Quasi partial equilibrium algebra and a graphical analysis
Let:
Where w is the log real wage, and y is log income; log income is a function of the real low income wage bill. Labor demand determines the amount of labor employed.
Take the partial differential with respect to the minimum wage, wmin, and rearrange:
There is kind of a “multiplier” here, in that changes in the real wage bill spur income changes that affect the demand for labor and in turn affect the real wage bill. Note that each component can be signed; however, the overall responsiveness of the real wage bill to the minimum wage cannot unless other assumptions are made. For instance, if one eliminates spillover effects:
Then the impact of the real minimum wage on the real wage bill is given by:
Finally, if the elasticity of the wage with respect to the minimum wage is unity, then the real wage bill rises as long as the (absolute value) of the labor demand elasticity is less than one.
This analysis can be depicted graphically, as in Figure 1 below.
Figure 1: Low wage labor market, initial equilibrium and after imposition of minimum wage.
Initially, quantity labor supplied equals quantity demanded at N1. With the imposition of a minimum (real) wage, the wage rate rises from W1 to W2. In standard partial equilibrium analysis, there is excess labor supply Ns2 – Nd2. However, labor demand is derived; the income variable shifts out the labor demand curve (plausible if the marginal propensity to consume is high for low income households, and the wage bill increases).
Then, quantity of labor demanded rises to Nd3. While unemployment rises, employment also rises. Hence, the standard Econ 1 prediction that employment necessarily falls in response to the imposition of a (binding) minimum wage is a special case of a more general model.
Notice that the impact on the real wage bill, even when no spillover effect is present, is ambiguous. The original real wage bill is the orange shaded area, while the bill afterwards (once again ignoring spillover effects) is the lined area. Clearly, if demand is inelastic, then the wage bill will increase.
The larger the response of income to the low income wage bill, the larger the ultimate increase in the wage bill (to the dotted area).
It’s important to recall that the proposed $9 minimum wage will be eroded by some inflation by the time it is fully implemented, by end-2015. Figure 2 depicts the time series of nominal and real minimum wage rates.
Figure 2: Nominal minimum wage per hour (blue), and real (in Dec. 2012$) (red). 2015M12 real value assumes 2% inflation from 2012M12 through 2015M12. Source: about.com, BLS and author’s calculations.
More discussion by Wonkblog, [Thoma/MoneyWatch], as well as this 2006 post. Here are 2007 CBO calculations of the impact of a minimum wage increase, assuming net employment impact is zero. For a full information/partial equilibrium approach, see Keith Hennessey (whose logic implies that we should immediately drop the minimum wage to zero).
Jared Bernstein also refers to this very good study about minimum wages:
http://www.cepr.net/documents/publications/min-wage-2013-02.pdf
Thanks for the real / nominal graph.
I saw on Colbert that some FoxNews commenter named Bob something or other said he was glad to be paid 85 cents an hour when he was in school. I saw he was 18 in 1965 – when the minimum wage was actually $1.25. GIven where the minimum wage is now, he would actually be making less now without the requested rise.
Frankly, this is getting bizarre. Playing around with the minimum wage will not benefit American wage earners. The only thing that might help would be to understand why their wages have stagnated – something the economics profession seems incapable of grasping. The truly bizarre aspect is that the stagnation of the real wage is a simple, predictable and direct consequence of basic trade theory, infact, it would only be remarkable if it did not occur.
When a capital abundant country (home) opens trade with a capital poor country (foreign) in a scenario where foreign can produce at near the efficiency of home, then both countries restructure their economies to produce at alternate and mutually beneficial points on their respective production possibilty frontiers (ppfs). So far so good. Typically, the real wage in both countries will rise . The reason this can happen at home is that a fall in the nominal wage due to more capital intensive production is offset by the income effect of a fall in prices post-trade.
However, that is the end of the good news for the wage earners at home. If the capital/labour ratios between home and foreign are far apart then trade in goods cannot equalize factor prices. This will leave wages lower and rents higher in foreign. If capital is internationally mobile – which it surely is – then rentiers (the owners of capital) will transfer productive capital from home to foreign in response to the higher rents. In a static model, the ppf at home shrinks and the ppf of foreign expands. The real wage must fall as wage earners at home have less capital to work with. As well, there is an even greater reduction in the labour share of national income. This is because rentiers earn higher rents at home (capital is now more scarce there) as well as earning even higher rents from the capital transferred abroad. Consequently, there is a big shift in the share of national income going to the owners of capital. The economy at home stagnates as capital formation is offset by the constant drain of capital transfer.
