In his economic address Wednesday, President Obama lamented, “since 1979, when I graduated from high school, our productivity is up by more than 90 percent, but the income of the typical family has increased by less than 8 percent.” In other words, the link between pay and productivity has been shattered. This would be appalling if it were true — but it is not.

This argument has nonetheless become conventional wisdom in many circles. The belief that workers’ pay no longer rises with their productivity helps explain why liberals’ policy focus has turned so sharply to redistributive policies. The president and others essentially argue that the American dream has died and the modern economy does not reward employees for their hard work.

Fortunately, they are wrong. I put out a comprehensive report on this issue for the Heritage Foundation over the summer that examined changes in pay and productivity since 1973. The data shows average compensation — which includes both wages and benefits — has risen in tandem with productivity over the past generation. This makes sense — market forces compel employers to raise pay along with productivity gains. If an employer pays workers less than their productivity, its workforce will take better job offers from competitors. A business that pays more than its workers produce usually goes out of business. Competition forces businesses to pay workers according to the value they create.

But the widespread belief they do not is understandable. Wage and productivity figures appear to diverge. Since 1973 average hourly productivity has doubled, while average real hourly wages measured by the payroll survey have fallen 7 percent. Anyone glancing at these figures would conclude pay no longer rises with productivity.

With economic statistics the devil often lies in the details. The wage and productivity data come from different surveys using different methods and covering different groups of workers: statistical apples and oranges. The facile comparison has several problems.

For one, it does not look at everything workers earn. Looking only at wages ignores the non-cash benefits that have become an increasingly large share of workers’ total compensation. Economists expect total compensation to rise with productivity. Nothing says that additional compensation will come entirely in cash.

Worse, the payroll survey records the pay of just a portion of the workforce. The Bureau of Labor Statistics (BLS) tells businesses to report the pay of their “production and nonsupervisory” employees. Most businesses have no idea what this means and report the wages of their hourly employees instead — only 60 percent of the workforce.

The total hourly compensation of the entire workforce has risen 30 percent since the early 1970s, a far cry from the slight decline in payroll-survey-reported wages.

Second, the Bureau of Labor Statistics adjusts compensation for inflation using the consumer price index (CPI). It adjusts productivity with the implicit price deflator (IPD). These indexes use different formulas that calculate different rates of inflation. This methodological difference has nothing to do with underlying growth rates. Adjusting compensation for inflation with the IPD shows it has risen 77 percent since 1973 — much closer to the 100 percent increase in productivity.

Finally, the BLS overstates productivity growth in several ways. Economists have discovered, for instance, that the agency misestimates the prices of foreign goods that domestic businesses use in production. This makes them appear to produce more output at less cost — also known as higher productivity.

Further, compensation rises with workers’ net productivity — what remains after subtracting depreciation. As businesses use more computers and software in production, depreciation rates have increased. However, the BLS only measures gross productivity. This makes it appear that useable productivity has risen more than it actually did. (In the words of the liberal economist Dean Baker, “no one can eat depreciation.”)

Measured correctly, employee compensation has risen in step with the value workers create. Gaps between productivity and compensation sometimes emerge in times of high unemployment — such as America is now experiencing — but over the long term workers’ pay closely matches the value of what they produce. Federal Reserve researchers and Harvard professor Martin Feldstein have also come to this conclusion.

Nonetheless, over the past generation, pay has not risen very quickly among some groups of workers, while technological changes have made highly skilled workers much more productive. Today a few engineers can operate computers that run vast assembly lines, so their wages have risen commensurately. Technology has not augmented the productivity of less-skilled workers in the same way: It takes as many workers to change sheets in a nursing home today as 40 years ago. Economists call this “skill-biased technological change.”

The solution is to help less-skilled workers become more productive. If they do, market forces will drive their compensation up. Online education — by reducing the cost of acquiring skills — could become an economic game changer in this regard. George Tech University has announced it will start offering online master’s degrees for just $7,000, and other schools are offering high-quality courses online for free.

President Obama is wrong: Workers’ pay remains closely connected to their productivity. The challenge for policymakers is removing barriers that make it harder for workers to become more productive.

- James Sherk is a senior policy analyst in labor economics at the Heritage Foundation.