Monetary and Financial Macroeconomics

Transcription

1 Monetary and Financial Macroeconomics Hernán D. Seoane Universidad Carlos III de Madrid

2 Introduction Last couple of weeks we introduce banks in our economies Financial intermediation arises naturally when there are spread (interest rate differentials) due to differences in liquidity Banks do not keep all deposits in liquid reserves Banks handle long term assets and short term liabilities This makes banks vulnerable

3 Introduction Today we study the exposure of banks to liquidity risks This risk appears when many clients decide to withdraw their deposits at the same time Should a government intervene during a banking crisis? How? Diamond and Dybvig (1983, JPE): today we cover a rather theoretical exposition and during the reducidos you will see the same theory oriented to exercises References: Diamond and Dybvig (1983, JPE), Freixas Rochet (1999) Ch7, Champ et al (2010) Ch 12

4 A model of liquidity risk We start with the key ingredients of a model of liquidity risk These ingredients can be easily introduced in the OLG setting, and we will do so later The is a one good economy populated with people that live for 3 periods t = 0, 1, 2 Ex-ante everybody is identical (ex post, i.e. after the realization of a shock, no) Agents receive 1 unit of a good as their endowment in period 0 No one want to consume in period 0. In period 0 only investment decisions are taken

5 A model of liquidity risk Investment Investment decisions in period 0 Agents can invest in a liquid technology that pays a gross return of 1 in 1 period (storage technology, short term and liquid) Agents can, instead, invest in an illiquid investment that takes 2 periods in mature and pays a gross return of R > 1 at maturity (long term and illiquid) The long term investment can be liquidated before maturity (i.e. the capital can be sold in an anticipated way at a loss), assume that for now if this is the case, investment will have a low return L < 1

6 A model of liquidity risk Liquidity shocks Agents are subject to liquidity risk Those agents that are hit by a liquidity shock will need to consume only in period 1 (type 1), while the rest want to consume in period 2 (type 2) Liquidity shock occurs with probability ρ and does not occur with probability (1 ρ) Ex- ante (i.e. before the realization of the shock) agents are all alike and have the following expected utility U = ρu(c 1 ) + (1 ρ)u(c 2 )

7 A model of liquidity risk Note that liquidity risk is an idiosyncratic risk We assume types are non-observable (they are private information) If we have many agents in the economy, law of large numbers hold and in the aggregate a fraction ρ of the population with be type 1 and (1 ρ) will be type 2 This implies that in the aggregate there is no risk

8 A model of liquidity risk Allocations 3 relevant market allocations depending on market assumptions 1 Autarky: what would happen if no trade is allowed 2 Financial Market: if we allow for trading assets 3 Optimal: if types are publicly observable (we could write optimal insurance contracts)

9 A model of liquidity risk Autarky Assume at t = 0 everybody chooses its level of capital investment, I, and keep 1 I in the storage technology to maximize U subject to c 1 = LI + 1 I, someone hit by the liquidity shock will have and c 2 = RI + 1 I, If not hit by the liquidity shock Given that L < 1 < R, c 1 1 and c 2 R... hence, ex-post everything is inefficient with positive probability If type 1, I should have been 0; else 1... we can do better with financial markets

10 A model of liquidity risk Financial Market Assume at t = 0 everybody chooses its level of capital investment, I, and keep 1 I in the storage technology to maximize U Types 1 can sell the product of his shares to capital investments at price, q each, c 1 = qri + 1 I Types 2 buy shares c 2 = RI + 1 I q Note that the 2 eq imply c 1 = qc 2 In an interior maximum we need qr = 1

11 A model of liquidity risk Financial Market Contracts are uncontingent in this setting as the shock is private information and there is no information revealling that can make the contract contingent on Given that everybody is identical in 0, there will be trade in claims in periods 1 and 2 Each agent has access to the same linear technology and can choose any positive linear combination of c 1 = 1 and c 2 = R Here c 1 = 1 and c 2 = R There is no early liquidation of investment

12 A model of liquidity risk Financial Market This allocation is not, in general, Pareto-optimal Reason: there is liquidity risk and those agents that suffer this risk should be insured for (i.e. no right allocation of risk) An optimal allocation requires that the marginal rate of substitution equals the marginal rate of transformation. That is, it will require here that u (1) = Ru (R)

13 A model of liquidity risk Optimal allocation max U = pu(c 1) + (1 p)u(c 2 ) c 1,c 2,I subject to pc 1 = 1 I (1 p)c 2 = RI This will give us the optimal symmetric allocation

