Abstract
We study the consequences and optimal design of bank deposit insurance and reinsurance in a general equilibrium setting. The model involves two production sectors, financed by bonds and bank loans, respectively. Financial intermediation by banks is required in the model as we assume that one of the production sectors is risky and requires monitoring by banks. Households fund banks through deposits and equity. Deposits are explicitly insured and banks pay a premium per unit of deposits. Any remaining shortfall is implicitly guaranteed by the government. Two types of equilibria emerge: One type of equilibria supports the Pareto optimal allocation. In the other type, bank lending and the default risk are excessively large. The intuition is as follows: the combination of financial intermediation by banks, limited liability of bank shareholders, and deposit insurance makes deposits risk-free from the individual households’ perspective, although they involve risk from the societal point of view. This distorts investment choices and the resulting input allocation to production sectors. We show, however, that a judicious combination of deposit insurance and reinsurance eliminates all non-optimal equilibrium allocations. Our paper thus may provide a benchmark result for policy proposals advocating deposit insurance cum reinsurance.
Highlights
1.1 MotivationMany countries have some form of deposit insurance for demand deposits, up to some fixed amount per account or per individual
We have shown that an equilibrium with banks and δ-deposit insurance can replicate the optimal allocation of the equilibrium without financial intermediation
Deposit insurance cum reinsurance does guarantee that the optimal allocation is achieved in equilibrium
Summary
Many countries have some form of deposit insurance for demand deposits, up to some fixed amount per account or per individual. When a government bail-out is needed, the required taxation of households is lump sum and does not lead to additional distortions Given this set-up, it is a priori unclear whether equilibria in such an economy yield the optimal allocations that would occur in an Arrow-Debreu version of the economy. Deposit insurance and reinsurance assets, there is over-investment in the risky sector and banks raise too many funds Such a situation is an equilibrium, as this investment pattern is consistent with the optimal portfolio choice of risk-averse households. Households anticipate that they have to pay taxes in the bad state to bail out banks and that they receive additional funds from the deposit insurance fund in the good state. Whereas the results will be derived in a general equilibrium setting, under certain assumptions on technologies and preferences, we argue in the concluding section that the underlying logic holds true more generally for economies with banks and aggregate risk
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