International capital transfer is a slow process. It will take many decades before average wages and rents approach those of the developed countries. While this slow equalization occurs, we will inevitably face all the above consequences.
The only thing I cannot explain is why this simple explanation is barely even considered by economists. It is backed by mathematical theory as well as strongly confirmed by computer simulations of trade (my own sphere of interest).
There’s also some literature suggesting that an increase in the minimum wage increases worker effort and productivity at roughly one-for-one…at least up to a point.
The downside of a higher minimum wage is that it increases the opportunity cost of going to school, and to the extent that the minimum wage is applicable to teenagers this may not be a good thing over the long run.
One of the keys is the elasticity of the labor demand curve. If the labor demand curve is highly elastic, then the micro econ 101 textbook version is mostly correct. If the labor demand curve is inelastic, then the wage bill will increase. However, if the labor demand curve is inelastic then it is also true that the incidence of the payroll tax falls primarily on owners of capital rather than labor. So a cut in the payroll tax would be a windfall to capital. If you’re for a higher minimum wage, then it might be a little hard to reconcile this view with wanting an extension of the payroll tax holiday. Such is life.
Thanks for the CPI adjusted minimum wage graph. It might be interesting to add an average wage or per capita GDP adjusted graph. It is frankly shocking how much the relative income status of a minimum wage earner has changed over the past 2 generations.
While I suspect W2xNd2 will be much greater than W1xN1 (if the demand elasticity is > -1), moving from the market clearing wage of W1 to a supra competitive wage of W2 will cause slight drop in employment of N1 – Nd2. This would show up as an incremental loss in real GDP. Since the demand for minimum wage labor is somewhat proportional to GDP,there will be a very minor shift of the demand curve to the left.
OTOH, let’s suppose minimum wage workers are being paid a below market clearing wage of Wo (Wo
There are more factors to take into account with minimum wage analysis… one for example is social costs of labor.
Here are two papers on this (by Bruce Kaufman) …
http://digitalcommons.ilr.cornell.edu/cgi/viewcontent.cgi?article=1458&context=ilrreview
http://www.ilo.org/public/libdoc/nonigo/2008/461482.pdf
A higher minimum wage can increase economic efficiency. He talks about how a neoclassical approach falls short of understanding the complete dynamics of a minimum wage.
Since a sizable percentage of low wage workers are illegal workers, what type of impact does raising the minimum wage have on these workers?
There would be one supply curve for legal workers and to the right a supply curve that includes both legal and illegal workers. Both of these curves see the same demand curve. If raising the minimum wage causes either an increase in the availability of legal workers, or an overall job decline, I suspect it will be at the expense of illegal workers.
Continued from my first post–
OTOH, let’s suppose minimum wage workers are being paid a below market clearing wage of W0 (W0 less than W1). Raising W0 to W1 will increase employment by N1-Ns0. This would show up as an incremental gain in real GDP. Since the demand for minimum wage labor is somewhat proportional to GDP, there will be a very minor shift of the demand curve to the right.
Neumark and Wascher use the data and prior authors’ own methodolodgy to pretty much demolish recent research suggesting that increasing the minimum wage does not reduce employment.
http://ftp.iza.org/dp7166.pdf
WSJ – David Neumark has looked at more than 100 major academic studies on the minimum wage, and he says the White House claim of de minimis job losses “grossly misstates the weight of the evidence.” About 85% of the studies “find a negative employment effect on low-skilled workers.”
The minimum wage should be adjusted upward in small increments from time to time. However, why do it now?
Employers are facing health care costs that are rising faster than output prices.
Employers are facing the prospect of rising energy costs as Obama and the EPA try to purge cheap energy from the system. Creating an increase in the cost of low skilled labor coupled with Obama’s health and energy policies is a recipe for disaster when it comes to reducing the unemployment rate of the low skilled.
The BLS says that ~5% of workers earn at or below the minimum wage. Certainly a few more percentage points of earners would be impacted by the proposed 25% increase, but you really have to question the claim that a ~25% increase in the minimum wage will increase the demand for low skilled labor. It flies in the face of reason.
