Appendix I. Numerical Solution Method
As argued in the paper, the purpose of the model is to illustrate how the mechanism of self-insurance arises in a qualitative form without aiming at generating quantitative implications. For this reason, the parameters are not chosen as to match particular patterns in the data and are simply chosen within the range of values seen in the literature. Bankruptcy costs are chosen so that the bank is more efficient than depositors in liquidating projects (ω > μ) and both are within the range of values used in the literature (Bernanke et al. (1999), Carlstrom and Fuerst (1997b), and others). The level of the risk-free rate is inconsequential in this model, so it is normalized to 0. The values are shown below.
The model is solved by backwards induction using Carroll (2006)’s endogenous gridpoints method. The method involves first finding the values of
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The author thanks Stijn Claessens, Giovanni Dell’Ariccia, Giovanni Ferri, Leonardo Gambacorta, Randall Kroszner, Luc Laeven, and seminar participants at the IMF, the Legatum Institute, the 2013 MoFir workshop, and the 2013 Society for Economic Dynamics conference in Seoul for comments and discussions and Jeanne Verrier for outstanding research assistance.
Knight (1921) argued that there is a fundamental difference between risk and uncertainty: the latter cannot be casted in a probability framework, while the former can. This argument implies that uncertainty is not measurable. But it may still be the case that agents use subjective probabilities to possible outcomes, with some residual probability assigned to unknown ones.
It is important to clarify that the actual number is not known because there is no comprehensive dataset on new loans that shows their characteristics. However, the STBL is conducted quarterly in a representative sample of over 300 banks, and the survey reports the fraction of C&I loans that are granted under pre-existing commitments.