Is Deposit Insurance a Good Thing, and if so, Who should pay for it?

1. Is Deposit Insurance a Good Thing, and if so, Who should pay for it? Alan Morrison, Merton College & Saïd Business School, Oxford Lucy White, Harvard Business School & FAME, Université de Lausanne

2. Why do we have deposit insurance? • Deposit Insurance Schemes increasingly adopted around the world. • Yet empirically they are associated with increasing the probability of a banking crisis. • So why are they adopted?

3. Literature on Deposit Insurance • Large literature (starting with Merton 1977) looks at how to price deposit insurance fairly. • Small literature considers that this may not be possible (Chan et al 1992) or desirable (Frexias and Rochet 1998). • These papers all take the existence of deposit insurance as given. • Closest in Spirit: Diamond and Dybvig (1983) and Matutes and Vives (1996). These papers provide a rationale for deposit insurance.

4. Rationales for Deposit Insurance • Diamond and Dybvig (1983): deposit insurance rules out a bad sun spot equilibrium where all depositors run. • Matutes and Vives (1996) deposit insurance reduces vertical differentiation and increases bank competition: may be good or bad. • We abstract from both of these. In our model, we show that deposit insurance can be a useful subsidy to the banking system that reduces moral hazard. • Basic intuition: a subsidised deposit insurance scheme increases rents for successful bankers.

5. The Model • N risk-neutral consumers per country, with $1 and CRS project: • Returns R if successful (probability pL) • 0 otherwise • Each country has bankers with $1 and a CRS project • A proportion g of bankers is sound; the rest are unsound • Sound bankers have a monitoring technology which at cost C per dollar increases the success probability to pH=pL+p • Banker type is unobservable: Adverse Selection problem • Monitoring is unobservable: Moral Hazard problem

6. Banks • A bank is a banker who takes depositor funds to augment the size of his project • Since bank investments are weakly more profitable than consumers, (utilitarian) welfare is maximised if consumers deposit in banks. • Banks receive fee Q from depositors (deposit rate = R-Q) • Return to size k bank is therefore R+(k-1)Q • Monitoring is efficient: Rp>C • …but must be incentive compatible (MIC): …and also better than the outside option (BIC): • Depositing IR constraint (DIR): • Where (g)=pL+gp is unconditional prob of investment success.

7. Banking without Deposit Insurance Q • Banking is possible only if UDIR>BIC: iff g big enough • The largest possible bank is of size kU. • But if kU<N+ then not all funds are invested in the banking system - there is rationing of deposits. • Deposit insurance will allow us to expand the banking system. MIC UDIR BIC k k=1 kU

8. What externality does deposit insurance correct? • The combination of adverse selection and Moral Hazard means that the banking sector is socially too small. • MH means that bankers must receive rents for managing deposits; AS makes depositors too reluctant to pay such rents: they may pay a fee and get no monitoring  banking sector is socially too small.

9. A Model with Deposit Insurance • Deposit Insurance fund collects lump sum taxes ex ante from Bankers (B), Depositors (D), and Non-Depositors (N). • All proceeds will be paid out ex post to depositors in failed banks. • Moral hazard incentive constraint unchanged (both sides multiplied by (1-B)). Intuition: bank does not get anything from deposit insurance directly, only indirectly from what depositors are willing to pay… • The DIR constraint is relaxed because (a) depositors will now receive a payout if the bank fails (b) non-depositors may be taxed more highly than depositors.

10. Deposit Insurance as a Way to Encourage Depositing • Thus, intuitively, deposit insurance raises the depositors’ IR constraint and increases the level of bank deposits. • Complete deposit insurance is not optimal as then banks could expand without bound – the MIC would be violated but depositors would not care. • The optimal scheme ensures that all funds are invested in the banking sector, and can be implemented in a number of ways, for example: • B= D =N a flat rate tax • B= D =0; N >0 through general taxation, constituting a net subsidy to the banking system.

11. Intuition • Taxation of bankers is welfare neutral: • It reduces their incentives to monitor by reducing their capital • BUT it raises their incentives to monitor by increasing what they can extract from depositors. • These two considerations exactly offset. • Similarly, taxing depositors ex ante to provide them with a subsidy ex post has no effect on deposits when depositors are risk neutral. • Thus only a general subsidy to the banking system through N has a beneficial effect.

12. Bank Size with Deposit Insurance Banking Sector With Deposit Insurance Q • Welfare effect of increasing deposit insurance up to the optimum level. MIC Banking sector without deposit insurance QN RDIR (D,N, g) QS RDIR (D,N,g) k k**(g)=N+ k*(g) k=1

13. Robustness Checks • We consider how the deposit insurance fund should be invested: in the banking system or in a less productive storage technology (T-bills). • We consider whether the taxation for deposit insurance should be raised ex ante or ex post. • We consider whether the adverse selection problem could be countered using capital requirements, cross subsidies or coinsurance schemes.

14. Comparative Statics • Level of Deposit Insurance should be larger the worse is the quality of the banking sector (given that it is still more productive than depositors’ outside option). • Low banking sector quality also associated with higher probability of financial crisis. • Shows that deposit insurance can be a good idea despite its empirical association with poor outcomes.

15. Conclusions • A new rationale for deposit insurance. • Previous literature has considered that deposit insurance should be “fairly priced”. • We show that if the banking sector exhibits both adverse selection and moral hazard, economic productivity can be enhanced by a net subsidy to the system which can take the form of deposit insurance.