Starting school

In New Zealand, every kid can begin school on the child's fifth birthday. There is then no particular birthday cut-off for schools, other than that kids might be stuck in Year 0 a little bit longer.

In much of the rest of the world, school starts on a particular date: if you turned 5 before some cut-off date, you're in; if not, it's another year of daycare, but you'll be one of the older kids in your class. This has consequences for timing of births.

New Zealand may be considering flipping to the "everyone starts on the same date" regime. And so you have the potential for a rather nice difference-in-difference study: none of the kids in the current cohort would have been born with parents anticipating school-start timing effects around a set start date, but if the regime changes, they will - in a few years. In the transition, there will be kids in one year who started on their birthday and others just starting on the set date.

If it happens, I wonder whether anybody will pick this up as a neat identification strategy.

Weak instruments are weak

More than a decade ago, back in the advanced econometrics course at George Mason, Thomas Stratmann taught us about the weak instruments problem. Looks like one of these was worse than I'd thought.

Suppose you wanted to know whether education affected earnings. And you saw that people with more education had higher incomes. But suppose that you also thought that people who were smarter (or more conscientious) would earn more regardless of education AND that those same people were more likely to select into more education. You then have an endogeneity problem: just running a wage regression with education on the right hand side doesn't really give you the effect of education on earnings. It tells you how much more those with more education earn compared to those with less education, but it's a total effect rather than a partial: it includes all the effect of selecting into more education as well as the effect of the education.

So, then, what to do? You need something that will affect the amount of education that somebody gets that isn't itself a predictor of income. Something exogenous to income that affects education. If you have that, you can use an instrumental variables approach to try to estimate the effect of education on income via the effect of the exogenous instrument on education.

And the typical early example is the old Angrist and Krueger measure of quarter of birth as instrument for education. Compulsory schooling laws in the US meant you couldn't quit school until you were some minimum age. Quarter of birth could then affect how much schooling you got: those who turned 16 early in the school year could drop out earlier than those who turned 16 later in the school year.

Then Prof Stratmann told us about the weak instruments problem. Quarter of birth is only really weakly correlated with education - it explains very little of actual differences in education levels. And so bad stuff can happen in the estimation.

So we've known for a while that quarter of birth might not be a great instrument. But it would still get used. Bound, Jaeger and Baker complained about it in 1995; I think we went through their critique in our 1999 metrics class. Jaeger got angry in 2009 when quarter of birth was still being cited as a decent instrument.

Fast-forward to today's news from the Freakonomics blog: Buckles and Hungerman have shown that season of birth is endogenous. (gated, ungated) Ka-boom.

Season of birth is associated with later outcomes; what drives this association remains unclear. We consider a new explanation: variation in maternal characteristics. We document large changes in maternal characteristics for births throughout the year; winter births are disproportionately realized by teenagers and the unmarried. Family background controls explain nearly half of season-of-birth’s relation to adult outcomes. Seasonality in maternal characteristics is driven by women trying to conceive; we find no seasonality among unwanted births. Prior seasonality-in-fertility research focuses on conditions at conception; here, expected conditions at birth drive variation in maternal characteristics, while conditions at conception are unimportant.

If different types of parents select different seasons in which to have kids, then there goes the exclusion restriction: IV just plum don't work right if the instrument affects outcomes via channels other than the one specified. I think that Dubner at Freakonomics understates the importance here when he says the finding's interesting because so many studies have found an association between birth month and later outcomes: the importance is rather that we have something much more serious than a weak instruments problem when using quarter of birth to get around endogeneity problems in estimating the effect of schooling on income.

@KevinMilligan points out that folks have moved toward regression discontinuity design for this kind of work anyway.

@colbycosh Certaily hurts QofBirth IVs, but most stuff now uses tight discontinuities. Season of birth effects no prob if trend smoothly.
— Kevin Milligan (@kevinmilligan) August 12, 2013

Agreed! But I still wonder whether loud cries of "WE TOLD YOU SO!" were coming from Jaeger, Bound or Baker's offices when the Buckles and Hungerman paper came out....

