The first study is reported in this NBER Working Paper (ungated here) by Ekaterina Jardim (University of Washington) and others. The paper investigates the impact of the rising minimum wage in Seattle:
The minimum wage rose from the state’s $9.47 minimum to as high as $11 on April 1, 2015. The second phase-in period started on January 1, 2016, when the minimum wage reached $13.00 for large employer...Given the starting point was already well above the U.S. federal minimum wage level of $7.25 per hour, this gives some evidence as to what might happen if a much higher minimum wage was introduced (although as the authors note they probably overstate the effect of more modest minimum wage changes). Jardim et al. find that:
...the rise from $9.47 to $11 produced disemployment effects that approximately offset wage effects, with elasticity estimates around -1. The subsequent increase to as much as $13 yielded more substantial disemployment effects, with net elasticity estimates closer to -3...
In other words, although workers earned more per hour worked after the $11 minimum wage was introduced, they worked fewer hours so that the overall impact on their earnings was approximately zero. When the minimum wage increased further to $13, the effect on hours was greater than the effect on hourly earnings, leading to a reduction in overall earnings. Students of ECON100 will recognise that when demand is elastic (here the price elasticity of demand for labour was estimated at -3, i.e. elastic), an increase in price (here, the wage) is more than offset by a decrease in quantity demanded, leading to a reduction in total revenue (in this case, a reduction in total earnings for workers). Jardim et al. estimate that the overall effect included the loss of over 6,300 low-wage jobs at single-site employers (or approximately 10,000 jobs if multi-site employers are also included, although their dataset could not accurately evaluate the impact on multi-site employers).
One of the interesting things about this study is that the authors were able to reconcile their results with those of earlier work, which has generally focused on all employees in one or more low-wage industries (whereas this study limited consideration to only low-wage workers, defined as those earning less than $19 per hour - that is, those most likely to be affected by the increased minimum wage). Often the focal industry of earlier studies has been the restaurant industry. Jardim et al. show that these earlier studies "may have substantially underestimated the impact of minimum wage increases on the target population".
The second study is reported in this CEPR Working Paper by Claus Thustrup Kreiner (University of Copenhagen), Daniel Reck (UC Berkeley), and Peer Ebbesen Skov (Auckland University of Technology). This paper investigates the impact of the Danish youth minimum wage, where:
The average hourly wage rate jumps by DKK46, or about $7, corresponding to a 40 percent change in the wage level at age 18 computed using the midpoint method.
That's quite a substantial change when someone turns 18, and Kreiner et al. demonstrate a substantial disemployment effect, summarised in their Figure 1:
Notice that average hourly wage (in the left panel) increases significantly at age 18, while the employment rate (in the right panel) decreases significantly at that same age (along with a small drop off slightly before age 18, which may be explained by employers anticipating the increase in wage that would occur a few months later). When it comes to the elasticity:
We observe that wages are relatively constant around 90 DKK beforehand, and then increase to about 135 DKK after the wage change... we estimate that this 46 DKK increase constitutes a 40 percent increase in hourly wages.
...In our preferred specification... we estimate a 15 percentage point drop in employment, equivalent to a 33 percent decrease in the number of employed workers. In other words, the presence of the wage hike causes roughly one in three workers employed before 18 to lose their jobs when they turn 18. Combining the percentage change in hourly wages and in employment, we obtain the implied elasticity of -0.82...
That's the elasticity of employment, rather than hours worked. Once they also account for reductions in hours for those who remain employed, the elasticity increases to -1.1, which is eerily similar to that for the Jardim et al. paper (though in a completely different context). An elasticity of -1 implies that when the wage rate increases, total earnings pretty much does not change (because the decrease in hours worked would offset the increase in the wage rate).
Kreiner et al. then go on to show that the effect of age 18 is almost entirely driven by labour market exits (lost jobs) at, or just before, age 18, and not by a decrease in hiring. And finally, the effects of that job loss are persistent:
...by one year after job separation at age 18, only 40 percent of separated individuals are employed, compared to just over 75 percent of individuals who did not experience a separation. Even two years after turning 18, individuals who kept their job at age 18 are about 20 percent more likely to be employed than individuals who did not...
Both papers have a similar advantage over earlier work, in that they are able to use the observed change in wage rates for workers to compute the elasticity, rather than relying on an implied increase in wage rates proxied by the percentage increase in the minimum wage. Given that many workers affected by the higher minimum wage would have had wage rates that were higher than the original minimum wage, this means that the increase in wages is overestimated in those earlier studies, leading to under-estimates of the elasticity.
Finally, with increases in minimum wages we can be fairly certain that at least some workers are made better off (those who retain jobs at the new, higher, minimum wage), whereas others are made worse off (those who lose their jobs, or now work substantially fewer hours, at the new minimum wage). Both papers are silent on these distributional impacts, and do not have the data to adequately address them. But those distributional impacts are also important for understanding the impact of the minimum wage.
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