This is what's in your wallet...and here's how you use it

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, for example, by using credit cards instead of cash. This paper utilizes data on credit and debit card holders from the 2012 Diary of Consumer Payment Choice to simultaneously analyze payment instrument choice and cash withdrawals. First, we show that even this subsample of consumers holds a substantial amount of cash and could settle 70% of their transactions by cash. Then, we extend existing payment instrument choice models to explicitly account for fixed withdrawal costs and cash holding costs. This complicates the estimation process substantially as the parameters of a dynamic single agent decision problem with both discrete and continuous choice variables will have to be recovered. We rely on the methodology developed by Bajari, Benkard and Levine (2007) to do this. The structural estimation reveals that the widely observed drop in cash use, as transaction values increase, is not due to a drop in the flow utility of cash payments, as previous static analysis suggested, but due to an increased likelihood of incurring a withdrawal cost. This has important policy implications, as the results imply that technological improvements that lowered the fixed cost of withdrawing cash (e.g. ATMs, debit card cash backs) must have contributed significantly to the high share of cash use still observed at point of sale transactions in the United States.