Why are so many workers struggling today?

Some union-backed analysts have a straightforward answer: "Their employers are cheating them." They claim businesses no longer compensate workers for their productivity. This argument demonstrates H.L. Mencken's point that "for every complex problem there is an answer that is clear, simple, and wrong."

Competition forces employers to base pay on productivity. Firms that consistently pay workers more than they produce go out of business, as Bethlehem Steel famously demonstrated. But firms that underpay their employees also don't last long.

Imagine a firm that tried paying some employees just half of what they produce. A competitor could reap large profits by hiring away those productive workers for slightly more. But then another competitor would offer even higher pay. Competition quickly bids up workers' pay to their productivity level. To keep good employees, businesses must pay them commensurately with their productivity.

This explains why over 95 percent of Americans make more than the minimum wage. Federal law does not require employers to pay above $7.25 an hour. Economic laws do. A company that wants a quality workforce has to pay for it.

Believers in a productivity-pay gap rarely note their theory's implication: that many employers pay their workers from the generosity of their heart. If competition does not drive pay, then high-wage companies could pay less. Why don't they pay lower wages and increase their profits? They must be incredibly generous.

Of course, many employers are generous. But few economists think Mark Zuckerberg's generosity explains why Facebook's average salaries exceed $100,000. Rather Facebook employs highly skilled and productive workers. Their skills command premium pay. This logic illustrates why few economists believe the pay-productivity gap exists. Even prominent liberal economists reject the theory.

Nonetheless a union-affiliated think tank has produced influential charts showing productivity nearly doubling since 1973, while wages stagnated. These charts persuaded President Obama that employers deny workers the fruit of their labor. Labor Secretary Tom Perez told reporters his new overtime regulations are meant to close this gap. If competition ties productivity to pay, why do these charts show otherwise?

Because, as Mark Twain noted, "there are lies, d----d lies, and statistics." These charts compare statistical apples and oranges. They juxtapose the productivity and pay of different workers. They also include the productivity growth of the self-employed (including sharing economy workers like Uber drivers) while excluding their pay growth. And they adjust productivity and pay for inflation differently. These choices systematically lower measured wage growth and increase measured productivity growth.

But when we compare apples to apples, the apparent divergence disappears. Since 1973, average productivity grew 81 percent in the private sector. Using the same measure of inflation and looking at the same workers, we find that average earnings also grew 77 percent. Workers enjoy the fruit of their labor.

However, it is also true that productivity has not grown at the same rate for all workers. Modern technology has made highly skilled workers even more productive. At the same time, it has reduced demand for many less-skilled workers' labor. A lot of workers face real economic challenges (on top of the slow recovery). But these challenges stem from a changing economy — not reduced corporate generosity.

The best way to help these workers is to help them become more productive. They will then be able to command better pay. Education reforms and reducing the cost of college would be a good start. States should also tear down barriers to better earnings, such as excessive licensing requirements that prevent workers from utilizing their skills. One-third of U.S. jobs now require a government license. Many of these licenses are unnecessary — barbers do not need to study for a year to safely cut hair. But the license mandates serve to keep many workers out of jobs in which they could excel — and increase their earnings.

Trying to increase productivity is a complex solution to workers' problems. But it is also the right solution.