The BLS data also shows that the largest group of minimum wage earners are in the 16 – 24 age group. Teen unemployment is between ~25%-45% depending on demographic breakdown. Can anyone (Menzie?) seriously assert that raising the minimum wage by ~25% will reduce teen unemployment?
The data and majority of studies simply do not support a policy that attempts to reduce unemployment and poverty by increasing the minimum wage by 25%.
WSJ – The average income of a family with a minimum wage earner is nearly $50,000.
WSJ – According to data from the Employment Policies Institute, about two of every three minimum-wage workers also get a raise within one year.
Obama says he is for jobs, but his actions prove otherwise. This is nothing more than another attempt to buy votes and/or create a campaign issue.
The proper wage mechanism to address poverty is the Earned Income Tax Credit. It provides an incentive to work.
http://online.wsj.com/article/SB10001424127887323478004578302510280314712.html?mod=WSJ_Opinion_LEADTop
tj First, let me say that I’m pretty much of an agnostic on Obama’s proposal to raise the minimum wage. On even numbered days I support it and on odd numbered days I don’t. Today’s an even numbered day, so I’ll correct some of the things you said.
The BLS data also shows that the largest group of minimum wage earners are in the 16 – 24 age group.
That is not what the BLS data shows.
http://www.bls.gov/cps/minwage2011tbls.htm#1
According to BLS data the 16-24 age group accounts for 43.7% of minimum wage workers. The largest group of workers is the over 25 age group. Perhaps not a big surprise given that they also represent the largest group of workers overall. Now it is true that those in the 16-24 age group are disproportionately affected by the minimum wage, but that too shouldn’t be a big surprise. But what’s more important is that it really isn’t right to lump those in the 16-19 category in with those in the 20-24 age group. Both groups seem like babies to me, but there really are some important differences. Of those making minimum wage or less, 76.5% are not teenagers.
It’s also a bad idea to use national BLS data when looking at the minimum wage because it’s not always a binding constraint.
anyone (Menzie?) seriously assert that raising the minimum wage by ~25% will reduce teen unemployment?
Is reducing teen employment a worthwhile policy goal? I’m not so sure. Maybe lower tuition rates would be better.
The data and majority of studies simply do not support a policy that attempts to reduce unemployment and poverty by increasing the minimum wage by 25%.
You’re assuming away the very question that Menzie is raising. I think the evidence is ambivalent and inconclusive one way or the other. Which is why I’m an agnostic. Or are you arguing that the minimum wage shouldn’t be raised by 25%, but 15% might be okay? I think it makes a difference.
WSJ – The average income of a family with a minimum wage earner is nearly $50,000.
So two workers earning $7.25/hr working full time equals 2 x $7.25/hr x 2080hrs = $30,160/yr. Hmmm…so obviously the WSJ is referring to those cases in which there is at least one family member making substantially more than $50K/yr (remember, the WSJ is talking about the average of all families, so ~half of the families will make less than $50K.
The proper wage mechanism to address poverty is the Earned Income Tax Credit. It provides an incentive to work.
So you and the WSJ are recent converts to the EITC? So much for the 47% slacker argument. Again, I’m very sympathetic to expanding the EITC, but one of the downsides is that it does tend to subsidize owners of small businesses.
You also might want to read up on the literature regarding something known as the “efficiency wage.” There’s not much doubt that the “efficiency wage” is very real and an important contributor to productivity growth. What’s less clear is if raising the minimum wage brings in these efficiency wage productivity shocks or not. It may just be the differential rather than the wage. But that’s an open question.
One final thought. If you have to link to the WSJ to support your argument, then you’ve probably already lost.
Since the minimum wage is rarely raised and is eroded by inflation, not to mention the out and out wage theft practiced by such as Walmart, you might think we would be in a capitalist utopia of low wage driven growth and employment. Doesn’t seem to happen, why not?
2slugs
The largest group of workers is the over 25 age group.
