Saturday, May 28, 2011

More on margins of comparison

In this post I talked about the problem of confusing different margins of comparison. This is what I mean w.r.t. the public school issue:

In the United States we are living in the left columns, with a mix of public and private schools where private school students generally have better outcomes than public school students (btw - I went to public schools through high school, William and Mary is public, and George Washington University and American University are both private). We often make this comparison between public and private school students - either formally and rigorously or informally - when we discuss these issues. Those comparisons have some value, of course. From a parents' perspective it helps them think about where to send their kids, and it also helps us think about the structure of public education and the wisdom of things like charter schools and vouchers. But when we pontificate on the role of government in education its exactly the wrong comparison to think about. When we talk about the role of government we have to compare the left columns with the right columns. That's an entirely different question, and it's harder because distributional issues start to enter the equation. Not to mention the problem that we have no data on that question!

Another place this pops up is the question of wage cyclicality. If you plot out the raw data, real wages seem to be high in recessions - it looks like wages are counter-cyclical. This bolsters both New Keynesians who think that sticky wages matter a lot and anti-intervention types who want to blame the minimum wage, labor laws, etc. The problem is its a big example of margin confusion again. If high wages were the culprit in recessions, what we would want to look at is the spot market for labor - the intensive margin. We would want to look at trends in the cost of one more unit of labor over the business cycle. Easy - that's the hourly wage data series that the Bureau of Labor Statistics produces, right? Wrong. Aggregate hourly wage statistics are influenced by fluctuations on the intensive and the extensive margin, and as such they can be very misleading in discussions of wage cyclicality. The problem is that different sorts of workers are employed at different points in the business cycle, so wage data is picking up fluctuations on the extensive margin - the decisions to hire or fire different types of workers, rather than fluctuations on the intensive margin for a constant pool of workers. Brad DeLong summarizes the literature on this problem in his excellent critique of Vedder and Gallaway here. The empirical evidence on this is very consistent - wages are not highly counter-cyclical. At most they are acyclical, although some find a modest pro-cyclicality. Abraham and Haltiwanger (1995) provide a survey of this literature, and I suggest anyone who thinks empirical economics is all over the map read it. The findings are very consistent and all point to the same conclusion. Your margin of comparison matters.

I don't have time to go over it now, but this also matters a lot for the economics of discrimination and the work that Becker did (which a lot of people get confused about and draw the wrong lessons from). I'll try to post on that in the near future. But out of curiosity I want to ask - what do people think Gary Becker concluded about discrimination in the labor market?


  1. A mix? Over 90% of the children above the age of six are in public schools. That's the primary problem I'd say. Public education is a vast field where competition is tamped down and kept at a minimum as much as possible. Well, that and the rampant corruption.

  2. As long as you make those assessments by thinking about the right margin of comparison, I'm happy Gary.

  3. My goal is primarily to decouple the state from education.

  4. Gary can you be more specific about how taking the "state" out of education will solve our woes? More importantly what do you think of Daniel's claim in his other entry about why private schools do better?

  5. After my time here in Scandinavia, I cannot help but be influenced by their system on this issue... Indeed, I would say that Public Education is perhaps the one aspect of "welfarism" that I unreservedly support.

    What is perhaps most interesting about the Nordic/Scandinavian countries' approach to schooling is their effective design and system of accountability. On that note, here's an interesting article that appeared yesterday on the Finnish education system, which is ostensibly ranked as the best in the world.

    [Disclaimer: Clearly, I'm not in a position to comment on the American schooling system, which nevertheless seems to be crying out for some kind of reform.]

  6. Couldn't help but chuckle at the comparison. I agree that we should be mindful of the "true" alternative. But other than that, your point - at least with respect to those argue for eliminating government schools - doesn't apply.

    The alternative column or "counterfactual" situation is a prediction, opinion, or hypothesis. Many who disagree simply have a different outcome in mind.

