MINIMUM WAGE MYTHS
The major argument used against raising the federal minimum wage is that because it would make the cost of labor greater, it would cause employers to cut their labor costs by cutting employees. That is, it would cause job loss. It is relatively easy to check that theory against the historical facts because the U.S. Bureau of Labor Statistics has vast tables of historical data on its website (www.bls.gov) giving unemployment rates, job growth rates, and minimum wage values. In what follows, all values are annual averages and statistical calculations are done using Origin®2015.
Minimum Wage
Before we can do any analysis, we must express the minimum wage in constant dollars; that is, we must correct for inflation. The Bureau of Labor Statistics website has an inflation calculator which allows one to change the nominal dollars of any year into dollars of another year. It doesn’t matter in which year’s dollars we choose to express the minimum wage as long as it is always the same year’s dollars. Figure 1 shows the minimum wage since 1950 expressed in 2012 dollars.
FIGURE 1
If we had used dollars from some year other than 2012 to express minimum wage, the graph would look just the same, but the scale on the left-hand side would be different. The maximum value was reached in 1968. The nominal minimum wage was raised to $7.25 in 2010, and since then it has decayed in constant dollars due to inflation. In the last year of the graph, 2014, the inflation-adjusted minimum wage was almost exactly the same as in the first year, 1950.
Unemployment
Does raising the minimum wage cause more unemployment? If that were true we would expect to see a statistically significant positive correlation between minimum wage in constant dollars and unemployment rate over the 65 year period: higher unemployment rates accompanying higher minimum wage. The actual case is shown in the scatterplot of Figure 2.
FIGURE 2
In fact there is a small positive correlation, but it is far below statistical significance. The correlation coefficient between the two variables is only 1.9% or 0.019. The correlation coefficient measures how much the two variables vary linearly together. A correlation of 1 means that the two vary exactly proportionately, and all the points would lie perfectly on a straight line (the regression line) with positive slope. A correlation of -1 would mean the same thing, but the regression line would have a negative slope: when one variable goes up the other goes down. A correlation of 0 means no discernible relation. The regression line in Figure 2 is the straight line that fits the data best, with minimum error. The very great scatter of points around that line is an indication of low correlation.
The square of the correlation coefficient gives the coefficient of determination (COD), a number that specifies how much of the variation in unemployment could possibly be due to the variation in minimum wage. In our case, that value is far below 1%. That means that above 99% of the variation seen in unemployment over 65 years must be due to factors other than minimum wage.
Unemployment for Low-Paid Workers
Often, when conservative commentators become aware of the negligible correlation of Figure 2, they switch their arguments to the assertion that raising the minimum wage will kill jobs for low-paid workers, the ones who might be making only minimum wage. However the Bureau of Labor Statistics keeps data on workers by age. We can check the effect on low-paid workers by just looking at the age cohort of 16 – 19 year olds. They should be the lowest paid in the workforce because they are just starting. Figure 3 shows the pertinent scatterplot.
FIGURE 3
Here the slope and correlation coefficient are about as close as you can get to 0, using real-world variables. The correlation coefficient is only -0.004. The unemployment rate for low-paid workers is even less dependent on minimum wage than that for all workers together.
Job Growth
A better measure of effect on jobs may be the job growth rate. That number measures the percentage change in the number of jobs over a year. Unemployment rate doesn’t take into account the people who stop looking for jobs because it measures unemployment as a percentage of the labor force and those who stop looking are not considered part of the labor force. If many jobs are created in a year, that is an absolute good regardless of whether people have dropped out of the labor force. Fortunately, the U.S. Bureau of Labor Statistics tracks job growth rate also. Figure 4 gives the scatterplot.
FIGURE 4
Here the slope is definitely positive: higher job growth rates with higher minimum wage, exactly the opposite of conservative economic theory. However the slope and correlation coefficient (20%) are still not considered statistically significant. The coefficient of determination is 0.04, so 4% of the variation in job growth rate could possibly be due variation in the minimum wage.
