Overview

We develop an equilibrium model of competing banks to analyze how a regulator should optimally respond to the risk of bank failure through several policy tools such as deposit insurance, tax/subsidy on bank’s investment, liquidity buffer requirements and equity constraints. In the model, banks raise deposit from risk averse depositors and equity capital from risk neutral equity holders through a competitive market, and invest it in a portfolio of safe asset, market index and entrepreneurial projects. The aggregate risk in our model stem from the risk of entrepreneurs projects’ failure which also affects market index as well. Since the market is incomplete the autarkic equilibrium depends only on the marginal probability of entrepreneur’s success and not on the correlation structure of entrepreneurs projects. We show that in the autarkic equilibrium banks always over invest in entrepreneurs’ projects. We show that the regulator can implement the first best when the aggregate risk is IOW. When the aggregate risk is high, the regulator imposes a liquidity buffer policy, which lowers the investment of banks in entrepreneurs’ projects.