An Intertemporal Model of Optimal Commercial Bank Reserves

The standard bank reserve model is extended by explicitly introducing the dimension of time. This feature has not been addressed in the literature which seem to be a very surprising omission given that that the concensus view of this financial institution is that of a (differentiated) microeconomic firm maximizing over terminal wealth. The results indicate that the solution across periods is stationary. All the information needed by the bank to make its choice is embodied in the various interest rates as well as in the penalty structure that institutionally defines the cost of illiquidity. Neither the contemporaneous level of portfolio variables nor its comparative levels in previous periods become relevant to the optimal rule. It is further shown that the stationary solution is in fact Markov stationary, that is, the intraperiod optima will be exactly the same as that in the static case. This literally suggests that the optimization in a multi-period horizon can be taken as a series of repeated one-period models, leading to the same set of optima. This result was shown to be robust, particularly when the allocation problems is modeled explicitly as a Marcov process. The model is extended to account for the possibility of loans with fixed term beyond one planning period. This means that resources for these type of instruments will have to be pre-committed by the bank and therefore would not be free to be allocated over the period in which the multi-period loan is in effect. The results lead to an ambiguity as to whether optimal reserves would either increase or decrease. This was explained in terms of the competing influence of what is labelled as an ?income-commitment effect? and an "income-option effect".