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September 04, 2007
The optimal amount of cash in your wallet
Bryan Caplan had some fun at lunch recently...
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. :-)
Greg Mankiw defends the textbook model:
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....
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.
He then gives two examples (neither of which he finds compelling). My answer to Caplan is that personally, I'm with "Economist A". I don't carry a lot of cash, but that's mainly because I use very little of the stuff and have extremely convenient access to an ATM on campus (which charges no fees as I am a customer of the bank that owns the ATM).
Mankiw's puzzle, however, is not really a puzzle to me. The problem for the model is that the value of time tends to be overestimated in examples like this. Perhaps I can bill my time at $60/hour, but that does not mean that I will at all times and in all places behave as if my time is literally worth $1/minute.
Consider the example that circulated a while back about how Bill Gates wouldn't even bother to pick up a $100 bill off the ground because he makes more money in the time that it would take him to bend over and pick it up. (A clever rendition of that story, complete with a chart, can be found here.) But there's something about the example that doesn't wash. Does Bill Gates literally get paid by the second? No. As clever as this example is, it is not literally true that Bill Gates would forgo the fraction of his income that could be attributed to 4 seconds out of his day when he bends over to pick up a $100 bill. The amount he would forgo might even be more, and is probably often less. Using the value of time as an explanation only makes sense if there is truly something given up. Think about it this way, would Bill Gates be more likely to stop and pick up a $100 bill on his way into an office building for a meeting or on his way out? On his way in, his mind is focused and he doesn't want anything interfering with getting to the meeting. On his way out, he may have a bit of "slack time" (unless he's late for the next meeting). The point is that the true opportunity cost of Bill Gates' time is not uniform throughout the day.
Or how about this one... A lot of people don't bother to pick up pennies. Is it because the value of their time is more than the value of the money that is picked up? Perhaps it is sometimes. But it seems more likely (and more in tune with my own experience) that you just don't want to carry a penny around, or maybe because you suffer disutility from bending over. The value of time matters, but it doesn't have to do all the heavy lifting in this example.
The fact of the matter is that most of us have a bit of "slack time" built into our day by accident or design. Suppose that it takes me 50 minutes to eat lunch and that I like to get to class 5 minutes early. If I'm passing by the ATM on my way to get lunch and it's 60 minutes until my class starts, the time that it takes me to get cash comes out of the 5 minute buffer that I have in my schedule. That's time that I would spend checking my e-mail, looking at my notes, or enjoying the view out my window while I get my thoughts in order. It's a low opportunity cost window of time--small enough to just be counted as the time equivalent of loose change. Those fleeting moments don't aggregate very well into billable $60/hour blocks.
Viewed that way, the puzzle disappears. Personally, ideas tend to come to me in low opportunity cost moments of time, so paradoxically, I value those moments highly. Discuss.
Posted by William Polley at September 4, 2007 11:30 PM
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Comments
If Mankiw really takes 10 minutes to get cash out of an ATM, the banks in the Cambridge area are really messing up.
From my vantage point by Grand Central Station, more than 90 seconds would be a Long Time at the lunch hour.
Posted by: Ken Houghton at September 5, 2007 12:16 PM
I've never timed myself, but 90 seconds is about right for my location (unless there's a line, which is rare except maybe on football Saturdays).
And that counts the approximately 10 steps (each way) that I need to go out of my way on a beeline for the food court.
Posted by: William Polley at September 5, 2007 12:56 PM
In large part it is how convenient is the ATM and are you there already. I would have to drive, wait in line as they are usually busy, and return, 20 minutes reasonably, or hunt for one and find one that didn't have a fee, probably also 20 minutes. I have to go to the bank more than 3 times a year anyway, so I don't need that much and I don't spend much cash either but do need some.
Posted by: Lord at September 5, 2007 05:33 PM
Yes, convenience is key. I would add that in determining your *average* cash holdings it is not whether you are there already, but how often you can reasonably be predicted to be near an ATM--for me that may be more often than for you.
Whether you choose to get the cash at that moment when you are passing the machine depends on the amount remaining in your wallet and the length of time you might reasonably expect to elapse before you are conveniently at a machine again.
These are two different problems both worth examining. More later, perhaps, if I have time. (That is to say, if the opportunity cost of my time is sufficiently low.)
Posted by: William Polley at September 5, 2007 06:58 PM
$100 per ATM transaction
But the reasons are only partially explainable in economic terms.
Generally speaking I walk everywhere, mostly to a small fixed set of locations and my goal is to minimize transit time and effort. I live in an old-fashioned city with rectangular blocks and a certain amount of slope (not being 25 anymore). But generally speaking transit time is the same anyway I go, that is as long as I never go outside the grid box of my two endpoints and never backtrack.
My free ATM is two blocks out of my way to my standard destination. The two fee ATMs on the direct route charge $1.25 flat and both are located in stores I make a daily purchase in anyway. Now the quickest transaction you can make is Quick Cash and on many machines $100 is the top amount without having to punch extra buttons. And since the fee doesn't vary by dollar withdrawn the choice is pretty obvious.
But the bigger point is that you can use this question as a case study in economic reductionism. Mankiw's calculation does not take into account the security of the money to theft, robbery or accident, or the effect of having that much more cash on average in wallets to the incidence of armed robbery. The ideal economic solution might lead to poor social outcomes, his $600 average leading to a higher odds of me losing my $100 and getting stabbed to boot.
Moreover it totally ignores the "money burning a whole in my pocket" phenomenom. In my state we have almost unlimited possibilities for gambling, but in each case you have to have converted assets to cash. I don't gamble much anymore, but I did at one time, and often it was a relief to walk into a bar and realize you only had $20 and not $300 to blow.
"From this information, the Baumol-Tobin model yields a very specific prediction:"
Yes, lots of things in life are simple. You just have to ignore the complexities. Mankiw is taking an act that is intertwined with all kinds of social, psychological and lifestyle variables and forcing it into a typical economic Procrustean bed.
Because the only true real world answer to the question is "It depends"
Posted by: Bruce Webb at September 7, 2007 11:31 AM
Good point about the $100 per transaction. Of course, there's always the teller window.
Actually, security and "money burning a hole in my pocket" were the two explanations Mankiw offered but rejected. He certainly recognizes that the threat of loss would decrease the amount withdrawn and increase the frequency, but he says, "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."
Given that everyone carries a smaller amount of cash than Baumol-Tobin would predict, would-be robbers have lower expectations. Individually, as long as no one knows that you're following Baumol-Tobin and carrying more cash, you can free ride on those lower expectations and not worry as much about theft. But if everyone acts like Baumol-Tobin would predict, criminals would figure it out and theft would increase.
But still, I don't think this accounts for the behavior that we see.
I still think that my explanation of slack time--the few extra minutes that we build into our schedule that have a very low opportunity cost once they are built in--does a pretty good job of eliminating the puzzle that Mankiw sees.
Since it is entirely reasonable that social, psychological, and lifestyle variables are what determine the way we build our schedules and live our days on a minute-to-minute basis, I think a combination of our approaches is probably a very useful way to think about this.
Posted by: William Polley at September 7, 2007 01:36 PM