Actually, I was referring to similar size age groups. But, even by your metric, it’s close. Look at Table 7 in your link. The distribution is almost 50/50 between 25 and younger and over 25. The fact that workers in the 16 – 25 group (a 10 year span) has as many minimum wage workers as the 25 and over group (a 50+ year span) demonstrates how concentrated minimum wage earners are in the younger age group. Combine that with the fact that younger workers have the highest rates of unemployment and it should be obvious even to you that Obama’s minimum wage policy is a gimmick. It won’t be long before he and his surrogates will be croaking about a Republican “War on low wage workers” or similar nonsense.
Hmmm…so obviously the WSJ is referring to those cases in which there is at least one family member making substantially more than $50K/yr
Yes, that’s the point. The vast majority are not near the poverty level. That’s another reason why the claim that raising the minimum wage will reduce the poverty rate is false.
“One final thought”, if you can’t refute Neumark and Wascher, then you’ve already lost. 😉 Take a look at that paper linked above, you might enjoy it.
I have long suspected the gain to workers from an increase in the minimum wage (the area from W2 to w1 at Nd2) is less than the total from lost employment (the yellow shaded area). Assessing the derivative effects without understanding the net revenue per an employee versus their cost strikes me as a bridge too far – without that evidence any conclusion you reach will be at best an educated guess.
tj You’re overstating the conclusions of the N&W paper. Their argument isn’t actually that higher minimum wages lower employment, but that studies demonstrating higher minimum wages have no effect on employment are flawed; therefore we shouldn’t just dismiss studies from an earlier era that did find a relationship. The reader is supposed to infer the conclusion that a higher minimum wage leads to higher unemployment.
But their critique of various papers is not without its own problems. For example, they consistently talk about “employment” effects, but in their regressions they use the unemployment rate. Not exactly the same thing, especially in the context of the minimum wage. Since the unemployment rate is a function of both the number of people unemployed and the number of people looking for work, we shouldn’t be surprised if a higher minimum wage increases the unemployment rate. We would expect that a higher minimum wage would induce the marginally attached worker (viz., middle-class teenagers) to enter the labor force. Another problem with their paper is that they calibrated the cross-county weights by using restaurant worker wages. This is a problem because in many of their 48 control counties restaurant workers are not typically the lowest skilled workers. For example, for the counties in the upper midwest as well as the Nevada/California/Oregon borders the low skill workers tend to be dominated by agri-business workers and not restaurant workers. Furthermore, most restaurant workers do not earn the minimum wage. For example, tipped employees are paid less (and in some states it’s quite a bit less) than non-tipped minimum wage employees. So their calibration assumptions do not match the real world. They also ignored the effects of BRACs on county employments (a topic about which I happen to have a great deal of detailed knowledge)…and by a strange coincidence many of the counties that they removed from Figure 5 (e.g., counties along the Michigan/Ohio/Indiana borders) were counties that saw very large employment gains during this timeframe due to BRACs. Or the Delaware/Pennsylvania/Maryland borders. And some of the counties that they retained in Figure 5.B were counties that saw very large employment losses due to BRACs. Or Bowie County Texas. Or as example, one of the counties in their calibration lost over 1,100 jobs with an average salary of $75K. Those are the kinds of exogenous shocks that they should have controlled for.
One valuable insight in their paper is their finding that a higher minimum wage tended to substitute rich white teenage employment at the expense of lower socioeconomic workers. This is something that I’ve always been concerned about. One interesting experiment might be to raise the minimum wage for those between ages 16-18. If this action lowered teen employment numbers (note I’m not talking about the teen unemployment rate, but rather teen employment numbers) and increased non-teen employment, then we might be able to conclude that the minimum wage does indeed reduce employment for the trial group. And perhaps we should use that fact to discourage teen employment.
2slugs
For example, they consistently talk about “employment” effects, but in their regressions they use the unemployment rate.
Did you even read the paper? They are using the same data sets as the authors who found no employment effects from an increaes in the minimum wage.
The unemployment rate is a control variable. The dependent variable is typically the employment to population ratio.
Their argument isn’t actually that higher minimum wages lower employment, but that studies demonstrating higher minimum wages have no effect on employment are flawed;
It’s clear now you didn’t read the paper. They certainly show the studies in question are flawed, but they also show that when the other studies are correclty specified, the other models produce the standard result that an increase in the minimum reduces employment.
