Propensity Score Models
I just saw a reference to “propensity score models” for “the effect of treatment
on the treated” which it seems are used by
many economists. Sascha Becker at Munich has
the best explanation I
could find in quick search. I could not understand it by reading it, but by thinking
I think this is the situation:
Suppose
some workers join a job training program (X) and we want to see how much their wages
(Y) go up, controlling for age (V). But other workers deliberately did not join the
program, and so we don’t
have a random comparison. Maybe the workers who joined would have done well anyway.
We are trying to estimate b in
Y = bX + cV + epsilon,
but X depends on epsilon, so we have an endogeneity problem.
One solution is to find an instrument Z for X that is correlated for X but not epsilon.
This is standard instrumental variables. I think the propensity score model uses IV
too, really, but in a more complex way. It first tries to estimate the X equation, and
then to do something with the data before running the Y equation. Thus, first you
run
X = dZ + epsilon
using a probit, and gets a propensity to choose X=1, to get the training. Then you find
matches pairs in the data of trained and untrained workers with the same propensity
score. Then you do something further, and eventually run the Y equation.
I don’t see what the advantage over simple IV is, and I’m not even sure there’s a
difference, but I can imagine there’s some kind of efficiency advantage.