Monday, August 8, 2011

Returns to education

I’ve been going over the econometrics literature on the returns to education (see for instance, Card) and it’s the first time I’ve looked at this and I’m a little surprised at how it’s presented. The estimated return is assumed to be linear in years of education and as a baseline method (first approximation) this works well although this is not how I would think of as a return to education. Unfortunately, the literature seems to be fixated on this method.

My natural inclination is to think of returns to a high school degree versus high school dropout or to measure directly the returns to a college degree. In terms of the latter, it would seem to be the wage premium of a BA over a HS but this premium when averaged over the population confounds years of experience, ability and time/year effects so that it becomes hard to separate.

If I’m about to invest $200,000 in a college degree I would like to know the return to this investment, not the return to an additional year’s of education. If I were to think of this as an investment project, I would I would first calculate the discounted PV of the lifetime stream of income that the completion of a college degree would confer versus say, the discounted PV of a HS graduate. Supposing that the PV of a college graduate is $2 million versus $1 million for a HS degree, the the NPV would be $1 million. Thus, the return would be ($1 million-$200,000)/$200,000 or 400%.

But the calculation of any streams of income is a road that is fraught with perils. It makes a lot of assumptions about baseline earnings and earnings growth (as well as inflation rates and interest rates) and in some cases, small differences can matter. If for some reason the PV of a college graduate is only $1.5 million, then the return falls to ($500,000-$200,000)/$200,000 or 50%. If the PV is $1.2 million for a college graduate then the NPV is 0 ($1.2 million - $1 million - $200,000) or a return of 0.

The lifetime incomes of $2 million, $1.5 million, and $1.2 million do not seem to be a large difference yet the return has fallen from 400 percent to 0 very quickly. Now, some would say that the PV of the lifetime income of HS graduate should not be deducted as a cost to calculate NPV and I would say perhaps but I need a way of comparing alternative investments and not getting a college degree represents an opportunity cost to getting a college.

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