Cash Burns: An Inventory Model with a Cash-Credit Choice

Abstract

We present a model that characterizes the relationship between optimal dynamic cash management and the choice of the means of payment. The novel feature of the model is the sequential nature of the payments choice: in each instant the agent can choose to pay with either cash or credit. This framework predicts that the current level of the stock of cash determines whether the agent uses cash or credit. Cash is used whenever the agent has enough of it, credit is used when cash holdings are low, a pattern recently documented by households data from several countries. The average level of cash and the average share of expenditures paid in cash depend on the opportunity cost of cash relative to the cost of credit. The model produces a rich set of over-identifying restrictions for consumers’ cash-management and payment choices which can be tested using recent households survey and diary data.Institutional subscribers to the NBER working paper series, and residents of developing countries may download this paper without additional charge at www.nber.org.