Bryan Caplan  

Sub-Prime Education

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Over at Cato Unbound, I praise Murray for highlighting the fact that many "investments" in education end in foreclosure - also known as "dropping out":

[L]abor economists normally estimate the return to completed education.  It only takes a small drop-out rate to drastically reduce the expected return of trying to complete a year of school.  If the rate of return for a completed year of education is 10%, but 6% of students who start a year don't finish (and waste a year of their lives plus tuition), the expected rate of return is only 3.4%!  If the marginal student is less likely to finish than the average student, the effect is even more drastic.
I conclude:

Murray's critics can't dismiss him merely by waving around standard estimates of the return to education.  One of Murray's main points is that for many students, the "standard" return is just a honey trap.
My point seems too obvious for labor economists who estimate the return to education to have overlooked.  But they've missed the obvious before...


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COMMENTS (19 to date)
Steve Sailer writes:

Excellent analogy.

Thanks.

William writes:

Your basic point is valid, I don't understand where you are getting your 3.4% figure.

I understand that you are evaluating this expression:

.94 * 1.1 + .06 * 0 = Expected Earnings

But I don't understand why.

.94 - Prob - successfully completes BA - BA
.06 - probability of non-success - ~BA

1.1 - expected lifetime earnings under BA (more precisely, factor of increase vs. making no attempt)
0 - This doesn't work. Your lifetime earnings are not 0 under ~BA, they are something like .95

As I say, your basic point still stands, but honestly, the cost of one wasted year of schooling just doesn't have as much of an effect as you claim.

frankcross writes:

Like William, I can't fathom how these numbers were produced. I would add that they contain an assumption that the drop out gains zero value from the education he or she received. Maybe right, but an unsupported assumption. It's certainly plausible that "some college" yields some economic value.

Mark Thoma writes:

This is about a previous post, so it's off topic and you should feel free to delete it.

It's about the post on oil prices and whether there was a bubble. This is meant to be friendly, not quarrelsome, but I wonder why you are so sure that we aren't in a negative bubble, i.e. why you are sure that prices haven't undershot their long-run fundamental values recently. Bubbles can work both ways - e.g. from positive or negative rumors or from other drivers - so could this be a negative bubble?

What I'm asking is if this is a potential case of confirmation bias. When prices go way up - it's a bubble - but when they crash - it's to fundamental values becasue that's what you have claimed previously.

But why couldn't the downward movement be from bandwagon type speculation, i.e. a departure from fundamentals? How do you know it isn't? Did you look at inventories, etc., or just assume it wasn't a negative bubble because it fits the story you want to tell?

Not saying claims are right or wrong, that's a different discussion - I've seen confirmation bias discussed here a lot and just wondering if you checked out the claim that confirms your prior position as closely as you checked out the evidence that runs counter to it.

Mark Thoma writes:

Oops - I should have added that was meant for Arnold (just noticed he didn't write this post..)

Unit writes:

Education is subsidized and what tax-payers should ask is what is the average class-attendance? They'll find that it's very similar to the empty flights of the subsidized airline industry, the empty buses, etc...How efficient!

Gary writes:

If 9 people get a 10% return on investment and 1 person gets a 0% return on investment, isn't the mean return over those 10 people 9%?

Or suppose 9 people get 10% and 1 person gets -20%, isn't the mean return 7%?

Gary writes:

To expand on William's point, either of these equations works fine:

0.94*.10 + 0.06*0 = 0.094

0.94*1.10 + 0.06*1.0 = 0.094

Both have an expected 9.4% return.

El Presidente writes:

Gary,

If 9 people get a 10% return on investment and 1 person gets a 0% return on investment, isn't the mean return over those 10 people 9%?

Or suppose 9 people get 10% and 1 person gets -20%, isn't the mean return 7%?

I think Bryan's point in his estimation is the opportunity costs of forgone wages, etc. amount to a less-than-zero return for the dropout. They amount to a loss which must be factored against the gains of those who complete and increase their salary. I think, as has been pointed out, that although the immediate return on investment may not be evident, the time period for analysis and the imputed value of externalities mean a great deal when comparing costs and benefits. The skills a person may learn, even if they do not complete their program of study, have value and can raise productivity. The possibility that the individual may not realize as large a gain in salary as those who complete the program does not negate the possibility that they may produce greater value than their salary reflects. Once again, price does not always equal value. The market equilibrium is usually different than the social equilibrium.

Gary writes:

El Presidente, it's reasonable to suppose a dropout gets a less than 0 return on investment. Is it reasonable, though, to assume a 100% loss?

Keep in mind that the return Kling supposes is probably annual (nobody would spend $20k in tuition to get a one-time gain of $2k). So it seems to me that a 100% loss assumes that the dropout earns nothing for the remainder of his career.

