The Minimum Wage: Evidence from a Danish Discontinuity

In addition to the Seattle study, another minimum wage paper crossed my path this week and it takes a very different approach than much of the literature. In Denmark the minimum wage jumps up by 40% when a worker turns 18. Thus the authors, Kreiner, Reck and Skov, ask what happens to the employment of young people when they hit their 18th birthday? Answer: employment drops dramatically, by one-third.

A picture tells the story. On the left is measured wages by age, the jump up due to the minimum wage law is evident at age 18. On the right is the employment rate–the jump down at age 18 is also evident as is a bit of pre-loss as workers approach their 18th birthday.

The authors have administrative data covering wages, employment and hours worked for the entire workforce of Denmark so their estimates are precise.

Denmark has laws making age discrimination illegal but these do not apply when a young person turns 18 and firms may legally search for under or over-18 age workers.

A variety of restrictions mean that under-18 age workers can do less than adults (e.g. they can’t legally lift more than 25 kilos or have a driver’s license.) Thus, productivity increases at age 18, making the employment loss at this age even more dramatic.

The authors can’t tell for certain if workers are quitting or getting fired but there are few other obvious discontinuities around exactly age 18. Students are eligible for certain benefits at age 18 but the authors are able to look at sub-samples where this objection doesn’t apply and the results are robust.

In a section of the paper that adds important new evidence to the debate, the authors look at the consequence of losing a job at age 18. One year after separation only 40% of the separated workers are employed but 75% of the non-separated workers are employed. Different interpretations of this are possible. The separated workers will tend to be of lower quality than the non-separated and maybe this is correlated with less desire to have a job. Without discounting that story entirely, however, the straightforward explanation seems to me to be the most likely. Namely, the minimum wage knocks low-skill workers off the job ladder and it’s difficult to get back on until their skills improve.

Hat tip: Ben Southwood.


And so the obvious gets pointed out again.

Quick - someone alert Paul Krugman.

And Nick Hanauer.

...and Robert Reich.

This article leaves out the major reason why 18 year olds might work less! At the age of 18, students qualify for STIPENDS paid by the Danish Government. They spend more time getting serious with school studies and have less time for after school jobs.

This is not proof that "increased wages causes unemployment" !!!

Please read the post again as both the post and the paper discuss that issue.

In Norway apprenticeships is a tightly regulated regime, part of vocational high school. It's for a fixed number of months, where they pay something like 20% of a regular wage. The employer definitively can't fire at will with a deal like that, quitting for the apprentice is very costly (they forfeit their Master's letter, the reason they accepted the low pay in the first place). Nor could you just drop into such a job on short notice (say, from being fired from your fast food job on turning 18). This isn't Donald Trump style apprenticeships/corporate internships. Think more medieval guilds.

I don't know how different it is in Denmark. From a quick search, it seems it's funded differently, and lasts longer, but otherwise similar.

So, I don't immediately see how the lack of a drop in apprentice employment would rule out the stipends as a factor. Of course apprentices don't quit their low-paid jobs when they get a stipend. Apprentices aren't short-term employees.

"I don’t immediately see how the lack of a drop in apprentice employment would rule out the stipends as a factor."

Why would anyone?

Unfortunately, Mary has a point. To be meaningful, a discontinuity design must be such that the individuals on the left of the discontinuity are exactly the same of those on the right except for the treatment. There are literally thousands of reasons to believe that people at 18 years and one day are systematically different than those at 17years and 364 days. That's why the paper at best provides biased coefficients.

". . .Students are eligible for certain benefits at age 18 but the authors are able to look at sub-samples where this objection doesn’t apply and the results are robust."

I suggest you take a look at Figure 6 and the related discussion :)

"At the age of 18, students qualify for STIPENDS paid by the Danish Government."

Yes, Figure 6b on page 31 is "Workers Never Receiving Social Assistance"

The debate is over the size of the dis employment effects, not over the existence. If you are serious, not insult people who have honest disagreements with you.

Interestingly, if people around the age of 18 were a single block that just wanted to maximize average income for working and nonworking individuals, they would still want this minimum wage increase, since the workers that remained made 40% more. 140% (gain in wages) * (100%-33%) (loss in employment) = 107.8%. Overall, they make more money, it's just less evenly distributed among 18-year olds than it is among 17-years olds.

