David R. Henderson  

Robert Murphy on Minimum Wage Studies

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Many economists who currently support large minimum wage hikes claim that the best research now shows that such an increase would not cause significant drops in employment. However, their conclusion relies on a dubious reading of the literature. Dozens of recent empirical studies show significant employment reductions from minimum wage hikes, with some of these analyses using the newer "case study" approach, as opposed to the traditional regression analysis. Furthermore, serious methodological criticisms have been leveled against even the best of the studies used to justify increases in the minimum wage. Finally, even on their own terms, the studies purporting to show that the minimum wage is benign can justify only modest hikes: these studies' own results are consistent with the claim that aggressive minimum wage hikes will cause many unskilled workers to lose jobs.
This is the second paragraph in this month's Econlib Feature Article "Large Increases in the Minimum Wage Are Likely to Destroy Jobs," by Robert P. Murphy.

Another excerpt:

However, in the present article, I focus on the narrow issue of the empirical estimates of the employment effect of a minimum wage hike. I cite the recent literature showing that this is still an open question even if we consider only modest hikes. Furthermore, even if we stipulate the results in the 2010 Dube et al. paper, we still should be wary of the popular minimum proposals, because the proposed increases are so large. Ironically, it would be more accurate to say that there is no evidence to justify large increases in the minimum wage.

One of the best paragraphs:
Now the interesting thing is that when we perform this exercise, it turns out that the lower bound falls smack dab within the traditional consensus. In terms of coefficients, the orthodox regressions found that the minimum wage variable fell in the range of negative 0.100 through negative 0.300, whereas (in the quotation above) Dube et al., in their preferred model, report that it's probably not worse than negative 0.147. This is neither the intellectual revolution nor the green light for policymakers that Krugman and others would have us believe.

The whole piece is excellent.

Comments and Sharing

COMMENTS (23 to date)
GinSlinger writes:

On the subject of minimum wage, I'd just like to offer an observation:

A few weeks ago I was working in Edinburgh, Scotland, at or near a governmental building. Outside, during my weeks there, the Scottish Socialist Party was collecting signatures for a ten pound per hour minimum wage.

Basically, that would be fifteen dollars an hour--the pound (no longer sterling) being roughly 1.5:1. Most of my expenses there made perfect sense in terms of dollars, i.e. a four pound pint, seven pound burger, etc.

So, in a very rough Big-Mac PPP comparison, the Scottish Socialist Party was asking for the near equivalent of what would be a ten dollar an hour minimum wage in the US. There may be some reasons to talk about Democratic Party proposals as socialist if they're 150% of what an actual socialist party is calling for.

magilson writes:


I can't imagine how telling a supporter of a $15/hour minimum wage in the United States that they're calling for more generous or more aggressive wage rates than anyone else, let alone a Scottish Socialist Party policy proposal, would do anything to deter their own policy position.

This is not about coefficients or regressions or evidence or analysis for every-day people.

Nick writes:

I have a lot of problems with this article. Let's start with the translation into English of Dube et. al.'s result.

"If we are discussing proposals to increase the minimum wage to $10.10, then Dube et al. are telling us that they are 95-percent confident that teenage employment will fall by no more than about 6 percent."

Let's put aside the fact that this is a basic statistical error (it has nothing to do with them being '95% confident'!)

Where did 6% come from? Assuming we're talking about states with the lowest minimum wage possible (7.25 / hour), a raise to 10.10 is a percentage increase of around 33% = (10.1 - 7.25)/(10.1/2 + 7.25/2), which with an elasticity of -0.147 is a lower bound of 4.8%.

(You appear to be using the current minimum wage as a baseline, which will produce an overestimate.) Similarly, for a raise to $15, the lower bound is around 10%, not 16%.

And at their actual estimates, the elasticity is positive. You omitted the negative sign in your quotation of the lower bound, which makes it seem as though you are looking at magnitudes, and so makes this fact ambiguous.

I have many more problems with this article than I have time to articulate. The only part of this article I agree with is

> ...in reality, the employment effect of the minimum wage is still an open question even for modest hikes.

