equate the marginal value of a loan made at time _t_ to the expected value of the loan at time _t_ + 1, taking into account the opportunity cost of making the loan as opposed to placing it in the investible assets (the relative price of which is given by<sup>_∂B_</sup><sup><u>(</u></sup><sup>_ait_</sup> _∂a_<sup>_<u>,li,</u>_</sup> _it_<sup>_t_</sup><sup><u>+1</u></sup><sup>_<u>,dit</u>_</sup><sup><u>)</u></sup> _/_<sup>_∂B_</sup><sup><u>(</u></sup><sup>_ai,t_</sup><sup><u>+1</u></sup> _∂a_<sup>_<u>,li,</u>_</sup> _it_<sup>_t_</sup><sup><u>+2</u></sup><sup>_<u>,di,t</u>_</sup><sup><u>+1)</u></sup> ). Moreover, any given bank will face a transversality condition where _λT_ +1 is the shadow price (multiplier) on the constraint (2).

Now, consider the behavior of the same bank during a financial crisis. While a financial crisis is likely to result in a first-moment shock to asset valuations, it is also likely to incorporate a second-moment element, where uncertainty becomes more pervasive. Following Bloom (2009), we call this crisis-induced change in the variance _σ_ an uncertainty shock, which leads to a revised density function given by _f_ ( _a_ ; _σ_ 2), where the variance of the function is now given by _σ_ 2 _> σ_ 1.<sup>6</sup> Repeating the exercise above yields the crisis-period analogue of (4): Taken together, (4), (6), and (5) characterize the three channels that impact a bank’s credit provision in and out of a financial crisis: its need for access to liquidity (the constraint (3) and the presence of next-period loans in the current-period derivative in the Euler,<sup>_∂B_</sup><sup><u>(</u></sup><sup>_ait_</sup> _∂a_<sup>_<u>,li,</u>_</sup> _it_<sup>_t_</sup><sup><u>+1</u></sup><sup>_<u>,dit</u>_</sup><sup><u>)</u></sup> ); balance sheet solvency considerations (the constraints (2) and (5), and the inclusion of the function _B_ ( _·_ )); and the impact of uncertainty (the presence of _σ_ 2 and _σ_ 1).

The importance of the solvency channel has been empirically verified for periods of tight money (Bernanke, Gertler & Gilchrist 1996), as well as, more specifically, in the context of financial crises (Duchin, Ozbas & Sensoy 2010). Likewise, the liquidity channel is an important conduit for monetary policy (Kashyap & Stein 2000), and was important in the propagation of the Great Depression (Bernanke 1983), and appears to be relevant for the recent financial crisis as well (Ivashina & Scharfstein 2010). Finally, Bloom (2009) has found that uncertainty shocks are crucial for understanding the dynamics of crises; the uncertainty channel has also been explored in the context of financial contagion by Kannan & Koehler-Geib (2011).<sup>7</sup> These three channels all appear to have been important in the 2007/09 financial crisis. Widespread concerns about the ability of counterparties to make good on unsecured loans dis-

> 6An alternative approach to capturing the role of risk is to directly introduce time-varying relative risk aversion into a utility function, as in Boschi & Goenka (2012). Crises are then modeled as shocks to the risk premia of portfolios held by international investors, which may give rise to contagion effects. Since this approach to modeling risk relies on _propensities_ as opposed to asset _volatility_ , it can have a material impact on the variables used to measure risk. We address this concern in our robustness section.

> 7Fern ́andez-Villaverde, Guerr ́on-Quintana, Rubio-Ram ́ırez & Uribe (2011) also explore the real impacts of what they call a volatility shock on small open economies, arguing that emerging economies often face timevarying volatility of real interest rates.

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