A static low-wage cutoff point, whether it be $19 or $100, automatically reduces the size of the treatment group (Seattle) if wages in the treatment group are increasing faster than the wage of the control group.This is not erudite statistical methodology. This is simple arithmetic. If the wages in the treatment group increase at a higher percentage rate than the wages in the control group, more workers are lifted above the $19 threshold in the treatment group than in the control group. This is true if the treatment group and the control group are otherwise absolutely identical. This is what I call wage-bracket creep. The extremely simplified example below shows how this looks, the yellow cells represent workers whose jobs and hours would be "lost" (to the study) as they pass the $19 threshold:
See how much worse off the treatment group is than the control group? The yellow cell occupants haven't lost their jobs, they have simply been excluded from their respective groups because their wage now exceeds the static cutoff amount.
Of course, I wondered if the study authors could be making such a simple arithmetic mistake. So I reached out to one of the authors, who generously replied but appeared to confirm that they relied on a static threshold. I say appeared because some of the replies were, shall we say, "ambiguous" but did not disclaim use of a static threshold when I sought explicit confirmation or denial.