Stability in a Model of Staggered-Reserve Accounting

Critics of staggered-reserve accounting have used simple models to show that a disturbance to deposits with no change in total reserves sets in motion an undamped cycle in which deposits oscillate above and below the equilibrium implied by the total reserve target. In this paper a simple reduced-form model of the money-supply process is used to investigate the nature of the dynamic process implied bystaggered-reserve accounting. The parameters in the model include the number of banking groups in the staggered regime, the reserve requirement, the response of banks to their own reserve position, and the response of banks to a deviation of the money supply from target.

Classical stability algorithms are used to find the range of parameters for which the model is stable. In this paper, the model is defined to be stable if the reduced-form difference equation for the money supply represents a converging process.

The results confirm the presence of a perpetual cycle found by others. This perpetual cycle depends on two special conditions: the first is that there are only two groups of banks in the staggering arrangement; the second is that banks ignore information about the money supply and Federal Reserve policy in making their asset portfolio decisions. When the model is extended to include more than two banking groups, or when banks are allowed to react to aggregate information, the money supply converges to the target level following a disturbance to equilibrium.