Does Size Matter? Bailouts with Large and Small Banks

Eduardo Dávila is Assistant Professor of Finance at New York University Stern School of Business and Ansgar Walther is Assistant Professor of Finance at the University of Warwick. This post is based on their recent paper.


The differential treatment of large financial institutions has drawn substantial interest in recent financial regulatory discussions. In particular, several regulatory measures put in place after the 2008 financial crisis have singled out large banks as subjects of increased regulatory scrutiny. At the same time, the U.S. banking industry has experienced a secular increase in concentration: The total number of U.S. banks has dropped from 25,000 in the 1920’s, to 14,000 in the 1970’s, to less than 6,000 as of today, while the top 10 bank holding companies now control more than 50% of total bank assets. These developments suggest that concerns about too-big-to-fail banks are now more important than ever before.

In our research, we study the effects of bank size on banks’ funding decisions in an environment with systemic bailouts. A simple example illustrates the underlying mechanism behind our results. Is the government’s decision problem different when it contemplates a bailout of 10 banks of size one versus a bailout of one bank of size 10? If we assume that the losses associated with bank failure are proportional to bank size, the naive answer to this question, from an ex-post perspective, is no. This can be called the too-many-to-fail critique to the too-big-to-fail problem, or the “clones” property of bailouts. The problem with this argument is that large banks are aware that their individual choices directly affect the likelihood and magnitude of a bailout, while small banks are individually unable to modify bailout policy responses. Therefore, anticipating the government’s policy response and internalizing the effect of their size, large banks decide to be more aggressive at an ex-ante stage, increasing their leverage in equilibrium and, consequently, the likelihood of a bailout. Moreover, this effect is amplified by strategic spillovers to small banks. Aggressive leverage choices by large banks increase the implicit bailout subsidy for the banking sector as a whole. Small banks, encouraged by this shield, respond by increasing their leverage beyond what they would optimally choose in the absence of large banks.

Taken together, these effects imply that all financial institutions, large and small, choose higher leverage when the banking industry becomes more concentrated. Therefore, the net worth of all banks becomes more volatile, which increases the risk of financial crises and government bailouts. We further show that, due to strategic spillovers between large and small banks, an increase in bank size is associated with a leverage multiplier that increases the quantitative significance of this mechanism.

We show that the optimal regulation can be implemented with size-dependent Pigouvian taxes. Large banks are charged a supplement tax on borrowing relative to small banks, which counteracts their incentive to increase leverage so as to maximize government subsidies. Our normative results provide a formal rationale to regulate large banks differently from small banks, simply because of their size. Our results further imply that there is a natural interaction between financial regulation and policies that directly control industry structure (i.e., antitrust policy, merger regulation, etc.). We quantitatively assess the predictions of our model calibrated to U.S. data over the period 1990Q1 to 2013Q4 and find that our model is able to rationalize roughly half of the observed differences in leverage between large and small banks.

We use our model as a laboratory to study the effects of industry concentration. We find an increasing and convex relation between the leverage choices of large and small banks and the degree of industry concentration. We show that moderate increases in industry concentration starting from the status quo, in which the top 5 largest banks hold around half of total bank’s assets, are associated with substantial increases in leverage by large and small banks. In particular, an increase from 50% to 70% in the share of assets held by the 5 largest banks is associated with a 3.5 percentage point increase in aggregate debt-to-asset ratios (from 90.1% to 93.6%), or equivalently with a 5.5 point increase in the aggregate leverage ratio (from 10.1 to 15.6), in the absence of regulation that counteracts large banks’ leverage incentives. Our quantitative exercise further highlights the importance of the “granular hypothesis”: The strategic incentives of large banks to take leverage, and therefore to increase aggregate volatility, are strengthened substantially when large institutions face idiosyncratic shocks that are not diversifiable.

With the goal of guiding policymakers on the magnitude of optimal corrective policies, we also compute the optimal “size tax”. Under the optimal policy, calculated for current levels of industry concentration, large banks pay a size tax of 40 basis points (0.4%) per dollar of debt issued, over and above the Pigouvian levy that is charged to small banks. This optimal size tax increases up to roughly 60 basis points per dollar of debt issued if the share of assets held by the 5 largest banks reaches 70%.

The complete paper is available for download here.

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