# Economists Do It With Models

## Follow Up: Read This Before Signing Up For Those Random Classes…

#### August 12th, 2010 · 7 CommentsFollow Ups · Fun With Data · Policy · The Simpsons

So yesterday I posted a little quiz asking what was wrong with with labeling the following graph with the headline “The benefits of a college degree in one graph”:

I was quite impressed with the comments on the post, since most of you passed with flying colors and even touched on issues that were more subtle than what I was going for, such as the way unemployment is calculated and whatnot. The fundamental point that I was making, of course, was regarding the correlation versus causation issue. In that sense, there is nothing wrong with the graph itself, since it just shows data about the world. The problem is with the caption on the graph that interprets the data as the benefits of education, since this implies that you can take a randomly selected person, give him some education and therefore bump him into a different one of these buckets. I particularly liked reader Warren’s J’s comment, which states “Even more pronounced is the correlation between employment and the education of your highest-educated parent. So, the conclusion is that you increase employment by sending parents to school, right?”

This discussion highlights the classic problem that labor economists face in trying to estimate the returns to education. On the up side, labor economists have a lot of data at their disposal- they can calculate wages versus education and can control for things like age, tenure at job, gender, race, etc. On the down side, they can only control for those things that they can see, and ability and motivation are, for the most part, not on that list of things. Why is this a problem? Let’s say that our regression tells us that a year of schooling is associated with a \$5000 increase in yearly wages. Does this mean that I can increase my income \$5000 a year by signing up for some night classes? I don’t know. What it does mean is that those people who have CHOSEN to have an extra year of schooling make \$5000 more. Put this way, it’s pretty clear that at least some of the \$5000 should be attributed to whatever qualities made the person choose the schooling in the first place. If it’s the case that smarter and/or more motivated people choose more schooling, then the \$5000 is an overestimate of the return to school itself. On the other hand, if people seek out extra education to make up for what they are lacking in terms of ability or motivation, then the \$5000 is an underestimate of the true return to schooling.

In an ideal world, economists would randomize people into different groups, each of which gets a different amount of schooling, and then compare the resulting wages and unemployment levels. Unfortunately, the government hasn’t gotten on board with that plan yet, so economists have to be more creative. For example, economists use the fact that there is an imperfect correlation between age and number of years in school to estimate the effect of mandatory schooling on financial outcomes. This works because most mandatory schooling laws are written such that a student must go to school until he reaches a particular age, often 16 years old. However, depending on when the student was born and/or allowed to enter school, this requirement could translate to completing 9th grade for some students and completing 10th grade for others. If you believe the assumption that birth month is not correlated with innate ability or motivation, this approach provides a limited but valid causal estimate of the return to a (particular) year of education.

When estimating these sorts of effects, it’s important to remember that even a causal interpretation merely answers the question “what does an extra year of school do for this person under the assumption that no one else decides to up and get more school also?” If a large number of people increase their level of schooling, the supply of workers for jobs that require higher education increases, which pushes down the wages that these workers get. (The baby boomers would probably be more than happy to shed some more light on this concept for you.) To some degree, the mix of available jobs might change to meet this supply, but it’s certainly not the case that if everyone went to college we’d end up all doing jobs that required or could financially reward a college education. (If nothing else, this would make your morning cup of coffee pretty expensive.) In fact, you’d likely see a ratcheting effect illustrated a few years back by one of my freshmen who earnestly explained to me that she was discussing with her parents how “grad school is the new college.” In a lot of ways, she’s not wrong.

I initially put this topic out there as a quiz because I feel like I’m beating a dead horse with this whole correlation vs. causation thing- I’ve tried stick figures, TV dinners, SAT scores, baseball, and boobs, and yet not everyone seems to grasp (or be willing to acknowledge) the concept. This wouldn’t really be a big deal if the distinction between correlation and causation were just a matter of nerdy semantics, but instead the issue has clear choice and policy implications. For example, there would be a lot of pissed off people if everyone saw this graph and ran out to get their University of Phoenix degrees, only to find that they were still unemployed and \$50,000 in debt afterwards. Before you say “that’s absurd, clearly people aren’t that dumb,” take a look at the following clip at around the 6:52 mark:

 The Daily Show With Jon Stewart Mon – Thurs 11p / 10c Deductible Me www.thedailyshow.com

“You want to create jobs as rapidly as China? The Chinese pay zero capital gains tax. If we had zero capital gains tax in the United States, we’d be building factories, founding companies, creating jobs, we’d be dramatically better off.”