    Many would say a test score of a "1" vs a "3" is both misleading and irrelevant with respect to consequences. A kid that can just read compared to a kid that can do calculus doesn't really indicate the "value-added" from school. It's just a signal of ability - calculus is almost never used in practice. In other words, your own complaint fails to locate the real extensive margin. These test scores are largely irrelevant.

    Government schooling is 99% waste. It's a daycare system, nothing more. The supposed "positive externalities" that rationalize it's existence don't even exist. All studies confuse causation with correlation. Rich countries can afford to waste their money on schooling - not the other way.

    As a TA I work with college kids every day. Except for the 1% who are already gifted, the others are just filing through, not learning material that will never be used. The gifted 1% are slowed by the slows. It's so popular in modern culture to praise the value of education and those who teach it. But honestly, besides reading, a bit of elementary mathematics, and some mediocre writing skills, what's the point of teach anything more to everyone? It's all waste if it's never used - which it most often never is. It should be catered to a specific purpose, which seems to be something only a system not plagued by bureaucratic machinery can do.

  7. edarniw -
    1. First, yes I said in the post we don't know what the alternative would be. I don't think mine is implausible at all.

    2. Substitute whatever metric you want - my point was only that comparing existing public schools with existing private schools is meaningless. Of course existing private schools do better. If they didn't they simply wouldn't exist. And it's not an argument against public schooling at all to have a free, vibrant, and successful private market in education. Only a central planner would want public schools as the only option. But when you consider public provision, you have to evaluate its value in a meaningful way and to many people evaluate it poorly.

  8. Because the state screws everything up. This axiomatic.

  9. Bryan Caplan has given a great talk about education. He states that education is mostly signalling and private alternative would do little to change that(as much as he wishes otherwise). And you know what? I agree. School fails to teach relevant jobs skills. You will end up forgetting most of the material you've learned, but that doesn't matter. The employer see's what he's looking for in that piece of paper and not the education behind it. Most likely you will be trained and fear not about having to discard junk trivia.

    "Government schooling is 99% waste"

    Thirteen years of gargantuan opportunity costs, in other words.

  10. Anonymous -
    Do you know why he says this? My understanding is that signaling is a 12-30% marginal effect for a BA, and the returns to a year of schooling is usually within the 5-12% range. That would put four years of undergrad at 20-42% return. I don't see how you get "mostly a return to signaling" out of that, although obviously it is an important part of it.

    We need to be careful about how we interpret "signaling" anyway. Finishing your degree says something about the quality of the education you received while you were at school, which is not as easily observed in simply reporting years of education. I don't see any obvious reason to assume that a signalling effect is necessarily a sign of waste. It's a mechanism for communicating otherwise unobservable information.

    Why do you agree with Bryan? Does Bryan say what you're saying here, or are you putting your own spin on his thoughts on signaling?

    This is a more readable overview for people:

    Card's chapter is the best overview I know of of the estimates:

    The measured returns to schooling have been increasing in the last several decades, btw. That's in Card - Goldin and Katz also cover that in their recent book.

  11. I imagine Caplan is drawing from Spence's signalling game model, one of the most popular signalling game models. One of it's predictions is that for low enough schooling costs, all different "types" - gifted, ungifted, etc. - will opt for acquiring education. For those not familiar to game theory, this is called a "pooling equilibrium". It's an equilibrium in which the signalers (eg high school graduates) all do the same thing. Because they all do the same thing, the employer doesn't acquire any extra information about their true nature.

    There is also the alternative situation in which no one gets an education. The employers would be in the same position as above, but in this case, the high school graduates didn't blow money on education. It's thus unambiguously welfare increasing. Of course, it depends on assumptions about the alternative benefits of schooling, and in reality the schools and majors aren't completely homogeneous, but it's a nice basic theoretic model that's able to produce certain institutional equilibria that may be sub-optimal. And of course, one of the main implications is that it's not obvious whether subsidization of college is beneficial.

  12. edarniw -
    I have no doubt what model he has in mind.

    I'm wondering where you and he are getting the magnitudes of the significance of signaling.


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