Carlos Parada writes:
Saw your blog post on the Heckman Curve. I went through Heckman’s response that you linked, and it seems to be logically sound but terribly explained, so I feel like I need to explain why Rea+Burton is great empirical work, but it doesn’t actually measure the Heckman curve.
The Heckman curve just says that, for any particular person, there exists a point where getting more education isn’t worth it anymore because the costs grow as you get older, or equivalently, the benefits get smaller. This is just trivially true. The most obvious example is that nobody should spend 100% of their life studying, since then they wouldn’t get any work done at all. Or, more tellingly, getting a PhD isn’t worth it for most people, because most people either don’t want to work in academia or aren’t smart enough to complete a PhD. (Judging by some of the submissions to PPNAS, I’m starting to suspect most of academia isn’t smart enough to work in academia.)
The work you linked finds that participant age doesn’t predict the success of educational programs. I have no reason to suspect these results are wrong, but the effect of age on benefit:cost ratios for government programs does not measure the Heckman curve.
To give a toy model, imagine everyone goes to school as long as the benefits of schooling are greater than the costs for them, then drops out as soon as they’re equal. So now, for high school dropouts, what is the benefit:cost ratio of an extra year of school? 1 — the costs roughly equal the benefits. For college dropouts, what’s the benefit:cost ratio? 1 — the costs roughly equal the benefits. And so on. By measuring the effects of government interventions on people who completed x years of school before dropping out, the paper is conditioning on a collider. This methodology would only work if when people dropped out of school was independent of the benefits/costs of an extra year of school.
(You don’t have to assume perfect rationality for this to work: If everyone goes to school until the benefit:cost ratio equals 1.1 or 0.9, you still won’t find a Heckman curve. Models that assume rational behavior tend to be robust to biases of this sort, although they can be very vulnerable in some other cases.)
Heckman seems to have made this mistake at some points too, though, so the authors are in good company. The quotes in the paper suggest he thought an individual Heckman curve would translate to a downwards-sloping curve for government programs’ benefits, when there’s no reason to believe they would. I’ve made very similar mistakes myself.
Sincerely,
An econ undergrad who really should be getting back to his Real Analysis homework
Interesting. This relates to the marginal-or-aggregate question that comes up a lot in economics. It’s a common problem that we care about marginal effects but the data more easily allow us to estimate average effects. (For the statisticians in the room, let me remind you that “margin” has opposite meanings in statistics and economics.)
But one problem that Parada doesn’t address with the Heckman curve is that the estimates of efficacy used by Heckman are biased, sometimes by a huge amount, because of selection on statistical significance; see section 2.1 of this article. All the economic theory in the world won’t fix that problem.
P.S. In an amusing example of blog overlap, Parada informs us that he also worked on the Minecraft speedrunning analysis. It’s good to see students keeping busy!
The marginal benefit = marginal cost criterion for efficiency (or rationality) depends on an often unstated assumption: that marginal benefits are a declining function and marginal costs an increasing function of the relevant quantity variable (in this case, age). The idea that marginal benefits of education decline with age while the marginal costs increase is far from clear to me. It presupposes that benefits can be measured by lifetime earnings and that costs can be measured by the opportunity costs of time (this one is far from clear – is it foregone earnings, other demands on time, such as having children, etc.?). In any case, the simple demonstration that moderation (in this case, don’t get too much education) is optimal is just too simplistic.
I used to ask introductory economics students to comment on the saying “anything worth doing is not worth doing (too) well,” which is an economic phrasing of the marginal benefit = marginal cost condition. It is trivially true, but also very disturbing. It actually rules out certain measures of benefits and costs. In the environmental effects literature, it rules out certain nonconvexities that give rise to declining marginal cost curves. Corner solutions (all or nothing optimal solutions rather than marginal benefit = marginal cost) can arise. These are generally exceptions, but can be important exceptions.
Back to the education context: certainly, it is rational to stop formal education after x* years, where 0<x<expected lifetime. But it also implies that informal learning should stop after some y* years. That conclusion is far less obvious to me, although it appears to be an empirical fact. Many people with academic careers appear to largely stop learning fairly early in their career (a skeptical view of this is that they stop learning right after getting tenure). The monetary rewards would certainly suggest that it is rational to stop learning new things at some point before your expected lifetime ends. But if your benefits include more than monetary rewards, then this is less clear.
As with many economic concepts, the seeming obvious principle that marginal benefits should be equated to marginal costs, presupposes particular measurements that are rarely explicitly stated.
Sounds like this our old friend the thermostat problem, but in an education guise: people adjust their thermostat of education-credential plans for their particular situation until they are neither too hot nor too cold but just-right. Thus, the simple correlations you might expect to find will be attenuated, disappear, or even reverse depending on how the underlying causal processes work.
I think it’s worth pointing out that many people do not enjoy learning or novelty at all, whether formal or informal, and this is a big influential individual-difference (which is why Openness makes it into the Big Five). Even if you max out your Openness because you’re an academic or something, you can’t cheat Father Time, and you will grow old & tired – where learning becomes much harder, more painful, more costly, quite aside from the intrinsic loss of value due to shorter horizons and being more locked into things like families or mortgages or jobs with pension plans. Essentially no one is like the recently deceased Freeman Dyson in being in their 90s and still writing or trying to learn new things (note that Dyson was killed by an unlucky accident, elder falling, and not dementia or a stroke or something).
Dear Econ undergrad who really should be getting back to his Real Analysis homework:
“Judging by some of the submissions to PPNAS, I’m starting to suspect most of academia isn’t smart enough to work in academia.”
You should look into a courses in logical reasoning and statistical inference.
Pretty sick levels of smugness for an undergrad
> courses in logical reasoning and statistical inference
Do you have some examples of ones you thought were good or can provide some sense of what they should cover and how?
“You should look into a courses in logical reasoning and statistical inference.”
You should look into courses about recognizing sarcasm.
not sure it’s even sarcasm. maybe exaggeration.
Some people would study forever (if they could) because they enjoy studying.
But not very many. :)
I wonder how this is among the kids of the super rich. I guess education doesn’t have that much economic return to them in the sense that they can already afford whatever. But then, don’t these kids usually get lots of education anyhow? I guess there’s cultural capital, or something like this, to be gained. Also, doing e.g. a PhD. is not so much fun if you’ve got bills and so on, but maybe its super fun when your existential security is maxed out?
My existential security was pretty well established when I entered my PhD in my mid 30’s. Doing the research was super fun. I feel like I ultimately made a contribution to my field that exceeded anything anyone at my university in Civil Engineering had ever done. Dealing with the dysfunction of Academia wasn’t super fun. I’m more or less scarred for life about the human race.
Short version: I love learning things, and I came out of Academia super bitter about the fact that Academia isn’t at all about learning things.
“But not very many. :)”
Probably everyone reading this list.