk (investment distortions still exists, otherwise can get 1 st best 30 optimal macroprudential 25 20 policy that removes endogenous risk household welfare 15 10 5 0-5 no policy -10-15 -20-20 -15-10 -5 0 5 10 15 20 25 intermediary welfare

Conclusion Unified macro model to analyze Financial stability Monetary stability - iquidity spiral - Fisher disinflation spiral Exogenous risk & Sector specific idiosyncratic Endogenous risk Time varying risk premia flight to safety Capitalization of intermediaries is key state variable Monetary policy rule Risk transfer to undercapitalized critical sectors Income/wealth effects are crucial instead of substitution effect Reduces endogenous risk better aggregate risk sharing Self-defeating in equilibrium excessive idiosyncratic risk taking Macro-prudential policies MacroPru + MoPo to achieve superior welfare optimum