A Note on the role of bank capital
This note explores how a bank’s balance sheet responds to a capital shock in a simple model of the banking firm where both loan demand and deposits are sensitive to a bank’s capital position relative to its competitors. An unconstrained bank shrinks its deposit base in the wake of a capital loss if loan demand is very sensitive to the bank’s relative capital position. The deposits of an unconstrained bank expand only if both deposit and loan demands are fairly immune to a bank’s relative capital position. In a simple model with reserves we show that in the wake of a capital loss the adjustment of loans and reserves under a binding constraint depends on the parameters of the model while the adjustment of total assets and liabilities does not. Loans decrease by the size of the capital loss plus the increase in reserves. If the constraint is not binding then loans generally decrease by more than the increase in reserves.