Inflation
A third argument used against any raise in the minimum wage is that such a raise would increase inflation. The story line goes that employers who have to pay more for labor will pass the increased cost on to customers and as such increases propagate through the economy, higher inflation is inevitable. That is not a very persuasive argument at the present time because the annual inflation rate was only 2.1% in 2012, has been below 2% for the last two years, and the consumer price index (CPI) was actually down (negative inflation rate) in the first half of 2015[1]. Still, it is worth investigating the validity of the claim that increasing the minimum wage will increase inflation, just as we have investigated the job loss claims.
It should first be noted that this is a more difficult investigation. We cannot just blithely use minimum wage in some constant dollars as our independent variable because inflation rates are used to calculate equivalent constant dollars; the variable we wish to make the dependent variable (annual inflation rate) is already mixed into the variable we would like to consider the independent variable (minimum wage in constant dollars). Minimum wage in nominal dollars (also known as current dollars) does not make a very good independent variable either because nominal dollars represent a changing measurement scale, like measuring length with a shrinking ruler. Besides, we are more interested in what effect a change in minimum wage has. However even changes in minimum wage in nominal dollars are affected by inflation: legislated change values are not pulled out of thin air, but are often established by considering cumulative inflation since the last change. We are faced with a “the chicken or the egg” conundrum: does inflation drive minimum wage or vice-versa?
With all these difficulties in mind, I decided to use percent change in minimum wage in nominal dollars as my independent variable. Percent change from one year to the next eliminates most of the effect of inflation, except perhaps for the inflation rate during the year in question. The change may be affected by lawmakers’ consideration of previous years’ inflation rates, but probably not much by the inflation rate of the year in which the change occurs. It is not an ideal candidate for the independent variable (there are other problems as we shall see), but it is the best I could find. This variable is shown in Figure 5. There are two features immediately noticeable in this graph: the first point is an extreme outlier and there are many zeroes.
The first point, in 1950, is more than twice as large in percent change as any of the other 64. That is because the minimum wage went from $0.40 in 1949 to $0.75 in 1950. In absolute terms that is just a 35ȼ increase, but it is a large percentage change because the starting base was so low. This is one more problem with the chosen independent variable. In 1956 minimum wage went to $1.00, and this became the second-largest percentage change at 33.3%. All the other increases are below 20%.
FIGURE 5
The zeroes come in the years when there were no increases in nominal dollars. Altogether there were 40 such years, along with 25 years when minimum wage was increased. However, zero is as good a number as any other and they are all entered into the calculations.
First we consider inflation rates as a function of the minimum wage change in the same year. Results are shown in Figure 6. The slope of the regression line is not significantly different from zero and COD is far less than 1%. We may conclude that increases in the minimum wage have had no statistically significant effect on inflation rates of the same year, a result that, conversely, gives some justification to the assertion that inflation rates of any year do not much affect the minimum wage change of that year.
FIGURE 6
We can pair the minimum wage changes with inflation rates in succeeding years, i.e. wage change in 1950 with inflation rate in 1951, wage change in 1951 with inflation rate in 1952, etc. This procedure gives the increased labor costs a year to percolate through the economy. It also has the advantage of only allowing one-way causation: later inflation rates can have had no influence on earlier minimum wage changes. We can similarly consider a two-year delay. These two cases are shown in Figures 7 and 8. The slope in Figure 7 is considered statistically significant, and since it is positive, represents evidence for increases in minimum wage causing increases in inflation in the following year. However COD = 7.4% in this case, so the effect is still small; minimum wage increases could possibly cause 7.4% of the inflation rate change in the next year. As shown in Figure 8, this effect disappears in the second year after a minimum wage increase. In this scatterplot the regression line slope is not significantly different from zero and the COD value is well below 1% again. So the evidence suggests that a minimum wage increase might cause a small, one-year bump in inflation rate in the year following the increase.
