An Analysis of Coordination Mechanisms for the U.S. Cash Supply Chain

The overuse of its currency processing facilities by depository institutions (DIs) has motivated the Federal Reserve (Fed) to impose its new cash recirculation policy. This overuse is characterized by the practice of cross-shipping, where a DI both deposits and withdraws cash of the same denomination in the same business week in the same geographical area. Under the new policy, which came into effect July 2007, the Fed has imposed a recirculation fee on cross-shipped cash. The Fed intends to use this fee to induce DIs to effectively recirculate cash so that the societal cost of providing cash to the public is lowered. To examine the efficacy of this mechanism, we first characterize the social optimum and then analyze the response of DIs under a recirculation fee levied on cross-shipped cash. We show that neither a linear recirculation fee, which is the Fed's current practice, nor a more sophisticated nonlinear fee is sufficient to guarantee a socially optimal response from DIs. We then derive a fundamentally different mechanism that induces DIs to self-select the social optimum. Our mechanism incorporates a fairness adjustment that avoids penalizing DIs that recirculate their fair share of cash and rewards DIs that recirculate more than this amount. We demonstrate that the mechanism is easy to implement and tolerates a reasonable amount of imprecision in the problem parameters. We also discuss a concept of welfare-preserving redistribution wherein the Fed allows a group of DIs to reallocate (amongst themselves) their deposits and demand if such a possibility does not increase societal cost. Finally, we analyze the impact of incorporating the custodial inventory program, another component of the Fed's new policy.