Interestingly they don't make more money. "[L]abor input (extensive and intensive margins) decreases by around 45 percent". Thus is 140%*(100%-45%) = 91%. They do note that the aggregate wage bill is "nearly unchanged". I guess a roughly 9 percentage point drop is "nearly unchanged. Sidenote: while I am happy they don't use decimals to give an false sense of accuracy, I love how the employment decrease is "33 percent" and the labor input decrease is "around 45 percent", as if the former wasn't an approximation.

Yes but should we force it considering:
1. Idle hand are the devils workshop.
2. Anyone working full time in the developed world is really not living in poverty. How I Live on $7,000 per year
3. Unemployment is depressing. The Grave Evil of Unemployment
4. People often learn skills on the job and BTW you would have to make internships pay minimum wage to fair.
5. Jobs integrate younger and older people and older people's life styles are better.
6. If you consider the difference in pay between the market rate and the min wage rate a tax, fair in my mind, the tax falls on employers of low wage labor in the short run and consumers of products produced by low wage labor in the longer run, why tax them more than others?
7. Many people are already working for less than minimum wage. WHy Drug Dealers Live with there Mom's
8. Black youth unemployment is already much to high.

I couldn't get past the point of dying laughing where you said "anyone working full time in the developed world is really not living in poverty" by citing to citing to some blogger who talks about his ultra frugal lifestyle of eating ramen every meal.

From the Q&A:

What’s your typical meal?
A very typical meal would be a salad from the garden (cucumber, tomato, lettuce, mesclun) with homemade thousand island dressing (vinegar+ketchup+mayonnaise, just try it, that’s all there is to it) followed with
pasta with a sauce based on beans, canned tomatoes, zucchini from the garden, onions, and olives. I douse this with hot sauce. For some strange reason, I’m famous for eating lentils. I did that when I was in grad school because it’s quick and easy but since my wife took over the cooking and I took over the dishes and laundry about seven years ago, this doesn’t happen anymore.

Although, this makes his gimmick obvious. He survives on $7,000/year by performing and consuming several thousand dollars of labor within his household.

I eat mostly pasta and tomato sauce in college.

If you have ample food to survive reasonably well, a few sets of decent clothes, and decent shelter, you are not in poverty. You may feel poor by American or west European standards, but you are not truly in poverty.

Well, having a place to live a food to eat pretty much leaves clothing and heat as the only items required to not be in poverty.
Full time at todays minimum wage would give you about double $7,000 after FICA and 2 weeks off.
One of my sons makes $11/hour and is doing great and saving a good amount.
I live in Honduras for a while where some folks working 40hours/week really are poor.

There are people who work fulltime and live in poverty, but it is rare. Typically people in poverty are in poverty because they aren't working.

The worldview of a hard-toiling poor and an idle rich may have been true at some time and some place, but it's not the case in current America.

"There are people who work fulltime and live in poverty, but it is rare. Typically people in poverty are in poverty because they aren’t working."

Where is you evidence?

Do you believe that the disabled will become employed at upper income wages if they simply look for a job hard enough? As in you will happily hire a worker with the mind of a 5 year old?

Should children work, perhaps work as victims of sexual predators, to get out of poverty?

Should half the population who have failed to move out of rural America move to wealthy suburbs where most people are working at upper income jobs because being homeless in such areas will ensure you get a high paying full time job quickly?

Should parents abandon their kids to work full time, or lock them in cars while at work, so they can work full time?

Maybe sell their kids to make the payments on a place to live in a high income suburb?

Here's data and analysis from the BLS:

"Full-time workers continued to be much less likely to be among the working poor than were part-time workers. Among persons in the labor force for 27 weeks or more, 3.4 percent of those usually employed full time were classified as working poor, compared with 14.1 percent of part-time workers "

That says about 5 million full time workers are working poor, living on a half or less of the median wage.

If 5 million people is "rare", then terrorism is for all intents non-existent, yet billions are spent every month by government because nonexistent terrorism is an existential threat to America.

