# Behind Seemingly ‘Objective’ Statistics

Statistics are often useful. Their careful collection and interpretation can improve both the practice of social science and the formation of public policies. But statistics also are often harmful. They must be handled with great care if we’re to avoid great mischief.

As is well-known to all who regularly deal with statistics, it’s surprisingly easy to tell lies with data that are truthful. If, for example, a country lowers barriers that obstruct the ability of low-skilled immigrants to find work, more low-skilled immigrants will find work. These new workers – being low-skilled – will earn wages below the national average. Thus, this policy of liberalized immigration will soon result in a lowering of both the median and mean wage – a fact that is easily trumpeted as evidence that allowing more low-skilled immigrants into the workforce is bad for the economy, or at least bad for the average worker.

But of course the fall, in this case, in the mean and median wage is a statistical artifact caused by expanding the size of the workforce by adding more low-skilled workers. While all too easy to do, it’s illegitimate to conclude from this statistic that the addition of low-skilled immigrants into the workforce caused the typical worker’s wage to fall. Only the most careful users of statistics will understand that the decline in the mean and median wage under these circumstances is consistent with every individual worker’s wages rising.

For those of you who are skeptical, consider this mental experiment. Suppose that on January 1st, 2020, the Jones’s calculated the average height of their two children – 5-year-old Sarah and 2-year-old Seth – and found it to be 39 inches. Now suppose that the Joneses had a third child, Sam, on December 31st, 2020. On January 1st, 2021, mom and dad again measured the average height of their children, who now are three in number. Newborn Sam is only 21 inches tall. The average height of the Jones’s children on New Year’s Day 2021 was, at 33 inches, six inches less than it was one year earlier. Yet no one would conclude that in 2020 one or more of the Jones’s kids shrunk or even failed to grow!

Using statistics to create false impressions about the individual elements – such as persons, events, or firms – that make up any statistical grouping is child’s play. But in the quotation at the top of this essay, economic historian Robert Higgs identifies a different and deeper problem with statistics. Let’s call this problem “Distorted Reality.”

Consider the so-called “distribution of income.” What does it mean? What is its relevance? These questions aren’t as inane as they at first appear.

As any sophomore can explain, the distribution of income is based on the record of how much monetary income is earned – usually during a calendar year, and for a specific country – by each of the many individuals or households. By arraying these monetary earnings from lowest to highest, a “distribution” of income is revealed.

This distribution can be sliced and diced in all sorts of different ways. A typical way is to divide it into quintiles. Under such a grouping, the 20 percent of all income earners whose incomes are higher than that of any of the remaining 80 percent are classified as being in the top quintile. The 20 percent of income earners whose incomes are lower than are the incomes in the top quintile, but are higher than are incomes earned by the remaining 60 percent of income earners, are classified as being in the second quintile. And so on.

Pretty simple. Yet what is this “distribution’s” significance, especially in a world – which ours (fortunately) is – where the amounts of income that different people earn are not determined consciously by some central authority?

Many people will insist that the “income distribution’s” significance is that it’s a – perhaps the – key piece of information to reveal just how economically equal, or unequal, is the society. But such a response is shallow, not least because the “distribution” of income says nothing about the flesh-and-blood individuals whose incomes are used to calculate it.

First, the individuals who are in each quintile change from year to year. This reality is of no small significance, as Thomas Sowell explains:

When some people are in the bottom quintile for life and others are in the top quintile for life, that is a very different situation from one in which most people move from one quintile to another within a decade. Only 11 percent of Americans 25 years old have been in a household within the top 20 percent of household incomes. But 70 percent of Americans 60 years old have been in such a household at some point in their lives. Since every 60-year-old was once a 25-year-old, increased income differences between age brackets are hardly an injustice to Americans who live a normal life span.

Second, monetary income, while important, is only one aspect of a person’s, or a household’s, economic condition. Always to some degree – and frequently to a large degree – monetary income is an offset to some significant non-monetary aspect of a person’s or a household’s economic condition. High income might reflect unusually dangerous or unpleasant work conditions, or unusually risky financial decisions. Low income might reflect a conscious decision to avoid such conditions and decisions.

A personal story is a lone data point, but in this case it’s one that plausibly conveys a general truth. As I neared graduation from the University of Virginia School of Law in May 1992 I received two offers of full-time employment. The first was for a tenure-track position as associate professor in Clemson University’s Department of Economics. The second was as a junior attorney at the prestigious Washington, DC, law firm for which I worked the previous summer. The annual monetary pay offered by the law firm was nearly three times higher than was the annual monetary pay offered by Clemson University. And also, I knew, the difference in lifetime monetary income earned as a lawyer, over the pay of a college professor, was even higher.

I remember talking on the telephone to the law-firm hiring partner who called with the job offer. After thanking her profusely, I turned the offer down without hesitation. It’s a decision that I’ve never regretted. The value to me of the leisure and task-flexibility enjoyed by a college professor was much higher than the additional monetary income of working as a lawyer. Or alternatively, the cost to me of the pressure and long hours of working at a big-city law firm is higher than is the value to me of the additional monetary income that I’d have been paid by working as a practicing attorney.

Therefore, a comparison of my monetary income to that of a practicing attorney reveals a distorted reality. Superficially, this comparison reveals that my economic welfare is lower than that of the attorney. But the deeper reality is otherwise. If the impossible were possible – specifically here, to observe and quantify subjectively experienced economic welfare – my welfare would be ranked as equivalent to, and perhaps even higher than, that of the attorney. Yet because monetary incomes are observable and quantifiable, they are what is seen and reported, while the many complex trade-offs that give rise to them remain hidden. The seemingly objective and straightforward reality is, in fact, a distorted reality. Government policy based upon such a distorted understanding of reality is likely to worsen the true reality.