Some early literature correlated the likelihood of systemic crises to banks’ anticipation of bailouts. Leitner (2005) develops a model of financial networks in which linkages not only spread contagion but also induce private sector bailouts, where liquid banks bail out illiquid banks because of the threat of contagion. Linkages can thus be optimal ex ante because they allow banks to obtain some form of mutual insurance even if formal commitments are impossible. However, in some cases, the whole network may collapse.
Acharya and Yarulmazer (2007) show that while the too-big-to-fail guarantee is explicitly a part of bank regulation in many countries, bank closure policies also suffer from an implicit too-many-to-fail problem: when the number of bank failures is large, the regulator finds it ex post optimal to bail out some or all failed banks, whereas when the number of bank failures is small, failed banks can be acquired by the surviving banks. This gives banks incentives to herd and increases the risk that many banks may fail together. The ex post optimal regulation may thus be time-inconsistent or sub-optimal from an ex antestandpoint.
Farhi and Tirole (2009) make a similar argument, showing that private leverage choices exhibit strategic complementarities through the reaction of monetary policy. In a context where monetary policy is non-targeted, the ex post benefits from a monetary bailout accrue in proportion to the number amount of leverage, while the distortion costs are to a large extent fixed. This insight has several consequences. First, banks choose to correlate their risk exposures. Second, private borrowers may deliberately choose to increase their interest-rate sensitivity following bad news about future needs for liquidity. Third, optimal monetary policy is time inconsistent. Fourth, there is a role for macro-prudential supervision.
Acharya, Shin and Yorulmazer (2010) look at how policy interventions aiming at resolving bank failures affect the ex ante choice of bank liquidity. They focus on three different policies: (1) liquidity support to failed banks (bailouts); (2) unconditional liquidity support to surviving banks; and (3) liquidity support to surviving banks conditional on the level of liquid assets in their portfolios. They show that the first two policies decrease banks' incentives to hold liquidity, as the first policy limits fire-sale opportunities and the second policy guarantees the liquidity desired by surviving banks for acquisitions at fire-sale prices. In contrast, the third policy increases banks' incentives to hold liquidity. While interventions to resolve banking crises may be desirable ex post, they thus affect bank liquidity in subtle ways.
Chari and Kehoe (2013) develop a model in which, in order to provide managerial incentives, it is optimal to have costly bankruptcy. If benevolent governments can commit to their policies, it is optimal not to interfere with private contracts. Such policies are time inconsistent: without commitment, governments have incentives to bail out firms by buying up the debt of distressed firms and renegotiating their contracts with managers. From an ex ante perspective, however, such bailouts are costly because they worsen incentives and thereby reduce welfare. Chari and Kehoe show that limits on the debt-to-value ratio of firms mitigate the time-inconsistency problem by eliminating the incentives of governments to undertake bailouts.
Keister (2016) studies the bailout vs. bail-in question in a model of financial intermediation with limited commitment. When a crisis occurs, the policy maker will respond with fiscal transfers that partially cover intermediaries' losses. The anticipation of this bailout distorts ex ante incentives, leading intermediaries to become excessively illiquid and increasing financial fragility. Prohibiting bailouts is not necessarily desirable, however: while it induces intermediaries to become more liquid, it may nevertheless lower welfare and leave the economy more susceptible to a crisis. A policy of taxing short-term liabilities, in contrast, can both improve the allocation of resources and promote financial stability.
Nolan, Sakellaris and Tsoukalas (2016) argue that banks and other firms which are bailed out should suffer a penalty contingent on that bailout. They demonstrate that optimal time-consistent macro-prudential policy that replicates an equilibrium with no bailouts and zero debt, is like a tax on bankers’ consumption and contingent on government's’ fiscal capacity which itself is a function of existing debt. That removes the incentive of bankers to take excessive risk because it makes them internalise the cost of bailouts. They also show that policies such as solvency or leverage constraints are sub-optimal because they are time inconsistent just at the point when governments and regulators confront the central problem of financial regulation. The government cannot commit not to bail out bankers with those policies in place. It follows that the non–zero correlations between credit spreads and bond spreads observed during periods of financial crisis reflect suboptimal government policies that do not remove bankers’ incentive to take excessive risks.
Keister and Mitkov (2016) study the interaction between a government’s bailout policy during a banking crisis and individual banks’ willingness to impose losses on their investors, in an environment in which banks and investors are free to write complete, state-contingent contracts. Their primary focus is on the timing of this contract’s response to an incipient crisis. In the constrained efficient allocation, banks facing losses immediately cut payments to withdrawing investors. In a competitive equilibrium, however, these banks often delay cutting payments in order to benefit more from the eventual bailout. In some cases, the costs associated with this delay are large enough that investors will choose to run on their bank, creating further distortions and deepening the crisis.
Bernard, Capponi and Stiglitz (2017) develop a framework to analyse the consequences of alternative designs for interbank networks, in which a failure of one bank may lead to others. They analyse the conditions under which governments can credibly implement a bail-in strategy, showing that this depends on the network structure. With bail-ins, government intervention becomes desirable even for relatively small shocks, but the critical shock size above which sparser networks perform better is decreased; with sparser networks, a bail-in strategy is more credible. The intuitions behind our findings are twofold: (i) the no-intervention threat is more credible in sparsely connected networks when the shock is large or interbank recovery rates are low and (ii) banks can be incentivised to make larger contributions to a subsidised bail-in if the network is more sparsely connected.