The second caveat is that we have allowed the bank to liquidate assets all the way to l++, rather than stopping at the stricter limit /+ < l++. This is permissible if a run occurs, in that liquidating up to l++ still allows the bank to service its debt of d. But notice: if the bank could precommit to liquidate only up to l+: then resources would be available in period 2 to repay creditors who had kept on lending in period 1, and no ongoing lending flight would not be an equilibrium outcome. Hence in our story, as in the self-fulfilling attacks by Obstfeld (1994), lack of precommitment by domestic financial institutions is crucial in generating this kind of multiple equilibria Here.
Short term debt
So far we have not been explicit about the maturity of the debt incurred by the bank in period 0. It made no difference whether it was a one-period bond that was rolled-over in period 1 or a two-period bond that matured in period 2, for we have always implicitly assumed that a one-period bond was automatically renewed, and in the same conditions, in the middle period.
Consider now the implications of being explicit about the maturity structure, and assuming that the initial debt indeed consists of one-period loans (bonds?). What happens if international creditors refuse to roll over the debt in period 1? This is an important question, for both in the Mexican 1994 crisis (recall the infamous Tesobonos) and in the recent Asian episode foreign bondholders have balked at purchasing new short term bonds when the old ones matured at a time of crisis.
With no roll-over the bank has no external debt to repay in period 2, and hence it can liquidate the full long term investment in case of need:
Clearly, if d is positive 24 is more stringent than both 15 and 19. That is to say, financial fragility is greater if lenders refuse to roll over existing debt in the event of a run.
Why would creditors refuse to roll over short term debts? Because they may expect that the bank will not be able to repay its debt. This may turn out to be a self-fulfilling prophecy as in the case of ongoing lending: if run condition 24 is indeed satisfied, then in the event of a run there would not be enough resources in period 2 to repay a loan of size d. Should a run occur, lenders are justified ex post in not having been willing to roll-over existing debts.
Here, as with ongoing lending, lenders’ fears on non-payment can be self fulfilling. If 24 holds but 19 does not, then a run is possible if and only if external holders of bonds panic in period 1 and demand immediate payment. In those circumstances, a panic by the creditors may cause a self-fulfilling run by both depositors and creditors; the resulting bank collapse need not have happened had the creditors behaved differently.