I should note at the outset that solving the TBTF [Too Big to Fail] problem has two distinct aspects. First, and most obviously, one goal is to get to the point where all market participants understand with certainty that if a large SIFI [Systemically Important Financial Institution] were to fail, the losses would fall on its shareholders and creditors, and taxpayers would have no exposure. However, this is only a necessary condition for success, but not a sufficient one. A second aim is that the failure of a SIFI must not impose significant spillovers on the rest of the financial system, in the form of contagion effects, fire sales, widespread credit crunches, and the like. Clearly, these two goals are closely related. If policy does a better job of mitigating spillovers, it becomes more credible to claim that a SIFI will be allowed to fail without government bailout.
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Still, we are quite a way from having fully solved the policy problems associated with SIFIs. For one thing, the market still appears to attach some probability to the government bailing out the creditors of a SIFI; this can be seen in the ratings uplift granted to large banks based on the ratings agencies' assessment of the probability of government support. While this uplift seems to have shrunk to some degree since the passage of Dodd-Frank, it is still significant. All else equal, this uplift confers a funding subsidy to the largest financial firms.
Moreover, as I noted earlier, even if bailouts were commonly understood to be a zero-probability event, the problem of spillovers remains. It is one thing to believe that a SIFI will be allowed to fail without government support; it is another to believe that such failure will not inflict significant damage on other parts of the financial system. In the presence of such externalities, financial firms may still have excessive private incentives to remain big, complicated, and interconnected, because they reap any benefits--for example, in terms of economies of scale and scope--but don't bear all the social costs.