FIGURE 7
FIGURE 8
One feature that stands out like a sore thumb in both Figure 7 and Figure 8 is the outlier point representing the 87.5% minimum wage change that took place in 1950. If we consider the data without that outlier, the results are different. Such a procedure is the same as just considering the 64 year period 1951 – 2014, because that extreme value appeared in 1950. Eliminating the outlier leads to the conclusion of no slope significantly different from zero for inflation rate the same year, or one year later, or two years later. For brevity I just show the scatterplot for one year later which is the only one that changes from a statistically significant slope to an insignificant, although still clearly positive, one. COD = 5.0%
FIGURE 9
Because I have tried to be scrupulous about avoiding data selection to fit a preconceived notion, I offer the above as of passing interest only. From all the data I stand by the previous conclusion that a minimum wage increase might cause a small, one-year bump in inflation rate in the year following the increase.
For the Skeptical Reader
It behooves the reader to be skeptical. If I were the reader instead of the author, I would be skeptical of a study that uses one measure of minimum wage in one part and another measure in another part, always reaching conclusions that seem to contradict conventional wisdom in economics. If minimum wage change in nominal dollars was a good enough measure at the end, why wasn’t it a good enough measure at the beginning?
Actually, to make sure I wasn’t deceiving myself, not to mention others, I did nine more linear regressions using the minimum wage change in nominal dollars as the independent variable. The dependent variables were same-year unemployment rate, 16-19 year old unemployment rate, and job growth rate. Then I repeated the same-year calculations with the 1950 outlier removed from the data. Then I repeated the calculations with a 1-year delay in the dependent variables (1950 point included). I shall not burden the reader with nine more scatterplots and COD values, but just assure him or her that none of the nine linear regression slopes were significantly different from zero. The largest COD value was 5.9%, for same-year job growth rate vs. minimum wage change (1950 data included), and that slope was positive (larger job growth with larger minimum wage change). In short, had I used only nominal dollar minimum wage change in all the calculations, I would not have reached any different conclusions.
Gary Waldman
December 2015
[1] www.bls.gov/cpi/#tables, CPI Detailed Report, Oct 2015, Table 24, pps. 71 & 73
MINIMUM WAGE AND SMALL BUSINESSES
Introduction
In a previous study[1] I showed that there is no evidence that higher federal minimum wage rates adversely affect unemployment rate, unemployment rate for 16-19 year-olds, or job growth rate. That study encompassed 65 years, 1950 through 2014.
Another argument used by conservatives against any increase in the minimum wage is that such a raise would harm small businesses, which presumably would be more affected than large businesses. Small businesses would feel the increased labor cost more and would have to lay off employees or close altogether, according to standard conservative arguments.
I have only been able to find data from the Small Business Administration for the period 1988 – 2014[2], 27 years. I would normally analyze a period of time more than twice as long, but I shall make do with what is available.
Small Businesses
The government (Small Business Administration) defines a small business as one with less than 500 employees. Small businesses can be broken down into Employer Small Businesses (1 or more employees) and Non-Employer Small Businesses in which the proprietors are the only workers. Although the latter category is much more numerous, only the former category would be affected by minimum wage. Figure 1 shows a history of numbers of the former.
The most prominent feature of the graph is the effect of The Great Recession, 2007 – 2010, which clearly reduced the number of Employer Small Businesses. Indeed, even the number of large businesses (500 or more employees) dropped in 2009 and again in 2010, and did not attain its 2008 value again until 2013. The number of Non-Employer Small Businesses dropped only in 2008.
Employer Small Businesses can be further broken down by size measured by the number of employees. Figure 2 shows this breakdown. This figure shows that the smallest firms (1 to 4 employees) are the most numerous (Non-Employer firms being more numerous still). Also the number of smaller firms seems to have been more severely reduced by The Great Recession.
FIGURE 1
FIGURE 2
The question remains as to whether the number of small businesses has also been adversely affected by higher minimum wages. To examine this question I shall use data from just the tail end of Figure 1 in Reference 1: minimum wage from 1988 to 2014, corrected for inflation by using constant dollars. Figure 3 shows this variable.
FIGURE 3
This plot shows the typical peaks from legislated increases, often in several steps, followed by the inevitable inflation-caused decays. The last legislated increase, ironically, was in 2007, just as the recession was about to strike. Therefore the minimum wage goes up as the number of small businesses comes down in the years 2008, 2009, and 2010. Are these three years enough to establish a significant negative correlation between number of small businesses and minimum wage?