Yes, of course! Even Paul Krugman endorses that viewpoint: "...There's just no evidence that raising the minimum wage costs jobs, at least when the starting point is as low as it is in modern America." It is a completely reasonable interpretation of the literature that, aggregating across many studies, we have failed to find consistent evidence on the sign or magnitude of minimum wage effects!

JLV writes:

Murphy can make the point in his title OR make the point at the end but not both. ALL empirical estimates of the effect of minimum wage hikes are local to the policy change full stop. So if you want to make an external validity claim, then be fair to both sides. There's strictly speaking no evidence that there are small or zero effects for a large change but there is also no evidence for large effects.

Daniel Kuehn writes:

Nick -
I'm not sure how substantial the 4.8% vs. 6% point is - the lower bound of the DLR estimate goes negative and the upper bound of the DLR estimate goes positive, which is what we'd expect of an essentially zero point estimate. I talked some with Bob about these bounds previously and I'm honestly a little surprised he leaned on that so heavily. But whether it's 4.8 or 6 the basic point still stands.

But I do agree very much with your last paragraph. It's interesting how Bob rhetorically flips things around from what I'm used to - I think of the no disemployment effect camp as being relatively conservative in the same way you do here. DLR highlight the big negative and big positive effects on certain county borders and Dube himself opposes a $15 minimum wage for precisely the reasons Bob raises here. It's the standard stance when you've got a null result.

David R. Henderson writes:

I’m sure that Bob Murphy will want to weigh in here, but here are my responses.
Where did 6% come from? Assuming we're talking about states with the lowest minimum wage possible (7.25 / hour), a raise to 10.10 is a percentage increase of around 33% = (10.1 - 7.25)/(10.1/2 + 7.25/2), which with an elasticity of -0.147 is a lower bound of 4.8%.
Bob was computing the increase from $7.25 to $10.10. You computed the increase from halfway between $7.25 and $10.10. I don’t know why.
(You appear to be using the current minimum wage as a baseline, which will produce an overestimate.)
Yes, that’s what he’s doing. Please explain why you think that using that wage gives an overestimate.
Even Paul Krugman endorses that viewpoint: "...There's just no evidence that raising the minimum wage costs jobs, at least when the starting point is as low as it is in modern America." It is a completely reasonable interpretation of the literature that, aggregating across many studies, we have failed to find consistent evidence on the sign or magnitude of minimum wage effects!
Failing to find consistent evidence is not the same thing as finding no evidence.
There's strictly speaking no evidence that there are small or zero effects for a large change but there is also no evidence for large effects.
Of course. There can’t be direct evidence of effects of large changes when we have never had such large changes. You’re misunderstanding what Bob is doing. He’s using Dube et al’s estimates, derived from relatively small increases in the minimum wage, to show that the effect of a large increase in the minimum wage could be large.

David R. Henderson writes:

P.S. I think you’re forgetting basic economics--the law of demand--and acting as if the fact that some evidence for small changes is inconsistent means that we should be equally agnostic about large changes. If you doubt that, ask yourself this: what would be the employment effect of immediately increasing the minimum wage to $30 an hour? Would you say that we can’t say much, or would you be willing to grant that probably tens of millions of U.S. workers would lose their jobs?

Floccina writes:

Do economist consider it a negative if a minimum wage increase results in some of the lowest skilled workers being replaced by people who would have waited for a better opportunity absent the minimum wage increase? That is some lowest skilled workers work less and some higher skilled workers work more because they are unemployed for a shorter periods of time because now they view that retail job as worth taking?

E. Harding writes:

The largest-ever Federal minimum wage increase (that of 1950), which only applied to workers covered by the Fair Labor Standards Act, roughly half of the U.S. work force, led to no significant impact on any kind of unemployment, including teen. 1950 was also as hard an economic boom as 2008 was a bust, though. Had the Federal minimum wage increase of 1950 applied to all workers, and not just half of them, I think we would have had a good natural experiment of the effect of large Federal minimum wage increases.

