Banking, Liquidity Effects, and Monetary Policy Te-Tsun Chang and Yiting Li NTU, NCNU May 28, 2016
Monetary policy Monetary policy can contribute to offsetting major disturbances in the economy that arise from other sources than monetary policy itself, and provide a stable background for the economy (Friedman 1968). A key objective of modern central banking is to keep inflation low and stable over some long time horizon, but they are also concerned with stabilizing the real economy in the short run. Need to balance the two objectives.
Banks holding reserves When people are subject to trading shocks, banks can play an efficiency role by channeling funds from people with idle money to those who are cash constrained. This role is limited by banks holding reserves, due to regulations and liquidity management considerations. Basel III: banks must have enough liquidity buffers e.g. liquidity coverage ratio: banks hold the short-term liquidity buffer to cover its net cash outflows over a 30-day period following a shock.
Objectives Study how banks holding liquidity buffers affect the monetary transmission mechanism and the conduct and effectiveness of monetary policy. What we do... Study liquidity effects and monetary policy in a model with fully flexible prices and explicit roles for money and banks. (Lagos and Wright, 2005; Berentsen, Camera and Waller, 2007) Establish the monetary transmission mechanism in the basic model with monetary shocks only. Incorporate temporary demand shocks to study optimal monetary policy. Motivate banks holding reserves by resorting to the need for liquidity management due to random deposit withdrawals.
Main features of the model Fiat money is used as the medium of exchange, due to limitations on record keeping, enforcement, and commitment. Agents are not subject to the standard CIA constraint because, before trading, they can borrow cash from banks. Banks hold some fractions of deposits and newly injected money as liquidity buffers. Money kept as bank reserves does not provide liquidity to lubricate economic activity, and the higher the fraction kept as reserves, the less liquid money is.
Key findings: liquidity effects Unexpected money injections raise output and lower nominal interest rates iff the newly injected money is more liquid than the initial money stocks. Liquidity effects are eliminated, if banks hold no liquidity buffers; or the newly injected money is as liquid as the initial money stocks. Though agents make portfolio choices before the realization of monetary shocks, the informational friction does not necessarily generate a liquidity effect.
Key findings: stabilization monetary policy Two types of optimal stabilization policy in response to temporary shocks Central bank promises to withdraw state-contingent money injections in the future. No promise to withdraw state-contingent money injections Failure to withdraw state-contingent money injections does not make the stabilization policy neutral. (Berentsen and Waller (2011): the promise of the central bank to undo state-contingent money injection is key to the existence of a liquidity effect and the effectiveness of stabilization policy. The economy may undergo higher short-run fluctuations than otherwise Success of stabilization policy relies on unexpected money injections being more liquid than the initial money stock.
Model The first subperiod preference shock: Prob(an agent is a buyer) = θ: u(q) Prob(an agent is a seller) = 1 θ: c(q) All goods trades are anonymous, and there is no public record of individuals trading histories: Money is the medium of exchange. The second subperiod All agents can produce and consume a good. Agents adjust money holdings, m.
Money injections evolution of (per capita) money stock: M t = (1+z t )M t 1. money growth rate: z t = µ+ε t µ: long-run money growth rate. ε t : monetary shock, with support, [ε,ε] The central bank injects money in 1st subperiod, τ t = z t M t 1, or it can levy nominal taxes from banks reserves to extract cash: τ t < 0 and z t < 0.
Banking Competitive banks accept nominal deposits and make nominal loans. They take as given the loan rate and deposit rate. Assume full enforcement of debt repayment, and so default is not possible (but see, e.g., Berentsen, Camera, and Waller, 2007, and Li and Li, 2013). The central bank injects money through banks, which extend funds to borrowers. A bank s profits are distributed to agents as dividends, or withdrawn from agents bank accounts if z t < 0.
Banks liquidity buffers Banks lend out ν (0,1] fraction of deposits, and χ m (0,1] fraction of injected money. 1 ν of deposits and 1 χ m of money injections are kept as reserves. zero marginal profit condition: νi = i d, liquidity buffer: a cost on the intermediation
Time sequence of events m zt = μ + εt 1st 2nd m t t+1 θ buyer borrow : b - (1+i) b 1 - θ seller deposit : d (1+id) d
Subperiod 2: maximization problem W(m,b,d) = max x,h,m +1 U(x) h+βv(m +1 ) s.t. x +φm +1 = h+φ(m +F)+φ(1+i d )d φ(1+i)b W(m,b,d) = φ(m +F)+φ(1+i d )d φ(1+i)b + max x,m +1 {U(x) x φm +1 +βv(m +1 )}. FOC U (x) = 1, βv m (m +1 ) φ, = if m +1 > 0 Envelope conditions W m = φ W b = φ(1+i) W d = φ(1+i d )
Subperiod 1: maximization problem Seller s problem max q s,d s.t. c(q s )+W(m d +pq s,d) d m FOC p = c (q s ) φ d = m if i d > 0 Buyer s problem max q b,b s.t. u(q b )+W(m+b pq b,b) pq b m+b FOC u (q b ) c (q s ) = 1+i
Subperiod 1: optimal money holdings V(m) = {θ[u(q b )+W(m+b pq b,b)] +(1 θ)[ c(q s )+W(m d +pq s,d)]}f(z)dz Optimal money holdings at period t 1 satisfy β [θ u (q b ) +(1 θ)φ(1+i d )]f(z)dz = φ 1 p
Subperiod 1: market clearing conditions Goods Money (1 θ)q s = θq b m = M 1 Loan loan demand per capita {}}{ θb = ν(1 θ)d }{{} +χ mzm 1 }{{} ν: fraction of deposits lent out deposits χ m : fraction of injected money lent out money injections
Liquidity effects: aggregate demand Total funds available per buyer: where m +b = (χ+χ mz) M 1, θ χ = θ+(1 θ)ν Substitute p = c (q s) φ into cash constraint, pq b = m+b, to get aggregate demand θq b c ( θq b 1 θ ) = χφ 1M 1 +χ m zφ 1 M 1 (1+z)
q b z = Liquidity effects: χ m > χ φ 1 M 1 (χ m χ) θ(1+z) 2 [c ( θq b 1 θ )+ θq b 1 θ c ( θq b 1 θ )] > > = 0 iff χ m = χ < < χ: fraction of initial money stock to finance spending. χ m : fraction of newly injected money to finance spending. A liquidity effect exists iff χ m > χ; i.e., newly injected money is more liquid than the initial money stock The larger the difference between χ m and χ, the stronger the liquidity effect. If banks hold no liquidity buffer (χ = χ m = 1): No liquidity Effect
Loanable fund effect vs Fisher effect Aggregate demand (suppose c (q) = 1): θq b = χ(1+ χm χ z)φ 1M 1. 1+z { loanable fund effect qb ;i Money injections Fisher effect q b ;i If χ m > χ, an increase in z causes a stronger loanable funds effect, which dominates the Fisher effect, raising a buyer s real balances to support higher consumption.
