Here is the abstract of a 1997 Peter Stella paper:
Central banks may operate perfectly well without capital as conventionally defined. A large negative net worth, however, is likely to compromise central bank independence and interfere with its ability to attain policy objectives. If society values an independent central bank capable of effectively implementing monetary policy, recapitalization may become essential. Proper accounting practice in determining central bank profit or loss and rules governing the transfer of the central bank`s operating result to the treasury are also important. A variety of country-specific central bank practices are reviewed to support the argument.
More concretely, I am not persuaded by the view that a kind of sheer internal commitment to good outcomes, however sincere, can sustain a peg or nominal target. The outside world always impinges on the logic of commitment, and thus capital is required. This is also why I do not agree with Scott Sumner’s claim that a truly credible Swiss target, eliminating the need to expand the SNB balance sheet to make it stick, is possible circa January 2015 or for that matter anytime soon.
I do not, however, see time inconsistency as the central problem. More likely the government either just doesn’t want to take the specified action (e.g., Germany with higher inflation), or part of the government would like to do something but it doesn’t have enough political capital (Draghi at the ECB). Time consistency models have some neat analytic properties but often they distract our attention from these more fundamental constraints.