Princeton University Udates: htt://www.rinceton.edu/~markus/research/aers/i_theory_slides.df
Motivation Main features Unified framework to study financial and monetary stability Model that combines money and intermediation inside money Value of money is endogenously determined liuidity value (Samuelson, Bewley, KM, ) Fisher (1933) deflationary siral Negative shock hits assets side of intermediaries balance sheets and is amlified through leverage and volatility dynamics Decline in inside money, leads to deflationary ressure hits intermediaries balance sheet on the liability side Inside money and outside money Endogenous money multilier = f(health of intermediary sector) Monetary olicy Redistribution from/towards intermediary sector Difference to New Keynesian framework Greensan ut - time-inconsistency Difference to examle in Kydland-Precott 2
Role of money some literature Medium of exchange Store of value & liuidity Samuelson s OLG Bewley Scheinkman-Weiss Homstrom-Tirole Kiyotaki-Moore 08 (New) Monetarists Save for future Precaution for Financial stability + monetary olicy Diamond-Rajan (2006) Stein (2010) Curdia-Woodford (2010) uninsurable endowment shocks to kee roject running new investment oortunity + resell constraint New Keynesian framework Macro with financial frictions BGG, KM97, He-Krishnamurthy 2009, BruSan 2010 3
Model outline roductive 2% Assets Liabilities less roductive 98% Assets Liabilities 4
Model outline roductive 2% Assets Liabilities less roductive 98% Assets Liabilities Caital
Allocation according to roductive 2% Assets Liabilities less roductive 98% Assets Liabilities Allocation according to Value of caital
Efficient allocation roductive 2% Assets Liabilities less roductive 98% Assets Liabilities Efficient allocation Value of caital 7
Frictionless economy roductive 2% less roductive 98% Assets Liabilities Assets Liabilities caital outside euity debt Issue outside euity because caital is risky stocks loans Value of caital caital
Allocation with euity constraint roductive 2% less roductive 98% Assets Liabilities Assets Liabilities caital net worth debt outside euity Must hold at least 60% of euity stocks loans caital Value of caital
Allocation with euity and debt constraint roductive 2% Assets caital Liabilities less roductive 98% Assets Liabilities caital Value of caital
Monetary economy w/o intermediaries roductive 2% less roductive 98% Assets Liabilities Assets Liabilities caital when agent A becomes unroductive and B becomes roductive, A exchanges his caital for B s money (Bewley, Samuelson) outcome more efficient than without money (roductive hold more than 2% of caital) caital money 11
Two olar cases Economy Assets Value of fiat money Frictionless Issue claims Euity Debt Low (zero) Frictions (severe) No claims high
Two olar cases introducing intermediaries Economy Assets Value of fiat money Frictionless Issue claims Euity Debt Low (zero) Intermediaries caitalization erfect Frictions (severe) No claims high defunct Role of intermediaries Relax financing constraint by monitoring roductive agents Have to take on roductive agent s euity risk (so that they have incentive to monitor) Intermediation deends on their ability to absorb risk of intermediaries
Monitoring technology Diamond (1984) Holmström-Tirole (1997) Allocation with intermediaries roductive 2% less roductive 98% Assets Liabilities Assets Liabilities caital outside euity debt intermediaries Assets entrereneur euity Liabilities entrereneur euity deosits loans deosits caital
Monetary economy w/o intermediaries roductive 2% Assets Liabilities less roductive 98% Assets Liabilities when agent A becomes unroductive and B becomes roductive, A exchanges his caital for B s money (Bewley, Samuelson) outcome more efficient than without money (roductive hold more than 2% of caital) relative to financing through intermediaries, less efficient allocation (roductive hold too little caital) valuation (rice of caital deressed by limited demand from roductive agents, leads to underinvestment) caital money 15