Actually the answer is “no”. When a linear regression analysis is performed for the whole 27 year period the slope of the regression line is not significantly different from zero, a value that indicates no relationship between the variables. In fact, the insignificant slope that does appear is positive, not negative. Figure 4 shows the scatterplot. Because of the large scatter of the points, the coefficient of determination (COD) is only 0.7%. The probability that the variables are unrelated (the null hypothesis) is 34%, far above the 5% limit for significance.
FIGURE 4
Perhaps only the smallest of Employer Small Businesses is hurt by higher minimum wage. To test this hypothesis I performed another regression analysis using only businesses with fewer than 20 employees as the dependent variable. The result shows a somewhat larger slope and higher COD, but it was still statistically insignificant at the 0.05 level, and, worse for the conservative argument, the slope was still positive! The COD value was 1.0% and the probability of the null hypothesis was 31%. Figure 5 shows the scatterplot.
FIGURE 5
Employment by Small Businesses
The analyses above still do not tell us if a higher minimum wage causes small businesses to cut back on the number of their employees. To investigate that question we need to look at the number of employees rather than the number of firms. The number of employees employed by small businesses is shown in the graph of Figure 6. It can be seen once again that the most prominent feature is The Great Recession. Otherwise there is a general upward trend.
As in the case of the businesses themselves, we can break down the number of employees according to the size of the business. This is shown in Figure 7. Most small business employees work for the bigger firms, although Figure 2 shows that there are a lot more of the small firms employing 1 to 4 people.
FIGURE 6
FIGURE 7
A linear regression analysis between the data in Figure 6 and minimum wage in constant dollars shows a regression line with a slope not significantly different from zero. Here the COD value is only 0.01%, meaning that the independent variable, minimum wage, can explain essentially none of the variation in small business employment. Probability of the null hypothesis is now 48%. The scatterplot is shown in Figure 8.
FIGURE 8
Once again I tested to see if minimum wage had an effect on employment by very small firms, ones with 1 to 19 employees. The answer is just as definitive as for employment by all small businesses. A regression line slope not significantly different from zero and a COD = 0.02%. Figure 9 shows the scatter plot.
In the 27 year period of recent history for which I have data, there is no empirical evidence that the federal minimum wage has any effect on either the number of small businesses or the number of employees in those businesses.
FIGURE 9
On the Other Hand
However there are other ways to view the data other than working with raw numbers of small businesses and their employees. Those numbers are not normalized in any way. For example, we could look at the small business share of total private sector employees, thereby normalizing by total employees. If the total number of employees has increased greatly, perhaps employment in small businesses has not kept pace and has been held back by minimum wage considerations. Figure 10 shows the actual case. It can be seen that the total number of employees has increased significantly from 1988 to 2014, with noticeable recession dips in 2002 and 2009, 2010. Small business employment has not been quite proportional, with small business share at 54.5% in 1988 and 47.8% in 2014. Figure 11 shows how the small business share has dropped almost monotonically over the period except for a brief gain in 2001 – 2004.
FIGURE 10
FIGURE 11
A glance at Figure 3 for minimum wage shows, despite the sharp peaks and valleys, a general upward trend, with each successive peak a little higher and the value in 2014 higher than the starting value in 1988. Could the opposite trends in Figures 3 and 11 lead to a statistically significant negative correlation between small business share of employment and minimum wage?
This time the answer is “yes”. The scatterplot is shown in Figure 12: the slope of the regression line is negative and significantly different from zero. COD = .25 meaning that up to 25% of the variation in small business share of employees could be due to minimum wage. Thus there is some evidence that higher minimum wage values tilt the playing field in favor of large businesses over small businesses. Still we must remember that this COD value implies that at least 75% of the decline in small business share must be due to factors other than minimum wage.
FIGURE 12
Gary Waldman
August 2017
[1] G. Waldman – Minimum Wage Myths – Dec. 2015
[2] www.sba.gov/advocacy/847. Under Research & Statistics click Firm Size Data; on the next page click Firm Size Data again; go to datasets, U.S data.
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