Can Robbery and Other Theft Help Explain the Textbook Currency-demand Puzzle?

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.