Optimal Minimum Wage?
David Lee of Princeton University and Emmanual Saez of University of California, Berkeley have an article in the Journal of Public Economics titled “Optimum Minimum Wage Policy in Competitive Labor Markets.” It has two strange results, one that I understand and that depends crucially on a strong assumption that they don’t even attempt to justify and the other that I don’t understand unless the concept of “Pareto improvement” has changed dramatically. Along the way, though, they admit something that has been at issue lately: the effect of the minimum wage in competitive labor markets.
Start with the last point, the effect of the minimum wage in competitive labor markets. Go to their Figure 1 and you’ll see the kind of graph the vast majority of us economics professors draw in class: a labor market, pre-minimum wage, in equilibrium in which the amount of labor supplied equals the amount demanded, with a minimum wage above the equilibrium wage that causes there to be less employment.
That graph alone is comforting for those of us who were wondering whether the consensus has frayed about the issue of whether the minimum causes there to be fewer jobs. Their figure supports that consensus: there are fewer jobs.
It’s possible that many of the economists who doubt whether the minimum wage destroys jobs have in mind, not a competitive labor market, but a monopsonistic one. In the latter case, a carefully set minimum wage that is above the free-market level could actually increase employment.
Anyway, on to Lee and Saez’s results. They show that under certain conditions, introducing a minimum wage increases social welfare. I want to highlight three assumptions that get them to this conclusion. One is that the government has a “social welfare function” in which it puts a higher weight on the utility of low-skilled workers than it does on the utility of high-skilled workers and owners of capital. The second is that somehow we can make interpersonal comparisons of utilities, even though we can’t.
The third assumption–the strong one I mentioned above–is that the workers who lose their jobs due to the minimum wage are the ones who get the least producer surplus from the jobs they would otherwise have had. In graphical terms, they are the ones who are highest up on the supply curve.
There is no good reason to make this assumption. It’s more likely that the workers who lose their jobs are randomly distributed along the supply curve. You might argue that the workers with the most producer surplus will “fight” hardest to keep their jobs, possibly telling the boss that if he keeps them, they will work extra hard. That’s possible. But then Lee and Saez would have to put that in their model. For one thing, that would reduce these workers’ producers’ surplus and, because they admit that their model depends on their previous assumption, the results would not necessarily be the same as the results they report.
Greg Mankiw highlights the following quote from Lee and Saez:
Finally, the desirability of the minimum wage hinges again crucially on the “efficient rationing” assumption. Under “uniform rationing”, where unemployment strikes independently of surplus, the minimum wage cannot improve upon the optimal tax allocation, a point formally proven in Lee and Saez (2008). Indeed, with efficient rationing, a minimum wage effectively reveals the marginal workers to the government. Since costs of work are unobservable, this is valuable because it allows the government to sort workers into a more socially (albeit not privately) efficient set of occupations, making the minimum wage desirable. In contrast, with uniform rationing, as unemployment strikes randomly, a minimum wage does not reveal anything about costs of work. As a result, it only creates (privately) inefficient sorting across occupations without revealing anything of value to the government. It is not surprising that minimum wages would not be desirable in this context. (italics added by DRH)
Greg says it well, writing:
Rather than providing a justification for minimum wages, the paper seems to do just the opposite. It shows that you need implausibly strong assumptions, such as efficient rationing, to make the case. I cannot see any compelling reason to believe that in the presence of excess supply of workers, the market will somehow manage to efficiently ration the scarce jobs.
I would add one other part that Greg does not mention. In one section, Lee and Saez write:
A Pareto improving policy consists of reducing the pre-tax minimum wage while keeping constant the post-tax minimum wage by increasing transfers to low-skilled workers, and financing this reform by increasing taxes on higher paid workers.
Hmmm. Recall that a Pareto improving policy is one that makes at least one person better off without making anyone worse off. With an increased tax on higher paid workers, can you think of some people who would be made worse off? Anyone? Anyone? Bueller?