Kevin Erdmann writes:

E. Harding, in 2015 $, that MW hike took us from about $4 to about $7. Even if it applied to all workers, I don't think anyone today would expect a rise from $4 to $7 to have nearly the effect of a rise from $7 to $10.

Subsequent hikes after 1950 did take the minimum wage to higher levels, and did seem to coincide with drops in employment.

Nathan W writes:

With zero analysis, even if the market could rationally handle it, I would a priori think that raising the minimum wage to $15 is too far too fast for many businesses to absorb. Spaced over time, probably many (most? almost all?) would manage, but faced with such a shock, many small operators would flail their arms, close shop, and go look for a job (perhaps all that entrepreneurial effort wouldn't be worth it if they could just get a job that pays $15 an hour).

Fast food and the Walmart's would easily manage - they will increase prices as much as they have to in order to maintain targeted ROI or margins, and since lower income people will have more money to spend (assuming the aggregate wage bill increases) they might even enjoy an increase in business. But, they may invest in some labour saving technologies which will reduce employment.

Aside from the purely economic debate, I think there is also an important political aspect to consider. In asking for $15 an hour, this allows proponents of minimum wage hikes to achieve a stated policy goal (higher minimum wages) while allowing significant room for opponents to claim victory in holding this increase to some smaller amount, say, $10 an hour. In such a process of political negotiation, both sides get to claim partial victory, and both sides face a partial loss. So long as the losses and gains appear relatively symmetrical, no one will be rubbing anyone's face in the dirt.


Instead of having to fight for minimum wage hikes every few years, I prefer a policy that is opposed by the right even more strongly than occasional hikes: a minimum wage that is indexed to the cost of living. A simple version would be to achieve the goal of a constant minimum wage in real terms, adjusted for inflation. I would go one step further. I suggest that the minimum wage should be indexed to inflation + some moderate real gain, say, 1%. I justify this for two reasons. First, the productivity of labour in the complementary labour-capital aggregates increases over time as it is matched with more and better capital. A landscaper who uses modern tools is more valuable not only because he/she has better capital, but because the labour itself is inherently more valuable when competently paired with that capital. Second, as productivity increases more broadly across the economy, the ability to pay the hair dresser and gardener should also increases. Not only can we afford it (vague redistributional ideals), but perhaps some individuals are not well positioned in time to enter these fields which ended up being the locus of productivity gains (the 40-year old landscaper may find that it's "too late" to retrain for software engineering). As a member of society in general, why shouldn't they be rewarded with some of the broader productivity gains being enjoyed in society?

I think implementing a real (inflation adjusted) minimum wage is a no brainer. Why should the lowest wages always stagnate, necessitating the periodic fight to keep them oh so very high as they were 50 years ago?

The case for implementing an annual real (inflation adjusted) pay raise for the lowest earners in society would is harder to justify. Some will argue that investors in technology "deserve" those gains, not the workers. But is it not just, if the worker's contribution to complementary labour-capital aggregates is higher, for them to enjoy the share of gains attributable to labour?

The case for justifying an annual real (inflation adjusted) pay raise for the lowest earners based on broader productivity gains is harder yet. Why should they benefit from productivity gains in sectors altogether unrelated to their area of activity? Well, first I appeal to the basic preference expressed by many, for moderate redistribution in the name of fairness - but I'm not sure that wage policy is the right place to address redistribution per se. Again, I appeal to notions of justice though. Surely there is a bit of luck involved in entering into a field which becomes a locus of high productivity gains. Why shouldn't these gains be enjoyed at a societal level, including those on the very bottom rung?

Do I go too far in suggesting that the minimum wage should include a real (inflation adjusted) annual pay raise of somewhere in the range of 1%? Perhaps, perhaps not, but having made this case, does it not seem exceedingly reasonable that minimum wages should at the very least keep pace with the cost of living?

john hare writes:

Nathan W

The problem I have with your scenario is that redistributing my productivity gains to an uninvolved third party tends to discourage me from trying as hard for those gains, so the consumer loses.

