The past two decades have been punctuated by a high incidence of financial crises in the world. In the period 1980–1996 itself, 133 out of 181 IMF member countries experienced significant banking problems, as documented by Lindgren, Garcia, and Saal (1996). Developed countries and emerging countries have been equally affected. These crises have been empirically shown to be associated with high real costs for the affected economies. Hoggarth, Reis, and Saporta (2001) document that the cumulative output losses have amounted to a whopping 15–20% of annual GDP in the banking crises of the past 25 years. The restructuring and output losses have been as high as 50–60% of annual GDP in some emerging-market banking crises.
Understanding bank failure risk, and especially systemic failure risk the risk that most or all banks in an economy will collapse together is considered the key to predicting and managing such financial crises. Indeed, the issue of systemic risk amongst banks has long been attributed as the raison d’etre for many aspects of bank regulation. Its causes, manifestations, and effects are however not yet fully understood. In this paper, we lay down a foundation that we hope will lead to an enhanced understanding of different forms of systemic risk.
In particular, we examine liability side contagion, asset side correlation, and their inter-actions. Liability side contagion arises when the failure of a bank leads to the failure of other banks due to a run by their depositors or a liquidation of their liabilities. Asset side correlation across banks arises if they lend to similar firms or industries. The paper’s goal is both positive as well as normative. On the positive side, we build a theoretical model whose assumptions and results are supported by empirical evidence. The normative aspects concern a welfare analysis of the costs and the benefits of systemic risk.
Recent models of contagion amongst banks include the work of Rochet and Tirole (1996), Kiyotaki and Moore (1997), Allen and Gale (2000), to cite a few. The primary focus of these studies is the characterization of contagion and financial fragility that arise due to the structure of inter-bank liabilities. By contrast, in our model there is no inter-bank linkage. Instead, we propose that systemic risk arises on the liability side of banks due to a revision in the cost of borrowing of surviving banks when some other banks have failed. Crucially, however, we also allow for systemic risk on the asset side of bank balance sheets. In particular, we show that banks choose a high correlation of returns on their investments by lending to firms in similar industries. The incentives for such action increase in the extent of systemic risk on the liability side. This interaction of liability side and asset side systemic risk is an important and novel contribution of this paper.
In our model, there are two periods and two banks with access to risky loans and deposits. The returns on each bank’s loans consist of a systematic component, say the overall state of the economy, and an idiosyncratic component. The nature of the ex-ante structure of each bank’s loan returns, specifically their exposure to systematic and idiosyncratic factors, is common knowledge; the ex-post performance of each bank’s loan returns is publicly observed. However, the exact realization of systematic and idiosyncratic components is not observed by the economic agents. Depositors in the economy are assumed fully rational, updating their beliefs about the prospects of the bank to which they lend based on the information received about not only that bank’s loan returns but also those of other banks. Ex-ante, banks choose whether to lend to similar industries and thereby maintain a high level of inter-bank correlation, or to lend to different industries.
When a bank’s loans incur losses, it may fail to pay its depositors their promised returns. Such failure conveys potential bad news about the overall state of the economy. Depositors of the surviving bank rationally update their priors and require a higher promised rate on their deposits. By contrast, if both banks experience good performance on their loans, then depositors rationally interpret it as good news about the overall state of the economy. Hence, they are willing to lend to banks at lower rates. The borrowing costs of banks are thus lower if they survive together than when one fails. This is an information spillover of one bank’s failure on the other bank’s borrowing costs, and in turn on its profits. Indeed, if the future profitability of loans is low, the surviving bank cannot afford to pay the revised borrowing rate and fails as well. An information contagion results.