For example:
Moreover, the evidence suggests that the linear state-specific trends used by ADR for these sample periods are influenced by the recessions in ways that apparently contaminate
their estimates of minimum wage effects on teen employment.15 More generally, our evidence shows that the estimated effects of minimum wages on teen employment are negative and significant
and,
(a) in most cases, there is little rationale for ADR’s choice to focus only on the withindivision
variation to identify minimum wage effects; and (b) when there is a good rationale for doing this,
the evidence shows negative and statistically significant effects of minimum wages on teen employment, with elasticities that are in or near the −0.1 to −0.2 range.
and
Our analysis suggests, however, that their methods are flawed and lead to incorrect conclusions.
and
Based on this evidence, we continue to believe
that the empirical evidence indicates that minimum wages pose a tradeoff of higher wages for some against job losses for others, and that policymakers need to bear this tradeoff in mind when making decisions about increasing the minimum wage.
The reader is supposed to infer the conclusion that a higher minimum wage leads to higher unemployment.
No, as shown above, they clearly state that the results show an increase in the minimum wage is associated with a decrease in employment.
tj: If you are familiar with academic debates, you will realize that no single paper is dispositive. In any case, here is an interesting point (A. Dube in The Atlantic):
So, before we make wholesale conclusions, I think we need to consider more closely the results in both authors’ papers. I for one plan to read them more closely before coming to a judgment (especially since one is published in REStat, and one is a working paper).
Part of the formula states that an increase in the wage bill increases the demand for low wage workers. The increase in the wage bill is mostly a transfer payment from consumers and, less so, from employers. If they have similar tastes to minimum wage workers (and they probably don’t), the net effect on the demand curve for the products produced by low wage workers would be zero. I have no idea what the divergence in tastes are between minimum wage workers and the consumers of their products, but I would guess that consumers of their products have a relatively greater preference for their products. In that case, the transfer would reduce the demand for the goods minimum wage workers produce. In any case, this is all, right now, an undetermined effect and most likely a very small effect.
tj As I said before, I think the minimum wage issue is far from settled empirically. Yes, all of the papers studied looked at the unemployment rate rather than the employment numbers; but the criticism has more bite when applied to the N&W paper. Why? Because the other papers found no increase in the unemployment rate, whereas N&W did find an increase in the unemployment rate. With an increase in the minimum wage we would expect to find that more marginal workers would enter the labor force, which would put upward pressure on the unemployment rate. But for those authors that reported “no change” this means that the number of employed must have increased along with the number of people entering the labor force. So while using the unemployment rate is a small problem for the other papers, it is a much bigger problem for the N&W paper.
My reading of the N&W paper is that it is primarily intended as a criticism of other papers that found no change in the unemployment rate. Way most of their effort is concerned with criticizing the methods of others. While they do claim that their take on the data shows that a higher minimum wage increases unemployment, they don’t make an extended defense of that claim. It’s more in the nature of “oh, by the way…” kind of thing. They are mainly interested in critiquing the methods of other papers and cautioning against overturning previous research indicating that there is a trade-off. They are on much weaker ground when they try to rerun the numbers using their “corrected” interpretation. As I said, I think their “corrections” have some serious problems. A lot of the counties they de-selected in Figure 5.B look cherry picked in the extreme. For example, the one MI border county immediately below Detroit is strongly affected by the automobile and to a greater degree the defense industries in that county. N&W exclude the MI and OH border counties below Detroit because they did not find any variation in the legal minimum wage. But does this make sense? Even though both MI and OH shared a common legal minimum wage, there is obviously a very significant difference in the effective minimum wage. For example, many of the defense firms on the MI side of the border were subject to Davis-Bacon wages, whereas those on the OH side of the border were not. So I would argue that N&W should not have excluded all of the counties along the MI, IN and OH borders. You could tell a similar story with Bowie County, TX, which they also removed from the original analysis. There are other problems with many of the 48 border county matches that N&W chose to retain. Towards the end of their time series there were very large exogenous negative BRAC related employment shocks (typically > $100M/yr) in Herlong County, CA, Scott County, IA, St. Louis, County, MO, Monmouth County, NJ and a bunch of others I could list. Did N&W control for these large employment shocks? No.
Menzie
You know better than I, but I think there is at least a 2 year lag between the time a researcher identifies a problem in a paper and is able to get a rebuttal in print. Thus, the working paper is all we have to work with.
