# Presentation: 011864

## 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***

***k******U***

## 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)*

*RDIR (****D**,****N**,g)*

*k**(g)=N+***

*k*(g)*

*Q**N*

*Q**S*

- 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.