## Tuesday, September 04, 2007

### How much cash to hold

Bryan Caplan asks about how much money he should hold in his wallet:

At a recent GMU lunch, two economists sparred over the optimal quantity of cash to keep in one's wallet. Economist A holds very little cash, on the grounds that you can pay for virtually everything with credit cards. Economist B holds lots of cash, on the grounds that the foregone interest is virtually nothing, and his time is very valuable.

Whose side do you take, and why? Value of time and foregone interest calculations are welcome.

P.S. Please don't repeat the textbook model of money demand. I'm asking for a concrete solution, not a general framework. :-)

Bryan dismisses the textbook model too quickly. The standard Baumol-Tobin model of cash management gives more than a general framework: It yields a concrete answer. A problem in chapter 18 of my intermediate macro textbook asks the student to apply the model to a simple numerical example describing his or her own behavior.

For example, suppose that the GMU economist spends \$10 per day in cash, takes 10 minutes to go get cash out of his ATM, has a value of time equal to \$60 an hour, and earns 5 percent annual interest on balances held at his bank. From this information, the Baumol-Tobin model yields a very specific prediction: The prof should take out \$1200 from his bank three times a year and hold an average of \$600 in his wallet. (See the textbook for the equations that back up this inference.)

Most people hold much less money on average and go to the ATM much more often than the model predicts for their parameter values. This is a puzzle. It is also a great example to work through in an intermediate macro class. You can generate a good classroom discussion about why the model fails to match behavior.

One possible answer is that people are worried about losing the money. A probability p of loss or theft would affect the opportunity cost of holding cash and thus effectively raise the interest rate that enters the model to r+p. But plugging in numbers makes this a hard case to make. To match behavior, such as a biweekly trip to the ATM, you would need people to lose their wallets far more often than they do.

Many students will then say that they don't hold as much cash as the model predicts because they are afraid they will spend it. This response raises an intriguing behavioral theory: Money burns a hole in your pocket, but the temptation is somehow removed if the money is left at the bank. I don't find this very compelling as a description of my own behavior, but my experience is that many students are more attracted to it.