Update: I'm going to give the last word on this one to Dr. Phil:

Finding a solid IV is a grueling task. Make it a little more fun by turning it into a scavenger hunt for the kids.
— Dr.Phil of Economics (@DrPhilofEconomi) August 13, 2013

Shame elasticity of demand

Here's a fun one. New Zealand supermarkets have started putting in self-checkouts. Turns out customers buying embarrassing or personal products are more likely to choose those checkouts than ones staffed by clerks.

Pak 'n Save Moorhouse Ave was the first supermarket in New Zealand to have them installed, in 2006.

Foodstuffs chief executive Steve Anderson said 20 to 30 per cent of transactions were now through self-checkouts. However, they accounted for a far lower proportion of customer spending.

Customer research showed people who used the self-checkouts tended to buy fewer items and were often mothers with children, the technology-minded or introverted.

"Embarrassing products", such as personal or indulgent items, were more commonly bought at the self-checkout.

Anderson said there had been some savings for the business, but "nothing major". It had not saved on employee numbers. "The idea was more about customer choice and convenience," he said. "You still need staff there." [emphasis added]

So here's a potential IV study for somebody. If people are more likely to buy condoms when these kinds of self-checkouts are introduced, and there's no correlation between self-checkout installation and underlying sexual behaviour trends, you could use the availability of self-checkouts as an instrument for condom use. Ta dah!

It would likely be a weak instrument, alas; the correlation isn't likely to be that high.

9/11 as an Instrument

It's hard to tell in cross-sectional data whether depression is cause, consequence, or spurious correlate of risky sexual activity. Susan Averett and Yang Wang try to figure it out in the latest AER. Their trick? AddHealth data collected over a period that spanned 9/11 that lets them use the terrorist attacks as an instrument for depression.

Some summary statistics:

Our full sample consists of 4,151 women aged 18 to 26 years. Most of our respondents are white (68 percent) or African American (25 percent). The average years of education are 13.5 and the average age is 21 years. Thirty-five percent smoked for at least 30 days in the past year, and during the year before interview 72 percent of these women drank alcohol and 31 percent used marijuana. Selfrated health averages 2.05, which is slightly worse than “very good.” The mean CESD score for the nine questions asked in the Wave III 95 percent of these women are sexually active in their relationships. Sixty-seven percent and 11 percent of them engage in oral and anal sex, respectively. Fewer than 2 percent of the women in our sample report using condoms.

An active sample. And, an active sample that showed a sharp jump in depression scores in the period right after 9/11. They then use 2SLS with 9/11 as instrument and find that OLS estimation underestimates the effect of depression on participation in risky sexual activity.

So a one point increase in the CESD (depression) score correlates with a 0.4% increased likelihood of vaginal sex by OLS, but a 2.1% increase by 2SLS - and a 1.9% reduction in the likelihood of using a condom. 

It's worth keeping this kind of result in mind when we hear findings that alcohol use correlates with risky sexual behaviour [and, let's not forget, with more positive consequences of sexual experiences]. If depression correlates with heavier drinking, then it's pretty easy to conflate the effects of alcohol with a covariate, like depression, that drives both drinking and risky sexual practices. 

Offsetting behaviour: vaccine edition

I'm more inclined to call stupidity over risk homeostasis on this one:

Some adolescent girls who get the HPV vaccine to prevent cervical cancer wrongly think they no longer need to practice safe sex, U.S. researchers said on Monday.

The study, published in the Archives of Pediatric & Adolescent Medicine, shows the need for better education about the vaccines and their limitations.

...The authors said the study was limited in that subjects came from a single urban clinic serving low-income clients so the findings may not apply to more general populations.

I wonder if anybody's running effects of vaccination on STD and condom use rates. It would be surprising if there weren't some drop-off in condom use with vaccination; the risk has indeed gone down. But I'd love to see numbers on it. Unfortunately, the kinds of things that would predict vaccination likely also predict sexual behaviour regardless of whether vaccination has taken place. Finding an exogenous instrument could be tough.

