Category Archives: Labor Economics

Rudimentary Foray into the Minimum Wage & African-American Unemployment

A commonly cited cause of relatively high African-American unemployment rates is the minimum wage. This argument is often made by libertarians. To detractors: it’s not just white, middle-class males who argue this. Walter Williams is well known for making the case — see his book, Race and Economics. Thomas Sowell, as well. The relationship is intuitive, if you assume that African-Americans, on average, are less productive than whites (and other ethnicities/races with lower unemployment rates) and perfect competition is the best model to apply to low-skill labor markets. My prior is that binding minimum wages do reduce unemployment, and so I’ve too repeated the argument, most recently today.

Knowing that intuition is deceiving, I want to develop a model to test — nothing too fancy, but not necessarily primitive, either. I don’t have that model yet. I’m looking at what data is available, what data is the best to use, and how I should manipulate the data, based on the model (e.g. should I compare rates of change or levels? what should be the functional form?).

In the meantime, here is the quick and dirty result, from the data I do have. All data is for California, including the African-American unemployment rate (BLS) and the inflation (CPI, less food and energy) adjusted minimum wage. The two compared,

Percent Change Minimum Wage v Percent Change African-American Unemployment (California)

The black trendline includes all data points (the blue diamonds); the red trendline excludes the highest blue diamond (-0.01942, 0.1963). The R2 are .0365 and .0311, respectively. Very low. Indeed, percent change in the minimum wage is not statistically significant. Also not statistically significant is the effect on the inflation adjusted minimum wage on the unemployment rate, and neither is the effect of ln(adjusted minimum wage) on ln(unemployment rate) — for those who may not know what the difference is, this last one measures elasticity; i.e. a one percent change in the real minimum wage causes a percent change in unemployment equal to the coefficient estimated for the former.

A “quick look” suggests that maybe the relationship between the minimum wage and African-American unemployment isn’t so obvious (or intuitive), after all.

CEPR Engages in Semantics

Reporting on the CBO’s recent study, claiming that the planned Federal increase in the minimum wage will lead to a loss of 500,000 jobs, CEPR writes,

The CBO projections imply that 500,000 fewer people will be employed at low wage jobs. It did not say that 500,000 people would lose their jobs. This is an important distinction. These jobs tend to be high turnover jobs, with workers often staying at their jobs for just a few months. While there will undoubtedly be cases where companies go out of business due to the minimum wage hike (many small businesses are always at the edge, so anything can push them over) the vast majority of the lost jobs are likely to be in a situations where businesses don’t replace a person who leaves or don’t hire additional workers as quickly in response to an uptick in demand.

The evolution of my reaction,

  1. When I first read the brief, yesterday, I thought that CEPR’s writers were trying to make the costs sound less costly than they actually are;
  2. Then, I started writing a post, and in the process of writing I realized that there is a good chance I was jumping the gun. So, I re-read the CEPR report and decided that they have a point (I’ll specify what made me re-think my position in a little);
  3. Today, motivated by this Intelligence Squared debate on the minimum wage, I decided to re-read the CEPR study, and I now find myself somewhere in between my initial reaction and my consequent reconsideration.

In reference to step (2), here is the part of the CEPR brief that caused me to reconsider,

With 25 million people projected to be in the pool of beneficiaries from a higher minimum wage, this means that we can expect affected workers to put in on average about 2 percent fewer hours a year. However when they do work, those at the bottom will see a 39.3 percent increase in pay.

That doesn’t sound like a bad deal. I don’t know what the average amount of hours worked by a minimum wage earner is, but I’ll assume it’s 40 per week — although, when I worked for minimum wage I’d be lucky to get 20. So, if the loss in hours is evenly distributed, the new minimum wage will affect total compensation as follows, more-or-less: 10.10(39.2) – 7.25(40) = $105.95. That’s $105.95 more per week minimum wage earners will make, even with a 2% loss in hours.