3.4%. I knew it was less than 5% but not sure where. Thanks for finding that!

I think that refutes Daniel's claim pretty well as it accounts for 3.4% is out of the working population. That would make them a substantial proportion of the poor.

Elementary Statistician needs to re-check that calculation:
(140%)*(100% - 33%) = 93.8% < 100%

+1, to Elementary Math

People don't work to maximize the average income. People work to maximize their own incomes.
You do make a good point about the money being less evenly distributed, however. Effective minimum wage (and by effective, I mean a minimum wage sufficiently above the minimal market value of labor to matter) increases income disparity rather than decreasing it. I personally don't see income disparity as being in any way fundamentally immoral, but imposing that income disparity on some (those who lose jobs and lose the opportunity to develop skills) by government force to benefit others (those who get paid more, who may well outnumber those who lose their jobs, and therefore result in a net gain in votes for politicians) is highly immoral.

"the minimum wage knocks low-skill workers off the job ladder and it’s difficult to get back on until their skills improve"

If the text purpose would not be criticizing the minimum wage, this would be called "a nudge" to improve worker skills. This situation begs for a lifetime analysis, what's the optimal outcome? Young people that becomes 40 with 3 kids while still working in low skills jobs or temporary unemployment while 18 year olds are adaptable and can learn valuable skills?

EITC and other wage subsidies. Keep people in the workforce. You could even target a 35-hour workweek if you wanted to leave time for evening classes, but realize that most people at the bottom of the scale really don't want to go back to school.

A decent fraction people at the bottom don't want to work or improve themselves AT ALL if it cuts into evening/weekend free time or their hippie lettuce habit.

Although living in America's East Germany probably skews my sample more towards degeneracy.

There's no minimum wage law in Denmark. This is the result of sectoral collective bargaining. The 18-year olds should take it up with their unions.

There is little economic difference between a state imposed minimum wage and a union bargained minimum wage. They have identical economic effects. Consider an alternative of a widespread voluntary minimum wage. Same effect.

Well, there's some difference in who it covers. Far from everyone is covered by the union rules and it's often, as in Denmark, negotiated on a sector by sector and/or firm by firm basis.

But obviously union negotiated minimum wages can have a large impact too as the data shows.

I'd guess union wages cause redistribution among union and non-union workers. The distributive effects of min wages are likely somewhat different.

How much of this loss is attributable to the decision to attend university? Or what is the rate of college enrollment in Denmark? It seems like that can confound an 18 yo cut off and employment rates. This same questions applies to the rate of those employed one year later, too.

I was thinking the same thing:

- college
- military service
- higher opportunity with a HS diploma

I have no idea which if any apply to Denmark, but other thresholds at the same time period confound event studies.

Because 17 year olds who are going to go to college aren't in school?

I just meant that the transition to college is often a natural breakpoint for people in terms of decision to maintain employment, especially regarding the question of maintenance of employment at one year after. As an example--if employment rate is 50% at age 17 and 90% of Danish kids ( go to college--if you just assume that 50% percent of kids going to college (that is free, and a 1000/month living stipend is included), then the labor rate probably drops to the number we see above--

I guess some math might look something like: 250k people turning 18. So 225k will start college. 125k are working at the age of 17. I will assume the likelihood of working is equally distributed across the entire population--not necessarily true, but this is a quick calculation. So, of the 125k working at 17 (50% labor rate), 112.5k start college. If 30 percent of them decide to stop working (33.75k people) then the labor rate changes to 36%. That is at least plausible.

I am not saying the idea is correct, but in a country where 90% of people go to college that is paid for and you a stipend for expenses, I am surprised the topic was not mentioned in the paper.

Sorry-- typo in the last sentence: should read "college that is paid for and you receive a stipends". Apologies.

The authors show that the effect occurs "the month" the person turns 18. The return rate of workers may be affected by the university decision, but the job severing is not (unless all 18 year olds in Denmark have the same birth month and that is the same month in which 18 year olds would quit work to go to uni.

Good point. Thanks for the note.

Please notice the "Mary in Denmark" comment earlier in the comments, and Alex Tabarrok's reply to her. They have addressed your question previously.

