The Minimum Wage Debate and Racial Inequality

There is an interesting post about the minimum wage debate here. Honestly, for this post, the tone felt a little off, and it seemed as if the evidence was selected in order to validate the preformed conclusion, but it raises an interesting point none the less(and as I struggle with tone, I’m sympathetic to the author). I’m first going to go into the 101 level economic reasoning that the minimum wage will decrease employment, then give some data to present a strange idea on preferential inequality.

Econ 101 would treat the minimum wage as a price floor. If you think of the wage rate as a price, a floor would be the point for which the minimum price occurs. If you think of this in simple terms, then when you enact a price floor for the wage rate, there will inevitably be some people would be willing to work for less than that wage rate, and many employers would would be willing to hire below that wage rate. This creates a surplus of labor, but the market cannot equalize because of the floor in place.

In reality however, the actual analysis of the minimum wage effects are much more complicated. The 101 level thinking on this matter assumes that the only thing a firm can do is change the number of workers hired, but this is not the only option. A firm really has three(or more) options in response to a minimum wage change. The first, is to change the number of workers hired. This occurs because at equilibrium, the wage rate is based on the extra revenue gained as a result of the last worker(marginal product of labor equals wage). If this equilibrium wage rate is below the minimum wage, this implies that the additional revenue gained from the last worker, is less than than the minimum wage as well, meaning having that worker hired at the new wage rate is costing the firm money. This however, holds prices constant, and does not consider benefits. If the firm simply raises prices, then the real wage can remain constant, and inflation increases. The firm could also decrease benefits, making the overall level of labor compensation the same.

Note that in the preceding paragraph I left out of of the more populist responses to a minimum wage increase: firms can just make less profits. While it is true that firms will probably lose some profit as a result of a minimum wage increase, it will not be a direct substitution to workers. A for profit firm, by definition maximizes its profit, and as long as it does not engage in rent seeking behavior, or regulatory capture, that’s not really a bad thing. As long as the firm has some other options aside from reducing prices, as listed above, there is no reason to expect it will decrease its profits.

This is a slightly more nuanced view of the minimum wage debate, and I should note that this is only the 201, or maybe 301 level of thinking. For those of you with JSTOR access, here is an even more reasoned discussion of the minimum wage idea. I’ll save discussion of the reasoning presented in that article for a later date, as it’s not really the focus of what I’m writing about today. The main point I want to make here, is that the minimum wage is an extremely complicated issue, and nobody should treat it as if they know exactly what will happen. In reality, the firm will probably use a mix of a bit of everything in response to a minimum wage change, and predicting the magnitude of a change is near impossible to do accurately at our current level of knowledge and forecasting models.

The topic of this article, is about racial inequality in a very limited scope. There are essentially two aspects I’ll be considering here. The first, is the relative effects on employment from a minimum wage increase for one societal group versus another. The second, is the relative effects on median wages for one societal group versus another.

I already discussed the employment effects on the minimum wage a bit before, but now I need to go into a bit more detail about how these could have racial disparities in their effects. I can readily identify two mechanisms for these disparities to occur. Both of these can be looked at with more rigor, but they follow a simple intuition. For the first, imagine you own a firm, and the minimum wage is $5. You have two employees, one earning $50 an hour, and the other earning $7 an hour. Suppose the minimum wage increases to $10 an hour. Do you fire the low wage worker or the high wage worker? It should be relatively obvious to see that there is no pressure here to fire the $50 per hour worker, as the new minimum wage does not impact how much you pay them. This can translate to a racial disparity, because workers belonging to historically disenfranchised groups tend to be clustered at the bottom of the wage spectrum. If there are more workers of one race clustered at the bottom, then they will be the people most impacted by the  new minimum wage, and thus disproportionately affected by the change. Note here, that if this is the correct hypothesis, these workers should be more strongly affected by both the negative, and positive effects. Historically disenfranchised workers should see the largest decrease in employment, and also the largest increase in wages. There is a second story however, that could lead to these workers experiencing more of the negative employment effects.

Imagine a new scenario. Again, you own a firm, and the beginning minimum wage is $5. This time however, you have two employees of different races, each making $7 per hour. Assume that you have a racial preference for one worker over the other. When the minimum wage increases to $10, you must fire one worker(the reason you don’t have to fire both involves diminishing marginal returns in the production function with respect to labor, but that would take some time to explain, and if anyone is interested, I’m happy to write a piece on it). Assuming these two workers are exactly the same in all ways except their race, you will fire the one that you least prefer. If you make the further assumption that people tend to prefer people of their own race, and in the US, whites own a larger proportion of means of production than any other race, it follows that the employees kept under this example will be the white workers. This is a very different case from the previous one. Not only will we see more people of disenfranchised groups lose their income as a result of the minimum wage increase, we will also see a disproportionate increases on the wages of the white workers.

