Dynamics of Debt Capacity

We propose a model that explains the build-up of short term debt when the creditors are strategic and have different beliefs about the prospects of the borrowers' fundamentals. We define a dynamic game among creditors, whose outcome is the short term debt process as a function of the borrower's fundamentals. As common in the literature, this game has multiple Nash equilibria. We give a refinement of the Nash equilibrium concept that leads to a unique equilibrium. For the resulting debt-to-asset process of the borrower we define a notion of stability. Bank runs are predictable: a bank run begins when the debt-to-asset process leaves the stability region and becomes a mean-fleeing sub-martingale with tendency to reach the debt ceiling, which is the point when the borrower becomes illiquid. The debt ceiling and the stability region are computed explicitly. A critical ingredient in our model is the distribution of capital across the beliefs of the creditors and we allow for a wide variety of specifications for this distribution