Mike Sconces asks:
Question: I have questions about "bad control" (BC) (Section 3.2.3, p.
64). Your prescription is to leave the BC out of the model, or else to
have strong theory for leaving it in. In the stats literature, there
is discussion of "principal stratification" (PS). Let w_0i, w_1i be
the potential outcome of a mediator variable (following the notation
on p. 65) for individual i. The idea of PS is to divide the sample
into, e.g., {i: w_0i = w_1i} and {i: w_0i != w_1i}. These strata are
generally unobservable, but we could otherwise use them as
pre-treatment covariates. Some stats papers argue that the LATE relies
on a special case of PS, where the sample is divided into those whose
treatment status is affected by the instrument, and those whose
treatment status is not. Here, the treatment would be a BC (in the
reduced form, I suppose...?). So why doesn't PS make us more hopeful
about BC? Also, given random treatment, why can't we just instrument
the BC, since it's just another endogenous variable?
One Comment