Optimal Deposit Insurance Eduardo Dávilla and Itay Goldstein By Eduardo Dávilla and Itay Goldstein Discussion Report Suresh Sundaresan

Depositors Date 0: Ex-ante identical depositors leave some deposits with the bank. This amount is exogenous. Date 1: Depositors discover their type. “Early” type depositors consume in date 1. (“Late” type depositors consume in date 2.) Early depositors receive their (fixed) endowment.

Depositors Both types of depositors have access to an inefficient storage technology. Date 2: Late depositors receive a state contingent endowment. Proceeds are shared. 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

Banks Date 0: Banks have access to a productive technology. Banks offer an interest rate to depositors, which can be withdrawn at Date 1. Date 1: Early liquidation of investment at Date 1 is costly. Bank may face illiquidity/insolvency issues. Banks act to maximize the welfare of depositors. ***************** Banks fully internalize how their choice of interest rate will affect failure probabilities, and the severity of losses. Banks do not internalize the fiscal costs of funding any insurance payouts.

Planner’s Problem Maximize the welfare of depositors. Choose the optimal coverage of insurance. Choose the interest rate on deposits, which depends on the insurance coverage.

Main Trade Offs Level of DI Bank Failure Probability. Fiscal Costs Externality. Consumption losses associated with failures.

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.

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.

Summary Elegant and rigorous analysis of an important problem. Results are well exposited. Model is stylized and it would be useful to caveat the policy predictions, and provide a few extensions to alleviate this concern. 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].

A high level look at policy tools Deposit Insurance (DI). Lender of Last Resort. Bank Supervision. Capital Requirements. Problem Bank Resolution. Depositor preference. These tools go together, complementing each other. Ignoring these tools will skew the importance of DI.

Comments and Suggestions 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. 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.

Comments and Suggestions What is the insurance premium, for the coverage? Who pays it? Banks actually pay the insurance premium in “good states”, ex-ante. This is not modeled. Money is raised by taxes at Date 2, ex-post.

Comments and Suggestions Bank Decisions are made by managers/equity holders. They typically do not necessarily act to maximize depositor’s welfare. How do we take the planner’s policies and make the bank’s equity holders implement them?

Possible extensions? With attractive investment opportunity sets, depositors need not entirely depend on inefficient storage technology or banks. 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.

Possible extensions? 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: Bank resolution policies. Minimum Capital Standards.

Very interesting paper. Worth reading!