Monetary economy with intermediaries roductive 2% less roductive 98% Assets Liabilities Assets Liabilities net worth outside euity entrereneur euity caital money debt intermediaries Assets entrereneur euity Liabilities deosits money loans deosits caital money Monitoring technology Diamond (1984) Holmström-Tirole (1997)
The big icture Intermediaries Zero: like economy with only outside money ( high) Very large: erfect lending (no frictions) ( low) Intermediate: Contracting friction: amlification (non-linear effects) money multilier changes outside money stays constant, inside money fluctuates Intermediaries have to hold α fraction of risk (in order to have incentive to monitor) No contracting on roductivity switch relation to Bewley (no distinction between cash flow news, k t, and SDF news)
Roadma Big icture overview 2 olar cases Imaired i-sector Perfect i-sector lending via outside money only erfect lending Passive monetary olicy: Gold standard Model setu General model (with aggregate risk) Lending and money multilier deends on of i-sector Deflation siral Active Monetary Policy Introduce long-term bond Short-term interest rate olicy Asset urchase and OMO Redistributional effects Greensan ut - Time-inconsistency
Model details (random) switches More roductive (θ=2%) Fraction of caital ζ t = θk t / [θk t + (1-θ)k t ] Less roductive (1-θ) y t = a(ζ t ) k t, DRS in ζ t y i t a(ζ t )k t 2% ζ t 0 t = (a i t ) k t dk t = (ϕ(i t ) δ) k t dt + k t dz t g t sector shock (exogenous risk) 19
Model details (random) switches More roductive (θ=2%) Fraction of caital ζ t = θk t / [θk t + (1-θ)k t ] y t = a(ζ t ) k t, DRS in ζ t Less roductive (1-θ) Fraction of caital 1-ζ t y t = a(1-ζ t ) k t, DRS in (1-ζ t ) y i t a(ζ t )k t y i t a(1-ζ t )k t 2% 0 t = (a i t ) k t ζ t 98% dk t = (ϕ(i t ) δ) k t dt + k t dz t o t = (a-i t ) k t dk t = (ϕ(i t ) δ) k t dt (1- ζ t ) g t dz t =0 20
g * = ϕ(i * ) δ Otimal investment decision: Examle 2% of agents are roductive and 98%, unroductive Each grou of agents has same decreasing returns to scale roduction function a ζ t i t k t dt dk t = where ζ t is the fraction of caital held by each grou Otimal investment: i = 1 ζ b 2 2 2b ζ t i t δ k t o, ζ = a ζ i = 1 ζ a b 2 2 net outut o * =a-i * g, ζ = 2b ζ i δ = 1 ζ b δ growth
Production and Pricing Assume constant returns to scale at individual level, but decreasing returns to scale at sector level a * and g * deend on caital allocation ζ t to entrereneur sector interior solution in euilibrium Caital held by roductive agents a * ( t, ζ t ) k t dt dk t = g * ( t, ζ t ) k t dt + σk t dz t Caital held by less roductive agents a * ( t, 1-ζ t ) k t dt dk t = g * ( t, 1-ζ t ) k t dt Price of caital (in terms of outut) d = µ t t dt + σ t t dz t
Risks Caital risk Assets Liabilities caital k t t net euity worth held by banks dk t = g * ( t, ζ t ) k t dt + k t dz t exogenous risk d t = t t dt + t t dz t endogenous risk d(k t t ) = (g * ( t, ζ t ) + t + t ) (k t t ) dt + ( t + ) (k t t ) dz t
Risks Caital risk d(k t t ) = (g * ( t, ζ t ) + t + t ) (k t t ) dt + ( t + ) (k t t ) dz t Money risk t K t dk t = (κ t g * ( t, ζ t ) + (1-ζ t ) g * ( t, 1-ζ t ) + h) K t dt + ζ t K t dz t endogenous risk d t = t t dt + t t dz t d( t K t ) = ( t K t ) dt + ( t + ζ t ) ( t K t ) dz t exogenous risk
Balance sheets roductive θ less roductive 1-θ Assets Liabilities Assets Liabilities net worth outside euity entrereneur euity caital constraint: debt entrereneurs and intermediaries must hold fraction of at least ψ of entrereneur euity intermediaries Assets entrereneur euity loans Liabilities deosits Monitoring technology Diamond (1984) Holmström-Tirole (1997) deosits money caital 26
