Abstract Thoughts on the Chance of Rain

I have a day in mind, but I'm not telling you. My question is: what is the chance that it rained that day in Washington DC?

You have no knowledge of the cloud formations, temperatures, or time of year. However, suppose that over the last four decades, it rained 15% of the time in DC. So your best guess is 15%, but you're not very confident.

Suppose that I told you that my mystery day was in September. You could look at historical September predictions and adjust your guess accordingly, now with slightly more confidence.

Yet when we look at the 10-day forecast, we routinely see that the chance of rain is around 50%. This could mean that, historically, it has rained about 50% of the time during this time of year. More likely, it means that historical patterns mean very little when we want to know if it will rain any particular day; instead, the forecast is primarily influenced by the latest meteorological readings.

If it's for sure not going to rain tomorrow, the chance is 0%. If it's for sure going to rain, the chance is 100%. It's amazing to me that, given modern technology, we so often see chance of rain predictions for the very near future around 50%, essentially a coin flip.

Trapped Inside During Snow? Make Some Babies

The Washington Post has an amusing story about whether there will be a surge in births in the D.C. region come September, which would be about 9 months after the snowstorms that paralyzed the region for days on end:

Outside, the white December snow piled higher. Relentlessly higher. Inside a Laurel home, a woman watched "Dexter" reruns while her boyfriend played "Batman: Arkham Asylum." They grew restless. They looked at each other.

"Once a day," Gineen Glenn, 27, admitted on a recent Tuesday.

"Twice a day," interjected John Cargo, 28.

No denial from Glenn, who is expecting to give birth to their first child, a boy, in early September. "You lose track of the days," she said, giggling. "It's just dark."

So it was during the historic snowstorms in December and February that folks trapped indoors searched for ways to relieve the boredom. Nearly nine months later, the things some residents did seem to be breeding results.

The story notes that the connection between natural disasters and copulation has been speculated about for decades, with several statisticians arguing that there is no real effect.

Count me among the skeptics. It's safe to assume that the amount of sex increases when there's few alternate activities available, but more sex does not necessarily mean more pregnancies.

Many couples have sex for years without getting pregnant, because they use the proper contraception. There's no reason to believe that the use of contraception would drop during the snowstorm.

Unless people are far less responsible than I give them credit for, couples are either trying to have a baby or they're not. The presence of the snowstorm and any increased sex it might bring about shouldn't be a factor.

And even if many children are "accidents," there are plenty of opportunities more or less evenly distributed throughout the year for them to be conceived.

Staying Open in the Snow: Differing Incentives for Workers and Owners

The view outside my apartment at 8 p.m. Wednesday.

Because of record snowfall in the Washington, DC, region, federal offices have been closed for a fourth straight day. However, quite a few private sector businesses have remained open.

To the owner at most large private sector businesses, staying open means making money and closing means losing money (assuming that customers will want to come to his store that day). So the decision to stay open is obvious.

To the worker, getting to work with such poor road conditions and the other inconveniences caused by the snow might not be worth it. But he may take a "loss" for the day--for example, earning only $100 for the day but incurring $200 worth of "costs" (including effort to get there) to do so--in order to keep his job for the long run.

The analysis differs, however, for smaller businesses. For one thing, the owner may also have an active management role, or his job may be very similar to that of his underlings. His calculus is the same as the worker's: he may be willing to forgo the day's profits if it means that he doesn't have to make the drive on snowy roads, either. In addition, the owner of a small business is more likely to have a personal relationship with his workers; it's easier for a CEO to insist that thousands of workers in a faraway branch show up than it is for a small-business owner to order in his workers, who also may be among his closest friends.

So, we would expect large businesses to be more likely to stay open than small businesses during a snowstorm.

Snow Storm Approaching! Time to Hit Up ... the Bank?

So reports the Washington Post.

In my prior post, I discussed how there's been stampedes at the local supermarkets. But why this happens at the banks is more puzzling. If most people are going to be trapped in their homes this weekend, why bother getting money from the bank if they can't spend it anywhere?

One woman is quoted as saying:

"I am just taking care of bills before the snow hits."

Well, doesn't that just involve signing checks?

HT to Sharon.

Stocking Up Before the Storm

CC Image Courtesy of Stephen Cummings on Flickr

The Washington, D.C., area is expecting a major snow storm this weekend. All reports I've heard point to major overcrowding and supply shortages at local grocery stores ahead of the storm. The Whole Foods near Logan Circle was closed for 30 minutes because the crowds were causing fire safety concerns, reports the Washington Post.

In theory, the grocery stores don't need to be chaos before storms. When demand exceeds supply, the price level rises until enough people don't want the good at the higher price. The most price-sensitive people buy other things or wait for the price to fall. Stores could have a policy of hiking prices 20% ahead of major disaster periods, for instance. However, for political reasons and for fear of customer backlash, they may choose not to (we saw what happened with the 5 cent bag fee). If you don't really need to go shopping, you'll wait until next weekend. If your cupboards are bare, you'll be willing to pay the premium.

Instead, the scarce good that is space in the grocery store is allocated by time wasted waiting in line. Again, only those who really need groceries today will be willing to bear the lines.

Which is the better way to sort customers? Economists generally prefer the former method. If customers have to pay a premium, they might as well do so in money instead of time. At least the higher prices transfer money to the stores and the local government (via sales taxes), and the higher prices (in the long run) induce more firms to provide the scarce good. In contrast, if people have to wait in long lines, that doesn't do anyone any good and is a waste of resources.

However, both methods create a sort of economic efficiency, by getting the goods to the people who most need them, and who are willing to "pay" the most, whether it be in time or money. But note that, to some people, time is relatively more expensive than it is for others. So the final allocation won't quite be the same.

Snow Days and Keynesian Beauty Contests

The view from outside my apartment this morning.

Overnight, 2 to 4 inches of snow fell in the D.C. area, and most local schools are closed (see this Washington Post story for more details).

For school administrators and others, deciding whether to shut down school is something of a Keynesian beauty contest. Old newspaper contests asked readers to select the most beautiful women among a series of photos. Entries were graded on how they fared against popular opinion. So, the game was to pick not the women whom the reader personally thought were the prettiest, but the ones the reader thought that most other people would judge as the prettiest.

What is the worst outcome for the school administrator? If he allows school to go on, someone might get injured or not be able to make it to school. However, if all the other local schools in the area are open, the onus shifts to the students. In contrast, a good case for negligence could be made if the other schools are closed and a student gets hurt at the one open school.

But school heads shouldn't always err on the side of closing, either. While students may appreciate such a school, parents and lawmakers will not. But a school cannot be blamed for closing on a day when all the other schools are closed as well.

In the sum, the school head's best play is to follow everyone else, as illustrated in the below payoff matrix (assuming that all the other schools more or less coordinate). In the game, the school head has a payoff of 0 if he follows the other schools and -1 if he doesn't, while the other schools are not affected by the choice of this one school. This is a version of the coordination game in game theory.

	Other schools: cancel	Other schools: don't cancel
Your school: cancel	0, 0	-1, 0
Your school: don't cancel	-1, 0	0, 0

Of course, if school is canceled, the more advanced the notice, the better. Canceling a 7:20 p.m. class at 7 p.m. isn't going to help anyone. So a school administrator is wise to wait and see how the field plays out but make a decision in enough time for students and parents to react.

Down the street.