Optimal Deposit Insurance
By
Eduardo Dávilla and Itay Goldstein
Discussion Report
Suresh Sundaresan
Depositors
Date 0:
o Ex-ante identical depositors leave some deposits
with the bank. This amount is exogenous.
Date 1:
o Depositors discover their type.
o “Early” type depositors consume in date 1.
o (“Late” type depositors consume in date 2.)
o Early depositors receive their (fixed) endowment.
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Depositors
o Both types of depositors have access to an
inefficient storage technology.
Date 2:
o Late depositors receive a state contingent
endowment. Proceeds are shared.
o Taxes are levied by the planner to fund
insurance payouts. These are borne by late
depositors.
The only decision of depositors is the amount of
deposits to keep at time 1
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Banks
Date 0:
o Banks have access to a productive technology.
o Banks offer an interest rate to depositors,
which can be withdrawn at Date 1.
Date 1:
o Early liquidation of investment at Date 1 is
costly. Bank may face illiquidity/insolvency issues.
o Banks act to maximize the welfare of depositors.
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o Banks fully internalize how their choice of interest rate
will affect failure probabilities, and the severity of losses.
o Banks do not internalize the fiscal costs of funding
any insurance payouts.
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Planner’s Problem
o Maximize the welfare of depositors.
o Choose the optimal coverage of insurance.
o Choose the interest rate on deposits, which
depends on the insurance coverage.
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Main Trade Offs
o Level of DI
o Bank Failure Probability.
o Fiscal Costs Externality.
o Consumption losses associated with failures.
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Main results
Results
Intuition
Propositions 1 and 2:
optimal level of insurance.
An increase in coverage
decreases the probability of
failure. But it can reduce the
consumption of late types in
failure states, through fiscal
costs.
Proposition 3: planner
controls the interest rate on
deposits in setting the optimal
insurance.
Fiscal externality disappears.
Planner can provide a higher
coverage. Planner also
introduces a wedge in the
deposit rates, relative to the
one that the banks will offer.
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Main results
Results
Intuition
Propositions 4: optimal level
of insurance with broader
investment opportunity set for
depositors and banks.
Basic results go through.
Depositors’ investment
opportunity set does not
influence the insurance policy,
but bank’s opportunity set
matters.
Deposits at t=0 are
exogenous and unaffected
by their opportunity set.
Propositions 5 and 6:
Equilibrium Selection &
Aggregate spillovers.
Shows some robustness of the
characterization of sufficient
statistics in the basic model.
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Summary
1. Elegant and rigorous analysis of an important problem.
2. Results are well exposited.
1. Model is stylized and it would be useful to caveat the policy
predictions, and provide a few extensions to alleviate this
concern.
2. Model predicts a relationship between the deposit rates and
the optimal insurance coverage. Can this be brought to the
data? [Quantity of deposits fixed, irrespective of DI].
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A high level look at policy tools
1. Deposit Insurance (DI).
2. Lender of Last Resort.
3. Bank Supervision.
4. Capital Requirements.
5. Problem Bank Resolution.
6. Depositor preference.
These tools go together, complementing each other.
Ignoring these tools will skew the importance of DI.
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Comments and Suggestions
o Banks in the model have no equity. No Tier 1
(equity) capital for the bank. This will overstate
the costs of funding insurance, and the fiscal
externality.
o Issuing equity to avoid illiquidity or failure
is precluded at Date 1. Again, minimum bank
capital will mitigate the effects that arise in this
model.
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Comments and Suggestions
oWhat is the insurance premium, for the
coverage? Who pays it?
oBanks actually pay the insurance premium in
“good states”, ex-ante. This is not modeled.
oMoney is raised by taxes at Date 2, ex-post.
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Comments and Suggestions
o Bank Decisions are made by managers/equity
holders. They typically do not necessarily act
to maximize depositor’s welfare.
o How do we take the planner’s policies and
make the bank’s equity holders implement
them?
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Possible extensions?
o With attractive investment opportunity sets,
depositors need not entirely depend on
inefficient storage technology or banks.
o This should affect endogenously the deposits
that they would leave at date 0. [Covariance
effects]. Deposits at time 0 ahould be
endogenous, relative to the premium, and
investment opportunity set.
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Possible extensions?
o Insurance premium for the coverage could be quantified
and paid, ex-ante.
4. The effects of DI are likely to be different in the
presence of other policy tools, especially:
o Bank resolution policies.
o Minimum Capital Standards.
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Very interesting paper. Worth reading!
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