Working Papers, Federal Reserve Bank of Boston 14-5
Models of money demand, in the Baumol (1952)-Tobin (1956) tradition, describe optimal cash management policy in terms of when and how much cash to withdraw, an (s, S) policy. However, today, a vast array of instruments can be used to make payments, opening additional ways to control cash holdings. This paper utilizes data from the 2012 Diary of Consumer Payment Choice to simultaneously analyze payment instrument choice and withdrawals. We use the insights in Rust (1987) to extend existing models of payment instrument choice into a dynamic setting to study cash management. Our estimates show that withdrawals are rather costly relative to the benefits of having cash. It takes 3-8 transactions to recoup the fixed withdrawal costs. The reason is that the shadow value of cash decreases substantially with the number of available payment instruments and, correspondingly, individuals are less likely to make withdrawals.