"I don't think that's the end of the story, though, because if you want to know whether the minimum wage is binding you really do have to think about trends in productivity, because that's what ought to determine labor demand. EPI has also done excellent work tracking what the minimum wage would look like if it had grown since the late sixties at the rate of productivity growth. Now productivity growth as it is measured is NOT the same thing as marginal productivity that we use in theory, but I think it's a fair proxy to consider when we're ballparking this sort of thing. And of course we don't have productivity information for minimum wage workers (although BLS now breaks it out by industry - perhaps someone should take a look at productivity growth in typical minimum wage industries)."It appears the same day I wrote that, someone did take a look at food services productivity growth. The result?:
"Taking a longer view, from 1987 to 2012 the same BLS data show that worker productivity in the food service sector rose by an average of 0.6 percent per year. In limited service restaurants, the gains were slightly lower, only averaging 0.5 percent per year. Meanwhile, unit labor costs have risen by an average of 3.6 percent. Over this period the minimum wage has risen from $3.35 to $7.25 per hour which is an average annual increase of 3.1 percent. In other words, at least in food service, the minimum wage has risen at a rate five or six times as fast as justified by the gains in worker productivity."Now at the end there he is doing the average nominal growth rate. Average annual real growth rate is about 0.96%*. So it's not quite as dire as the author suggests, but it should move your priors towards the idea that a 39% nominal increase to $10.10 is not a "modest" increase by the standards of the empirical literature and guesses at what the binding level would be (we still don't know that, of course - this data just gives you less room to make that argument).
* So I say "about" because I'm using Larry Mishel's real minimum wage values for 1989 and 2011 rather than the author's nominal values for 1987 and 2012, because I can't find immediately at hand real numbers for those years.