An outstanding paper by Currie, DellaVigna, Moretti, and Pathania (aka et al. ungated) in this month's AEJ: Ec Policy does a pretty credible job identifying causal effects of fast food restaurants on 9th graders and pregnant women. Identification rests on the assumption that, once a restaurant has self-selected itself into a site within a quarter mile of a school, it is random where within that quarter mile circle it lands. Put another way, the most fattening restaurants can't guarantee a spot across the street from the high school ... or a particular pregnant mother. With several million observations and detailed geographic information, they are able to get very precise standard errors.
They find a significant difference for 9th graders (and 5th graders when school fixed effects are included): obesity rates increase by 5% (1.7 percentage points) when there is a fast food restaurant within 0.1 miles vs. when it is within 0.25 miles. That's 30-100 calories more per day.
Pregnant mothers have access to a car, so the small difference in distance does not matter. much. 1-4 calories on average. But, interestingly, the effect on African-American women is 3 times that for white women, and while there is no effect on educated women, less educated women are impacted. Note also, this is the change in weight gain between pregnancies: they know how much that woman gained in her last pregnancy and can compare weight gain in the second pregnancy between women who now have a close fast food restaurant to the second pregnancies for women who don't.
Among their numerous robustness checks, they even identified the effect of future fast food restaurants (0), ruling out much of the possible demand-side effect.
The only mild down side is that this is still at a population level. It would be nice to know if the effects were from many people at the borderline just barely crossing over or if we are talking about large changes in behavior for fewer people.
Hat tip: Blattman