"Thanks for delving into this. Wanted to note a few things. Meer and West do not really offer a critique of the methodology of Dube Lester Reich (2010, 2012/3). That is because DLR's main specification does NOT rely on a county or state specific trends - the main methodology is to use compare only across counties within a pair (operationalized by using county-pair-specific time-period dummies that wash out variation between pairs.) So the primary border-discontinuity specification is not subject to any criticism from Meer and West. Indeed, Meer and West merely cite the Neumark Salas and Wascher study (I'd say more for support rather than illumination) as a critique of the border discontinuity methodology.
Now, it is true that besides our preferred discontinuity specification, we *also* show results using "intermediate" specifications with state linear trends - as a way of showing that even less granular types of controls for spatial heterogeneity kills the disemployment estimate in the "canonical" place and time fixed effects. (And in Appendix Table A1 we additionally subject our discontinuity specification to state linear trends as a robustness check and show results are the same.) So in principle these specifications (but NOT our primary discontinuity specification) are subject to the issues with linear trends that Meer and West raise.
Even there, however, there are two important pieces of evidence that suggest Meer and West's critique is off base. First, we show dynamic specifications with 16 quarters of lags. This means that in models with state trends, those state trends are estimated WITHOUT using the first 16 quarters of post-intervention data - so they are largely PRE-existing trends; see the original Wolfers 2006 paper on this. (As Meer and West point out, most minimum wage differences last around 4 years).
Yet there is not an indication that the "long run elasticity" [associated with the t+16 value in Figure 4] in linear trend specification, that is largely estimated using PRE-existing state trends, is any more negative - as would be the case if Meer and West's explanation were correct. Moreover, during these 16 quarters, there is no indication of falling employment as suggested by Meer and West's simulation.
In general, if you estimate a set of flexible distributed lags (as we always do in DLR as well as Allegretto Dube and Reich), you should catch falling employment levels if there is a growth reduction. But we don't see that anywhere. Which raises serious doubts about the explanation Meer and West offer for the discrepancy between levels and growth as outcomes.
Finally, see this post by John Schmitt about the Meer and West paper's own findings regarding industries: http://www.cepr.net/index.php/blogs/cepr-blog/more-on-meer-and-wests-minimum-wage-study"