Population Stats + Individual Advice = Bad Idea

In a recent EconTalk podcast on parenting, the guest economist presented evidence for strong hereditary effects and weak parental effects on children’s outcomes, in a nutshell. I get the general argument, and I’m generally amenable to the idea. As a big fan of personal agency, I’d like to think that my kids will get to determine who they will be and not be “pre-determined” by me despite my best intentions.

There’s one point, however, that didn’t come up in the conversation that I think is really important. The point: it’s dangerous to try to use population statistics to guide individual behavior. I think the medical profession exemplifies this danger really well. When doctors study diseases and therapies, they tend to experiment at the population level. As an oversimplification, when the FDA approves a drug it is because the drug had positive net effects on the population as a whole. However, each drug also comes with warnings about all the possible side effects—side effects that happened to individuals during those same trails that yielded net positive benefits. I can’t help but laugh to see that these side effects seem to always include “death,” however innocuous the drug or remote the possibility.

As an individual patient, I couldn’t care less what the effect of a drug on a population will be. My interest is the drug’s effect on me, a population of one. To the doctor, patients are delivered to the exam room like numbers from a roulette wheel, and the effect of a drug on the distribution of all patients might take on a nice Gaussian curve. To the patient entering the doctor’s office, the distribution of effects is uniform, and if you’re in the unlucky tail of the Gaussian patient curve, then that uniform distribution says “you + drug = death.” The grand majority of doctors do not treat individuals; they treat means of population distributions one individual at a time.

As for parenting, it’s not terribly surprising that the cacophony of parenting skills and techniques across large populations yields a cacophony of child outcomes netting something close to zero at the mean. But who cares? These glib stats say nothing about the few dots in the corner of the scatter plot representing the children whose lives were dramatically affected by the “nurturing” of a parent, for better or worse. It doesn’t even say anything about the dots in the middle of the graph because nobody knows where those exact dots might land if the study were somehow “replicated.” The complexities of raising a child may wash out for whole populations, so policy makers may safely be parenting agnostic. For the individual family, however, those complexities may make the difference between some very desirable and very undesirable outcomes. Parents should carefully treat individual and complex children, not means of child populations superimposed on individual children.

Population stats yield population advice. The next time someone starts giving individual advice based on population stats, you might call them out.

((Bouncy))

[This is a repost of an earlier version. This version has updated data, better graphs, and more accurate/precise statistics.]

Has anyone else noticed that the market is a bit bouncy lately? Perhaps "bouncy" is not the most erudite economic expression of my life, but it's descriptive. I remember, way back in the day, when swings of 100 or 200 points in the DOW got headlines in major newspapers. No longer. Only a titanic jolt that sends brokers scurrying for the bathroom seems to get any attention these days.

All this bouncing nags me with a question: are analysts crazy? How do they manage to value stocks through the roof one day, through the floor the next, and then fly back up to the roof the day after? I have no answer. Analysis, however, I do have.

I recently downloaded the daily close for the DOW over the past, oh, 80 years (over 20,000 rows of data—thank you Yahoo Finance). I converted these into daily percentage gains/losses[1], and then I plotted the trailing 100-day standard deviation in these gains/losses between 1928 and now (see the top figure).[2]

If it's a comfort to anyone, the Great Depression still takes first prize in volatility both in terms of quantity and duration.[3] We also see that the financial scare of the late 80's briefly produced volatility on par with the present. As a further comfort, we see that the DOW is presently running out of bounce even if it's still in the crazy-volatile range. (The blue line, by the way, shows the growth in the DOW over its history plotted on a logarithmic scale. While there was greater volatility during the depression, the absolute size of the DOW's movements were tiny compared with its movements today).

The second figure (center) brings a bit more granularity to our present condition. As of 5/29, the 30 day trailing standard deviation for change in the DOW was about 1.5. In other words, if I had to put money on where the DOW will close tomorrow, I'd say it will probably close within 1.5% (up or down) from where it closed today.[4] If I wanted to be 95% sure that tomorrow's price will be within a given range, I'd bet today's price give or take 3%. That information isn't nearly precise enough to be useful in the short term, but hey, at least that's more accurate than saying, "Where it closed today, give or take 9%," which is roughly what the 95% confident stat would have been near the end of last year.

So, after a bit of analysis, do I have some idea how to tell when things will calm down? Well, not yet. A comparison would be helpful. The final figure (bottom) shows the bouncy Great Depression, and then some. The volatility of the Great Depression was, well, very volatile. Looking from left to right, you can see that prices got really bouncy really fast and then dropped precipitously for a brief time. Prices then gradually became bouncier until they were almost as bouncy as they had been at their peak. After a tumultuous period, prices finally settled down around the beginning of 1934 and remained stable for over three years. And then World War II broke out. Another story.

What does this tell us about today? Well, our current drop in bounce might signal the beginning of a new, stable financial period. Or—perhaps more likely given its rather precipitous drop—something will slap the ball and make it fly right back up for a while just as it did in the great depression. There's a rally after the bottom of every bear market, and following every post-bear rally, there is a volatile period of price settling as the market digests all of that activity.[5]

When the trailing 100 day SD has remained between 1% and 1.5% for several months, I'll say the crisis has run out of steam. I can't forecast the future, but I at least have a somewhat rigorous way to recognize the present.

[1] This was hard. Lots and lots of coding. I'm kinda proud that it worked so well.

[2] Summary stats for the DOW's daily percentage change over its entire history: Min = -22.6%, Median = 0.04%, Mean = .02%, Max = 15.3%.

[3] Summary stats for the DOW's 100-day trailing SD over its entire history: Min = 0.31, Median = 0.80, Mean = 0.99, Max = 3.94, SD 0.60. Yes, that's the standard deviation of all the standard deviations in the history of the DOW, i.e. measuring the volatility in the changes in the DOW's volatility. Forget I said anything.

[4] And, assuming a normal distribution, I have about a 68% chance of being right, for those of you who care.

[5] See this piece by the senior editor of Money Magazine.