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

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?

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.

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.

The Model N risk-neutral consumers per country, with $1 and CRS project: –Returns R if successful (probability p L ) – 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 p H =p L +  p Banker type is unobservable: Adverse Selection problem Monitoring is unobservable: Moral Hazard problem

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)=p L +g  p is unconditional prob of investment success.

Banking without Deposit Insurance Banking is possible only if UDIR>BIC: iff g big enough The largest possible bank is of size k U. But if  k U <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. k=1 k Q BIC MIC UDIR kUkU

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.

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.

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.

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.

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

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.

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.

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.