General Equilibrium Implications of the Capital Adequacy Regulation for Banks

Capital adequacy regulations specify a minimum capital-to-assets ratio for banks in the economy. The effects of these regulations on the level of economic activity have not been thoroughly studied by the banking regulation literature. Specifically, the fact that as proposed by the Basle Accords, a constant ratio tying bank lending to bank equity may reinforce macroeconomic fluctuations has been looked at by only a few existing theoretical papers. This paper proposes a stochastic dynamic general equilibrium model to study the interactions between the banking sector and the aggregate level of economic activity. Banks behavior is fully micro-founded. Banks financing decisions (equity versus deposits) are constrained not only by the regulation but also by a financial imperfection arising from the fact that during bad times banks find it difficult to recapitalize by raising equity. Thus, higher borrower bankruptcy rates during recessions imply that banks have to cut new loans until the ratio is restored to the required level. Since production firms can only imperfectly substitute bank lending with other forms of financing, a negative macroeconomic shock affects production and investment both directly and indirectly through the bank loan supply. This banking regulation and the financial imperfection imply two different constraints to the banks problem that bind only occasionally in the stochastic steady state. This prevents the use of standard linearization techniques to solve the model numerically. Alternatively, using some discretization of the state space methods such as Value Function Iteration is difficult because the model cannot be written in terms of a central planner problem. Following Fackler (2003) I solve the decentralized general equilibrium problem by using a very general Function Approximation technique that nests the Parameterized Expectation Approach as a particular case. The method allows to approximate numerically either the policy functions or the expectation functions. It is also flexible as regards the choice of approximating functions, including Chebyshev polynomials and piecewise polynomial splines. The technique relies on the Collocation Method to solve for the polynomial coefficients in combination with either generic root-finding algorithms or a fixed-point iteration scheme. Numerical results suggest that banks try to anticipate aggregate shocks by accumulating a buffer of capital over the regulatory minimum. Nevertheless, a series of bad shocks may be strong enough to eventually undermine these "reserves" and to make banks cut back on lending. This suggests the existence of a financial accelerator, since the supply of loans shrinks together with the demand during recessions. This mechanism has interesting policy implications and provides grounds for a procyclical value of the required capital-to-assets ratio