In his most recent State of the Union address, President Barack Obama advocated for an increase in the minimum wage. “Let’s declare that, in the wealthiest nation on Earth, no one who works full time should have to live in poverty,” he said, “and raise the federal minimum wage to $9 an hour.” In the aftermath of that address, debate has bounced back and forth on the effects that such a policy might have, and supporters of both sides have flocked to make their opinions on the matter heard.
In an editorial published in The New York Times, for example, Paul Krugman lent his support to President Obama’s proposal. “There are strong reasons to believe,” the Nobel Prize-winning economist wrote last month, “that the kind of minimum wage increase the president is proposing would have overwhelmingly positive effects.” As evidence for his position, Krugman cited the rise in productivity that the United States has seen over the past several decades. “In real terms the minimum wage is substantially lower than it was in the 1960s. Meanwhile, worker productivity has doubled. Isn’t it time for a raise?”
Krugman is not alone. In a recent Senate Committee on Health, Education, Labor, and Pensions hearing, Sen. Elizabeth Warren (D-Mass.) reiterated the claim that increases in productivity justify a policy of increasing the minimum wage. “If we started in 1960 and we said that as productivity goes up, that is as workers are producing more, then the minimum wage is going to go up the same … then the minimum wage today would be about $22 an hour,” Warren explained during the hearing last week. “So my question is … with a minimum wage of $7.25 an hour, what happened to the other $14.75? It sure didn’t go the worker.”
(First of all, neither Krugman nor Warren is actually arguing for such an expansive increase in the minimum wage. Both are simply trying to make a point, and actually support a modest increase of about $2-3 an hour. In order to understand what they actually are arguing, however, a closer look at the data they provide is in order.)
Krugman’s argument is based on data from the U.S. Department of Labor that show an increase in real GDP per hour worked over the past several decades. Warren’s data, similarly, comes from a remarkably sparse Center for Economic and Policy Research report that compares stagnant real minimum wages with increasing total productivity over the same time period. In arguing that this data unquestionably justifies an increase in the minimum wage, then, Paul Krugman and Elizabeth Warren are implicitly committing the fallacy of division.
The fallacy of division occurs when something that is true of a thing is reasoned to be true of all of the different parts of that thing. In this case, Krugman and Warren are implicitly arguing that an increase in the productivity of the entire American labor force suggests an identical increase in the productivity of just those workers earning the minimum wage. They are using the total increase in productivity on the part of all workers as a proxy to justify raising incomes for just some of those workers. No matter your moral stance on this issue, their interpretations of the data that they cite are dubious at best. A less-than-controversial example may help to demonstrate why this is the case.
Over the course of the 2009-2010 season, the Miami Heat scored an average of 96.5 points per basketball game. In the following 2010-2011 season, however, the Heat upped their scoring to an average of 102.1 points per game, representing an increase in total productivity of 5.8 percent. If we look only at this increase in total productivity as a basis for wage increases, then, we would have to conclude that Dwayne Wade and his teammates should have earned an extra 5.8 percent as a result of their increased total productivity during the 2010-2011 season.
But wait a minute. Does this increase in total productivity necessarily imply an increase in the marginal productivity of each player on the team? In order to find out, we can take a closer look at just Wade’s numbers.
During the 2009-2010 season, Dwayne Wade averaged 36.3 minutes, 26.6 points and 6.5 assists per game. Over the course of the 2010-2011 season, however, Wade played more minutes per game (37.1) but scored fewer points (25.5) and had fewer assists (4.6), meaning that—despite the team’s overall 5.8 percent increase in total productivity—Wade’s marginal productivity actually fell from one season to the next. In fact, of the seven players who remained with the Heat from the first season to the second, a total of five exhibited decreases in marginal productivity (in terms of average points scored per average minutes played) during that time. (It should be noted here that my measurements are crude, that this is intended as nothing more than a playful analogy, and that there are dozens of different ways to gauge the productivity of a basketball player.)
All of this, of course, suggests that something other than an increase in the marginal productivity of the existing players is probably responsible for the Heat’s total productivity increase. (Most would probably point to the addition of Chris Bosh and LeBron James in 2010 as the primary reason for the spike in productivity.) It can still be argued that Wade and his teammates deserve bumps in their salaries nonetheless, but to do so by implying increased personal production from the increase in overall production would be a serious misreading of the data.
In the end, the minimum wage is a highly complex issue, and the case for it cannot be made or broken on the basis of two bad readings of economic data. There are any number of alternative moral, social, economic, statistical and political arguments that can be put forward either in favor of or against increasing the minimum wage, which is all the more reason to leave murky economic data and hasty statistical analyses out of it.
Chris Bassil, Trinity ’12, is currently working in Boston, Mass. His column runs every Wednesday. You can follow Chris on Twitter @HamsterdamEcon.
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