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When facts aren’t facts

One standard explanation for the increase in measured inequality over the last few decades is that innovation has enhanced the productivity of highly educated people more than the productivity of less educated people. That in turn has increased the wages of college graduates relative to those who have only graduated high school. In the New York Times, Eduardo Porter refers to Larry Mishel of the Economic Policy Institute who is skeptical of this phenomenon. Porter writes:

This rendition of history suggests that improvements in technology — coupled with a college graduation rate that slowed sharply in the 1980s — have been principal drivers of the nation’s widening income gap, leaving workers with less education behind.

But critics like Mr. Mishel point out that this theory has important blind spots.

For instance, why have wages for college graduates stagnated over the last decade, even as innovation continues at a breathtaking pace? Between 2000 and 2008 the typical earnings of men with at least a bachelor’s degree fell by more than $2,000, after inflation, to $70,332 a year. Between 2008 and last year they fell a further $3,500. Though somewhat less pronounced, the pattern is similar for women.

This seems to refute the claim that technology gives college graduates an advantage. Surely there was technological change between 2000 and 2008, yet earnings of college grads fell. This calls into question the relationship between technology and inequality, but it’s alarming in its own right. It suggests that the rules of the game are rigged in some way. People are doing the right thing–they are going to college–and yet their salaries are falling. Here’s the key claim:

Between 2000 and 2008 the typical earnings of men with at least a bachelor’s degree fell by more than $2,000, after inflation, to $70,332 a year.

What does that mean? It seems pretty straightforward. But it’s easy to misinterpret. Here is what it does not mean. It does not mean that people who had a college degree in 2000 found themselves with lower income eight years later. Let me say that again. It does not mean that people who had a college degree in 2000 found themselves with lower income eight years later. It COULD mean that. But it doesn’t have to.

Why not? Because the people who were sampled in 2000 and 2008 are not the same people. What the statement does mean, is that if you take the median income of people with at least a bachelor’s degree in 2008, that number is lower than the median income of all the people with at least a bachelor’s degree in 2000. (This assumes that prices are measured correctly. All of the income comparison in this post correct for inflation using standard methods. There are problems with those methods, but let’s put that issue aside.)

You might think that this is a nit-pick. How much can the population of highly educated people change in just eight years? Sure, some people retire or die. Others enter the labor force. But those effects must be small.

They’re not. They’re potentially huge and they make the comparison meaningless for trying to figure out if it’s a good idea to go to college or if the economy is rewarding college graduates. Stick with me and you will learn one of the coolest things there is to learn about statistics and data and the elusiveness of truth. Sometimes something that looks like a fact isn’t close to a fact. And you’ll discover something pretty amazing that happened between 2000 and 2012 that you might not know about.

If you want the details, go below the fold…

Comparisons between 2000 and 2012 might not show what you think they show because there could be changes in not just who is working but in how much they work and when they work. So it’s possible that the proportion of the work force that works full-time is different, or all year vs. part-year. And even when you hold those things constant, men make more than women. So another variable that can change over twelve years is the proportion of the work force that is male vs. female. So to hold all those factors approximately constant, I’m going to look at just women who work full-time, year-round and who are over 25. I pick the age point just because that’s how the Census lists it.

I’m going to use a slightly longer time horizon, 2000 to 2012, so I can use the latest data. It also makes the point I want to make a little more dramatic.  But if I did it for 2000-2008, I’d get the same effect. The bottom line is that you can’t draw simple conclusions from what look like simple transparent changes.

Between 2000 and 2012, here are the changes in real median income for women 25 and older who were defined as working full-time, year-round by education level. The data I’m using are census data from here.

Less than 9th grade                    -3.7%

9th-12th but didn’t finish          -6.7%

High school graduate                 -3.3%

Some college but no degree       -3.7%

Associate’s degree                     -10.0%

Bachelor’s degree or more        -2.7%

Looks like a pretty bleak 12 years, doesn’t it? And sure enough, these numbers echo the Mishel claim listed above–college grads seem to be doing worse.

Given those numbers, what do you think happened to the median income for all women, regardless of education level? If you don’t think about it very much, you’d take an average of the six decreases in the data for each income group. Remember, those six categories are exhaustive–they cover all women 25 and over who work full-time year-round in the workforce. The average change across all groups turns out to be almost exactly 5%. So if you didn’t think about it much, you’d guess that for all women 25 and over who worked full time, income fell about 5%. You’d think that might be a pretty good approximation. But you’d be wrong.

Or maybe you’d realize that all the groups aren’t the same size, so maybe you shouldn’t just take the average. Maybe you should take a weighted average. But you’d be pretty confident that the overall change in the median income of women would be somewhere between -2.7 and -10, the range between the smallest change and the biggest change.

But you’d be wrong. The income of women over the age of 25 who worked full time actually increased between 2000 and 2012. It went up 2.8%. (Again, all these numbers are corrected for inflation.) Not a great twelve years. But very different from a 5% drop.

Now that seems impossible. I must have made a mistake. If every sub-group went down, how could the total for the whole group go up?

But it is possible. How? The answer is that the women in the full-time workforce 25 and over in 2000 were not the same women in 2012. In particular, they were a lot better educated. But how much better educated could they be in twelve years? Or a better way to put it, how much could the educational composition of the full-time female labor force change in a mere 12 years?

A lot. More than I would possibly have come close to guessing. In 2000 30.5% of all female workers who were 25 and older and who worked full-time and year-round had at least a bachelor’s degree. In only 12 years, that number had increased to 41.8%. That’s an enormous change, a 37% increase in the proportion. And it’s the category that has the highest overall pay of all six categories. So if you increase the proportion of the population in the highest paying group, the overall average can go up even when each group, including the group that pays the most, goes down.

Here’s another way to see it. In 2000, 11.6 million women 25 and over who were working full-time had at least a bachelor’s degree. Twelve years later there were 17.2 million women 25 and older working full-time with at least a bachelor’s degree.

That’s incredible. Between 2000 and 2012, the number of women with at least a bachelor’s degree increased by 48% in absolute numbers. That’s a silent revolution in the work force. (This phenomenon is called Simpson’s Paradox by the way. Floyd Norris of the New York Times has a similar example here.)

And now you can understand the complexity of claiming that college grads are doing worse than they did before. They’re not the same people. When a lot more women are going to college and entering the labor force with a college degree, you wouldn’t expect them to necessarily have the same income as the people who have already been to college. For one reason, they’re likely to be younger with less experience. But as the number of people going to college increases, you might expect their starting salaries to be lower than workers from before. The pool is less selective. And of course, there are a hundred other reasons their salaries could be lower–maybe they major in different things than people did in the past.

My point is that you can’t prove much by observing that salaries for people with a college education are going down over some period. It doesn’t mean that people who already have college degrees are doing worse. They could be doing better, but the starting salaries of the newcomers can pull down the median and the average as well.

The bottom line is that the “stagnation of college grad salaries” is misleading as a measure of the health of the economy and even of the health of being who have already graduated and who are working. It can actually be an encouraging measure–one of the reasons college grad salaries can stagnate is because more people are going to college and the new grads have lower salaries than the existing median. But the new grads are better off than they would be than if they had not gone and their salaries do not necessarily mean that those who would have gone no matter what are doing worse.


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