David R. Henderson  

Optimal Minimum Wage?

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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?


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CATEGORIES: Labor Market



COMMENTS (21 to date)

Great post! Any chance they mean Kaldor-Hicks optimality, though?

Andy writes:

They explicitly say that on net the higher paid workers would be unaffected even with higher taxes because of the stimulating effects of the lower minimum wage on low-skilled employment and thus the high-skill workers' marginal product and wage. And so, a Pareto improvement.

BJ Terry writes:

It seems particularly dubious to apply efficient rationing in this situation given that (1) people who are at the bottom of the labor food chain are those least likely to be fully-rational utility maximizing agents, and (2) if there is any deviation from rationality in these populations, you would actually expect the opposite effect. People who have the least producer surplus from a job are those who are very nearly qualified for work that pays more than the minimum wage, so they are the highest-value/highest-paid workers before instituting the minimum wage.

David R. Henderson writes:

@Jonathan Finegold,
Great post!
Thanks.
Any chance they mean Kaldor-Hicks optimality, though?
Possible, but you would have expected the editors and/or referees to catch that mistake.
@Andy,
They explicitly say that on net the higher paid workers would be unaffected even with higher taxes because of the stimulating effects of the lower minimum wage on low-skilled employment and thus the high-skill workers' marginal product and wage. And so, a Pareto improvement.
I missed that, but thank you.
To the substantive point, I'm sure they can build a model that way. I doubt it has much to do with the real world. The only taxes I know of that could relatively easily single out high-skilled workers are the Social Security tax and the Medicare tax. The income tax is a tax on high-income people but that includes people who are not working and yet making substantial income. But even aside from that, it's hard to believe that lowering the minimum wage would increase marginal product just enough for all high-skilled workers, as would be required for a Pareto improvement.

Charley Hooper writes:

Interesting post and I liked the YouTube clip.

I agree with BJ Terry's last point. And, if anything, Lee and Saez appear to have it exactly wrong.

With a minimum wage law, low-value employees cost the same as high-value employees (as long as they all get the same minimum wage). If the minimum wage causes jobs to be lost and therefore there are fewer jobs overall, the employees most likely to lose their job or not be hired in the first place are those with the least value to their employers. We would also expect that these employees would be on the low side on the supply curve, not the high side, because they have few other opportunities.

So I would conclude that the workers with the greatest producer surpluses would be the ones losing their jobs or not getting jobs due to the minimum wage law.

Jeremy writes:

If the efficient rationing assumption does not hold, wouldn't the case for its undesirability indeed be strengthened because it would suggest that the conventional model underestimates the deadweight loss resulting from the minimum wage?

David R. Henderson writes:

@Charley Hooper,
If the minimum wage causes jobs to be lost and therefore there are fewer jobs overall, the employees most likely to lose their job or not be hired in the first place are those with the least value to their employers. We would also expect that these employees would be on the low side on the supply curve, not the high side, because they have few other opportunities.
I was working within their model in which the workers are homogeneous to this employer, although clearly, given their different supply prices, not to other employers. If workers aren't homogenous, you can't draw a demand curve.
But I think you make a good point. In the real world, there's a lot of heterogeneity and the workers with higher supply prices also probably have, on average, higher productivity. So that does argue for your point.
@Jeremy,
If the efficient rationing assumption does not hold, wouldn't the case for its undesirability indeed be strengthened because it would suggest that the conventional model underestimates the deadweight loss resulting from the minimum wage?
I'm not sure, because I'm not sure what the conventional model says about deadweight loss. Presumably that's in the Lee and Saez (2008) article that they cite. Most economists notice that a binding minimum wage causes people to lose their jobs and we stop our analysis there, without going into measuring welfare losses.

Bill writes:

I just checked and Journal of Public Economics charges $1800 to the author of accepted papers for publication. Perhaps the high price makes the journal a kind of vanity press and drives out high quality papers.

David R. Henderson writes:

@Bill,
I just checked and Journal of Public Economics charges $1800 to the author of accepted papers for publication.
Wow!
Perhaps the high price makes the journal a kind of vanity press and drives out high quality papers.
No. The JPubE is thought of by most economists as a very high-quality publication. The vast majority of economists, including me, would love to get a piece accepted in it. So essentially what the publisher is doing is charging for shelf space.