But, assuming an even distribution of hour loss seems like a very unreasonable assumption. If the average minimum wage worker works less than 40 hours a week, it’s also safe to suppose that some employees work more hours than others — this was my experience. Three main reasons come to mind: (1) firms don’t like perfect work sharing, because it reduces productivity; (2) firms discriminate between workers; (3) some minimum wage earners work two jobs, others don’t. So, the distribution of benefits from an increase in the minimum wage will be uneven. The problem seems worse when we think about some working two jobs, and others working only one, where some will land two jobs at the new minimum wage, making the spread of hour loss even more unequal.

Note how losses and benefits are distributed. That the quantity of labor will fall by an equivalent of a loss of 500,000 jobs suggests that significant chunk of the cost of a minimum wage is being passed on to minimum wage earners, not capital owners. This means that whatever benefits x fraction of minimum wage workers earn from the increase, they are receiving these at the cost of other minimum wage workers.

The minimum wage seems like a regressive welfare program, since some are becoming better off at the expense of the worst off. Even if the minimum wage is Kaldor-Hicks optimal (which I doubt, especially when we look at other margins), is that really a policy liberals want to support?

A Simple Argument for the Minimum Wage

Apparently, some people can’t figure out what a strong argument for the minimum wage might look like. In what follows, I will provide what I think is a reasonable case for minimum wage legislation.  What I’m not saying is that the argument is right. I’m claiming it’s reasonable. It is perceivable (there is some probability) that that it could be right. Neither am I saying that this is the argument I agree with. I don’t think the minimum wage is good policy.

The case for a minimum wage. Many people believe that all people deserve a minimum standard of living, and that one method of pursuing this is by paying minimum wage workers an hourly income above the market value of their labor. The classic economic argument against the minimum wage is that it creates unemployment, by pricing many workers out of the market. However, much of the recent evidence fails to reveal disemployment costs, meaning that firms raise their minimum wage without having to let workers go. In fact, some studies show that the minimum wage increases employment, as the monopsony theory of markets predicts. The implication is that the most cited cost to minimum wage may actually not be a cost at all.

Note what I don’t say,

  1. Minimum wage…liberals…marxists. There has to be something analogous to Godwin’s law for this. As the discussion grows longer, the probability that a libertarian will bring up socialism/Marxism approaches one.
  2. Minimum wage advocates are assuming labor markets are non-consensual. Or, they assume that the only alternative to taking a low wage job is death, meaning the contract is as good as slavery.

I’m sure there are people who do believe in these things. But, those who want to take part in the debate on the minimum wage know, or should know, that these are relatively weak arguments. And critiques of these arguments do not address the stronger ones. It should not be surprising to you if you are attacking the weak ideas, but your criticism is not persuading anybody who doesn’t already agree with you. And, you are misleading your readers, because you’re guiding them into taking a position by ridiculing the weakest form of opposition against it.

P.S. Here is a strong argument against the minimum wage, that does address the strong arguments for the minimum wage.

Minimum Wage and Prices

Most commentators probably realize that there are various ways a firm can respond to increases in the minimum wage. But, from what I’ve seen in the media (not in academic circles), most people only consider what the minimum wage will cost to the consumer if firms respond by increasing the prices of their product. But, thinking about, this strikes me as a strange way to talk about the costs of the minimum wage.

We know that how much of the minimum wage the firm can pass on to the consumer depends on the elasticity of demand,

demand elastic and inelastic

In the illustration above, the graph on the left has a demand curve that is inelastic relative to the graph on the right. Suppose each graph represents a different firm. The left-hand firm will be able to pass on more of the minimum wage cost to the consumer, because quantity demanded will fall to a lesser degree than for the firm represented on the right. (By the way, this is why labor unions are more effective when they’re unionizing labor for competitive monopolists. This is also why labor unions lobby their government to pass regulations — e.g. tariffs — that offer their industries monopoly rents.)

The demand curves for the industries most likely affected by the minimum wage — e.g. fast food, other restaurants, grocery stores, et cetera — are probably relatively elastic. What this means is that the firm’s ability to pass on the additional cost of the minimum wage to the consumer will be rather limited. This is one reason talking about product price and the minimum wage doesn’t make much sense to me.

