Daniel Kuehn has a very interesting new paper on possible spillover bias when using a “contiguous county” approach in economic analysis. For example, this is the approach in the influential Dube et al. (2010) minimum wage paper, which Paul Krugman for example singled out as epitomizing the new research that overturned the old view about the minimum wage hurting teen employment.
The basic logic of Dube et al. (2010) is that traditional panel data studies erroneously took one region of the US as a good “control” for every other region. Sure, they’d control for things like the national unemployment rate, but if there were local trends that just so happened to hit states that raised their minimum wage, then it would falsely bias the estimated coefficient on the minimum wage variable. (I’m making this up, but: Suppose only the Rust Belt states were the ones that raised the minimum wage above the federal level. Then a nation-wide panel data approach covering the years 1960 – 1990 might conclude that the minimum wage caused serious job losses [particularly in manufacturing]. But that would be overestimating the harm of the minimum wage.)
So to correct for that potential problem, Dube et al. instead construct pairs of contiguous counties that straddle a state border. Thus when we run the regression, each county is only being directly compared with a contiguous county that may have a different minimum wage. Any regional differences are thus assumed to be washed out, because a county in (say) Michigan is only being compared with other counties that are also in the Rust Belt.
What Daniel does in his paper is show that construction of pairs of contiguous counties might not be the perfect control group after all. If county A is in a state that raises its minimum wage, while adjacent county B is in a state that doesn’t raise its minimum wage, then we can’t simply look at the growth in employment in the two counties to assess the impact of the minimum wage hike. This is because workers are allowed to cross state borders, and so commuter flows might change in response to the minimum wage hike in county A, giving a false impression of the effect.
The following is MY illustration of what Daniel is talking about. (Note that in practice Daniel found that Dube et al.’s approach UNDERstated the harmful effects of the minimum wage, but in principle it could’ve gone the other way. I’m going to flesh out how their approach could understate it, but the following is my explanation, which Daniel might not endorse.)
Suppose county A has 9,000 teenage workers with a bad work ethic and 1,000 teenage workers with a great attitude. County B has the same. Initially neither county has a minimum wage. Every worker is employed. Specifically, the bad workers earn $5/hour and the good workers earn $7/hour.
Now county A imposes a new $6/hour minimum wage. The firms in county A lay off lots of the bad workers, and they bid up the wages of good workers, as they re-staff their operations. The firms in county B respond to the changes in worker availability.
In the new equilibrium, county A’s *employment* (not residence) is now 8,000 bad workers and 1,500 good workers, while county B’s employment is 10,000 bad workers and 500 good workers. In both counties, the good workers earn $8/hour. In county A, the bad workers earn $6/hour, but in county B, they earn $4/hour.
So if we “naively” looked at these numbers, without considering the commuter flows, we would conclude that the imposition of a $6/hour minimum wage caused county A to lose 1,000 teenage jobs relative to county B: namely, 9,500 teenagers vs. 10,500 teenagers.
However, if originally BOTH counties A and B had imposed $6/hour minimum wage laws, then maybe the new equilibrium would look like this: Both would have 7,000 bad workers earning $6/hr, and both would have 1,000 good workers earning $9/hour. (Don’t read too much into the specific employment and wage levels; I don’t have a full-blown model in my mind. Maybe some of these numbers don’t make sense, I’m just trying to show the potential problem.)
So in this case, it’s clear that the “real” impact of the minimum wage is to reduce teen employment in a given county from 10,000 down to 8,000, meaning a loss of 2,000 teenage jobs per county. But when we only applied the minimum wage to one county and used the adjacent one as a “control,” the commuter response made us erroneously conclude that the minimum wage would only cost 1,000 teenage jobs for a given county. I.e. the contiguous county approach, in this contrived example, would make us conclude that the minimum wage’s harm was half of its true value.