A Schelling Point?

Yes, but people also take gap years and/or go to college at that age - the latter of which is heavily subsidized by the government. I'd be weary of taking too much from this.

college is heavily subsidized while they're paying their own way to go to high school? try again

Yes, sort of.

College and high school are both subsidized. Students are not paid additional money to attend high school. They are paid additional money to attend university (the stipend which is intended to ensure they have more time to focus on their studies, which serves both skills-building objectives and also inequality-reducing objectives by improving access to opportunity of those from lower income families).

The authors show that the effect occurs “the month” the person turns 18. The return rate of workers may be affected by the university decision, but the job severing is not (unless all 18 year olds in Denmark have the same birth month and that is the same month in which 18 year olds would quit work to go to uni or take a gap year).!

It is a funny graph. 16 year olds and 18 year olds have the same unemployment? But there is a surge 16-18?

There might be some Danish life patterns going on here that we don't know about. Internships or apprenticeships for 11th and 12th grades? Then less employment in freshman year?

I welcome a Danish perspective.

What is funny about it? Isn't that precisely what you would expect to see?

At 18 you'd still be in high school or vocational/technical schools/apprenticeships unless you skipped a year. Many Danish youths get part time after school jobs but they are heavily regulated. From she 13 you can bring out news papers and do other simple jobs. At 15 or when you graduate from lower secondary (folkeskolen) you can work jobs like cashier in a supermarket. At 18 restrictions like supervision and in working hours are lifted.

In my experience many shops and supermarkets thrive on having cheap staff for low skill work. They can easily train new staff when someone turns 18 and demand a higher wage. Some stay after 18 since it makes for more flexibility in tasks and working hours that may make up for the increased wages. But employers already have full time staff that command the same wages and have more experience so it makes sense to only keep the promising 18 yo, fire the rest and hire some at 16 again. Not a surprising finding.

What is interesting is that part time jobs for college students is huge in Denmark. Jobs that require some skills upon up too.

Here is an article on US trends. Our 16-18 employment rate is falling fast.

i suspect that this RD estimate will overestimate the effect of a regular minimum wage increase by quite some margin because in this case there is a close (to perfect) substitute (cheaper 17-year-old) available.

one could even be surprised that the effect is not bigger

For jobs like busboy there would be a strong incentive to cycle 17 year olds, which might not be bad. 18 year olds should be moving to skilled work.

"In a section of the paper that adds important new evidence to the debate ...": which debate? The notion that, other things being equal, an imposed increase in wages won't lead to people being sacked, or fewer people being hired, is surely bogus. Of course prices increased in that way reduce demand. To argue otherwise is a foolish as believing that absurd old story about why Ford raised his workers' wages. In the age of fake news it's a fake debate.

If, however, you mean that the debate is about how difficult it is to do empirical research that shows the effect in a reasonably unambiguous manner, against all the noise and confounding that tend to occur in economies, fair enough.

The graphs say a lot about substitution between two labor groups (pre and post 18 year olds) and just a little about the minimum wage. It does not say how total employment would go down if pre 18 year olds cost the firm the same amount as post 18 year olds, nor does it say what would happen if the government imposed a minimum wage so that the cost of hiring both groups went up by x percent. It does show the importance of substitution, which could mean the substation of capital for labor.

This is the important comment. Of course if employers can hire basically the same skills for less money, they will do that. The relevant question for minimum wage laws is what they do when the _cannot_ hire for less than a certain amount.

True, the decomposition of the effect into the substitution and income effects is probably needed here. The majority if not all would probably be a substitution effect since people under the age of 18 are cheaper to employ. The income effect would be a rise in prices and/or a drop in supply by the business which in this case probably wouldn't occur unless the supply of under-18 workers drops in Denmark. This is the exact decomposition of the min-wage debate which focuses on substituting for more automation and/or an increase in prices.

Agree, this was exactly the reaction I had. Has anyone addressed this critique?

As a tangent, this substitution logic is consistent with anecdotal observations that higher mandatory legal wages seem to go hand in hand with gray-market employment rising... Whether undocumented workers or just folks getting paid in cash for local jobs that can slip under the radar.

