Counting Defiers  Amanda E. Kowalski

Counting Defiers  by Amanda E. Kowalski
The LATE monotonicity assumption of Imbens and Angrist (1994) precludes “defiers,” individuals whose treatment always runs counter to the instrument, in the terminology of Balke and Pearl (1993) and Angrist et al. (1996). I allow for defiers in a model with a binary instrument and a binary treatment. The model is explicit about the randomization process that gives rise to the instrument. I use the model to develop estimators of the counts of defiers, always takers, compliers, and never takers. I propose separate versions of the estimators for contexts in which the parameter of the randomization process is unspecified, which I intend for use with natural experiments with virtual random assignment. I present an empirical application that revisits Angrist and Evans (1998), which examines the impact of virtual random assignment of the sex of the first two children on subsequent fertility. I find that subsequent fertility is much more responsive to the sex mix of the first two children when defiers are allowed.
http://papers.nber.org/papers/w25671.pdf 
this paper is embarrassingly wrong
How so. I get that traditionally we assume away defiers but if we know Pr(Z) exactly what is wrong with the additional assumptions?
Look, the basic point is that in an RCT with Z randomly assigned and outcome D the joint distribution of potentials (D_1,D_0) is not identified  only the marginal distributions of D_1 and D_0. Here complier/defier/etc is a function of both D_1 and D_0 and thus not identified the way Kowalski claims. It's embarrassing that she doesn't know this, and furthermore that she didn't bother to circulate the draft to anyone who might before posting two(!) totally misguided NBER WPs.

this paper is embarrassingly wrong
How so. I get that traditionally we assume away defiers but if we know Pr(Z) exactly what is wrong with the additional assumptions?
Look, the basic point is that in an RCT with Z randomly assigned and outcome D the joint distribution of potentials (D_1,D_0) is not identified  only the marginal distributions of D_1 and D_0. Here complier/defier/etc is a function of both D_1 and D_0 and thus not identified the way Kowalski claims. It's embarrassing that she doesn't know this, and furthermore that she didn't bother to circulate the draft to anyone who might before posting two(!) totally misguided NBER WPs.
it's also just super arrogant to think you're the first to think about identification of complier/defier shares  why didn't she send this to, e.g., Angrist before posting?