Erdmann, Empiricism, and the Minimum Wage

Erdmann's MW and teen unemployment graph
Pre-trend lines are for period from 27 to 3 months before MW hike. MW Trend lines are for period from 3 month before to 27 months after initial MW hike. [Y axis = Teen Employment To Population Ratio]
Kevin Erdmann, over at Idiosyncratic Whisk, posted a graph similar to the one shown above,* demonstrating that the trend in the US teen employment rate after a minimum wage hike was lower in all but one case than the trend before the hike.

There have been many responses, but I would like to focus on one over at Angry Bear that captures the worst of the criticism.** The writer goes way over the top in criticizing Erdmann, saying that people who oppose the minimum wage “apparently believe that the business cycle never impacts teen employment or unemployment.” To read this article, you’d think think that the only opposition to the minimum wage came in blog-post form. Frankly, no empirical analysis coming from a blog (including Angry Bear) can offer anything but a prima facie case for or against some proposition. I don’t read Erdmann as claiming that his little graph is the final word on the minimum wage.

The Angry Bear post goes on to use some very questionable econometrics to show that the minimum wage doesn’t have a big impact on teen unemployment. The author doesn’t use the inflation-adjusted minimum wage in his graphs (and presumably in his regression) for reasons unknown, making them pretty irrelevant. He then naively regresses the teen unemployment rate against adult unemployment, a recession dummy, the teen population, and the minimum wage to find that (surprise!) the minimum wage doesn’t have a big effect on teen unemployment. For someone who criticizes others about omitted variables, this regression should be pretty embarrassing. That’s time-series data! You don’t just apply OLS regression to time-series data. OLS regression assumes uncorrelated error terms, and the fact that adult (and teen) unemployment last month is highly correlated with adult (and teen) unemployment this month destroys that assumption.

To put it in layman’s terms, this statistical technique would find any two things that trend over time to be highly significantly related. It’s not a great way to do econometrics.

That said, I think if the author of this post had used good econometrics, he still would have found little connection between the minimum wage and teen unemployment. The economy is big and complicated, and it’s nearly impossible to distinguish real causal connections between economic variables from spurious correlations and white noise. Minimum wage hikes are typically small, so it’s hard to tease their effect out from all the other things going on.

Given that it’s so hard to get anything out of the data, the winner of any empirical argument is nearly always going to be determined by our assignment of the burden of proof. If one side says “A causes B” and the other side says “A does not cause B,” then the former side will win if the burden of proof is on the latter side, and the latter side will win if the burden of proof is on the former side. If the burden of proof is shared equally by both sides, the one that says “A does not cause B” will probably win, because teasing out the effect of any A on any B is very difficult without the opportunity to conduct controlled experiments.

I can think of three reasons why the burden of proof should be on the minimum wage law’s proponents to show that it has positive effects:

  1. Economic theory clearly implies that the minimum wage reduces opportunities for low-skilled workers, not only because it makes it hard for them to get a job, but because it prevents them from having a full range of contracting options with their employers. Minimum wage proponents need to justify their position with strange assumptions like monopsony in the market for low-skilled labour or efficient rationing. Weak theoretical arguments should require strong empirical backing to be taken seriously.
  2. The minimum wage law is a case of the political class overriding the decisions of millions of workers and employers engaging in peaceful contracting. In general, when a third party such as the government steps in to override other people’s decisions, the third party should provide a good reason for its meddling. Without this presumption, we would quickly descend into totalitarian rule.
  3. If the proponents of the minimum wage are wrong, the burden falls on the poorest members of society. If other anti-poverty programs fail, such as those programs that just give money to the poor, the burden is on the taxpayers who paid for the ineffective program. Taxpayers are richer than those who could be unemployed by the minimum wage law, so it’s better that they should bear the risk. (This argument was made recently by Janet Neilson.)

There are my arguments. I leave it to minimum wage proponents to prove that the minimum wage should exist. Until then, I will happily oppose it.

 

* This graph was added in a later update. Erdmann realized that the teen employment to population ratio was a more relevant variable than simply teen employment.

** Kevin Erdmann’s follow-up post deals with many of Angry Bear’s complaints. He also responded directly to the Angry Bear post in a comment on Marginal Revolution.

8 thoughts on “Erdmann, Empiricism, and the Minimum Wage”

  1. Erdmann’s regressions also are rather flawed, more so than Angry Bear’s. For one thing there is a high degree of model mining evidenced—selectively picking only periods of minimum wage increases, somehow cutting off a minimum wage increase in the early 50s. A true econometric model would have to explain periods in which there was no minimum wage increase also.

    Also, the issue of autocorrelated errors: The estimates of the coefficients would be unbiased, but the estimates of their uncertainty would be understated. The primary result would be overstating the significance of some coefficients (which Angry Bear doesn’t quote).

    Finally I should add that while economic theory indicates that raising the minimum wage decrease employment, it does not give us the relevant coefficient. Proponents of the minimum wage increase argue that currently the coefficient is extremely close to zero.

  2. Correction–I should have stated “assymptotically” unbias; any bias decreases towards zero as sample size increases.

      1. Kevin:
        Given that so many regressions have already been published, included those that look at local labor markets, I don’t hold out much hope for an additional regression resolving the question; certainly at a macro level. There are too many interacting factors over time.

        If you want to keep trying for a macro model try a partial equilibrium (error correction or cointegrated series model).

        A model needs to cover all datapoints–whether or not the minimum wage was hiked. And one needs to look for other trends and effects that may be also have an impact–other changes in work laws, changes that affect a teenager’s interest in working, and changes in business compositions for example.

        A simple one might be one where there is an equilibrium between youth employment, real or relative minimum wage, and the GDP. This means that

        ln(Y(t))=ln(Y(t-1))-G*(Y(t-1)-(A*WY(t-1)/WA(t-1))+B*GDP+C))

        G is the equilibration rate and A,B, and C give the equilibirum values.

        ln(Y(t)/Y(t-1)) = a*(WY(t-1)/WA(t-1))+bln(GDP(t-1))+c*ln(Y(t-1))

        where Y=Youth employment[if you normalize by Youth population use a difference instead of a log of ratios)
        WY=minimum wage.
        WA=average wage or a price index (There may be a problem in that there is strong autocorrelation of this variable as over long periods there have been time trends in both this and youth employment)
        GDP=real GDP
        (t-1)=means value in variable in prior period

        1. Thanks again for the input, Jon.

          My analysis certainly isn’t going to be published in any econometrics journals, but I don’t think what I’m doing lends itself to time series regressions. I’ve got 7 systematically defined observations, that cover 30 month periods around each series of MW hikes, and I’m attempting to make some attempt at controlling for recessions through RGDP. Did you look at the post I linked to in my comment? I think what I’ve done there is similar to what you have shown here. Even though I don’t think I could use every point in time as an observation, I have tried to choose the data points in a way that would not introduce bias.

          1. You have chosen the data points and method of analysis, including the sampling periods for the slopes (and even the usage of the slope) in a rather bias way.

            For example there are 10 sets of minimum wage hikes in the data:
            1950, 1956, 1961, 1963,1967-68, 1974-76, 1978-80, 1990-91, 1996-97, and 2007-2008. In 5 of these the slope in of the teen employment is higher in the 12 months after the last minimum wage hike than it is in the 12 months before the first.

            Hence those “7” regression points aren’t really so pure.

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