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While systemic risk-the risk of wholesale failure of banks and other financial institutions-is generally considered to be the primary reason for supervision and regulation of the banking industry, almost all regulatory rules treat such risk in isolation. In particular, they do not account for the very features that create systemic risk in the first place, such as correlation among banks' investments (Acharya 2009; Acharya and Yorulmazer 2007, 2008); the large size of some banks (O'Hara and Shaw 1990),1 which leads to "fire-sale"-related pecuniary externalities; and bank interconnectedness (Allen and Gale 2000; Kahn and Santos 2005). In this paper, we aim to fill this important gap in the design of regulatory tools by providing a normative analysis of how deposit insurance premiums could best be structured to account for systemic risk.
Demand deposits are explicitly or implicitly insured in most countries up to some threshold amount per individual (or deposit account). While regulators in some countries have realized the need to establish a deposit insurance fund only during the 2007-09 financial crisis, others have established funds much earlier. Demirgüç-Kunt, Karacaovali, and Laeven (2005) show that most countries provide deposit insurance. Furthermore, during the crisis of 2007-09, some countries, including developed countries such as Australia and New Zealand, introduced guarantees for the first time, whereas a significant majority of others increased their insurance coverage. In most cases, the capital in these deposit insurance funds is the reserve built up over time through the collection of insurance premiums from banks that receive the benefits of deposit insurance. Yet how should such premiums be charged?
We argue that the extent of systemic risk in the financial sector is a key determinant of efficient deposit insurance premiums. The basic argument is as follows. When a bank with insured deposits fails, the deposit insurance fund takes over the bank and sells it as a going concern or piecemeal. During periods of widespread bank failure, it is difficult to sell failed banks at attractive prices because other banks are also experiencing financial constraints (Shleifer and Vishny 1992; Allen and Gale 1994). Hence, in a systemic crisis, the deposit insurance fund suffers from low recovery from the liquidation of failed banks' assets. This, in turn, leads to higher drawdowns per dollar of insured deposits. This argument gives our first result: the actuarially fair deposit insurance premium-the premium that exactly covers the expected cost to the deposit insurance provider-should not only increase in relation to individual bank failure risk but also in relation to joint bank failure risk.2
In addition, the failures of large banks lead to greater firesale discounts. This occurrence has the potential to generate a significant pecuniary externality that can have adverse contagion-style effects on other banks and the real economy (compared with the effects stemming from the failure of smaller banks).3 Hence, the resolution of large banks is more costly for the deposit insurance regulator, directly in terms of losses from liquidating large banks and indirectly from contagion effects. This leads to our second result: the premium for large banks should be higher per dollar of insured deposit compared with that for small banks.
Furthermore, bank closure policies reflect a timeinconsistency problem (see, for example, Mailath and Mester  and Acharya and Yorulmazer [2007, 2008]). In particular, regulators ex ante would like to commit to being tough on banks even when there are wholesale failures to discourage banks from ending up in that situation. However, this strategy is not credible ex post, and regulators show greater forbearance during systemic crises. While such forbearance among most regulators around the world has been a feature of the current crisis, it has a strong precedent. …