Tuesday, October 02, 2007

Do I LOOK like a taxi? 

This morning Littlest Scholar heads out the door to the car, checks the back seat to see that her football is in tow, and upon arriving to school tells me her diorama she had made last night had been forgotten at home. It must be brought now. Because of road and bridge construction, it takes me forty minutes to go home, retrieve the diorama and bring it to school.

This caused me to miss my normal bagel-and-coffee with friends. Should I charge her for this?

When I finally get to my computer, a letter from the teacher at school, and it contains in part:
Would you please be able to get (her) to school a few minutes earlier in the morning? We start our day at 7:40, and that has been when she has walked in the door the last few days. Maybe about 7:35 or so. Thanks very much.
I'm a bit tempted to be flip with the teacher (who, btw, sent this at 7:45, so whatever was being done right at 7:40 didn't require his full attention.) After all, the bridge construction has changed traffic flows three times in the last four weeks, and predicting the time to leave the house to have her arrive at 7:35 is an estimate with much greater uncertainty now than in time passed. So I decided to reflect a little economics on the problem.

So, you might say, how about waking up Miss Forget-Your-Diorama a little earlier and setting off to school earlier? So what if she's early? Not so easy there, either. Teachers are preparing for classes at 7:20 or so, so if you show up that early you get a note asking you not to bring the kid so soon. (I know, I've received that note too.) Besides, as Mike Munger points out in an essay on lateness today (how convenient!), showing up early is seldom a good thing either. Kids in particular can be disruptive before class, wander around outside, gossip with other students, or otherwise not be prepared for the opening bell. And the bell never rings early, so that reduces the incentive to come in early. Munger notes five rules mostly in the context of academic meetings, but they apply more generally. From them he concludes a theory of lateness:

We all give other people a (small) credit for being early, a reputational effect. But we dislike waiting. Most important, people would choose a shorter wait instead of receiving the credit given to those who arrive early.

Indeed, since the school sends me a note equally for bring the child early or late, the credit I get for a 7:25 arrival is zero. Maybe something closer to 7:32 might bring a smile, hardly enough payment for forgoing that last article in the sports pages with my breakfast.

With that set-up, a simple economic analysis predicts several things. First, everybody would like to arrive on-time (no damage to reputation), and be the last to arrive (no waiting for meeting to start). Unless everyone literally walks into the room at the same time, this can't happen.

Which is what Littlest, now a teen, is thinking: She wants to be the last one in and on time. With teacher now moving the goalpost, we're redefined late. But this is also a problem for the teacher -- everyone wants to be the last one in, so if he permits Littlest to arrive with zero time on the clock, other students are incented to try to come in ten seconds after her. Which leads to Munger's next point:

Second, the outcome that everyone arrives (approximately) on time is still possible, and is in fact what economists call an "equilibrium," or possible stable outcome. But it is very fragile, because if even one person is occasionally tardy, everyone sits and kills time. Next time, everyone comes later. So any random factor can upset the "arrive on time" outcome.

Which is what has happened here: The bridge construction is the random factor that could lead to a cascade effect of all students (particularly the eighth graders) showing up late, which of course is a bad outcome. I'm sure the equilibrium is less stable for academic meetings than school starting times, but given it's a small school she goes to, it's more like a committee meeting than if this were a school of a thousand students (like each of our two junior highs.)

Third, meeting-goers can assure themselves of not having to wait, or at least not having to wait very long, by being late. And, since lots of people think that way, everyone is late sometimes. Some people, in fact, are late all of the time.

So what can we do? I'd suggest putting the pain onto the students (of course, since that's not me) by perhaps giving them "the tardy chair" and telling them their recess or lunch starts five minutes after everyone else's (but ends on time.) One of my colleagues does this in his classes, and it seems to work. Or make her stand until recess. (I note in comments on Munger's blog that his co-blogger Kevin Greir's wife locked university students out of the classroom when they were late. That option is not available to Littlest's teacher.) Small incentives should matter in this case; the student can be on time. Now Littlest would complain this is unfair because the bridge traffic is not her fault. I agree, but a lesson to learn is to be prepared for unexpected events and to evaluate uncertain outcomes. I would not let her off the hook for that.

(I note that Tyler Cowen has explained why paying her to be on time is not going to work, and why I need to have the teacher impose the negative incentive rather than providing a positive one myself.)

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