Peer effects aren't an externality

Suppose you started hanging out with Canadians. After a couple of months, a social scientist found that you had increased your likelihood of wearing plaid. And, you'd started listening to Rush. Does this mean that a taste for good fashion and good music constitutes a policy-relevant externality and we should subsidize flights to New Zealand from Canada to facilitate these positive interactions?

How about if you started skiing more after you started dating a skier? If folks generally disapproved of skiing, would this provide an argument for taxing skiers' romantic encounters?

Well, poor fitness may be contageous. Now forthcoming in the Journal of Public Economics, here's the paper by Carrell, Hoekstra and West. Air Force Academy Cadets were randomly assigned to residential social networks to test the effects of social connections on fitness.

We find statistically significant peer effects that are 40 to 70 percent as large as the own effect of prior fitness scores on current fitness outcomes. Evidence suggests that the effects are caused primarily by friends who were the least fit, thus supporting the provocative notion that poor physical fitness spreads on a person-to-person basis.

It's not at all implausible that peer effects of this sort matter. If you hang out with a bunch of fitness buffs, an extra five pounds will make you feel like a slob and you'll be more likely to do something about it than if all your friends are twenty pounds overweight and you're the (relatively) thin one.

I'm happy to take the empirics on this one. But I'm pretty sceptical about what folks are drawing as policy conclusion. Here's Kevin Milligan, via Twitter:

Forthcoming in J.Pub. Econ: http://bit.ly/i3GzZK. Finds obesity affected by peers--externality cld be corrected by pigouvian measure?

That's not an endorsement of fitness tax credits. But it does suggest that obesity has more than individual consequences; invites policy.

There's one case where I can agree with Kevin that it could be a policy-relevant externality: where you're coerced into being part of a particular social network. If you're forced to be in a public school where all your classmates are obese, the effect of their obesity on your fitness habits could be seen as an externality. Or, symmetrically, if your classmates are fitness nuts, the costs they impose on you to keep up could be an externality. This breaks down as soon as folks start being able to form their own peer groups as subsets of the people with whom they're mandated to share a class, and it's nowhere shown that the external effect is actually Pareto relevant, but it's not crazy to think about. The same would hold true for prison cellmates.

But out in the normal world, people choose their peers. Interpersonal effects within these voluntary arrangements can hardly be seen as externalities. As always, I follow the Buchanan and Stubblebine delineation of external costs. An external cost is only Pareto-relevant when there is the potential for gains from trade: if the gains to the affected party would be sufficient to compensate the affecting party for a marginal change in behaviour. How could we ever presume that a cost one friend imposes on his peers isn't part of an optimal equilibrium involving potentially complex side-payments? If people voluntarily choose to continue to associate with one another, shouldn't our presumption be that they've sorted things out? We all impose burdens on our friends and family; where the relationships continue, it's pretty likely that the abatement costs exceed the costs imposed.

Now maybe you could start building a case if you added in information market failures: that you didn't know that hanging out with your particular chosen peer group would have you adopt more of their habits. I'm pretty sure a whole chunk of the self-help book industry centres around picking friends who aren't bad influences. But it's still a big leap to claim failure; it's at least as plausible that the person with the less fit peer group realizes that his less fit friends are healthy and happy and that the folks over in that other peer group are wasting their time (and suffering a whole lot) by exercising too much and forgoing too many tasty treats. Further, we can build as strong a case for that too-fit people impose an external cost through peer effects in forcing others to exercise more. The case for a gym tax is as strong as the case for fat taxes if we worry about peer effects and don't want to presume to decide whose norm is the right one.

And even if we were to assume that the external cost existed, and we assume that it's the less fit that are imposing the relevant cost rather than the gym nuts, policy solutions can only be efficient where the burden avoided is less than the burden imposed. Is it really likely that the benefits to the thinner members of peer groups exceed the rather large costs imposed on everybody by any plausible policy targeted at obesity?

I worry when we assume that all interpersonal effects constitute Pareto relevant externalities as the scope for government intervention is then without bound. Suppose the Air Force study cited above sorted people into social network groupings where the behaviour of interest weren't fitness but rather were sexual activity. And suppose they found that being put in a grouping with more promiscuous peers made cadets more likely to become more sexually active. Such a result wouldn't be surprising. Would it make your sex life the legitimate object of policy because of potential effects on your non-participating peers? Only if we're willing to forget the difference between interpersonal effects and externalities.