As discussed in several previous posts (for example, here ), former U.S. Secretary of Labor Robert Reich’s recent case for raising the minimum wage  is a cascade of confusions. Here’s another: Reich gets his basic economics wrong about the relationship between worker pay and worker productivity.
Starting at around the 0:50 mark in his video , Reich says that if the minimum wage as set by Uncle Sam had “kept up with the added productivity of American workers since then , it would be more than twenty-one dollars an hour today.” Specifically, according to the graph that accompanies Reich’s claim, a minimum wage that had kept pace with “the added productivity of American workers” since 1968 would now be $21.72 per hour.
I can find in Reich’s video no sources for the data he offers there. With just a bit of googling, though, I found the likely source of Reich’s claims about the minimum wage hypothetically keeping up since 1968 with both inflation and with worker productivity: it’s this March 2012 report by John Schmitt  for the Center for Economic and Policy Research.
Every principles-of-economics student knows that a worker’s pay is determined on the market by the value of that worker’s marginal product and not by the value of workers’ average product (or even by the value of the average product of any large class – e.g., “workers age 16-19” – of workers). Yet Reich (following Schmitt), in order to determine what the minimum wage would be today if it had kept pace with worker productivity, tracks over time (1968-2010) the change in average worker productivity. According to the Data Appendix of Schmitt’s paper, he – Schmitt – uses Bureau of Labor Statistics data to calculate “output per hour of all persons” in the nonfarm business sector. The change over time in the average productivity of all workers in the nonfarm business sector is utterly irrelevant to any discussion of what the minimum wage ‘should’ be even if we agree that the minimum wage should keep pace with changes in the productivity of minimum-wage workers.
Reich’s error here is worse than sophomoric. It, and it alone, should label him forever as someone not to be trusted to analyze any economic matter, including the economics of minimum-wage legislation.
(See also this related 2013 Forbes essay by Adam Ozimek , which takes issue with Elizabeth Warren for committing the same embarrassing error as committed more recently by Reich.)
Although the minimum wage is set by legislative fiat and not by market forces which account for worker productivity, the legislature’s setting of the wage nevertheless affects the productivity of minimum-wage workers. In particular, the higher the minimum wage, the higher is the marginal productivity of minimum-wage workers (but, as explained below, this increased productivity is nothing to celebrate). This artifactual increase in the productivity of minimum-wage workers occurs for four reasons.
First, one response of some, perhaps many, employers to a hike in the minimum wage is to work their minimum-wage employees harder than before. Thus, these workers’ marginal productivity rises (even if our presumption must be that the value of the forced higher wages to these workers is less than the subjective cost to these workers of the worsening of their on-the-job work experiences).
Second, because the minimum wage creates a surplus of workers at that wage – in part because it attracts into the labor force some relatively higher-skilled workers (such as trustworthy and experienced retirees) who voluntarily remain out of the labor force at the lower wage – employers can exercise the greater choice that Reich himself recognizes is afforded to employers by a rise in the minimum wage . Employers, in short, can be more picky in choosing their workers. The result is a minimum-wage workforce consisting, on average and at the margin, of more-productive workers.
Third, because the minimum-wage makes substitution of capital (machinery) for low-skilled workers more attractive at the margin, the workers who retain their jobs at the higher minimum wage have more capital on the job to complement their work efforts – making these workers more productive at the margin.
The fourth reason that raising the minimum wage results in an artifactual increase in the productivity of minimum-wage workers is simply that fewer low-skilled workers are employed at the higher minimum wage than are employed at the lower wage. Even if the talents and trustworthiness of all low-skilled workers is the same after the hike in the minimum wage as before, and even if there is no change in the capital-labor ratio, because the value of the output of the marginal minimum-wage worker does not increase simply because the minimum wage is raised, it is unprofitable for employers to employ as many low-skilled workers at the higher minimum wage as it is at the lower wage. Put differently, the value to a firm of the marginal product of the each of its minimum-wage workers if it employs (say) ten such workers is lower than is the value to this firm of the marginal product of each of its minimum-wage workers if it employs only nine minimum-wage workers. A hike in the minimum wage, therefore, causes this firm to reduce the number of low-skilled workers it employs until the value of the marginal product of each of these workers rises so that it is at least equal to the higher minimum wage.
Note that regardless of the relative importance in reality of any of the above four artifactual changes in minimum-wage workers’ marginal productivity, the resulting government-induced rise in the marginal productivity of such workers is the consequence of a policy that nevertheless harms at least some low-skilled workers. To the extent (which is likely significant) that employers cannot profitably intensify the work-effort put forward by all of their low-wage workers, the artificially mandated higher pay of low-skilled workers means that some of them will lose their jobs (or not be hired to begin with). And the pattern of job losses will not be random: the very workers that the most ardent, if naive, supporters of the minimum wage wish especially to help are the ones who will most likely suffer the worst consequences of minimum-wage legislation, while the resulting artificially high wages will be paid disproportionately to workers – such as teens from affluent suburban families – who need a raise far less desperately than do those poor workers who lose their jobs need the incomes they lose.
Because the minimum wage is arbitrarily set by government diktat rather than by market forces, I do not discuss in this post the likely errors in the many claims that worker pay has not kept pace with productivity.* This 2006 post by Greg Mankiw is worth reading on this matter  – as is, I boast, this March 7, 2014, Wall Street Journal essay by freshly minted GMU Econ PhD Liya Palagashvili and me .
* If one were to develop a positive theory of the determination of minimum wages, any such theory that predicted that legislated minimum wages would keep pace with the value of low-skilled workers’ marginal productivity would be highly implausible (as, ironically, is shown by the very complaints, issued by Reich and others, that the minimum wage does not keep pace with worker productivity!).
First, such a positive theory would have to include a reasonable explanation for why government officials would consistently outperform competitive market forces at discovering the value of low-skilled workers’ marginal productivities and then ensuring that the actual wages paid to these workers accurately reflect this discovered and ever-changing information. The proposition that any such theory would include this sort of believable explanation strikes me as too far-fetched to take seriously. Second, a plausible, predictive positive theory of minimum-wage setting would likely zero-in on some rent-seeking account (such as best explains the origin of the national minimum wage in the United States ) or on some account of how politicians cater to the economic ignorance of the general population with fine-sounding legislative interventions – interventions the actual results of which, although often quite the opposite of those that their proponents predict, are difficult to see and isolate in the great complexity of the modern economy.