"The claim that “for older workers, the two effects offset one another” is only true if you count the utility of keeping a job as offsetting the disutility of not being able to find one. I am surprised how quick people are to accept this is not only a neutral development but a positive one, arguing that less turnover in the labor market is a good thing. I am more concerned that more stable but harder to get jobs is not what you want during a time of problematically high long-term unemployment."
Adam makes a good point, but there is an important counterpoint. For those who do manage to find or keep their jobs after a minimum wage hike, the jobs will not only be more stable, they will be higher paying. These pecuniary benefits might accrue completely to those workers who hold onto their jobs, but they may not. Plenty may have friends or relatives who are long term unemployed to whom they may transfer resources. If we accept that minimum wage hikes represent a tradeoff of unemployment for some versus higher wages and job security for others, should we not also accept that it is, at least in principle, possible for some of the gains to be transferred to those who lose out. Depending on the elasticity of labor demand, it may even be possible for it to be a Pareto-improvement from the workers perspective. It would be interesting to see some data on this if any exists.