Euilibrium definition An euilibrium consists of functions that for each history of macro shocks {Z s, s [0, t]} secify the rice of caital t, the value of money t and fees f t that insiders (entrereneurs and banks) charge for managing assets caital holdings ζ t and 1 ζ t and rates of investment of roductive and unroductive households Euity holdings of entrereneurs, ψ e, banks, ψ i and households 1- ψ e - ψ i rates of consumtion of entrereneurs, banks and households such that given rices and fees all agents choose asset holdings and consumtion to maximize utility markets for caital, entrereneur outside euity and loans/money clear. 27
Solving for the euilibrium Key idea: summarize sector s, sector risks, asset allocations, and make sure that asset returns match reuired risk remia Net worth Banks: N t Entrereneurs: θ (( t + t ) K t - N t ) HH: (1-θ) (( t + t ) K t - N t ) Risk (N t + θ (( t + t )K t - N t )) ( t + ζ t ) + ψ t ζ t K t ( t (1-θ) (( t + t )K t - N t )) ( t + ζ t ) + (1-ψ t ) ζ t K t ( t (1-ζ t ) K t ( t - t Money has risk t + ζ t Caital has risk t + Caital money t + - t - ζ t
Valuation of Entrereneur Caital Net worth Risk Banks: N t Entrereneurs: θ (( t + t ) K t - N t ) HH: (1-θ) (( t + t ) K t - N t ) â( t,ζ t )/ t + ĝ( t,ζ t ) + t + t - ( t K + t + t ) = (N t + θ (( t + t )K t - N t )) ( t + ζ t ) + ψ t ζ t K t ( t (1-θ) (( t + t )K t - N t )) ( t + ζ t ) + (1-ψ t ) ζ t K t ( t (1-ζ t ) K t ( t - t Return on money: ( K t + t + t ) dt + ( t + ζ t ) dz t Return on caital: (â( t,ζ t )/ t + ĝ( t,ζ t ) + t + t ) dt + ( t + ) dz t
Valuation of Entrereneur Caital Net worth Risk Banks: N t Entrereneurs: θ (( t + t ) K t - N t ) HH: (1-θ) (( t + t ) K t - N t ) â( t,ζ t )/ t + ĝ( t,ζ t ) + t + t - ( t K + t + t ) = (N t + θ (( t + t )K t - N t )) ( t + ζ t ) + ψ t ζ t K t ( t (1-θ) (( t + t )K t - N t )) ( t + ζ t ) + (1-ψ t ) ζ t K t ( t (1-ζ t ) K t ( t - t = ( t Return on money: ( K t + t + t ) dt + ( t + ζ t ) dz t Return on caital: (â( t,ζ t )/ t + ĝ( t,ζ t ) + t + t ) dt + ( t + ) dz t
Valuation of Entrereneur Caital Net worth Risk Banks: N t Entrereneurs: θ (( t + t ) K t - N t ) HH: (1-θ) (( t + t ) K t - N t ) â( t,ζ t )/ t + ĝ( t,ζ t ) + t + t - ( t K + t + t ) = (N t + θ (( t + t )K t - N t )) ( t + ζ t ) + ψ t ζ t K t ( t (1-θ) (( t + t )K t - N t )) ( t + ζ t ) + (1-ψ t ) ζ t K t ( t (1-ζ t ) K t ( t - t = ( t ψ t (N t + θ (( t + t )K t - N t )) ( t + ζ t ) + ψ t ζ t K t ( t N t + θ (( t + t )K t - N t ) Return on money: ( K t + t + t ) dt + ( t + ζ t ) dz t Return on caital: (â( t,ζ t )/ t + ĝ( t,ζ t ) + t + t ) dt + ( t + ) dz t
Valuation of Entrereneur Caital Net worth Risk Banks: N t Entrereneurs: θ (( t + t ) K t - N t ) HH: (1-θ) (( t + t ) K t - N t ) â( t,ζ t )/ t + ĝ( t,ζ t ) + t + t - ( t K + t + t ) = (N t + θ (( t + t )K t - N t )) ( t + ζ t ) + ψ t ζ t K t ( t (1-θ) (( t + t )K t - N t )) ( t + ζ t ) + (1-ψ t ) ζ t K t ( t (1-ζ t ) K t ( t - t = ( t ψ t (N t + θ (( t + t )K t - N t )) ( t + ζ t ) + ψ t ζ t K t ( t N t + θ (( t + t )K t - N t ) (1-θ) (( t + t )K t - N t )) ( t + ζ t ) + (1-ψ t ) ζ t K t ( t + - t (1-ζ + (1-ψ t ) t ) K t ( t - t (1-θ) (( t + t )K t - N t ) Return on money: ( K t + t + t ) dt + ( t + ζ t ) dz t Return on caital: (â( t,ζ t )/ t + ĝ( t,ζ t ) + t + t ) dt + ( t + ) dz t
Valuation of HH Caital Net worth Risk Banks: N t Entrereneurs: θ (( t + t ) K t - N t ) HH: (1-θ) (( t + t ) K t - N t ) â( t,ζ t )/ t + ĝ( t,ζ t ) + t + t - ( t K + t + t ) = (N t + θ (( t + t )K t - N t )) ( t + ζ t ) + ψ t ζ t K t ( t (1-θ) (( t + t )K t - N t )) ( t + ζ t ) + (1-ψ t ) ζ t K t ( t (1-ζ t ) K t ( t - t = ( t (1-θ) (( t + t )K t - N t )) ( t + ζ t ) + (1-ψ t ) ζ t K t ( t (1-ζ t ) K t ( t - t (1-θ) (( t + t )K t - N t ) Return on money: ( K t + t + t ) dt + ( t + ζ t ) dz t Return on caital: (â( t,ζ t )/ t + ĝ( t,ζ t ) + t + t ) dt + ( t + ) dz t
