Don Boudreaux has an excellent article in the Pitsburge Tribune-Review on statistics and how one has to be careful with reading statistics.
Here’s an example: Go back to 1977, the year America began its current string of annual trade deficits, and look at what’s happened since then to manufacturing employment as a percentage of total U.S. employment.
You’ll see that since that year the percent of manufacturing jobs in the U.S. has steadily declined. Today it’s about half of what it was 30 years ago. It appears as if trade deficits cause, or are at least associated with, declining jobs in manufacturing industries.
This appearance, though, is illusory. While the percentage of Americans today employed in manufacturing occupations is indeed about half of what it was in the mid-1970s (14 percent today compared with about 28 percent back then), the decline in manufacturing jobs as a percentage of all American jobs started way back in 1945 (when it was about 44 percent of all jobs). Because for most of the period between the end of World War II and 1977 America ran annual trade surpluses, it is illegitimate to read the data as saying that trade deficits reduce manufacturing employment.
Basically a cautionary example that correlation is not causation. This idea is well known to most people, even those with an aversion to mathematics and statistics. However, here is an other interesting danger that is often overlooked in statistics,
The average wage rate can fall even though everyone’s wages rise. Here’s how. Suppose that America’s average wage rate is now $18 per hour. Now suppose that many low-skilled immigrants arrive and find employment here at wages higher than they could earn in their home countries. Possessing lower-than-average skills means that the wages these immigrant workers earn will likely be lower than the U.S. average — say $10 per hour.
America’s average wage rate will be pulled down even though no individual’s wages fall. Indeed, it is possible for every American’s wages to rise and the average still fall.
This is indeed quite possible. The table below demonstrates how it is possible for everyone’s wage to increase, but for the average to still go down.
|
Initial Work Force |
|
| Workers | Wage |
| 10 | 10 |
| 10 | 12 |
| 10 | 14 |
| 10 | 18 |
| Average Wage | 13.5 |
|
After Immigration |
|
| Workers | Wage |
| 25 | 11 |
| 10 | 13 |
| 10 | 15 |
| 10 | 19 |
| Average Wage | 12.55 |
The problem is that there was influx of immigrants at the lower wage rates which increased the number of people at that wage rate. Thus, when calculating the (weighted) average wage the average declines even though everybody is making $1/hour more.
Prof. Boudreaux’s conclusion at the end of the article is a good one,
Statistics seem like straightforward, unambiguous facts; they’re not. Care is required not only in their gathering but also in your interpretation of them.
Keep this in mind next time you read about some statistic. Even though it might fit your world view, it could still hold some bits of information that would lead to a different conclusion. For example, how much of the stagnant wages that we hear about is a result of immigration? I’m not saying all of the stagnation is due to immigration, but you’d want to control for the effect above. If you are adding over a decade or two millions of low wage/low skill workers to the labor force then it stands to reason that this could pull down the average wage rate. Demographic shifts can have very large effects. Just look at the massive shortfall in Medicare. That is due in large part to a demographic shift.
