Is deposit insurance a good thing and if so who should pay for it
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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?.

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

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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 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


  • 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.

Banking without Deposit Insurance


  • 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.







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.


  • 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

Banking Sector


Deposit Insurance


  • Welfare effect of increasing deposit insurance up to the optimum level.


Banking sector without deposit



RDIR (D,N, g)


RDIR (D,N,g)





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.


  • 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.

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