Dynamic Banking and the Value of Deposits

Abstract

We propose a dynamic theory of banking where deposits play the role of productive capital as in the classical Q-theory of investment for non-financial firms. A key conceptual innovation of our theory is that the stock of deposits cannot be perfectly controlled by the bank. Demand deposit accounts commit the bank to allow holders to withdraw or deposit funds at will. The resultant uncertainty in deposit flows exposes the bank to the risk of violating regulatory restrictions on leverage. Deposits create value for the bank except when it is close to hitting the leverage restrictions, because sudden deposit inflows can force the bank into costly equity issuance. We show that the bank is endogenously risk averse with respect to both the deposit flow risk and standard loan return risk. Our model predictions on dynamic bank valuation and asset-liability management are broadly consistent with the evidence. Moreover, our model lends itself to a quantitative evaluation of the costs and benefits of leverage regulations.

Keywords: Deposits, Dynamic Banking, Liquidity, Financial Constraint, Inside Money, Outside Money, Franchise Value, Payment System

JEL Classification: E4, E5, G21, G3