The effects of a minimum wage are most likely seen elsewhere. Unemployment is the obvious alternative, but factors that give firms the ability to exploit labor may mitigate this to some extent. (“Exploit” has a specific, positive — not normative — definition: [MRP-W]/W; or the inverse of the labor supply’s elasticity.) Increasing the cost of labor can also reduce profits, which may be a disincentive to investment in the firm. One way or the other, the consumer is hurt by the minimum wage, but the least likely route is the direct one between increased input cost and increased output price.

Illegal Immigration and the Minimum Wage

Browsing this website campaigning for a higher minimum wage, I came across this Bruce Bartlett blog post discussing one of Ron Unz’ rationales that supposedly favors increasing it. Unz suggests that setting wages at $12 will price illegal immigrants out of the market, helping to mitigate the “problem” of illegal immigration. I’m surprised that Bartlett didn’t include any criticisms of the idea.

In 2003, 20 percent of the low-wage labor force was composed of immigrants. About one fourth of those earned less than the minimum wage. I don’t know what the cut-off for “low wage” is, but it’s probably a few dollars over 12. Nevertheless, there are a substantial amount of non-immigrants who work in low-wage industries that would also see themselves priced out of the market. The firm then has a choice between employing less natives at a higher price, or try to hire more illegal immigrants at lower wages. There is a unique cost to hiring illegal labor, which is a probabilistic legal cost, but if a quarter of low-wage immigrants were earning below the minimum wage, I think it’s safe to say that this cost is relatively low.

Raising the minimum wage to $12 an hour would not only put many natives out of work, but it would also make hiring illegally a much more attractive option. The Federal minimum wage is $7.25 ($8 in California) and a ~quarter of the low-wage immigrant labor force is making less than that. Now, imagine a minimum wage of $12. Illegal immigrants, or legal immigrants working under the table, will become relatively attractive. The implication is that a higher minimum wage will raise the demand for illegal labor — labor willing and able to work for less than $12, without the legal recourse to complain that the firm isn’t paying the legal minimum.

Unz argues that a higher minimum wage will be a disincentive to immigrants. The logic is that few people will be willing to migrate to a country where there’s no work for them. But, it’s very possible that raising the minimum wage will have the exact opposite effect! Instead of pricing immigrants out of the market, it would make them relatively cheaper.

Monopsony and Minimum Wage Logic

Monopsony models of labor markets can be used by economists to provide a theoretical justification for the minimum wage. One criticism of the theory, that I’ve read, is something akin to if the firms’ demand curve is downward sloping this somehow should hurt the positive case for a minimum wage. But, this simply isn’t true. Or, alternatively, what am I missing?

Labor Monopsony

To avoid controversy that might divert attention from this posts’ point, I am not saying that the simple monopsony model is a good theoretical justification for the minimum wage. And, of course, a theoretical justification is not an empirical justification. I, personally, do not think the minimum wage is a good welfare program (I think something like basic income is better).

The above graph uses completely arbitrary numbers. I took a textbook example of monopsony (I copied the figures from their table) and then I built another table with the minimum wage. This is what it looks like (minimum wage on the right; the highlighted row is where MC=MRP, or is just below it, because we’re dealing with finite and discrete units),

monopsony and min wage tableThe intuition behind a profit maximization model is that the firm will employ one additional unit of labor, if and only if the marginal benefits (marginal revenue product being the marginal increase in productivity) exceed or are equal to the marginal costs. If the marginal benefits are less than the marginal costs, the firm is earning a net loss on that additional employee. Because the minimum wage implies constant marginal costs on some segment of the marginal cost curve, if this segment crosses the demand (or marginal revenue product) curve, total employment will increase, despite the rise in wage, all else equal (if there are other factors that determine employment, including the availability of funds through, say, the stock market, how will an increase in the total wage bill affect these functions?). See also the second paragraph in this post by David Henderson for a verbal explanation of the intuition behind monopsony and the minimum wage.

