My friend Marlene is the fittest of the 50-somethings I know: she isn’t just lean, she’s strong. She figure skates, and she works out at one of those upscale gyms that also has a spa.
Someone could do a study of whether having a gym membership actually improves your fitness. But it wouldn’t be that easy. Because if you just compared members and non-members, you could easily find better health among members for all sorts of reasons that had nothing to do with working out. For instance, I’m fairly certain that none of the areas that the USDA identifies as food deserts—areas where you can’t buy fresh, healthful food—are in the same census tracts as boutique gyms. Plus it is likely that the person who can afford the gym membership can access healthy food even if it isn’t in their neighborhood because they can afford a car, too. So you have what we academics call selection bias: because people are selected into membership on the basis of things that predict health, members would be healthier even if nothing good happened in the gym.
Part of that difficulty is easily overcome. We can compare people of the same income level who are members and non-members and conclude that any remaining difference in, say, blood pressure, is no longer due to selection into membership on the basis of income. Even if you repeat this process to include other things that predict both blood pressure and gym membership (like age, smoking, alcohol consumption, education, etc.), you can’t observe everything that matters. For instance, it is very difficult to observe temperament—but very reasonable to argue that those who are happy being couch potatoes don’t join. Therefore even after controlling for a bunch of observable factors, there could still be a difference in blood pressure explained by selection into gym membership on the basis of temperament.
Similar problems with unobservable selection bias crop up in many other areas of research. Kasey S. Buckles and Joseph Price tackled the issue directly in their August 2013 Demography article, “Selection and the Marriage Premium for Infant Health.” Children born to married parents are healthier: they are less likely to be born prematurely, less likely to have low birthweight, and less likely to die in infancy. But as marriage is supposedly becoming a luxury good, it isn’t surprising that children born to married parents would be healthier just based on their parents’ education, income, and the like. Buckles and Price estimated that at least half of the marriage premium for infant health is due to selection on observables, but that a meaningful marriage premium remained.
So they tackled unobservables: they compared health outcomes for marital and non-marital births to the same woman. Using this method, no consistent characteristic of the mother could affect the size of the marriage premium for infant health, even if it was unobservable. The estimated premium shrunk in size again, just as it did when controlling for observable selection factors. Buckles and Price conclude that their results “find little scope for a large causal effect of marriage on infant health.”
There are two problems with their conclusion. First, they emphasize how much of the marriage premium for infant health they have explained away by accounting for selection, and downplay that it still remained. The magnitude of the marriage premium did drop a lot when accounting for selection: babies born to married mothers were on average 248 grams heavier than those born to unmarried mothers, and the difference after accounting for selection was 96 grams.
Still, women getting married between two births had healthier later babies; women becoming single between two births had healthier earlier babies. Buckles and Price emphasize that it is important not to interpret this as establishing that marriage has a causal effect on infant health since the transitions themselves (not the resulting marital state) could drive the effects. But how much does that matter? If getting married improves infant health and getting divorced compromises it, how is that practically different from marriage being good for infant health?
Second, they introduce selection bias in order to deal with unobservables. It is true that comparing marital and non-marital births to the same woman gives you an estimate of the marriage premium that is not biased by selection into marriage—but only among women who have had both marital and non-marital births. It seems quite plausible that children of continuously married women could experience a greater marriage premium. I’m pretty sure Marlene has had her gym membership continuously for decades. If we were to take blood pressure measurements while someone was an active gym member and while their membership was lapsed, we would control for unobservables that predict both membership and health, but we would never measure Marlene. Doesn’t it seem plausible that remaining a member helps more than having just become one?