As I am reading the most recent post in Greg Mankiw's Blog, I find the data he presents intriguing. He is comparing two years (2007 and 2010) to show that workers being paid the minimum wage has increased, measured as a % of all workers, from 2.3% to 6%. In those years the federal minimum wage increased from $5.15 to $7.25 in nominal terms. Greg is asking his students to evaluate the link between the two. As one of his former students I feel obliged to look at the data in more detailed to see what I can say.
My quick reaction is that there is an automatic relation between increasing the minimum wage and the % of individuals who are paid that wage. If we assume that firms keep employment constant and simply pay the higher wage, this increase will simply be those who were paid in between the old minimum wage and the new minimum wage. There is the possibility that some workers are fired, in which case the increase would be smaller.
My second reaction was about the fact that the period 2007-10 is special. Not only we have seen an increase in the minimum wage but also a deep recession. It is possible that some wages have fallen and old employees have been replaced by new ones who are now paid a lower wage - right at the level of the minimum wage. This would also cause an increase in the number of workers paid the minimum wage. But, of course, there is a potential second effect of a recession going in the opposite direction: it can be that during recessions those who lose their jobs are workers that are being paid lower wages and, as a result, you might see the percentage then decreasing as opposed to increasing.
So I was curious to see how this figure - the % of workers being paid the minimum wage- has changed over the last business cycles and whether this could also be behind its recent increase.
So I plotted three variables from 1979-2010. In blue you see the % of workers paid minimum wage (Greg's variable). As we can see this percentage has been decreasing since 1979. In that downward trend we also see three spikes: around 1991, around 1997 and 2008-10. The shape of this line, including the spikes correlate very well with the minimum wage (in green). It is measured in real terms (1996 dollars) and the scale is on the right hand side of my chart (the scale does not start at zero to see some meaningful variation). The real minimum wage has also been decreasing since 1979. A decrease that has been interrupted with increases in 1991, 1997 and 2007-09. These three increases coincide with the spikes in the blue line, the % of workers being paid the minimum wage. So the mechanical explanation is very visible in the chart, as you raise the minimum wage you see more workers being paid that rate.
What about the business cycle or labor market conditions in general? The unemployment rate is in red (left hand side axis). Interestingly, the unemployment rate, or the business cycle more generally, is also correlated with the blue line. Recessions are period where we generally see spikes in the blue line. Although there is an exception, the recession of 2001 saw unemployment increase without any change in the % of workers that were paid the minimum wage.
The difficulty in the figure above is that there is a correlation between the three variables and it is difficult to establish causality or assess the strength of each of the two effects. Two of the last three increases in minimum wages are not far from recessionary episodes which makes it very difficult to understand the potential role of the business cycle [Yes, there is a possible reading of those episodes as an increase in the minimum wage causing the recessions, but as we know well this is not what led to the 1990 or 2007 recessions].
One thing that might tell the two factors apart is to realize that we have an episode of increasing the minimum wage without a recession (1997) and we still see the mechanical effect very clearly; and we also have a recession (2001) without and increase in the minimum wage and the blue line does not change much. So based on that evidence it seems that the business cycle effect is not as visible as the simple mechanical effect of raising the minimum wage.
[For those who like econometrics: A more formal, but still very weak, test is to run a regression to see which of the two variables is more significant when put in a regression. The race is won by the minimum wage. Both the minimum wage and unemployment are significant when used in a regression by themselves. When you include them together only the minimum wage is. This regression is, of course, full of econometric problems because everything is endogenous, so still no causality inference can be made.]