1. What Do Banks Do? Liquidity Provision Systemic Risk and Financial Regulation Bonn 2015, Lecture 4 MPI Collective Goods Martin Hellwig

2. Deposit finance  Banks are unique in funding by deposits, funds that can be withdrawn at will  Why?  History: This is how banking got started  Deposits and letters of credit in long-distance trade in the late middle ages  Deposits and „bank notes“ in 17th century England (goldsmiths)  Function: Transactions services, insurance against uncertainty about timing of need for cash

3. Transactions services  Availability at many locations (bearer notes, ATMs)  Payments by bank transfers, checks, credit cards, debit cards, letters of credit  An aside on 2008/IV: disruptions in international payments system (letters of credit) played a significant role in the breakdown of international trade  Effects of „bank holidays“, US 1933, Germany 1931, Greece ?

4. Liquidity provision (Diamond- Dybvig 1983)  Consumers do not know when they will need cash  Bank leaves it to them to withdraw when they want  Reaction to information asymmetry/non- verifiability of „need“  Leaves bank open to the risk of a „run“

5. Liquidity provision (Diamond- Dybvig 1983), ctd.  Modelling consumer uncertainty  Three periods, 0,1,2, one good in each period  Im period zero, consumers have k to invest; they do not know when they will need to consume, with probability p in t=1, with 1-p in t=2.  Utility in one case: u(c 1 )  Utility in the other case: u(c 2 )  Expected utility: p u(c 1 ) + (1-p) u(c 2 )

6. Liquidity provision (Diamond- Dybvig 1983), ctd.  Investment opportunities  Storage: 1 unit returns 1 unit in the next period  Long-term investment: 1 unit in t=0 returns R>1 units in t=2; 1 unit (nothing?) in t=1  Assume that consumers‘ preference shocks satisfy a law of large numbers: a fraction p of the population consists of impatient consumers, a fraction 1-p of patient consumers

7. Liquidity provision (Diamond- Dybvig 1983), ctd.  An efficient arrangement specifies a pair (c 1, c 2 ), to maximize the expected utility p u(c 1 ) + (1-p) u(c 2 )  Under the constraint (1-p) c 2 <= R(k – p c 1 )  First-order condition: u‘(c 1 ) = R u‘(c 2 )

8. Liquidity provision (Diamond- Dybvig 1983), ctd.  If u‘‘(c)c/u‘(c) < -1, this implies c 1 > k and c 2 < R k  Insurance?  R>1 has an income effect and a substitution effect; the income effect raises c 1, the substitution effect lowers c 1  The assumption about u(.) implies that the substitution effect is dominated by the income effect

9. Liquidity provision (Diamond- Dybvig 1983), ctd.  If types are observable, there is nothing more to say.  If types are not observable, consumers can be given a contract in which they withdraw „on demand“, hopefully according to type.  Implementation by Bertrand competition between „banks“  Equilibrium of this competition has at least two banks offering the first-best contract, consumers going to one of them.

10. Liquidity provision (Diamond- Dybvig 1983), ctd.  Problem: In t=1, there may be a run  If patient consumers, expect other patient consumers to make withdrawals, they have an incentive to withdraw as well  If more than a fraction p of the population asks for c 1 in t=1, the bank cannot fulfil its obligations in t=2.  A run resulting from an equilibrium with self- fulfilling expectations  Multiplicity of equilibria

11. Liquidity provision (Diamond- Dybvig 1983), ctd. Remedies:  Deposit insurance  „Suspension of convertibility“ – have the bank in t=1 stop payments when it has served a fraction p of the population

12. Assessment  Is the „insurance“ idea crucial?  Von Thadden (EER 1997, JFI 1998, JMathE 2002):  In a continuous-time setting, the Diamond- Dybvig contract is not feasible.  Liquidity provision is still meaningful as a form of market making. Banks relieve investors from the limitations of autarky  Intermediation may be required for reasons given in Diamond 1984 (delegated monitoring)  Runs may still be a problem if liquidation is costly.

13. Assessment (ctd.)  Do runs result from „sunspots equilibria“?  Empirically: No, as reactions to information (Calomiris – Gorton 1991)  Are runs necessarily harmful? Could people run because information has it that it is more efficient to liquidate the assets? (Postlewaite- Vives, JPE 1986, Chari-Jagannathan JF 1988)

14. Incomplete Information  Incomplete information can eliminate equilibrium multiplicity  Morris-Shin AER 1998, Goldstein-Pauzner JF 2005, Rochet – Vives JEEA 2004  Bank solvency depends on a fundamental, the return on investment.  Each investor has noisy private information about the fundamental  Equilibrium is unique  Involves run if the fundamental is bad, no run is good. Transition?

15. Incomplete Information, ctd.  Uniqueness of equilibrium disappears if people also observe a noisy public signal (C.Hellwig JET 2002)  If the bank has outside equity as well as deposits, the stock price provides a noisy public signal (Angeletos-Werning AER 2006)  Who has incentives to invest in information? Shareholders or depositors?

16. How much liquidity do we need?  Gorton: Unbounded demand for liquidity ... At what price?  Putting money in money market funds...  Having money market funds put money in banks....  Having banks put money in ABS CDO‘s of MBS  An unbounded scarcity of collateral?  Efficiency? Social Costs?