Some inferences we might be able to draw from this relationship:
1) The relationship is surprisingly linear, which suggests that a linear relationship between minimum wage levels and employment may be a reasonably accurate assumption.
2) For each 1 percentage point increase in the MW, relative to the Average Wage (AHETPI), the wages of an additional approx. .44% of workers fall below the MW.
3) Historical correlations associate about .4%-.44% in lost employment for each 1 percentage point increase in MW/AW. This suggests that a total of .9% of workers are affected, with about 1/2 losing employment.
4) In the 2007-2011 period, 1.6% of additional workers' wages fell below the new minimum. An estimated 3.4% of workers were associated with MW job losses. The relative amount of estimated lost employment was especially high in this episode. As can be seen in the graph, this could be because the minimum wage had reached a level below the natural minimum. After the first two MW hikes in 2007 & 2008, the proportion of the labor force at or below MW was still at 1.7% in 2008. After the third rise in 2009, the proportion of workers earning MW finally topped out at 2.8% in 2010.
This probably means that I need to revisit my employment estimates for the recent period, because a linear relationship probably overstated the effect of the first hike in 2007. That hike probably didn't have as great an effect as the nominal dollar amount would indicate.
6) In a context of increasing income inequality, or variance in wages, we might expect a shift up in the relationship (more MW workers at a given MW level). We see the opposite, though. There appear to be periods roughly parallel to the trend, but with a shift down in the 1990's, so that there are relatively fewer MW workers now than there were in the 1980's. This also shows up if we graph the relationship in terms of constant dollars instead of as a proportion of average wages.
This could be the result of a change in the middle class life cycle. Young people have much lower labor force participation than they used to. So, this could be a product of middle class workers choosing not to work during the low-wage portion of their potential work life.
7) In 1980, about 60% of combined MW workers were at minimum wage and about 40% were below minimum wage. By 2008, nearly 90% of the combined MW workers were below the minimum. I take this as another sign that the MW was at an ineffective level by that time. This suggests that most jobs reported as MW involved tips or some similar characteristic. By 2012, the portion of combined MW workers working below the minimum was back down to 56%. This figure topped out in 2008, even though the first MW hike was in 2007, which again suggests that I need to lighten up my estimates of job losses during the early part of the recent episode.
Yet, my preliminary tests of the data show that, with some differences in character, male and female employment are roughly similar in their sensitivity to MW hikes. This poses a challenge to my model. Women are concentrated at MW jobs at nearly 3 times the rate of men. That should lead to greater sensitivity to job loss.
There are caveats. Female employment has different cyclical behavior than male employment. And, whatever the differences in labor force behavior among the genders, their proportions are pretty stable, so whatever differences there are, they shouldn't undermine the stable relationships of the aggregate population.
It is also likely that some of the employment losses from MW shocks comes through supervisory positions or other jobs with complementary relationships to MW jobs. This is one reason why studies that track individuals working at MW would not capture the complete effect of MW hikes.
But, still, the inability to explain this would be a strike against my model. The higher proportion of young workers at MW meant higher sensitivity to shocks, and I would have expected to see the same thing among genders.