William writes:

Thanks, Gary, you managed to be clearer and more concise than I was (though Caplan wrote this post, not Kling).

.04 * 0, as far as I can tell, means that the 4% of people who drop out earn nothing for the rest of their lives. I would imagine .95 is a more realistic number (assuming you have a 20 year working life and miss one year due to wasted schooling).

I think the 1.1 is supposed to be the excess income as a multiple of the opportunity costs.

So if you graduate, the present value of your additional lifetime earnings are 110% of tution plus foregone wages.

But if you don't graduate, you still pay tuition and you still miss out on the wages you could have earned if you were working full time, but you don't get a dime of additional income after you leave school over what you would have gotten if you had not attended school.

Gary writes:

Woops, sorry about the author attribution mixup.

Eric, I'm not even sure that William's equation is what Bryan had in mind (although it certainly looks like it). In any case, unless 6 people in 100 suffer a catastrophic loss while the other 94 achieve a decent return, I can't figure a way to get the average so low.

Bryan, defend yourself!

El Presidente writes:

Gary,

El Presidente, it's reasonable to suppose a dropout gets a less than 0 return on investment. Is it reasonable, though, to assume a 100% loss?

I would say, no.

It is true that the opportunity costs are an important consideration in measuring the value of education. I object to the characterization of the value of education on a more general level: social equilibrium almost never equals market equilibrium. The difference is the aggregated or net error between the socially preferred outcomes for all individuals and that which actually occurs. That's not to say that it is preferable or even possible for every outcome to be identical, only that the pricing involved in estimating whether this is a "subprime education" resulting in "foreclosure" ignores the externalities and makes the fundamental error of assuming that the average is ubiquitous. Many people have variations in pay owing to experience or skill (loosely 'performance'). These variations in pay may result from their formal education even if they posess no credentials. The point of education is to impart knowledge and skill, to increase the efficiency of labor, not merely to certify completion of rudimentary tasks or give credit for time served. If it wasn't so, any market premium on posession of a degree of any sort would be a confounding prejudice not worthy of consideration in an analysis of the VALUE of education.

ryan yin writes:

Gary and William,
I think you might be misunderstanding what is meant by return to education. As Eric points out, when someone says the return to education is X%, that's not 1+X times lifetime income, but 1+X times the cost of education. Note this implies that the "catastrophic failure" you're looking for is simply if you spent a year plus tuition w/ nothing to show for it (that is, your wages don't go down: they just don't go up). The stakes in either direction aren't nearly as extreme as you're assuming.

ryan yin writes:

El Presidente,
Is it clear that there are strong externalities to education, and if so, that they're always positive? If one thinks education is partly a signal (which you imply), wouldn't we think that there might be large negative externalities that might very well swamp any effect going the other way?

William writes:

ryan yin,

It's possible that I'm misunderstanding return to schooling, but I think that standard usage of the term "return to education" means the value of B2 in the following equation (copying a model from my econometrics textbook):

log(wage) = B1 + B2* BA

where B1 is the base wage and B2 is the coefficient on the dummy variable representing BA or no BA

If you are trying to estimate the expected effect on log(wage) of attempting to get a BA, where you get the BA with probability .94 and don't get it with probability .06, the expected value of B2*BA in your wage equation will turn out to be
.94 *.1 + .06*0 = .094

Which is an estimated return of 9.4%.

I just don't find it plausible that "return to BA" means:

[(total income|BA) - (total income|no BA)] / (total cost of BA attempt)

You're probably right that the math is okay in this case, but it seems to me that the factors in that latter equation are fiendishly difficult to estimate.

El Presidente writes:

El Presidente,

Is it clear that there are strong externalities to education, and if so, that they're always positive? If one thinks education is partly a signal (which you imply), wouldn't we think that there might be large negative externalities that might very well swamp any effect going the other way?

I would say externalities are nearly ubiquitous, and it is safe to assume they apply to education. I would not suggest they are always positive. In fact, there are a great deal of things one can learn which might be profitable, however we define that, but would produce negative externalities in application. Profits, as we commonly define them, can occur in a zero-sum or even negative-sum interaction. If our concern is the return on education to society, then we have to look beyond profits and focus on positive-sum interactions.

Cost-benefit analysis is a manifestation of the values of the analyst. They must choose which externalitites to include, and how to value them. They must choose the period for evaluation. They must choose the benchmark or standard rate of return with which to compare the investment. When we see analysis, it is important to ask whether they have valued the inputs and outcomes the way we would.

Gary writes:

ryan yin, as far as I can tell, the loss of tuition money and the lost opportunity of a year of schooling is not nearly catastrophic enough to get Bryan's figure.

The kind of catastrophe that might do it is for dropouts to be dropped off a cliff (literally).

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