In the wake of the financial crisis, financial regulators have developed new tools. Among these tools are countercyclical capital buffers, which aim to decrease the procyclicality of bank lending. The idea is that capital buffers should rise in good times, to build up high levels of equity capital. Then in bad times, capital requirements can be loosened, to encourage banks to lend more during the downturn, in an attempt to stimulate the economy.
One difficulty of this is that banks may not wish to lend more during a downturn, even if their capital requirements are loosened. In particular, banks may display a precautionary motive : They might seek to build up capital stocks in a downturn, to avoid coming near their capital constraint, as this would involve costly adjustments. Hence, banks might optimally choose to reduce lending in a downturn, even if capital constraints were loosened. As a result, the countercyclical effects desired by regulators might be undermined.
The objective of this paper is to examine the lending behaviour and capital levels over the cycle of a bank which has an explicit precautionary motive. Precautionary effects are 3rd order, and so require 3rd order approximation schemes to capture them. Moreover, a capital constraint only binds occasionally, and models with occasionally binding constraints are known to be quite challenging to solve using non-linear methods.