Truth, Lies and Statistics

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.

FILED UNDER: Economics and Business
Steve Verdon
About Steve Verdon
Steve has a B.A. in Economics from the University of California, Los Angeles and attended graduate school at The George Washington University, leaving school shortly before staring work on his dissertation when his first child was born. He works in the energy industry and prior to that worked at the Bureau of Labor Statistics in the Division of Price Index and Number Research. He joined the staff at OTB in November 2004.

Comments

  1. RJN says:

    “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.”

    This is so flawed that I can barely get my head around it. He is saying that mfg. employment is lower now than when we ran trade surpluses (of mfg. goods). Duh. Then he says; but, but, but, a trade deficit is not the same as a negative surplus (which of course it is), so the fact that we have lower mfg. jobs when deficits appear is ????, but certainly not correlated to trade deficits.

    Please break the news to me gently, I am old; have I slipped into dementia.

  2. spencer says:

    We start with 30 domestic workers and go to a state where we still have 30 domestic workers but we also have added 25 foreign workers.

    so in this example foreign worker have expanded from zero (0%) of the workforce to 45% of the workforce while the domestic workforce has not grown.

    Do you actually believe that this example has any relationship to reality?

  3. Steve Verdon says:

    Spencer,

    Do you actually believe that this example has any relationship to reality?

    I never claimed it was supposed to be reality and second you are reading in some assumptions such as that there are no foreign workers intially. The point is that wages can go up for everybody and the average still go down. We saw it recently with the median price of housing.

    Clearly you have no other point than to make dopey comments about how an illustrative example is not reflective of reality. No shit Sherlock, reality is messy and often confusing. This is why economists use models, to simplify things. I’d thought you of all people would realize this. Guess I was wrong.

    RJN,

    The problem with manufacturing jobs and the trade deficit is that it isn’t clear that the correlation would hold up using a longer time series. Also, world wide manufacturing employment has been declining. Why there is a decline in manufacturing is not something as simple as the U.S. is running a trade deficit.

  4. madmatt says:

    by the same standards a few millionaires in the mix and wage growth seems to go up even though wages may be stagnant.

  5. spencer says:

    The example seems to make it self evident that the original 30 workers did not include foreign workers.

    I believe the point of the article was to demonstrate that the average hourly earnings data that show average real incomes of hourly wage employment to be down can not be relied on because Don can come up with a set of data that
    shows that the decline in real average wages was due to an influx of foreign workers at lower wages. If the purpose of the example is to discredit what the actual data shows, then the example should have some relationship to what
    the actual data measures.

    If, as Don is claiming the weak real wage data is due to an influx of foreign workers he should make some effort to demonstrate that the share of foreign workers in the labor force is somewhat similar to the example he constructs. Otherwise, anyone that can do simple math or wants to base their analysis on something approaching reality is unlikely to take his argument seriously.

  6. spencer says:

    should have read your comment more carefully.

    You said:
    “I never claimed it was supposed to be reality.”

    Why am I not surprised.

    In other words anything you make up is better evidence the the facts.

  7. Steve Verdon says:

    The example seems to make it self evident that the original 30 workers did not include foreign workers.

    You keep writing 30, but apparently arithmetic is not your strong suit, the initial number was 40.

    I believe the point of the article was to demonstrate that the average hourly earnings data that show average real incomes of hourly wage employment to be down can not be relied on because Don can come up with a set of data that shows that the decline in real average wages was due to an influx of foreign workers at lower wages.

    Really, and what data set would that be? I just read the article again and Boudreaux makes no mention of any such data set. What he does do is point out that relying simply on averages can be problematic no matter what point you are trying to make (e.g. madmatt is [sorta] right also that the average could go up, even if everyone’s wages fall).

    If the purpose of the example is to discredit what the actual data shows, then the example should have some relationship to what the actual data measures.

    The example wasn’t to discredit anything, but to point out that sometimes what people think a statistic means doesn’t necessarily have to be the case. We just saw it a couple of months ago with housing prices. In fact, in all regions the median price went up, but nationally the median price went down, by alot. So I have a clearly made up example illustrating the problem, I also have a real world example of these kinds of problem, yet you still have your panties all in a knot.

    Why am I not surprised.

    In other words anything you make up is better evidence the the facts.

    Spencer are you acting like an jerk because you enjoy it or simply can’t help it? It is quite clear that my post was discussing that people need to be careful when using statistics such as an average. Anything else, is just your own fantasy.

    Oh, and here is a bit of advice, I’d recommend enrolling in a reading program. Maybe the Sylvan Learning Centre.