This fall semester, I was fortunate enough to take a Law and Econ class from the puissant Alex Tabarrok. Instead of writing a term paper on the partial effects of slinging empty oil cans at the heads of drag racers, I elected to investigate some of the myths of... wait for it... the DRUGS!
If you're of a certain age, a supercilious sneer ought to set up base camp at the corners of your lips, preparing a push to the summit once the weather clears a little bit. Drugs are bad, right? Drugs ruin lives, turn users into abusers into total trainwrecks, right? This is your celebrity; this is your celebrity on meth... not even once. DARE to keep your Gummi Bears off dat juice.
Or whatever.
Point is, there's a lot of propaganda surrounding drug abuse, and the (occasionally explicit, often implict) claim that drugs lead to a life in tatters, implying causality, is sort of at odds with what I would consider common sense. Indeed, it seems as reasonable to me that someone who is having a rough go of it would turn to self-medication as that drugs veer an otherwise decent life off-track. Ordinary statistical treatments have a tough time getting at actual causality. Ordinary Least Squares regressions can show whether or not two factors move together, but are mostly silent when it comes to saying what causes what. That's what theory is for.
Or a clever two-stage regression.
What now? What's all this? Well, look, if we can make the claim that a proxy for individual drug use predicts some sort of individual adversity and we can't plausibly make the claim that the adversity can affect the proxy, then we've got a good case for actual causality.
That's sort of confusing, so let me be a little more specific. I've got some data on positive urinalysis results. I've also got crime data from the FBI and some community drug use stats from the CDC. Basically, what I've done is used the crime data of the individual's hometown (specifically, the home town of record, at the time of enlistment) to predict the probability of drug use by the individual. Nice. So, if the property crime rate of Hookset, New Hampshire is 7.4 per 100,000, then we can say that people (Soldiers) from this charming burg have, oh a 0.43% chance of pissing hot for weed (numbers simulated, natch). Take this number and slap it into an equation that tries to predict some adverse outcome, like divorce or AWOL or non-availability or whatever, and hey-presto, we should be able to show actual causality, right?
Well, maybe. Of course, the 2-stage regression didn't work. I got the first stage numbers to fit pretty well. Indeed, I think I can comfortably claim that growing up in a high-crime community probably predisposes folks to use drugs and to a rather strong degree. However, while I was able to show that drugs and adversity correlate, I was unable to show the two-stage relationship.
Now, this is consistent with my claims, but I've still got a bunch of nagging problems. Yeah, my instrument passed the first condition (first-stage correlation) with flying colors, but it clearly fails on the second condition. All this tells us is that it's a bad instrument. To put it delicately, BFD. I was looking for a bad instrument, and by golly, I found it, but this (and this is crucial) does not imply that it's a bad instument for the reasons I claim. At best, it's a rather weak tea. In short, I found no evidence to support the claim that drugs unidirectionally lead to individual adversity. Not exactly an overwhelming claim.
Still, better than nothing, I reckon. Maybe I can buff this turd out and try to get it published. At best, it can maybe knock a little wind out of the abolitionist argument. Fat chance on that though.
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