Why Do We Need Countercyclical Capital Requirements?

See Repullo and Suarez (2013) for a review of the relevant literature. The mechanism works as follows. Banks’ capital requirements may become binding in recessions as losses occur and risk-sensitive capital requirements increase as a result of increasing risk measures. Consequently, banks may have to cut back lending as in a recession new external capital is hard to come by. As a result, economic activity may be further dampened. See also, e.g., Kashyap and Stein (2004), Pennacchi (2005), and Gordy and Howells (2006).

Numerous studies provide an account of the developments preceding the crisis; see e.g. Acharya et al. (2010).

Since we wish to use our model for studying the allocational effects of bank capital requirements, we postulate that the considered loans are granted by banks. However, as the banks are entirely passive, our model could easily be turned into a model of public debt markets, in which capital requirements are not relevant. In such markets similar allocational effects might be achieved with other policy instruments such as tax-like payments levied directly upon entrepreneurs.

To further justify our model as a model of bank loans, we point out two things. Firstly, the problems of asymmetric information with which the model is concerned may be most typical of small and medium size enterprises which are often dependent on bank debt. Alternatively, such firms could turn to venture capital but, in fact, De Meza and Webb (1987) have shown that debt is the optimal financing contract in the current type of setting.

Secondly, our model involving adverse selection could be particularly well suited for representing credit boom periods in which the customer base of banks grows rapidly so that problems of asymmetric information may be particularly pronounced. This is in contrast with models of relationship banking in which banks obtain private information of their customers.

It may sound contradictory to call capital requirements “countercyclical”, if these are set high in good times when the output gap is high, and low in bad times when the output gap is low. However, we stick to this terminology as it appears to be an established practice. The term “countercyclical” apparently refers to the effect that high capital requirements in good times help curb the lending boom, and vice versa.

It would be interesting to extend the current model to a model with a monopoly or an oligopoly in the banking sector. In such a model the market failure which we consider and which tends to make banks finance excessively risky projects, would be counteracted by the market power of the bank(s). This would tend to increase interest rates and decrease the incentives of entrepreneurs to take socially excessive risks. Hence, one may expect that the effects that we consider would be present in a less pronounced form in a model with a monopoly or an oligopoly in the banking sector.

The model of De Meza and Webb (1987) provides an alternative to Stiglitz and Weiss (1981) who find that there will be credit rationing (under-investment) in equilibrium, based on the assumption that all projects have the same expected payoff (the entrepreneurial type affects the project success probabilities and hence project risks). As already noted in footnote 3 above, one advantage of the De Meza and Webb (1987) model is that they show the optimality of debt as a financing contract in the current type of setting.

See e.g. Repullo and Suarez (2013) and the studies cited therein for why equity, in addition to the reasons given in the corporate finance literature, is a relatively costly form of finance, in particular to banks.

Our assumption is approximately valid in the model which motivates the internal ratings based (IRB) capital requirements of the Basel II and Basel III frameworks. These requirements aim at guaranteeing the sufficiency of bank capital for unexpected losses with the probability of at least 99.9 %, and they are based on an asymptotic single risk factor (ASRF) model which is due to Merton (1974) and Vasicek (2002). The probability distibution of the share of defaulting loans (which directly determines also the share of non-defaulting loans) in this model is given by (4) in Vasicek (2002), p. 160. This distribution is heavily concentrated in a narrow region between 0 and 1 (although, in principle, the model allows for cases in which almost 0 % or almost 100 % of the loans of a bank default), and if the model is correct, it is clearly possible to choose s _{η, min} and s _{η, max} so that the probability with which s _η is outside [s _{η, min} , s _{η, max} ] is almost zero.

In other words, we implicitly assume that s _{η, min} is sufficiently large to ensure bank solvency for the optimal capital requirements that we derive in Section 3. In the special case that loan defaults are independent, and given our assumption of the fully diversified loan portfolio, there is no variation in s _η so that s _{η, min} (as well as s _{η, max} ) equals the expected success probability, \(\widehat{p}_{_{\eta }}\). Hence, in this case, banks would be solvent under any capital requirements, including zero requirements, because the equilibrium interest rate margin on loans would alone suffice to ensure banks’ solvency.

Clearly, as the capital requirement for a mixed-portfolio bank is simply the sum of the requirements that apply to its low-risk and high-risk loans, mixed portfolio banks do not fail if specialized banks never fail. Further, when there are no bank failures, the expected profit of a mixed portfolio bank is simply the sum of the expected profits from its low-risk and high-risk loans, which is zero when Eqs. 9 and 11 are valid.

The assumption 2 implies that if some entrepreneurs choose the outside option in the market equilibrium, the set of the entrepreneurs choosing it must be an interval \(\left[ 0,\underline{ \theta }\right] \). However, the assumptions we have made so far do not guarantee that all three options get chosen in the market equilibrium, neither do they eliminate the implausible case in which the interval \(\left( \underline{ \theta },\bar{\theta}\right) \) would be divided into several subintervals, some of which contained low-risk entrepreneurs and some high-risk entrepreneurs. This possibility would be eliminated by, e.g,. the additional assumption that \(p {\acute{}} _{H}\left( \theta \right) >p {\acute{}} _{L}\left( \theta \right) \), i.e. that for each value of θ competence has a stronger influence on the success probability of high-risk projects than of low-risk projects.

In a calibrated version of our model, not reported here, this effect appears quite small.

More rigorously, the average success probabilities of the projects will change in the context of our model for two reasons in a recession. The success probability of the project of each entrepreneur will decrease in a recession when considered separately, but at the same time the average quality of the entrepreneurs will increase (as both the low-risk and high-risk investment projects become less attractive for insufficiently competent entrepreneurs as a result of lower success probabilities). The former effect tends to decrease and the latter one to increase the average success probabilities in recessions. Empirically, the increased number of defaults and hightened default probabilities of firms during recessions (see e.g. Nickell et al. 2000) suggest that the former effect dominates the latter one. Further evidence that success probabilities particularly of new firms decline in cyclical downturns is provided e.g. by Audretsch and Mahmood (1995) and Hampe and Steininger (2001). However, if the latter effect were dominant, then the average success probabilities would be higher, rather than lower, in recessions. By Proposition 3 below, we would then have a case that it would be optimal to adjust capital requirements in a procyclical manner.

Note that the proof of Proposition 3 is based on the fact that the values of \(p_{L}\left( \underline{\theta }^{om}\right) \) and \(p_{L}\left( \underline{ \theta }^{om}\right) /p_{H}\left( \underline{\theta }^{om}\right) \) are not changed by the recession, since they are deduced from the conditions 16 and 17. These values remain unchanged also when the values v _L , v _H , the investment I = R, and w are multiplied by the same constant in Eqs. 16 and 17. However, if e.g. the value of the outside option decreased without a corresponding decrease in the revenue of the successful entrepreneurs, the market failure which is associated with low-risk projects might well increase. Hence the output-maximizing low-risk capital requirement would also increase.

See Eq. 47 in the proof of part (c) of Proposition 3 in the Appendix.

Note from Remark 1 that the countercyclicality of capital requirements obtains also in a constant capital requirement regime, if the capital requirement is used to implement the optimal lower threshold of the entrepreneurial type. That is, if the average success probability of low-risk projects declines (in a recession), then the constant capital requirement, optimal in the above mentioned sense, would be lower. The reason is the same as already discussed in this section that the size of the market failure, related to the lower threshold, would decline.