I also include some cautions about how to apply this research to policy. These are every bit as important. I've had one discussion with a journalist so far about the paper and the fast-food strike for a $15 minimum. I did the math for him on how big an increase that $15 would entail and compared it to Figure A in my paper and flatly told him that you can't justify this with the existing research - our strong priors ought to be that it will reduce employment, with perhaps a few high wage metropolitan areas as the exception.
An excerpt from the report I like ("matching methods" is a more user-friendly term that I use to talk about quasi-experimental methods - that is all well-defined up front and defined in even more detail in the endnotes - the idea is that in all quasi-experimental methods you are matching some treatment case to some comparison case):
"It is difficult to overstate how uncontroversial it is in the field of labor market policy evaluation to assert the superiority of matching methods to the nonmatching approaches described above.9 The seminal evaluations of the effects of job training programs, work-sharing arrangements, employment tax credits, educational interventions, and housing vouchers all use at least some sort of matching method, if not an actual randomized experiment. In their widely cited survey article on non-experimental evaluation, Blundell and Costa Dias (2000) do not even mention state-level fixed-effects models when they list the five major categories of evaluation methods. In a similar article, Imbens and Wooldridge (2009) do mention fixed-effects models as a tool for policy evaluation, but clarify that these were used before more advanced methods were developed, noting that the modern use of fixed-effects models is typically in combination with other more sophisticated techniques. For example, Dube, Lester, and Reich (2010) also use a fixed-effects model, but more importantly it is a fixed-effects model that utilizes rigorous matching strategy to identify the effect of the minimum wage. Sometimes fixed-effects models are the best available option if no natural experiment or other matching opportunity emerges to provide a more rigorous approach. Well specified fixed-effects models can still be informative. But faced with the choice between a well matched comparison group and a fixed-effects model, the former is unambiguously the stronger study design."