The last thing I want to go in to before presenting some data and basic analysis, is a short discussion of which data sets to use. The idea of employment in the economy can be looked at in a few different ways. Here is an article detailing some history of them. Given the differences in what these different categories of data represent, picking the right one to look at employment effects of the minimum wage can be tricky. If one uses the unemployment rate, it leaves out workers that have dropped out of the labor force, and given that a minimum wage change is permanent, it is dubious to assume that workers displaced as a result will infinitely continue to search for work. If one uses the employment to population ratio(EPOP) workers that have retired, and more secular trends in the labor force will be included in the analysis. If one uses U6(unemployed, plus discouraged, marginally attached, and part time for economic reasons), then there is only data going back to 1994, which does not give many minimum wage increases to look at trends over. As this is not intended to be a formal article, and I’m only trying to present an idea to think about, I’m going to use EPOP, controlling for time, to look at the unemployment effects of the minimum wage, but keep in mind this is a very limited way of looking at the issue.

Just to give you an idea of what this looks like, here are two graphs showing the real minimum wage plotted against the EPOP for white and black/African American workers. Note that these are both negatively correlated, though there is no control for secular effects, so that may only be due to longer term forces pushing the real minimum wage up, and the EPOP down.

EPOPWB

The data sources here come from the St. Louis Fed here, and all calculations are done by the author. The data series used are LNS12300003, LNS12300006, FEDMINNFRWG, and PCECTPI.

When controlling for time, for white workers, a $1 increase in the real minimum wage would correspond with a 2.57% decrease in the employment to population ratio. For black/African American workers, as $1 increase in the real minimum wage would correspond to a 2.66% decrease in the employment to population ratio. It’s important to note that while both of these negative correlations are significant to a high degree(10^-28, and 10^-18 respectively), that does not imply that they are significantly different, and further analysis, with better controls should be done to determine that. If we take the numbers are face value however, it seems to give evidence toward the idea that there is a discrepancy in the effects of a minimum wage increase on this particular labor market indicator, so let’s move on to the question of wages. Here’s two similar charts to the EPOP series.

WageBW.jpgThe data sources here come from the St. Louis Fed here, and all calculations are done by the author. The data series used are LEU0262884500Q, LEU0262883600Q, FEDMINNFRWG, and PCECTPI.

Note here that the wages here are the median usual weekly earnings of workers employed part time, as very few full time workers earn the minimum wage. Also note here, that there is much less data here, only going back to 2000. Again, these are not controlled for time effects, and are just an illustration of  what I’m looking at here.

For both of these series, the positive correlation between median weekly wages and the minimum wage loses significance when controlled for time, so I won’t go through the analysis on that, but it’s important to note that due to globalization forces, and slow and unequal growth, the case that there is a strong secular trend for increased real wages toward the bottom of the income bracket is not as strong as one might assume. Once again, I will reiterate that this is not a rigorous analysis, it’s simply a thought experiment designed to look at some interesting issues.

For the uncontrolled regressions, both white, and black/African American workers face a significant(.00083  and .022 respectively) positive correlation between the real minimum wage, and real median weekly earnings for part time workers.  For white part time workers, a $1 increase in the minimum wage would correspond to a $4.56 increase in weekly earnings. For black/African American part time workers,  a $1 increase in the minimum wage would correspond to a $4.07 increase in weekly earnings. Note again here that I’m not testing for significance in the difference between these coefficients across workers, but taken at face value, we have that white workers seem to enjoy the benefits of a minimum wage increase more than black/African American workers. Taken in addition to the employment to population ratio story, this would seem to point to the racial preference story, instead of simply a structural clustering of disenfranchised workers at lower wage levels.

These are certainly interesting things to consider, but what does this information actually tell us? The correct interpretation for these findings is that they tell us absolutely nothing. This isn’t a rigorous study, and to actually get a result, one must much more carefully consider the appropriate data series to use, the best controls to use, and even factors involving data collection. I also presented no tests for significance in the difference between these, because it would be pointless to do so without a more carefully constructed methodology. Further more, nothing I’ve done here implies causation, I’m only looking at correlations. This was all simply an exercise designed to present questions, and a possible direction to go in when studying the issue, not to present any particular finding. Given the results of this exercise when taken at face value however, I would argue there is a strong case to ask, and carefully consider the question of how the minimum wage affects different groups in society. I would also argue for careful consideration of the question of how racial preferences might drive these effects.

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