Money, debit card, gross-settlement risk, and central banking

A monetary model is constructed to explore the effects of a new source of inefficiency of gross settlement with an operational risk on the choice of cash that is risky to hold and a debit card that is costly to use. During inflation, gross settlement would entail the deposit of a larger amount of money as payments and collaterals for the finality of the settlement process, thereby leading to a consumption loss. The endogenous adjustment between gross and net settlement may alleviate this distortion from inflation. Hence, the optimal monetary policy is to decrease the money supply so as to minimize the cost of theft and transaction costs of a debit card usage.