Nick writes:

@David R. Henderson

We could take the original or the final value as the baseline. In the latter case it's only a 4.1% change. In the former it's a 6% change. The discrepancy comes from the fact that elasticity is a measure of curvature of a continuous function. The actual percentage change is somewhere between 4.1 and 6, but requires calculus to compute exactly. For small changes it's approximately midway between 4.1 and 6, which is why most economics textbooks give the midpoint formula I used. I agree now with Daniel Kuehn though that this isn't very important.

But Bob Murphy makes quite a lot out of the statement that we're '95% confident' that a raise in the minimum wage to 15$ will lead to at most a 16% drop in teen employment. This is a misleading way of characterizing the paper. The true number is closer to 10%, we're not '95% confident' about anything, and phrasing it that way obscures the fact that the real message is that the point estimate is basically zero. Bob Murphy could just as easily translated it into English as follows:

If we increase the minimum wage to $10.10, then Dube et al. are telling us that they are 95-percent confident that teenage employment will rise by no more than about 6 percent. If, instead, we consider the more aggressive proposals to raise the minimum wage to $15 per hour, then Dube et al.'s results assure us with 95-percent confidence that teen employment will rise by no more than 16 percent. (!)

Do you see that this is a misleading way of translating into English? It makes it sound like Dube et. al. are telling us that they found employment will rise, but by no more than 16%.

Anonymous writes:

Is it not possible - maybe even likely - that employers will respond to minimum wage increases by substituting higher wages in place of non-wage benefits, leaving workers no better off?

Is it not also possible that, to the extent that the work part of low wage work is preferable to the work part of slightly higher wage work, increasing the wage of the former to that of the latter will encourage higher-skilled workers who would otherwise have done the latter to take the place of the lower-skilled workers who would have done the former?

Maurice de Sully writes:

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Nathan W writes:

john hare - point absolutely accepted. I hadn't been considering that, and it significantly weakers the ethical case. I think the weaker two "demands" in the argument are still pretty valid - for a) at least a constant real minimum wage, and b) perhaps that some real increases are also reasonable to reflect the higher value of labour in the capital-labour aggregate.

Anonymous - minimum wage workers almost never receive additional non-wage benefits.

An additional comment on the article itself - In this context, it seems ridiculously more relevant to focus on the confidence interval than the 95% threshold. Having studied quite a lot of natural sciences in undergrad, when I started higher level study in economics, I often complained that economists too often focus on the threshold and average effects, whereas it is standard practice in "good science" to include the error bars on almost every graph. I had forgotten about this, but I think it's a really important issue.

ThomasH writes:

Rather than just be skeptical about a "large" increase in the minimum wage, why not just plunge in and analyze one, say the President's. Using the parameter estimates thought best, how many people will loose/not gain jobs, how much income will they loose, how much income will job retainers gain? What increase in the EITC could give the same net income gain? Point estimates and confidence intervals.

Bob Murphy writes:


You are raising two separate objections. Let me deal with them separately.

First, regarding the use of elasticities. The typical way to report something like this is to say, "A 10% increase in the minimum wage will lead to a 1.47% drop in teen employment."

So if the minimum wage is currently $10 and they raise it to $11, and teen employment is currently 1 million, wouldn't that imply a drop in teen employment of 14,700 workers?

I understand what you're talking about, when they do stuff like compute price elasticity of demand and they use a midpoint formula, but I don't think that's what goes in a typical regression when you take logs of all the variables and get your OLS coefficients.

For example, try in Excel doing something goofy like having length in meters regressed on length in feet. I think you'd find that a 10% increase in length in meters corresponds to a 10% increase in length in feet.

And yet, if the length in meters of an object went from 1000 to 1100, then I think you'd be telling me that the length measured in feet would actually only go up 5%, because I need to take the midpoint as the starting point.

If you think I'm wrong, please spell it out, because obviously I want to get this point right. But I haven't been convinced yet that I did something wrong with those numbers.

Bob Murphy writes:


Regarding your more substantive objection, I would agree with you that if I merely took their positive coefficient and then "translated" it into the stuff about 95% confidence of a loss no great than such-and-such, then I would be misleading the reader.

