Optimal forbearance of bank resolution

This paper analyzes optimal strategic delay of bank resolution (forbearance) in a setting where partially insured depositors can run on the bank after observing bad news on the bank's assets. A resolution authority (RA) observes withdrawals of deposits at the bank level and needs to decide when to intervene to protect a deposit insurance fund. Intervention means the authority seizes the bank's assets and impose a mandatory stay for depositors, liquidates assets at market terms and evenly distributes proceeds among all remaining depositors. We show, there exists a hidden trade-off when resolving banks, late intervention increases costs to insurance but early intervention increases depositors' propensity to run, by this making the run and subsequent resolution more likely. This trade-off crucially depends on the amount of deposit insurance provided. Under low insurance depositors are too sensitive to bad news and inefficient runs exist, under high insurance, depositors start ignoring bad news on the bank fundamental, roll over to often and there is inefficient investment. As main result of the paper, under low deposit insurance, the optimal policy is to never intervene during a run, even if the run is ex post inefficient; a stricter intervention policy would alter depositors' behavior in a way that inefficient runs become even more likely. Under high insurance it is optimal to intervene as soon as possible. Further, for every intervention policy the optimal amount of insurance coverage is strictly between zero and one. There exist infinitely many pairs of intervention threshold and insurance coverage which achieve the first best outcome. Thus, there is room for a policy parameter reduction: RA can fix the intervention threshold and achieve first best solely by choosing the amount of insurance coverage. But not the other way around suggesting that insurance coverage is the stronger parameter: Under too high insurance coverage inefficient investment exists, under too low coverage inefficient runs exist, both for every intervention threshold.