Law of motion of N t So far, asset valuation for given N t only Net worth Risk Banks: N t Entrereneurs: θ (( t + t ) K t - N t ) HH: (1-θ) (( t + t ) K t - N t ) tn = (N t + θ (( t + t )K t - N t )) ( t + ζ t ) + ψ t ζ t K t ( t N t + θ (( t + t )K t - N t ) (N t + θ (( t + t )K t - N t )) ( t + ζ t ) + ψ t ζ t K t ( t (1-θ) (( t + t )K t - N t )) ( t + ζ t ) + (1-ψ t ) ζ t K t ( t (1-ζ t ) K t ( t - t = risk remium earned on incremental risk over Return on money: ( t K + t + t ) dt + ( t + ζ t ) dz t
Law of motion of N t So far, asset valuation for given N t only Net worth Risk Banks: N t Entrereneurs: θ (( t + t ) K t - N t ) HH: (1-θ) (( t + t ) K t - N t ) tn = (N t + θ (( t + t )K t - N t )) ( t + ζ t ) + ψ t ζ t K t ( t N t + θ (( t + t )K t - N t ) (N t + θ (( t + t )K t - N t )) ( t + ζ t ) + ψ t ζ t K t ( t (1-θ) (( t + t )K t - N t )) ( t + ζ t ) + (1-ψ t ) ζ t K t ( t (1-ζ t ) K t ( t - t = risk remium earned on incremental risk over dn t /N t = ( t K + t + t ) dt - ρ dt + σ t N (σ t N - ( t + ζ t )) dt + σ t N dz t Return on money: ( t K + t + t ) dt + ( t + ζ t ) dz t
Scale invariance Our model is scale invariant in N t (total intermediary ) an K t (aggregate caital) t = N t /K t Solve for ζ t = fraction of caital managed by roductive HH t = rice of hysical caital t = rice of money ψ t = fraction of risk held by entrereneurs and i-sector f t = fee for intermediation (sread) as a functions of the state variable t = N t /K t Mechanic alication of Ito s lemma euilibrium conditions get transformed into ordinary differential euations for ζ (η), (η), (η) and ψ(η)
Euilibrium: and
Euilibrium - unconstrained ζ
Observations As η goes u: Intermediaries take on more risk, cometition increases and fees for intermediation services go down Caital is allocated more efficiently, more roductively The rice of caital increases due to higher demand greater roductive efficiency Unroductive agents hold more inside money (deosits in financial institutions) and less outside fiat money The rice of fiat money goes down (so it would go u in the event that η falls, leading to deflation) There is an additional source of amlification relative to an economy without money: as η goes down, the value of assets fall, while the value of liabilities increase (due to deflation)
Amlification through deflation siral As intermediaries declines Intermediation + inside money shrinks Money multilier collases Economic activity declines Value of outside money rises deflation Externality effect (within i-sector) Intermediaries are doubly hit Asset side: Liability side: Deflationary siral asset values decrease real debt value increases
Roadma Big icture overview Passive monetary olicy: Gold standard Model setu General model with aggregate risk Lending and money multilier deends on of i-sector Deflation siral Active Monetary Policy Introduce long-term bond Short-term interest rate olicy Asset urchase and OMO Redistributional effects Greensan ut - Time-inconsistency
Motivation some stylized facts/emirics Stylized facts from current crisis Deflationary ressure Money multilier collased (see e.g. Goodhart 2010) Monetary base increased M3 stayed roughly constant Banking sector rofits were heled by monetary olicy Aggressive risk-taking before crisis Emirical findings Mervin King (1994) more indebted countries suffered sharer downturn in 1990s recession Eisfeld-Ramini (2008) less caital reallocation in downturns King-Ploser (1984) inside money has significantly more ower for outut than monetary base Friedman (1982) debt/gdp more stable than o-money/gdp 43