Liquidity effects: interpretations Usually χ m > χ because central banks impose reserve requirements against deposits, while no such requirements on reserves acquired from open market operations. The recent financial crisis may present a case in which χ m < χ. Cochrance (2014): Fed has bought about $3 trillion of assets, and created about $3 trillion of bank reserves, in which required reserves are only $80 billion. Banks only held $50 billion of reserves before the crisis. Almost all of the $3 trillion were excess reserves. One can interpret this case as χ m being extremely small.
Optimal monetary policy Aggregate demand shock, η g(η). u(q b ) = e η (1 e q b) Two types of stabilization policy whereby central bank implements the policy through state-contingent money injections. state-contingent stabilization policy Central bank does not promise to withdraw the state-contingent money injection. price-level targeting stabilization policy Central bank promises to withdraw the state-contingent money injection in subperiod 2 (Berentsen and Waller, 2011).
State-contingent stabilization policy Consider the case χ m = 1 > χ so a liquidity effect exists. Substituting buyer s binding cash constraint, q b (η) = [χ+z(η)]φ 1M 1 θ[1+z(η)], into agents optimality condition of holding money, β η η 1+χi 1+z(η) g(η)dη = 1: we obtain the central bank s problem: max x,q b W = U(x) x + s.t. η β η η η θ [θu(q b ) (1 θ)c( 1 θ q b)]g(η)dη (1+χi)(φ 1 M 1 θq b ) g(η)dη = 1 φ 1 M 1 (1 χ) FOC: U (x) = 1, and i(η) = βλ A[θ(1 χη)+χφ 1 M 1 ] θ[(1 χ)φ 1 M 1 2βλ A χ] λ A : multiplier of the constraint on optimal money holding
Implementation of state-contingent stabilization policy i(η) = βλ A[θ(1 χη)+χφ 1 M 1 ] θ[(1 χ)φ 1 M 1 2βλ A χ] Because 1+i = u (q b ) c (q s) = eη q b, we use the approximation, log(1+y) y, to get i(η) η q b (η). In response to higher aggregate demand, the central bank chooses higher money injections to increase consumption. When choosing the state-contingent money injection, the central bank weighs the payoff to managing inflation expectations, measured by the multiplier of the constraint on optimal money holding, λ A, against the effectiveness of implementing policy, measured by the magnitude of a liquidity effect.
Price-level targeting stabilization policy z(η) = µ+ε(η), where µ is the long-run money growth rate, and ε(η) is the state-contingent money injection, withdrawn in subperiod 2. The central bank s problem: max W = U(x) x + x,q b s.t. β Result: η η η η 1+χi 1+µ g(η)dη = 1 θ [θu(q b ) (1 θ)c( 1 θ q b)]g(η)dη i = 1+µ β ; z(η) = θq b(η)(1+µ) χφ 1 M 1 βχ φ 1 M 1 The central bank increases the state-contingent money injection in response to higher aggregate demand.
Comparing two policy regimes Optimality condition of holding money: State-contingent policy β η 1+χi η 1+z(η) g(η)dη = 1 Price-level targeting policy β η η 1+χi 1+µ g(η)dη = 1 Under price-level targeting policy, central bank controls long-run inflation expectations. The price-level targeting policy results in smaller fluctuations in consumption than the state-contingent policy. If central bank lacks the ability to withdraw state-contingent money injections, the existence of a liquidity effect and the success of stabilization policy rely on unexpected money injections being more liquid than the initial money stock.
Conclusion A liquidity effect exists iff the fraction of money injections used to finance spending is larger than that of the initial money stock. If banks hold no liquidity buffers, the liquidity effect is eliminated. In contrast to Berentsen and Waller (2011), failure to unravel state-contingent money injections in our model does not make the stabilization policy neutral. When the central bank cannot commit itself to a price-level path, the existence of a liquidity effect and the success of stabilization policy rely on unexpected money injections being more liquid than the initial money stock.