I'm confused how is this a valid identification strategy with respect to the minimum wage. The minimum wage isn't the only thing that is discontinuous at the age if the tasks they are legally allowed to do also change at the exact same age threshold.

This is definitely a really cool paper, the approach is creative, but claiming specific elasticities of the min. wage seems odd when you are identifying the causal interactive impact of these two things.

I only briefly skimmed the paper so I could have missed it but do they address this in the paper? Is there an existing literature analyzing discontinuities in the tasks you are allowed to do shifting (I'm sure there is)?

Ahh it doesn't matter. Minimum wage discussion are a perfect example of people just going with their priors regardless of what they see. I for one can say this has no bearing on my thoughts that minimum wages have modest dis-employment effects.

Simple solution obviously is not to have a big-jump, two-tiered minimum wage. This minimum wage practice is setup for a fall.

In Chicago (where I live) half of gang-age, minority males are in drug dealing street gangs because American born workers wont work for the "one-tiered" minimum wage. The federal minimum wage is now almost $4/hr below what it was in 1968 (adjusted) DOUBLE the per capita income later (see chart -- hope it loads better than last time). If we foretold Americans of 1968 this was going to happen what could they have conjectured: a comet strike, a limited nuclear exchange, multiple plagues? Simple loss of labor market and political bargaining power due to the banishment of unions did the trick.

(2013 dollars)
yr..per capita...real...nominal...dbl-index...%-of


"The federal minimum wage is now almost $4/hr below what it was in 1968"

The legal job market was exclusionary for women and blacks in 1968. There were plenty of those groups that had effective wages much lower than the listed minimum wage.

Are there controls for other things that happen at 18 that might impact employment? The do mention the student benefits but also say "a few other" factors contribute so controlling only for the student factor and claiming results are robust might be a bit premature. May well be solid per the logic of P-Q but that's only assumed here.

Also interesting that one sees something of a similar graph before and after 18 in terms of totals and slope.

It's amazing how everyone here is congratulating themselves based on a study that is obviously not measuring the same effect as increasing the global minimum wage across an entire market. This study explores the impact of workforce selection that have two different wage rates and EXIST SIMULTANEOUSLY. This is completely and utterly different from a market that has to make sense of a wage floor.

You guys need to go back to the drawing board in order to justify your exploitation and suppression of the working class. But keep at it! I'm sure you'll come up with something.

That is a key insight.

What this result actually says, is 'if population A has to be paid 40% more than population B population A will have a harder time finding work because employers will favor hiring from B'.

The political arguments about would surely be about solidarity and sector wide unionization.

Hrm that hadn't occurred to me. I was reflecting on regulatory price floors but you're right, that price floor can be negotiated through collective bargaining or labor action rather than laws.

Offering a job and having the job offer be accepted = exploitation and suppression?

"Exploitation and suppression of the working class." Talk about sanctimonious posturing.

"they can’t legally lift more than 25 kilos"


Mainstream economics Does not talk about this.

Huge coverup.

That's troubling, but it sounds like they recover relatively quickly. By age 24 the employment rate is back up again to the pre-18 level and still growing.

"By age 24 the employment rate is back up again to the pre-18 level and still growing."

That's 6 years of underemployment and lack of skill development at a minimum.

'That’s 6 years of underemployment and lack of skill development at a minimum.'

One could have a sneaking suspicion that this is 6 years of a government stipend involving studying, in the main. Including various varieties of something along the lines of internships/Praktika/apprenticeships/etc.

Actually it is two years; the scale is months after turning 18.

Besides as others pointed out it is a poor proxy for a minimum wage change applied to everyone.

I don't think you are reading the x-axis correctly. It's labelled "months since 18th birthday". So the point you are talking about is 24 months since 18th birthday. They are age 20, not 24.

At age 20, the cohort is back to where it was at age 17 in terms of employment rate. This doesn't seem like a big problem to me. That's a big transitional time in people's lives. It seems that the Danes have added one more item to the rite of passage to adulthood - they have a set of jobs that mostly people under 18 do.

Australia's youth and entry level wages would be a better test.

