<p>
[quote]
NotQuiteOld writes: I don't know why you're debating this in hypotheticals. Krueger and Dale did do a systematic study <a href="http://www.nber.org/digest/dec99/w7322.html%5B/url%5D">http://www.nber.org/digest/dec99/w7322.html</a> and found there is little or no significant income difference over the lifetimes of those who went to an elite school vs those who were also accepted but instead went to a school outside the top 25.
[/quote]
This study keeps getting mentioned in the press (and on this board) as if it settles the question, but if you dig a little deeper you find it does not. Furthermore it is clear that Krueger buried evidence that opposed his conclusion. I apologize for the length to follow, but its important to understand what the study actual did & found in order to reach a solid judgement. </p>
<p>Krueger starts by assuming each applicant has a quality X and each college has criteria C. If X > C, then admit. However X is composed of 2 parts: x(1) comes from factors such as SAT scores, race, parental income, etc. that can be observed later by researchers. x(2) comes from factors such as motivation, attitude, etc. that are determined thru recs, interviews, essays, etc. x(2) is seen by the colleges but not later researchers.</p>
<p>Next Krueger says the literature typically estimates the effect of college on earnings thru regression to find the constants (J,K,L) in an equation of the form log (income) = J + K<em>avgSAT + L *x(1). avgSAT is the average SAT of the school attended and is used by Krueger as a proxy for college selectivity. Krueger continues by saying that if employers as well as colleges care about X instead of just x(1) then the true equation is log (income) = J + K</em>avgSAT + L <em>x(1) + M</em>x(2) and leaving out x(2) causes the other variables to by overestimated. Most importantly, it will cause K to too high. As Krueger notes in his paper, if both income and admission to schools with higher avg. SATs (eg. more selective) are postively correlated with x(2) then omitting x(2) in the regression will cause K to be overestimated. </p>
<p>The problem Krueger faced in how to get x(2) into the equation, and he can't see it directly any more than anyone else can. So he came up with a very clever approach. Even if he can't see X directly, the colleges presumably did. So students that got into/rejected from the same sets of colleges have very similar values for X. Krueger identified matched students from the data and ran the regression on them. One important complication to be noted is there are thousands of colleges and Krueger wanted to find enough admit/reject matches in his data to make it meaningful. So he assumed that colleges with average SAT scores within a 25 point band were the SAME in selectivity. </p>
<p>When Krueger does his calculations on these matched pairs of students he plugs in the same data everyone else had, but the variables for accept/reject get the weight belonging to x(2). The value of K now tells us how important the college attended really is. In particular, if the value of K turns out to be zero then the college actually attended didn't matter. And this is just what he found.</p>
<p>Now that you have more than the sound-bite press release understanding of what Krueger did, problems should be obvious in this "systematic" study. Even if his approach was clever, what about the assumtions that he used? For one thing, does average SAT score really reflect selectivity? This is crucial, because it is used both to place students into matched pairs and later in the regression equation to stand for selectivity. </p>
<p>For an answer, lets turn to Krueger himself. More specifically, to a draft of his paper you can see on his department's site at <a href="http://www.irs.princeton.edu/pubs/pdfs/409.pdf%5B/url%5D">http://www.irs.princeton.edu/pubs/pdfs/409.pdf</a> In the draft Krueger noted that other estimates of selectivity existed at that pre-US News time, such as Barron's. Krueger writes "Interestingly, the Barron's ratings do not bear a monotonic relationship with school SAT scores. Notre Dame, for example, is ranked higher in the Barron's ratings than many schools with higher average SAT scores" Even Krueger admits some doubt around the assumption selectivity is captured completely SAT averages. Not only that, but you have to wonder about the assumption that the 25-point SAT bands really put schools into bands of equal selectivity.</p>
<p>So if the assumptions are flawed, what about the conclusions? As they say, GIGO. Furthermore I mentioned that Krueger buried evidence that opposed the sound-bite conclusion. Lets take a look at that.</p>
<p>If you take a look at the draft on the Princeton U website, you can see it mentions a second running of the data. Matched pairs were still created using the 25-point SAT band, but then the regression was run using the Barron's list for the selectivity variables instead of the average SAT score. And what do you know? Krueger found a link between the college attended and income!! He writes an F test of the null hypothesis that the Barron's ratings jointly have no effect on earnings is rejected at the .05 level in the matched applicant model for men". </p>
<p>Curiously enough, this didn't make it into the final report (which you can read at <a href="http://tinyurl.com/4lzhk;%5B/url%5D">http://tinyurl.com/4lzhk;</a> the link by NotQuiteOld is just to the abstract). The Barron's regression simply disappeared. It should be kept in mind that Krueger is well known for his populist approach to economics; for example he is also a advocate of raising the minimum wage and claims that raising the minimum wage has no effect on employment of those workers (contrary to virtually all other studies and econ texts). Hence it would not be surprising that he would want to find that pricy elite colleges don't help future earnings.</p>
<p>My take is that the body of research (including Krueger's study) shows there is a significant impact to attending a more selective college. Virtually all other studies have found this effect, and even the pre-publication version of this study acknowledged it and labeled it as "significant". Whether it is the smaller classes, higher expectations of the faculty, just having access to more opportunities by virtue of being surrounded by privileged students, or some other factors, it is impossible to say. But it seems there are economic reasons as well as other more personal reasons to prefer to attend a selective college.</p>