Special Report

## Inequality Doesn’t Measure Up

Statistics on income disparities invariably mislead and confuse.

Income inequality has been an issue of considerable contention among intellectuals as of late. Unfortunately, there are few areas where the relevant statistics are fraught with so many shortcomings. Thus, people who are intellectually honest may unintentionally mislead because the numbers they use do not show what they think such numbers do. For example, a blog post by the *American Prospect*'s Ezra Klein shows why statistics on income inequality can make inequality look worse than it really is:

I was thinking through Robert Reich's proposal to mandate that countries who want to trade with us set a minimum wage of half their median wage, and I ended up digging into some median wage statistics domestically. For those fuzzy on the terms here, median means, essentially, in the middle. If I make $6, and Matt makes $7, and Tom Friedman makes $150, the median wage is $7. The mean is the average, so in this example, it would be $54.33. If we outsource Tom's job to a bright Bangladeshi making $1, my wage is now the median, and the mean is $4.66.America's mean wage in 2005 was $35,448.93. That's the number you generally hear quoted. Its median, however, was $23,962.20. And if you want another example of rising inequality, in 1990, the median was 71% of the mean. In 2005, it was 67%. Indeed, over the same time period, the mean wage increased by 75%. The median only increased by 65%.

The mean and median numbers Klein uses suggest that the incomes at the top are growing much faster than those at the bottom. However, data on wages are some of the most misleading as this excellent article by Tim Worstall shows.

The fact is our economy has expanded over the last two-plus decades so that people who previously would have a hard time entering the labor force now do so with much less difficulty. As a result, more housewives are able to get jobs (see table 584 of the 2007 statistical abstract (pdf)). Also finding access to such jobs are immigrants. This nation has seen more legal immigration in the last 25 years than at any time since the beginning of the last century (see table 5 of the 2007 abstract (pdf)). However, such jobs are often low wage because those getting them usually either want part-time work or are entering the labor force with few skills.

This increase in low-wage workers results in downward pressure on means and medians. Yet the numbers Klein points to have gone up. That can only happen if those already in the workforce are seeing their wages rise. When those two phenomena converge, it's also likely the difference between the mean and median will, as Klein noted, increase, making inequality appear as though it has risen.

Consider a hypothetical example. Suppose that you have three workers, John, Sally and Matt. John makes $11 per hour, Sally makes $9, and Matt makes $7. For inequality, let's use both a comparison of the highest and lowest paid workers and the difference between the median and mean. On the first measure, Matt makes about 64 percent of what John does. On the second, the median wage is $9, while the mean (27 divided by 3) is also $9, which means that the median is 100 percent of the mean.

Now let's assume that a number of years go by, and two new workers, Tony and Lisa, enter the workforce for the first time, Tony being hired at $7 per hour while Lisa is hired at $5. Meanwhile, the three other workers have received a number of raises, so that both John and Sally make $15 per hour and Matt makes $10.

Who under this situation is any worse off? John, Sally and Matt now make more money than they did a few years ago. Tony and Lisa have gone from having no income to having income, and they are on their way to earning valuable job experience which will benefit them later on. Indeed, everyone is better off.

Yet look at what has happened to our measures of inequality. A comparison of the lowest to highest paid worker shows that Lisa makes only 33 percent of what John does. The difference between the mean and median has also worsened. The median is now $10, while the mean (52 divided by 5) is $10.40. The median has dropped to 96 percent of the mean.

However, it is hard to argue with a straight face that inequality has really increased -- after all, the *real* gap between John and Lisa has declined, since Lisa went from earning $0 per hour to earning $5. Unfortunately, actual government wage statistics don't count the folks who are not yet in the workforce, leaving us with an inaccurate picture of inequality.

That one has to very careful with income statistics lest they be misleading is not the only lesson to be derived here. More important, as Diana Furchtgott-Roth recently suggested, is that income inequality isn't very important. Rather, our focus should be on whether entry-level jobs remain open and abundant for those at the bottom of the income scale and whether, over time, people are able to move up the income ladder.

**David Hogberg is a senior analyst at the National Center for Public Policy Research. He also hosts his own website, Hog Haven.**