Monetary olicy So far, outside money fixed, ays no interest ( Gold Standard ) = no central bank Short-term interest rate olicy Central bank accets deosits & ays interest rate (by rinting money) E.g. short-term interest rate is lowered when η becomes small Introduce consul (eretual) bond ays interest rate in ST (outside) money Budget neutral olicies Asset urchases Bond oen market oerations (OMO) Outside euity Risky caital k t Perfect commitment (Ramsey) vs. imerfect commitment Markovian (in η)
Monetary economy with intermediaries roductive 2% less roductive 98% Assets Liabilities Assets Liabilities net worth outside euity entrereneur euity caital money debt intermediaries Assets entrereneur euity Liabilities deosits money loans deosits caital money LT bonds
Instrument 1: short-term interest rate Without long maturity assets changes in short-term interest rate has no effect Interest rate change euals instantaneous inflation change With long-term bond (monetary instruments: fraction χ is cash and 1 χ are bonds) with bonds, deflationary siral is less ronounced because as η goes down, growing demand for money is absorbed by increase in value of long-term bonds Effectiveness of monetary olicy deend on maturity structure (duration) of government debt
Moral hazard Liuidity bubbles Accommodating Monetary olicy rule Greensan ut Ex-ost efficient recaitalizes intermediary sector Ex-ante inefficient if excessive stimulates risk taking on behalf of intermediaries Liuidity bubble Time consistency roblem with Intermediaries/bankers instead of workers/labor unions Rationale for banking regulation To reduce robability of low η realizations 49
Otimality of monetary olicy Lowers risk on liability side of intermediaries ( t - κ t ) Signal = fundamental risk + valuation risk + money risk Signal recision increases Imroves incentives
Roadma Big icture overview Passive monetary olicy: Gold standard Active Monetary Policy Introduce long-term bond Short-term interest rate olicy Asset urchase and OMO Redistributional effects Greensan ut - Time-inconsistency Differences to New Keynesian framework
New Keynesian I-Theory Key friction Price stickiness Financial friction Driver Monetary olicy First order effects Second order effects Time consistency Demand driven as firms are obliged to meet demand at sticky rice Affect HH s intertemoral trade-off Nominal interest rate imact real interest rate due to rice stickiness Redistributional between firms which could (not) adjust rice Wage stickiness Price stickiness + monoolistic cometition Misallocation of funds increases incentive roblems and restrains firms/banks from exloiting their otential Ex-ost: redistributional effects between financial and non-financial sector Ex-ante: insurance effect leading to moral hazard in risk taking (bubbles) - Greensan ut - Moral hazard 52
Risk build-u hase New Keynesian I-Theory Net worth dynamics zero rofit no dynamics dynamic State variables Many exogenous shocks Intermediation/friction shock Endogenous due to accommodating monetary olicy Endogenous intermediation shock Monetary olicy rule Policy instrument Taylor rule (is aroximately otimal only if difference in u is well roxied by outut ga) sreads credit aggregates (?) Short-term interest rate + exectations Deends on signal uality and timeliness of various observables Short-term interest rate + long-term bond + exectations Role of money In utility function (no deflation siral) Storage Precautionary savings 53
Conclusions/further research Unified macromodel to analyze both Financial stability Monetary stability Liuidity sirals Fisher deflation siral Caitalization of banking sector is key state variable Price stickiness lays no role (unlike in New Keynesian models) Monetary olicy rule Redistributional feature Time inconsistency roblem Greensan ut Future research Persistent roductivity shocks Maturity mismatch in i-sector Minsky cycles 54