Monthly Archives: September 2017

WSJ reports that Americans losing faith in the value of college

Josh Mitchell and Douglas Belkin of the Wall Street Journal report that Americans are losing faith in the value of college, as represented in these survey results:
The most shocking results to me are that 30% of college degree holders do not think a college degree is worth it, as do over half of men and over half of 18-34 year olds.

Andrew Gelman and Hal Varian on Instrumental Variables

Andrew Gelmen

The trick: how to think about IV’s without getting too confused

Suppose z is your instrument, T is your treatment, and y is your outcome. So the causal model is z -> T -> y. The trick is to think of (T,y) as a joint outcome and to think of the effect of z on each. For example, an increase of 1 in z is associated with an increase of 0.8 in T and an increase of 10 in y. The usual “instrumental variables” summary is to just say the estimated effect of T on y is 10/0.8=12.5, but I’d rather just keep it separate and report the effects on T and y separately…

If there’s any problem with the simple correlation, I see the same problems with the more elaborate analysis–the pair of correlations which is given the label “instrumental variables analysis.” I’m not opposed to instrumental variables in general, but when I get stuck, I find it extremely helpful to go back and see what I’ve learned from separately thinking about the correlation of z with T, and the correlation of z with y. Since that’s ultimately what instrumental variables analysis is doing.

Hal Varian adds

You have to assume that the only way that z affects Y is through the treatment, T. So the IV model is
T = az + e
y = bT + d
It follows that
E(y|z) = b E(T|z) + E(d|z)
Now if we
1) assume E(d|z) = 0
2) verify that E(T|z) != 0
we can solve for b by division. Of course, assumption 1 is untestable.

An extreme case is a purely randomized experiment, where e=0 and z is a coin flip.