Can robbery and other theft help explain the textbook currency-demand puzzle? Two dreadful models of money demand with an endogenous probability of crime

This paper attempts to explain one version of an empirical puzzle noted by Mankiw (2003): a Baumol-Tobin inventory-theoretic money demand equation predicts that the average adult American should have held approximately $551.05 in currency and coin in 1995, while data show an average of $100. The models in this paper help explain this discrepancy using two assumptions: (1) the probabilities of being robbed or pick-pocketed, or having a purse snatched, depend on the amount of cash held; and (2) there are costs of being robbed other than loss of cash, such as injury, medical bills, lost time at work, and trauma. Two models are presented: a dynamic, stochastic model with both instantaneous and decaying noncash costs of robbery, and a revised version of the inventory-theoretic model that includes one-period noncash costs. The former model yields an easily interpreted first-order condition for money demand involving various marginal costs and benefits of holding cash. The latter model gives quantitative solutions for money demand that come much closer to matching the 1995 data$75.98 for one plausible set of parameters. This figure implies that consumers held approximately $96 billion less cash in May 1995 than they would have in a world without crime. The modified Baumol-Tobin model predicts a large increase in household money demand in 2005, mostly due to reduced crime rates.