Snow pro tips for Kiwis

A few things everybody from my part of the world knows, but you Kiwis may not:

• The slush on your driveway and sidewalk will freeze tonight into a slippery mess that will not melt until mid-day if you did not shovel it.
• If you postpone shoveling until the snow stops, that just makes the job harder later.
• Fresh snow falling on hard-frozen slushy muck makes things even worse.
• Cat litter and a shovel in the back of the car can be really helpful. Similarly, cat litter under tyres on an icy driveway also helps. A bucket of beach sand is just as good.
• If you're in a rear wheel drive, adding throttle on loss of traction rarely helps. And spinning your tyres is far worse than rocking back and forth.

One thing that I didn't see today that I ought to have: rosy-faced kids coming to the door offering to shovel the sidewalk and driveway for $20. I'd have paid it.

Despite 27.5% youth unemployment AND the schools closed for snow, no kids came round looking to work. And so I had to do it myself.

 I'll hazard a guess that this was due to lack of anticipated demand. If most Kiwis reckon that snow's not worth worrying about because it'll just melt, kids might well expect no demand, and so Say's Law holds: lack of demand means no supply is brought forth. When the 3-year old and I took a walk around the block, I counted no more than 4 driveways that had been shoveled; only two had also bothered to shovel the sidewalk.

I'll put that difference partially to differences in liability law. In Pittsburgh, for example, if you don't clear the sidewalk in reasonable time, you're liable for injuries incurred by pedestrians. Things vary across states, and even county to county. I wonder if anybody's done anything interesting playing around with differences in sidewalk liability regimes. Maybe you could use it as an instrument for entrepreneurship: kids in high liability regimes may expect to have clients and so will find returns to early entrepreneurship, setting them on the path to future greatness. But only in places where snow is infrequent enough that homeowners don't just contract with Mr. Plow.

Once Ira is 8 years old, if we're still here and if there's snow again, I'll send him out to test whether the problem is on the supply or the demand side....

Hidden meanings

It's usually Alex that gives a plain English interpretation of something that Tyler only hinted at. This time, it's Alex that buries the point. He writes:

Are IVs Going the Way of the Atlantic Cod?

It's hard to come up with a good instrumental variable (plausible source of exogenous randomization) so when someone does come up with one (e.g. legal origin) it's tempting to want to use it again and again. Unfortunately, as Randall Morck and Bernard Yeung point out in Economics, History and Causation, IVs with more than one use are deeply problematic. If a variable is a good IV for X then it can't also be a good IV for Y without also controlling for X and vice-versa. What this means is that every new use of an IV casts doubt on every previous use.

As Alex well knows, if these latent variables are a problem, they're a problem regardless of whether the additional IV studies are conducted or published.

But he still points to a Tragedy of the Commons and suggests overfishing. What then is the Commons that is exploited when the kth paper is published using a well-used instrument? It isn't the technical validity of the instrument. And it isn't the soundness of prior work using that instrument. Rather it's the continued plausibility of the instrument at all - whether we still believe in it. Unintentionally helping reveal that certain prior results are less sound, I would have thought, is more a public good than a public bad. So what's then the Commons that's being overfished? Perhaps the plausibility of results reliant on complex econometric techniques as a whole. Overfishing it brings the whole enterprise into disrepute.

And so maybe Alex's hidden message is that a lot of empirical results are a sham. The Commons is public credibility. And the private incentive is to publish the incremental result that gets you another line on the vita but helps slowly to bring down the whole edifice. I'm not sure that anybody has successfully answered DeLong and Lang.

Karl Smith also suggests we ought to be raising the status of good narratives.

I tend to be pretty skeptical of results that aren't grounded in basic price theory or that aren't confirmed by a lot of different methods, including both Ocular and Ordinary Least Squares.