14 max U = pu c 1,c 2,I A model of liquidity risk ( 1 I p Optimal allocation ) ( ) RI + (1 p)u 1 p gives u (c 1) + Ru (c 2) = 0 An interesting case will arise when u (1) > Ru (R)... here in the optimum we will need to provide more consumption to impatient agents... they need to be insured against liquidity shocks (this happens when elasticity of substitution between periods is less than 1

15 A model of liquidity risk Fractional banking system? Can banks decentralize the optimal allocation? Offer a deposit contract, in period 0 agents deposit their endowment and they can withdraw c1 deposit in period or c 2 in period 2 This contract can be implemented as a Nash Equilibrium: no-one will gain from unilateraly deviating from the following strategy Type 1: withdraw c1 in period 1 and c1 2 = 0 in period 2 A type 2: withdraw c2 in period 2 and c2 1 = 0 in period 1 With unobservable types, there will be self-revelation

16 A model of liquidity risk Bank runs There is another Nash equilibrium in which type 2 agents pretend to be type 1 they withdraw their deposits in period 1 and store them until period 2 To withdraw, agents have to que: first come first serve bank If everybody withdraw their deposits at once, the bank might have a liquidity problem Banks will need to borrow or liquidate assets

17 A model of liquidity risk Bank runs Bank run is an inefficient equilibrium Arises from a coordination failure in the game among depositors Sunspot equilibrium: could there be a shock that coordinate agents into the good equilibrium? A confidence shock?

18 Bank runs: how to avoid them? interbank lending identifying unnecessary withdrawals suspension of withdrawals government deposit insurance

19 Interbank loans run makes banks insolvent by forcing them to sell off assets at loss if banks can borrow enough to meet withdrawals: avoid losses banks can be repaid in the following period when capital matures key: no type 2 person would have an incentive to withdraw early borrow from whom? (i) other banks not subject to run; (ii) young people of next generation (recall: prohibited intergenerational loans)

20 Identifying unnecessary withdraws if banks can learn an individual s type, they could simply refuse to allow type 2 people to withdraw early historically: banks often refused to allow large withdrawals without verifying that withdrawal was genuinely needed (e.g. bill, payroll) Problem: you own your deposit

21 Withdraw suspensions close the doors temporarily when reserves are used up next period capital matures and everybody gets paid; incentive for type 2 people to withdraw early vanishes if a bank has the right to suspend withdrawals, it may actually never have to do so because depositors will no longer panic Problem: this can solve a liquidity problem, not a solvency problem (our model is not a model of solvency crisis)

22 Government deposit insurance government guarantees to pay promised return if bank is insolvent how to fulfill promise in case of a run? ) needs some revenue to pay off the depositors of an insolvent bank! e.g. may tax the young generation to bail out insolvent bank if government promise is credible, bank runs do not occur but: if bank assets are risky, a bail out may occur now: introduce riskiness of bank assets

23 Bank failures on average more than 2,000 bank failures per year ( ) on average five bank failures per year almost all assets involve some element of risk in their return how can banks protect its depositors from risk? hold a large fraction of riskless assets attract investors as shareholders in the bank if shareholders invest in a bank, its net worth is positive

24 Bank Risk If bank investment are risky, even if depositors dont want to withdraw deposits at once, bank might become insolvent how can banks protect its depositors from risk? hold a large fraction of riskless assets attract investors as shareholders in the bank if shareholders invest in a bank, its net worth is positive Depositantes tienen prioridad

25 Problemas de Moral Hazard y Seguros de depositos if banks are not insured: careful evaluation of risks and average returns in order to attract shareholders and depositors a bank that is exposed to too much risk will not attract investors typically: trade-off between risk and average return but what happens if banks are partially/fully insured? only care about high average rate of return ignore risk of loss because deposits are insured moral hazard problem: insurance removes incentives government may try to regulate the types of assets banks hold

26 Capital Requirements capital requirement: net worth must exceed a fraction of total assets provides a cushion to absorb asset losses before depositors (or the insurer of deposits) suffer any losses since shareholders are exposed to more risk, they will exercise more care when selecting a portfolio of potentially risky assets by contrast, if the bank s net worth falls to zero, shareholders have an incentive to gamble heavily because they have nothing to lose Basel I - III: set of regulatory standards for banks; involves capital requirements; equity ratio: shareholder s equity divided by total assets

27 Insolvent banks Closing an insolvent bank isan option As long as deposits are insured, this is no problem to the depositor Shareholder would loose their assets. There would be no incentives to invest in riskless assets once the bank is insolvent The best option for a shareholder is to gamble for redepmtion