If you are not already aware, the dissertation can make just about anyone feel like Sisyphus. I am probably on version 28 of this paper, but that should not deter you from taking a look at the recently updated draft for “The Minimum Wage, Self-Employment, and the Online Gig Economy.” If you saw the previous draft, you’ll notice a few changes have been made. The largest is certainly the transition from using urban and rural dummy variables as a proxy for labor market competitiveness to using a quasi-Herfindahl-Hirschman Index (HHI). If you don’t recognize the HHI, which is a completely understandable thing to not have memorized, it is a measure of market concentration, or labor market competitiveness.
This change produces similar results to what I found using the urban/rural dummies, but now it has a cooler name, which is really what it is all about. You’ll also notice that now I am clustering standard errors at the state level, including the two-digit NAICS industry breakdown, and evaluating a measure of average receipts as well as establishments per member of the labor force. All in all, the last six weeks have seen some major revisions to the draft, with limited changes in the conclusion, so academia in a nutshell. I think the results are best summarized in two plots.
First, we can look at the aggregate effects of changes to the minimum wage across all nonemployer establishments and then in the representative low-barrier marketplace most likely to be impacted by the expansion of the online gig economy:

Overall, what we can see is that transportation and warehousing services respond as one would expect in the competitive model of the minimum wage, but the aggregate effect on all nonemployer establishments is insignificant. This is due to a substantial amount of heterogeneity across NAICS industries and labor market competitiveness. The next figure shows how competitive labor markets matter:

Turns out the real impact is a combination of labor market competitiveness and the presence of an applicable low-barrier labor market, like Uber. This was my hypothesized conclusion from the previous draft, now on full display. Give it a read if you want to learn more.