This actually made me look up Newt Gingrich’s educational background to confirm that he had not gone to law school, since I can’t imagine him scoring very well on the LSAT with this sort of logic. The most frustrating thing is that I don’t actually think that Newt or others are actually unintelligent or incompetent, so I feel to a large degree that they should know better than to go around trying to convince people that if something leads to a particular result in China that it’s going to lead to a similar result in the U.S. I’m not sure I could think of a worse natural experiment if I tried. Maybe Newt was suffering from the same lack of recollection as Homer Simpson:

Communism vs. Rudimentary Free Markets

On a side note, it seems like Jon Stewart is on Paul Krugman’s side of the octagon. I am also pleased that my readers seem to be more with it than the average politician. (What’s the line about damning with faint praise again? 🙂 )

### 7 responses so far ↓

• 1 David // Aug 12, 2010 at 9:12 pm

I’m sure Newt Gingrich knows that correlation does not equal causation… but he’s also a politician, and he favors cutting the capital gains tax. I’m not aware of research suggesting that a higher capital gains tax is bad (or, at least, worse than other taxes), and I can think of reasons not to subsidize capital gains. In any case, there’s little reason to make an academic argument when you can just point at examples out of context and drum up support for your policies.

As for education: what about its effect as a signaling device? It may well be that someone is intrinsically more motivated, but that does her no good if the employer doesn’t recognize (and thus compensate) it.

If we assume that more motivated/smarter people have a lower cost of attaining an additional year of schooling (less work for the same outcome), then they will be more willing to get more education. Firms would then be well advised to use years of schooling as an indicator for motivation/intelligence. If that is the firm’s belief, it doesn’t matter if it’s really true: additional education will lead to higher compensation.

Then, it makes a lot of sense to take those night classes, even if they add nothing to your skill set. As unfortunate as it is (given that education is costly), I think it’s not an unreasonable claim that firms operate under this assumption. Many jobs require applicants to have a college degree, but don’t care if they majored in economics or basketweaving.

The problem, of course, is that this may be the equivalent of an arms race. Soon, a graduate degree may be required to distinct oneself in an application process. Given the cost of education, that’s not a good outcome. The best way to guard against it is, I believe, to not water down standards. Only if the cost of education (not just monetary) is high enough can it serve as a proper signaling device.

• 2 Warren J // Aug 13, 2010 at 12:16 am

Ha! I’m glad you liked my observation and I hope others did too. Nothing like beating people across the head to expose logical fallacy.

And don’t be too hard on people. Most people are too busy in their lives to really think or care about analyzing what they read or hear, and the way politicians, special interest groups, and other people with an axe to grind present data to support their argument, who can blame people for thinking that illegal immigrants account for 2/3 of Medicaid patients in California (true only if every Hispanic using the system were an illegal immigrant…)

If only my employer would allow me to write stuff like this in our newsletter. Thanks for the opportunity to vent!

• 3 Daniel // Aug 13, 2010 at 12:36 am

Warren J’s comment calls to mind the discussion in “”Freakonomics” on scholastic achievement in the Illinois (I believe) primary schools. They found that the highest achievers came from families with lots of books in the household, so the legislature decided, in its infinite wisdom, to try to pass a measure to provide books to households, in the hopes that this alone would increase scholastic achievement/test results!
Talk about faulty reasoning regarding correlation/causation!

• 4 Michael L. // Aug 13, 2010 at 2:19 pm

I’m not familiar with the situation in China but I believe Newt is right about the capital gains tax hurting an economy.

A capital gains tax discourages both savings and work, because most people work to invest.

True, not everything China does is going to give us good economic policy. However, research backs up Newt’s claim.

In other words, sorry this is a causation.

• 5 Joao Pedro Afonso // Aug 13, 2010 at 7:33 pm

I agree with David: if the difference between correlation (which may denounce or not a causation) and causation is so difficult to grasp by the common people as you acknowledge, then the graph in itself may become a causation of what it wants to show. After all, it is not as if the graph is too explicit about what is claiming: the title is enough ambiguous to allow different interpretations. For instance, we could claim that part of better success is indeed due to those characteristics that lead the people to choose more education. However, this doesn’t explain why they chose more education… after all, stories about self-made-millionaires who started earlier abound, and it makes sense to think the sooner someone starts to work, the sooner they’ll start to climb up and get promoted. If achievement appears correlated with education, then we must suspect that achievers look for education to get what they need to succeed… otherwise, they would be wiser to skip it in order to start earlier (time is money). My point is, since we can make a reasonable defense about not wasting time in education for achievers, the correlation must indeed hint benefices from education. And the graph’s title becomes true then.

About zero capital gain taxes, I have a small question: If governments loose that income source, what motivation they have to defend capital “rights”?

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