If you are familiar with academic debates, you will realize that no single paper is dispositive.
85% of studies in the area find a negative relationship between the minimum wage and employment. If we use the same logic that is applied to the global warming debate to guide policy, then surely 85% agreement on the minimum wage issue is sufficient to guide policy. 😉
on average, for 21-44 year olds (the broadest group they studied), a 10% increase in minimum wages reduces poverty by around 3%.
That’s unfortunate for everyone else. The point of the 2011 study was that there is a lot of variation in policy outcomes within various demographic groups. Some win, some lose, but in total the net is a negative.
There is nothing wrong with periodically raising the minimum wage, but why now? Hiring is anemic and has stagnated at historically low levels. http://data.bls.gov/timeseries/JTS00000000HIR
Now is the time to stimulate hiring with policies that make it easier for firms to hire, not more difficult.
Obama is doing the opposite. He is increasing business expenses every chance he gets. He is raising benefits and energy costs. He wants to close loopholes. He sells these measures as stand-alone pieces of policy. However, when taken in sum, they are putting a cap on job creation.
tj Just because the WSJ claims 85% of the studies show the minimum wage reduces employment does not make it so. You are afterall quoting the print version of Fox News.
And as your own preferred paper pointed out, the general consensus on the minimum wage that prevailed 30 years ago is no longer the case. If you want to get to the 85% figure then you will have to include some very old studies.
I think the evidence on the minimum wage is a lot like the evidence on the effect of immigration on wages; i.e., it’s all over the ballpark.
In the years I have been following this blog, it is amazing how bad the economics is.
Why is it that people “need” to have the minimum wage work?
Economics has a basic theory that when prices go up demand declines and vice versa. This can be seen day in and day out. The evidence is irrefutable.
On Friday, leaked emails showed that the first part of February was a sales disaster for Wal-mart. Does anyone think they are going to respond by increasing prices? For sure, if Ben Bernanke ran the company it might, since he would argue, consumers fearing rising prices would move forward their spending. But like all profit motivated actors, since demand has dropped, Wal-mart will respond by cutting prices.
More to the point, this blog and its supporters pretend like they are in a scientific pursuit when their responses are more like a cult.
For an example of how science would tackle this issue, we only have to look at the recent example of a research team making a public appeal to help them sort out an anomalous research result. http://www.nytimes.com/2012/03/17/science/einstein-challenge-falls-in-retest-of-neutrinos-speed.html?_r=0 Seems their research resulted in a violation of Einstein’s theory that nothing can exceed the speed of light. Obviously, great glory would befall anyone who could find a violation. But what did these researchers do, they assumed that their results were wrong, and looked for problems with their study. When they could find none, did they declare victory and come up with some cockamamie theory as to why their experiment broke Einstein’s theory. No. They openly revealed their results and asked for help in finding out what was going on. No doubt, they hoped there were no problems and that they did discover a violation of the Special Theory of Relativity. Unfortunately for them, the wider community found a problem in the experiment.
Are there known violations of the price theory? Yes. They are called asset bubbles. They are well documented. From tulip manias, to stocks, to our very recent housing bubble, which the astute James Hamilton popped by using exquisite mathematically [expletive deleted – mdc] to prove there was no housing bubble. As such, they require a theory to explain why people buy more when prices go up.
The evidence that a minimum wage increases employment, reduces unemployment, or otherwise generally helps human welfare, simply does not exist in a manner which would cause one to throw out the fundamental price theory that rising prices reduces demand. It doesn’t matter if the analysis supporting basic price theory regarding the minimum wage doesn’t produce statistically irrefutable proof. As others have posted here, there are an overwhelming number of variables that influence the data that is looked at that can’t all be controlled.
Those who glom onto such pathetic evidence of positive returns to increasing the minimum wage can only have other desires. Exactly, what they are (and there are probably many), it most certainly isn’t to benefit the least among us. If I had to posit an overarching theory, it is probably less about helping those who have the least skills and more about sticking it to the “rich.” Because the theory that people will hurt themselves if it hurts others more to improve social standing is well documented through anecdotes and experiments.
2slugs
Umm…that 85% quote was a recent quote by Nuemark. Why don’t you quibble with Menzie when cites The Atlantic and a quote by Dube?
It seems popular press quotes that support your ideology are ok.