Bank Capital and Aggregate Credit

This paper seeks to explain the role of bank capital in uctuations of lending and output. We build a continuous time model of an economy in which commercial banks nance their loans by deposits and equity, while facing issuance costs when they raise new equity. The dynamics of the loan rate and the volume of lending in the economy are driven by aggregate bank capitalization. The model has a unique Markovian competitive equilibrium that can be solved in closed form. We show that the competitive equilibrium is constrained ine cient: banks lend too much and hold too little equity, since they do not internalize the impact of their lending decisions on the cost of credit and the social costs of bank distress. We also examine the impact of two regulatory tools: a standard capital ratio and a tax on dividends, showing that the latter is more e cient in dealing with the distortions inherent in the competitive equilibrium.