Bryan Caplan wrote:
> But there's a great deal of evidence that AFQT is a very accurate
> measure of IQ; indeed there's probably nothing else in psychology that
> can be measured so reliably.
I disagree. For instance, Heckman, Cawley, and Vytlacil (1998) show
that the correlation between AFQT scores and the first principle
component of ASVAB scores, g, is only 0.83. That is, even if we
take g as a perfect measure of IQ, AFQT is a pretty noisy measure
of IQ. They also note that "many features of personality and
motivation" that may be part of what we think of as "cognitive
ability" are not captured by the ASVAB scores, such that there's
noise there too.
I did a wee Monte Carlo to see how this might affect wage regressions
like Bryan ran. I set the sample size equal to Bryan's, and
generated some weakly correlated noise for equations determining
wages, afqt scores, and education levels:
. set obs 4293
. gen u1=invnorm(uniform())
. gen u2=invnorm(uniform())*10+0.2*u1
. gen u3=invnorm(uniform())*2+0.1*u1+0.002*u2
. corr
(obs=4293)
| u1 u2 u3
--------+---------------------------
u1| 1.0000
u2| 0.0392 1.0000
u3| 0.0994 0.0226 1.0000
I then generated IQ, log wages, education, and afqt as:
. gen iq=20*invnorm(uniform())+100
. gen educ=-6+(1/6)*iq+u3
. gen afqt=iq+u2
. gen w=8+(0.005)*iq + 0.103*educ + u1
Such that all that determines wages is IQ and education,
and education is in turn imperfectly determined by IQ.
The true effect of IQ on wages is 0.005, which is what
Bryan found in his regression, as is the true return to
education at 10.3%. AFQT is just IQ plus a little mean
zero noise, and unobservables increasing any one outcome
are also, to a minor degree, likely to increase other
unobservables, reflecting those omitted personality
variables.
I then regressed log wages on education and AFQT:
. regress w afqt educ
Source | SS df MS Number of obs = 4293
---------+------------------------------ F( 2, 4290) = 623.31
Model | 1216.84642 2 608.423208 Prob > F = 0.0000
Residual | 4187.52751 4290 .976113639 R-squared = 0.2252
---------+------------------------------ Adj R-squared = 0.2248
Total | 5404.37393 4292 1.25917379 Root MSE = .98798
------------------------------------------------------------------------------
w | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
afqt | -.0000628 .0010443 -0.060 0.952 -.0021102 .0019846
educ | .1360265 .006005 22.652 0.000 .1242536 .1477994
_cons | 8.175557 .0700054 116.785 0.000 8.03831 8.312803
------------------------------------------------------------------------------
My results significantly overstate the returns to education and
significantly understate the returns to cognitive ability. Even
small measurement error and endogeneity problems can have big impacts
on estimates, particularly in the presence of high colinearity.
So, again: I do not agree that running a regression such as Bryan's
provides anything resembling "bounds" on the structural parameters
under question. Notice I'm also ignoring all the other problems
here: mismeasurement of education, selectivity into employment,
selectivity into occupations, and so on. Further, in a recent
working paper Heckman and Vytlacil argue a problem I previously
noted, the high correlation beween education and IQ, is so bad that
"it is not possible, even over a wide range of variation in schooling
and ability, to ... estimate their seperate impacts." Heckman and
coauthors in other work, using the same data as Bryan, show that
the returns to IQ vary with race and other characteristics, and are
sensitive to specification.
> I will say that I'm puzzled when you call this literature "massive."
> The return to education literature in economics is massive, but only a
> small fraction of that even tries to control for cognitive ability.
Again, cognitive ability and many other covariates are highly
correlated. That induces correlation between the parameter estimates,
so if we're mis-estimating the returns to, say, education, we are also
likely to be mis-estimating the returns to cognitive ability. The
whole literature on wage determinants is relevant to this question,
and the jury is still out on the answers. It is anything but a "pretty
easy" problem.
> amount on that too). From all that I've heard, a lot of the stuff in
> the Bell Curve hadn't been done before.
The Bell Curve is chock full of, to use the technical jargon, craptastic
econometrics. It's useful as a guide in how not to proceed with
scientific inquiry, but not much more.
And now for something completely different: Playstation 2 was introduced
today, with a retail price of $300 and "only" 500,000 units available.
They're selling on Ebay for over $1,500. Sure wish I'd pre-ordered a
thousand or so....
Chris Auld (403)220-4098
Economics, University of Calgary <mailto:[EMAIL PROTECTED]>
Calgary, Alberta, Canada <URL:http://jerry.ss.ucalgary.ca/>
