{"id":5321,"date":"2012-09-23T07:15:37","date_gmt":"2012-09-23T11:15:37","guid":{"rendered":"http:\/\/shermandorn.com\/wordpress\/?p=5321"},"modified":"2012-09-23T07:22:54","modified_gmt":"2012-09-23T11:22:54","slug":"peer-effects-modeling-the-terrible-horrible-no-good-very-bad-day-phenomenon","status":"publish","type":"post","link":"https:\/\/shermandorn.com\/?p=5321","title":{"rendered":"Peer effects: modeling the Terrible, Horrible, No Good, Very Bad Day phenomenon"},"content":{"rendered":"

There is a substantial literature on peer effects on achievement, something with important implications for how schools assign students to classes, schools, etc., as well as thinking about how such assignments mediate the judgments we make of school and classroom effectiveness. Most attempts to tackle the problem look at cross-sectional data and assume that the group mean of some characteristic has a linear (or at least continuous) relationship to outcomes. On the one hand, that’s better than assuming that group characteristics are irrelevant. On the other hand, the group-mean approach is highly unlikely to be a reasonable approximation of real group dynamics in real classes.<\/p>\n

A 2006 AEA paper coauthored by Caroline Hoxby<\/a> addresses some of the conceptual issues involved, primarily the difference between group means (what Hoxby and Gretchen Weingarth call the Linear-in-Means assumption) and the effects of outliers, critical masses, and either homogeneity or heterogeneity. They are correct to point out that group means are not the only path for peer effects. This post addresses a different concern, the assumption of a relatively continuous relationship between peers and outcomes. In my experience and observation, there is a range of small and moderate peer effects that\u00a0are<\/em> continuous, but there are plenty of ways in which the group dynamics in a class can lead to dramatically different outcomes — the most common example is of a class or a day when nothing gets done and the best a teacher or a student can hope for is a reboot the next school day. Above some threshold, learning can be bumped a little bit by a student having a bad day or everyone inspired a little bit by something a student says, but you don’t get dramatic effects above that threshold… but below some threshold of group functioning, events quickly collapse to “well, let’s try again tomorrow.” Enough of those “need a reboot” days, and the term or year is shot for most students.<\/p>\n

As far as I can tell from my limited knowledge of the peer-effects literature, this discontinuity is nowhere to be found in formal models. And because of that gap, I don’t think researchers have tried to wrestle with the causal models that tie “one kid having a bad day” to “is it the full moon or what?” ((I do\u00a0not\u00a0<\/em>think that the full moon affects student moods, but it’s a common-enough belief to symbolize a day gone to heck and back. Some days are like that, even in Australia<\/a>.)) So here is my speculation on a few ways that peer effects can show up in discontinuous fashion:<\/p>\n