From age 16-20, minimum wages rise each year from 37% of adult minimum wage to 98% of adult minimum wage.

This is interesting, but as many people point out, it is likely that some portion of the change in employment rate at 18 is driven by the choice to attend college.

The fact that Danish university students receive a wage from the government while they study ( likely makes them less likely to work in University than while in High School, and may also affect their decision of whether to stay in the work force or attend University.

I also wonder if this minimum wage cutoff is designed with the intention to encourage University attendance: Faced with lower job prospects versus similairly qualified 17-year olds, 18-year olds might see the prospect of free University plus a monthly stipend as a more attractive option.

Very few people start college in the month they turn 18

It is interesting (but certainly circumstantial) that this wage increase is 40%, which is roughly the change in the Seattle minimum wage that exhibited a significant effect. Thay might be a pretty good starting guess at the upper bound of a threshold on the tipping point.

Also, note that the drop in employment is 32%, so the wage hike is beneficial for the group of all 18-year-olds, but probably does penalize the lowest skilled.

"Also, note that the drop in employment is 32%, so the wage hike is beneficial for the group of all 18-year-olds, but probably does penalize the lowest skilled."

Does nobody do math anymore?

(100-32)*1.4 = 95

So, no it's a not beneficial for the group.

How do they address the fact that young people turning 18 will be eligible for education stipends?

Figure 6b on page 31 is “Workers Never Receiving Social Assistance”.

They specifically look at this group and chart the gap. There's a clear and significant employment disjunction at the 18 year old's birth month. I'm unsure that Social assistance is the same as Education stipend. But does the Education stipend kick in the very month that you turn 18?

Yep, as long as you're in some form of school.

This is a very impressive and compelling chart
Yet 40% wage increase is huge - especially so for low skilled labor.
So it remains unclear (to me) that the impact is a linearly applicable to other ages or lower wage step up say 10%.
Knowing the marginal impact would clearly help designing public policy/ colllective choices which need to encompass a broader scope than simply 18yr-20yr unemployment such as education policy, labor productivity and poverty among other things.

Be careful--this is *not* a RDD as it uses assignment by age and has "unavoidable treatment". See Lee and Lemieux. There is no quasi-randomness in this. Not every discontinuity justifies a quasi-experimental approach.

The +18 wage isn't the minimum wage because there is a wage that is less than it i.e. the under 18 minimum wage. This study is measuring something other than an effect of a minimum wage - how substitutable cheaper 17 year olds are for more expensive 18 year olds possibly.

It's probably more a measure of wage stickiness or what proportion of beginers fall into a job they are worth persisting with than anything.

People should also see the Figure 2 graph. After age 18, total earnings shoot up. By age 20, they are about 3X the earnings at age 18. Likewise, although hours worked drop at age 18 rather sharply, they recover to their prior peak at around age 19 and are double their prior peak by age 20.

There is probably a dynamic effect. Once someone reach's 18 they must quit their low paying job, but then they find a higher paying one. Thus the elasticity coefficient calculated is not extremely useful for policy purposes.

So, many youth are priced out of the market by cheaper high school students just at the moment they are expected to go invest time in a specialization. And those who were doing activities which are worth the 40% premium at the over-18 rate are more likely to be working in a year's time.

Of the ones who stopped working, how many left fast food or similar jobs and went to study towards more specialized skills?

The sad thing is that this New Evidence is needed at all, considering that we had plenty of old evidence in the form of numerous studies around the globe that minimum wages depress low income employment. Also, the idea that you can raise the price floor of a product with no impact on demand contradicts the basic tenets of economics, and so the burden of proof should be on those who claim increasing wages have no effect on demand for labor.

Against all this we had one very limited study that looked at one industry in a state that had a modest wage increase, and that't all it took for 'everyone to know' that minimum wages have no effect on labor demand.

This reminds me of the rebirth of Keynesian Fiscal Stimulus, after decades in the doghouse,

Do you know why physicists will not suddenly discover that Newton was completly wrong? Because physics is a science. Real sciences advance on hard data and falsifiable, testable hypotheses. If your 'science' is constantly being overturned by new consensus based on the changing political inclinations of its intellectuals, you are doing it wrong.

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