How do banks respond to minimize the impact of such liability side contagion on their profits? We argue that the response of banks manifests itself in ex-ante investment choices. The greater the correlation between the loan returns of banks, the greater is the likelihood that they will survive together; in turn, the lower is their expected cost of borrowing in the future and higher are their expected profits. Consequently, banks lend to similar industries and increase the inter-bank correlation. In other words, banks herd. Intuitively, banks prefer to survive together rather than surviving individually. In the latter case, they face the risk of information contagion. By contrast, given their limited liability, bank owners view failing individually and failing together with other banks in a similar light. While information contagion sequentially transforms losses (or failure) at one bank into losses (or failure) at the other bank, greater inter-bank correlation increases the risk of simultaneous bank failure if the industries they lend to suffer a common shock.
We extend the model to allow the depositors of the failed bank to migrate to the surviving bank, if any exists. Intuitively, this captures a flight to quality phenomenon sometimes observed upon bank failures. Such flight to quality enables surviving banks to gain from the failure of another bank by scaling up their own operations. In this sense, flight to quality counteracts herding incentives by reducing the costs of banks from information contagion. Nevertheless, if the future profitability of loans is expected to be low, depositors may rationally choose not to lend even to the surviving bank. Formally, in the presence of flight to quality, the extent of ex-ante herding measured through inter-bank correlation is decreasing in the expected profitability of loans tomorrow. If the expected profitability of loans tomorrow is high, inter-bank correlation is low, and vice versa. Thus, we call this phenomenon the procyclicality of herding. Competition amongst banks for loans, whereby banks earn lower returns on loans if they lend to the same industry, gives rise to similar effects as flight to quality. Numerical examples illustrate the effect on procyclicality of the extent of systematic risk in bank loans and the relative likelihoods of good and bad states of the economy.
Next, we introduce a “foreign” bank in the model to study the direction and the scope of information contagion and herding. The foreign bank’s loan returns are assumed to be affected by a systematic factor that is different from the one affecting the loan returns of domestic banks. We argue that information contagion and herding are likely to be localized phenomena. The failure of a domestic bank affects other domestic banks more than it affects the foreign bank. Conversely, the failure of a foreign bank has little information spillover to the domestic banks. By implication, the incentives of banks to herd with each other are stronger within the class of domestic banks than between domestic and foreign banks. This localization could be interpreted as purely geographic in nature, or as a metaphor for some richer heterogeneity amongst banks in their specialization, for example, due to wholesale vs. retail focus, small business lending vs. large business lending, etc.
Finally, we conduct a welfare analysis. To do so, we allow for the possibility that banks can earn better returns by lending to some industries. In this setting, a potential welfare cost of herding arises when loans to more profitable industries are passed up in favor of loans correlated with other banks. Compared to the first-best investments, herding can sometimes produce investments in firms and industries that are less profitable. Similarly, while flight to quality mitigates herding, it can sometimes be inefficient relative to the first-best: it gives banks competitive incentives to lend to different industries, even if a particular industry in the economy is more profitable for all banks.
In the context of our model, however, it is difficult to argue that herding is constrained inefficient. Herding is undertaken ex-ante to mitigate the ex-post costs that bank owners face from information contagion. Furthermore, these ex-post costs comprise social costs for the planner charged with maximizing the value of banking sector in the economy, specifically the sum of the values of bank equity values and deposits. Thus, taking financial intermediation as given, herding occurs in equilibrium only when it is also socially constrained) efficient. In turn, the systemic risk arising from herding is also (constrained) efficient in our model. This is an interesting result since it is in contrast to the inefficiency that arises in other herding models. We suggest possible mechanisms via which our result on the constrained efficiency of herding may be overturned. The regulatory assessment of systemic risk must thus take careful account of its different manifestations and delineate the social costs of systemic risk that exceed the costs to bank owners.
Section 2 discusses the related literature. Sections 3 and 4 present the model. Section 5 derives the information contagion. Section 6 demonstrates the herding behavior in response to information contagion and incorporates flight to quality. Section 8 presents the welfare analysis. Sections 9 and 10, respectively, discuss the robustness of the model to extensions and the incorporation of bank regulation. Section 11 concludes. Throughout the paper, empirical evidence is provided to support the theoretical results. All proofs are in the Appendix.
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