Note, also, why the argument, “why not a $10,000 minimum wage,” is not a good one (in this case). In our example, increasing the minimum wage to eight dollars would decrease total employment (and the total wage bill). To eliminate the welfare loss entirely, the optimal wage would be set at where the labor supply curve (the solid red line) intersects the demand curve (the solid green line). There are definitely limits to where the minimum wage should be set (of course, different models may have different optima). But, the government doesn’t necessarily have to set the minimum wage at the optimal value; there’s a range of wages where the outcome is still welfare improving compared to the market outcome, again all within the context of this limited model.


I have a related thought, although this is one of those “spur of the moment” ideas. The reason why the marginal cost curve lies above the labor supply curve in the monopsony model, is because the firm has to raise the wage of all other employees as it draws a new laborer from the market. This is where the marginal wage cost figures come from in the tables above. Say that we’re looking at the monopsonist firm (without minimum wage) in the above example, and this firm originally employs two workers at three dollars each (total wage bill of six dollars). The firm wants to employ one more person, who will join the company if and only if she’s paid four dollars. In the model, the firm not only has to pay the additional four dollars to hire the marginal employee, but it also has to pay an additional dollar per each employee already hired, for a total marginal wage cost of six dollars (the total wage bill being $12, 12 – 6 = $6).

How well does this represent real world marginal cost curves in markets where the firm is not a “wage taker” (the labor supply curve is upward sloping, or, amounting to the same thing, the labor supply curve is not perfectly elastic)? There is evidence that there is wage dispersion within firms (see, for example, Edward P. Lazear and Kathryn L. Shaw, “Wage Structure, Raises, and Mobility,” in The Structure of Wages: An International Comparison). This suggests that, to some degree, firms can price discriminate when they set wages (price discrimination means that the firm can charge different prices to different customers, or in this case different employees). If this is true, won’t the marginal cost curve exist somewhere closer to the labor supply curve (or, in the case of perfect discrimination, the marginal wage cost curve would be the labor supply curve)?

Of course, the straightforward monopsony model is not usually what minimum wage proponents have in mind. In introductory micro, monopsony is presented as the case where there is a single buyer (analogous to the basic monopoly model, where there is a single seller). Instead, they rely on theories like differentiation, where employees prefer one firm or another for some reason — if firm attractiveness varies, the reservation wage (the minimum wage a person is willing to accept in exchange for her labor) will vary by firm and the supply curve will be upward sloping. Other factors which can give employers market power include moving costs (the cost an employee has to pay to move between firms) and search considerations (imperfect information). So, these factors have to be considered alongside factors which may make monopsonistic elements less relevant. (A very good review of various theories of labor monopsony and empirical studies is William M. Boal and Michael R. Ransom, “Monopsony in the Labor Market,” Journal of Economic Literature 35, 1 [1997], pp. 86–112; although, I get the feeling that they are skeptical of the minimum wage and monopsony models in general, so the literature they review may be an incomplete picture of the evidence [selection bias, of sorts].)

Supply-Side Unemployment: Surface Data

2007 Shadow Econ v  2009 Unemployment

An informal sector forms, because the alternative of exchange through the formal economy is comparatively expensive. So, I thought that the size of the informal sector (as a percentage of GDP) serves as a decent proxy for the the additional transaction costs imposed by government — these are the supply-side issues that some economists say hold back economic recovery. The graph above shows the relationship between estimated sizes of informal sectors for 21 OECD countries for 2007 (the most recent data I can find) and the 2009 average unemployment rate.

2012 Labor Freedom v 2013 UnemploymentAn alternative way of giving a superficial look at the impact of these transaction costs is to compare the 2012 Heritage labor freedom index and the respective current unemployment rates of the same 21 OECD countries. A larger number on the labor freedom index indicates greater freedom.

Both graphs show a relationship that seems to support the supply-side explanation of unemployment. But, I’m not sure the relationship is very strong (excluding outliers, the slope is probably closer to zero).