A couple more points on the Murphies...
Ryan Murphy has a good post here. I think he goes a little overboard with his first point on market socialism and Hayek. Market socialism is silly. The minimum wage is "different" because wage earnings are how people make ends meet in the modern market economy. It's the same sort of concern that got Hayek to endorse the basic income but not a "basic profit" or a "basic rent" (which has its own distortions associated with it - Hayek liked it because it met some of his ethical tests). So the center-left is not as loopy as Ryan is worried about, I think. There are good reasons here. And I suspect a lot of the center-left is like me: if we were able to design the system ourselves it would not feature a minimum wage. Remember that was one of the first safety net programs to go into effect - if we had had other better designed supports I doubt anyone would have gotten so enthusiastic about it. But it doesn't seem to be introducing all that many problems - probably because it's stayed so low - so it's certainly not going to be something I'm going to be marching on Washington for. If it stays low I could even see some welfare gains. The most appealing thing to me about discussions of the minimum wage are the scientific questions it raises, not the policy questions. Hence my initial blase reaction to the announcement. What is also getting people energized is the smearing of people like Card and Krueger as unscientific or the "no real effect" side as abandoning Econ 101.
On the second point - Ryan seems to be missing my point. I'm not proposing controlling for local price levels. I'm proposing dividing the value of the minimum wage by either a price level or a median wage or a fair market rent or something like that, because the real value of the minimum wage in Alabama is actually higher than it is in California. I got my fair market rents from here. Ryan doesn't do this - he keeps his dummy variable for the state minimum wage in there and then controls for price level. Before he goes through a lot more leg work to run it again, that's still not going to be quite right to me. You just can't look at this in the cross-section. The U.S. is a very diverse place and you at least need to look at changes in the minimum wage longitudinally to control for time-invariant state level factors. I know he's put work into it, but I have no idea what to make of it in the cross-section with a dummy variable for the minimum wage. It's certainly not going to make me budge an inch from my current assessment of Card and Krueger, Neumark and Wascher, and Dube, Lester, and Reich. If it could, these studies would all be state level cross sections with dummy variables for the minimum wage variable too.
He is concerned about correction for state-specific trends. Dube, Lester, and Reich do additional correction in their analysis for state (and region)-specific time-variant factors. This is fairly standard in the literature. I've done this in an evaluation of some child welfare reforms in Connecticut, in an evaluation of the Bush administration's High Growth Job Training Initiative, and in my analysis of the Georgia job creation tax credit which I'm preparing for submission right now. Why do people do this?
If you have only time-invariant characteristics that might affect the employment level the solution is easy: do a pre-post test. This is unrealistic which is why you never see pre-post tests.
If you have time-invariant observation-specific characteristics and time-variant characteristics common to two observations the solution is a difference-in-difference. Now it's critical here that the time-variant characteristics are common between the two observations - that's why Dube, Lester, and Reich use contiguous counties (and why Card and Krueger looked at a state border).
But even this isn't going to be perfect. Things still vary. Things always vary and our job is to hold all the variation except what we're interested in constant. Sometimes this is done by another differencing: difference in difference in differences (or DDD). For example, you might do a DID within county for adult and teenage unemployment (to clean out county-specific trends), and then do difference out the contiguous county differences (to deal with the trends common to both counties). Another strategy is to match across counties, which is useful if you've got a lot of data. This is what we did for the child welfare analysis - we did propensity score matching to control for compositional change in the child welfare case load over time that would have impacted outcomes.
Dube, Lester, and Reich - because they are working with county data - instead just choose to include state-specific and region-specific trend variables.
OK - so all of this is entirely above board. There's nothing "magical" about this as Bob's title suggests. The approach is right.
How about the execution?
Bob is suggesting that controlling for these state specific trends will over-correct because states that adopt minimum wage laws will adopt other progressive policies that we all know are just awful and will slow adult employment growth more substantially than employment growth for those earning a minimum wage.
Remember they're not just looking at people earning the minimum wage - they're looking at restaurant employment and all private employment.
Ryan Murphy, in Bob's comment thread, suggests that it's going to affect the efficiency rather than the bias of the estimate. This is basically right - collinearity should just blow up your standard errors. In this case that probably matters a little more than usual since we've got studies hovering around a zero estimate. But collinearity can actually bias the estimate if the model is misspecified. Given the trouble with identifying impacts in these sorts of policies I would err on the side of caution.
I think there's a more fundamental problem with Bob's argument. Remember, estimation is going to be off of changes in the minimum wage, not levels - that's the whole point of this exercise. In 2007 you had a bunch of conservative, right-to-work, no-state-minimum wage states increasing their minimum wage against the liberal, union-friendly, state-minimum wage states because of federal action on the matter. The same is true of every federal minimum wage increase. So if Bob thinks that these state level trends are taking too much growth off of the conservative states by attributing good policies that don't affect the minimum wage workforce to the minimum wage workforce, that would suggest that Dube, Lester, and Reich might even be underestimating the positive impact.
Ultimately I don't buy Bob's argument because my impression is that regional growth trends that have nothing to do with the liberalism or conservatism of the state probably dominate these state-specific trends. The South was conservative when it was growing really slow too, after all. The Midwest and the Northeast had a lot of unions in their period of strong growth. I just don't buy the argument.
But it's not a bad argument under certain circumstances. If he's right that liberal policies matter that much (and in the direction he thinks they matter) this would be something to worry about if it were the liberal states increasing their minimum wage. But in a lot (at least as many? more? I don't know) of cases since it's the federal minimum wage that's increases it's actually conservative states that are doing the increasing.