Pajser writes:
"We're perfectly free to make any deal that government allows businesses to make with us."
The citizens own the country. If you want to do any business in our country, you should ask for permission first. You cannot make the rules on your own.
Pajser writes:

Wrong post, sorry David.

Walter Wessels writes:

If you believe there is a social utility function, that the government knows what it is, and that it can compare utilities, then there are a lot of ways to increase social utility far more efficiently than the minimum wage. Using the minimum wage is pure Rube Goldberg stupidity in this case. There is one main reason one would consider the minimum wage as a way of helping the poor: the voting public believes it won't have to pay the cost of raising wages. Also involved is the primitive belief that employers are responsible for workers, apartment owners are responsible for renters, and so on. In contrast, an alternative is that "society" is responsible and should be willing to bear the taxes needed to help the poor.

Manfred writes:

I confess I did not read the paper.
I do not have a ready link to JPubE, unless I physically go to a university library.
Thus, I go by what Mankiw and David say.
Mankiw points out Assumption 1 in the paper.
Like Mankiw, I believe this assumption is very strong. But I would go further, this assumption ALMOST assumes the outcome, it seems to me.
Then, they probabably clothe everything in terms of equations and elasticities (typical Saez modus operandi), and voila, they get an optimal min wage. With assumption 1, they generate the optimal min wage.
The trick would be to generate one *without* that assumption. Not sure this is possible.
But, Saez IS the editor of JPubEc, and thus he can publish whatever he wants in his own journal.

David R. Henderson writes:

@Manfred,
The trick would be to generate one *without* that assumption. Not sure this is possible.
Manfred, Check out my second comment above. They show that without that assumption, the optimal minimum wage is zero.
But, Saez IS the editor of JPubEc, and thus he can publish whatever he wants in his own journal.
Unless the web site is out of date, that's false. He is an advisory editor. Certainly that helps get him published, ceteris paribus, but that's very different from being the editor.

steve writes:

Why do you assume that employers will randomly get rid of workers? Certainly not what I would do with my employees.

Steve

David R. Henderson writes:

@steve,
Why do you assume that employers will randomly get rid of workers? Certainly not what I would do with my employees.
Because I'm working within their other assumptions. In their model, workers have the same productivity.
Like you, I would not do that with real-world workers. As I pointed out in my comment above, in response to Charley Hooper, Charley is right that the ones with the highest opportunity costs are the ones whom the employer would most likely keep, which is the opposite of the authors' assumption.

Manfred writes:

David, thanks, I do stand corrected. I was under the impression that Chetty and Saez were the editors now of JPubE.

ThomasH writes:

I always thought that the justification for a minimum wage was as an nth best way to redistribute income from higher income forks to those who are still employed after the minimum wage takes effect, the loss of income of those who lose jobs (cross your fingers and hope it's not many and that means tested programs keep them from falling too far) being one of the reasons it is an nth best policy rather than a first best policy.

Interpersonal comparison of utility are, of course, impossible, but we all do it all the time, anyway.

MikeM writes:

While I recognize that some economists may be knowledgable, rational and forthright in regards to their output, it is papers like this that make me regard academia as a form of clown college where people have gone from deriving a conclusion from the facts to the selecting facts and creating assumptions in order to "prove" their foregone conclusion.

rvman writes:
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.

This is pretty standard - it is the implication of calculating deadweight loss from a regulatory act as the area between the supply and demand curves, between the equilibrium quantity and the actual, post-intervention quantity. For that matter, the assumption of comparable utilities is implicit in the standard analysis as well.

The social welfare function favoring low-skill folks over high-skill is a pretty straightforward implication of the standard model with its diminishing marginal utility combined with the comparable utility assumption - an additional $1 to Bill W, the homeless guy who has few of them, is very likely more utility-creating than an additional $1 to Bill G, the software magnate who has many of them already.

David R. Henderson writes:

@rvman,
For that matter, the assumption of comparable utilities is implicit in the standard analysis as well.
No, it's not. The standard analysis adds dollar values, not utilities.
an additional $1 to Bill W, the homeless guy who has few of them, is very likely more utility-creating than an additional $1 to Bill G, the software magnate who has many of them already.
Although I agree with you that the intuition for this is strong, there is no way to make interpersonal utility comparisons. Utility is ordinal, not cardinal.

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