Statistics can mislead as easily as they can enlighten

Not long ago, Corinne Maier boasted in The New York Times that "... in many years French workers have a higher productivity rate than their American counterparts."

Measures of productivity do regularly reveal French workers to be more productive than American workers. So Ms. Maier, a trained economist, must be right to conclude that this statistic is "proof that you can work better by working less."

In fact, she's probably mistaken.

France's labor regulations are much more burdensome than those in the US. By artificially raising the cost of hiring workers in France, these regulations make it unprofitable to hire the lowest-skilled workers. One result is that only higher-skilled workers get jobs in France. But because US labor regulations are less restrictive, a higher proportion of low-skilled workers find jobs in America.

With a larger proportion of highly skilled workers, France's average productivity is bound to be higher.

But the French shouldn't be cheering.

I drive this point home to my students by asking them what would happen to average worker productivity if Uncle Sam were to impose a minimum wage of $500 per hour. The correct answer is: "The productivity of the average worker would skyrocket!" This achievement, however, would be no cause for celebration, for this higher productivity would result chiefly from the firing of all workers incapable of producing at least $500 worth of output per hour. Measured productivity in America would jump impressively even as the US economy tanked and most workers were cast into lasting unemployment.

The larger lesson is that proper interpretations of statistics often are surprisingly counterintuitive.

After all, our intuition tells us that countries with higher labor productivity do better economically than do countries with lower worker productivity. But our intuition is wrong.

Statistics can also fool us when averages change over time. Suppose that the average real-wage rate in the US falls. Do we conclude that American workers are worse off? That's one possible explanation. But before jumping to that conclusion, be aware that another, very different, explanation might better fit the facts.

If lower-skilled workers enter the labor force in unusually large numbers, the average wage rate will fall without necessarily reducing any worker's pay. Indeed, the typical worker can even see his real-wage rate rise while the average rate falls!

To see how, suppose that you calculate the average height of people in the room where you now sit and find that it is 5 ft., 6 in. Now suppose a 2-year-old child enters the room. The average height of people in that room suddenly falls. Few of us would make the mistake of concluding that those people were shrinking in size. Some of them might even have grown taller. Yet how often do we hear politicians use statistics in just this specious manner.

The same logic applies to the calculation of average wage rates. Changes in this figure can be caused by changes in the composition of the labor force rather than by changes in the wages of individual workers.

For example, if teenagers, immigrants, and other lower-skilled workers start entering the labor force in larger numbers, they will lower the average wage rate because lower-skilled workers generally are paid lower wages than those paid to higher-skilled workers.

This fall in the average wage rate, however, does not signal that workers' fortunes are declining. In fact, in this case it is evidence of economic health: The economy is sufficiently flexible to provide jobs to workers who haven't yet acquired valuable skills.

A less-flexible economy, such as France's, which makes it difficult for lower-skilled workers to find jobs, will not "suffer" any such fall in its average wage rate. But that fact, surely, is small comfort to the many poor people left unemployed.

Of course, in the other direction, if higher-skilled workers begin entering the labor force in unusually large numbers, they can pull up the average wage rate even if the wages of ordinary workers don't change.

None of this is to suggest that statistics are useless. Quite the contrary, statistics are indispensable to grasp reality better and to distinguish explanations that are correct from explanations that are merely plausible or even downright erroneous. But statistics will assist us in our quest for understanding only if we approach them critically, aware that they can mislead as easily as they can enlighten.

• Donald J. Boudreaux is chairman of the economics department at George Mason University.