However, *they* focused on the negative lower bound. It's not only in the quote I put in the paper, it's also in their introduction, right on page 1, in the fourth paragraph. So Dube et al. certainly thought that it was very important to show people they had "capped" how bad the negative values could plausibly be.

Last thing: You said above that I didn't include the negative sign, and that I was therefore misleading the reader. Actually, I wrote out the whole word "negative" to make sure people saw it; I was afraid an actual negative sign might be too small. Look again at the quotation in David's excerpt from me; the word "negative" appears all three times.

Nick writes:

@Bob Murphy

Regarding elasticity:

Here's a stark way of putting it: Let's say the minimum wage is $5, and the employment elasticity is -1. Let's say I raise the minimum wage to $15. By how much will employment fall?

Using your method, it will fall by

-1*(15 - 5)/5 = -200%.

But employment can't fall by more than 100%. The issue is that as you start raising the minimum wage variable, the employment variable starts falling, and so the baseline shifts downward continuously. The 'average' baseline is somewhere between 5 and 15, computing it exactly requires calculus. Using the midpoint is a rough approximation, using the original value is an overestimate.

Regarding the more substantive stuff:

You're right that you included the word negative in the quote. My (very small) issue is that you did not include it in your excerpt from Dube et. al. Since there is a convention of reporting the magnitude of demand elasticities, this makes the sign of the numbers ambiguous.

Finally, I suspect I will not convince you that your translation into English of the paper is misleading. So I'll just say this:

Who is the intended audience for your article? Not economists, who will not be convinced by sentences like 'We are 95-percent confident that employment will not fall by more than 16%'. Not laypeople who already support the minimum wage and presumably do not find esoteric econometric debates particularly compelling. Am I the audience? I think the minimum wage is a terrible policy. So I find it strange and aggravating that so many opponents of the minimum wage insist on opposing it on such shaky theoretical, statistical, and rhetorical grounds.

Anonymous writes:

@Nathan W

"Anonymous - minimum wage workers almost never receive additional non-wage benefits."

Perhaps I have a broader definition of non-wage benefits than you. What about work cafeterias? Employee discounts? What about everything that you could classify as "a nicer working environment", from frequently cleaned staff toilets to not being pushed to their absolute limit by their manager?

BeccaB writes:

I believe that aggressive hikes in the minimum wage would do more harm than good. The reason it seems like a good idea is because of the outrageous cost of living. Minimum wage is meant to allow a person to keep a house, transportation, and feed themselves. $7.25 an hour will not do that. However, raising the minimum wage to $15 an hour will not help. Raising minimum wage will only bring the cost of living up.

Not only that, but it would cause a significant decrease in jobs available for unskilled labor. Many teenagers gather valuable skills and maturity from working, but no business owner wants to pay $15 for someone who has no idea how to do a job. The value of college degrees would increase and therefore the cost of University would rise. Fewer people would attend college and we would enter a world with an uneducated populace.

Bob Murphy writes:


Thanks for alerting me to the missing minus sign in the quotation from Dube; that was unintentional. They put it back in.

Regarding your other issues:

==> Now we have each offered a reductio ad absurdum to show the potential problem with how the other guy wants to use a reported elasticity. (Note that with a sufficiently large increase in the minimum wage, even using your midpoint approach would "predict" a 200% drop in employment.) I am still not convinced that your approach is how most economists would apply such an elasticity in the real world, but maybe it is.

==> You ask who the audience is, since (you claim) no economist would be moved by my shaky arguments. Well, *I* liked them, and David liked them, and we're both economists. The graduate student here at Texas Tech was surprised when I first pointed out to him the point about the left end of Dube et al.'s confidence interval. He doesn't yet have a PhD in economics but he will eventually, so I'm going to count him too.

The point is, a lot of professional economists are skeptical of the "new" minimum wage research, because they find it hard to believe that across numerous episodes and in the long run, making unskilled labor a lot more expensive will induce employers to hire more unskilled workers. But they don't have the time to go wading through the literature, to see if people like Krugman are right in how they describe it. So yes, I think there are some professional economists who would like articles like this one.

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