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The authors thank Christopher Carroll, Stijn Claessens, Giovanni Dell’Ariccia, Gregory de Walque, Robert Kollmann, Luc Laeven, José Luis Peydro, Jose Victor Rios-Rull, Thierry Tressel, Kenneth West, and seminar participants at the NBER Summer Institute, the IMF, the CEPR-EBC-HEC-NYSE/Euronext-RoF Conference on “Financial Intermediation and the Real Economy”, the National Bank of Poland’s conference “DSGE and Beyond”, and CEPR-National Bank of Belgium-JMCB-ECARES-Ghent University conference on “Macroeconomics and Financial Intermediation” for comments and discussions.
Recent papers that give a prominent role to uncertainty shocks include Arellano, Bai and Kehoe (2011), Bloom, Floetotto and Jaimovich (2011), Christiano, Motto and Rostagno (2009), and Gilchrist, Sim and Zakrajšek (2010)
Notice that we assume that idiosyncratic risk affects profits rather than revenues as it would under a traditional productivity shock interpretation. This is done for two reasons: first, it allows us to preserve linearity of the problem, facilitating aggregation as it will be seen momentarily, and second, it means the wage is not affected by the idiosyncratic risk since workers collect it before the shock is realized.
The average market return rt will be determined in equilibrium and is the return earned by the financial intermediary on a fully diversified lending portfolio.
This follows simply from the fact that Equation (6) can be expressed in terms of spreads (or ratios) relative to At. Similarly, Equation (7) can also be normalized in the same way, resulting in an equivalent problem in which the key argument is the ratio At/(1 + rt).
In Bernanke et al. (1999) Dr is the fraction of entrepreneurs who die in each period who consume their net worth at the moment of death. We instead assume that money flows back to the household so that there is a unique value function in the model that is used to assess the welfare gains from recapitalization.
This can be thought of as a mutual fund investment.
In the context of our model, we can shut down financial frictions in the financial sector by either setting the monitoring cost μf or the variance of idiosyncratic shocks ωf to zero.
It is important to note however that our model does not incorporate endogenous asset prices, which in the financial accelerator literature is a key mechanism to generate quantitatively important amplification effects (Bernanke et al. (1999) and others).
This is because the maximization problem solved by financial intermediaries is linear and aggregate shocks do not affect borrowing spreads since they are realized after the within-period debt is repaid.
Note that the knowledge that shocks affecting the financial sector will be passed to the household through recapitalization policies reduces the expected rate of return on savings. However, this negative impact on expected returns is more than compensated from avoiding the negative real interest rates that would be associated with a financial crisis.