Say I have a binary treatment, X, and I'm interested in its (local average treatment) effect on a binary outcome variable, Y. I find (binary) instrument T that directly affects X but not Y.
How do I estimate this? I get that linear models like TSLS might not be ideal, but Angrist and Pischke's "Mostly Harmless Econometrics" seems to suggest that the effect estimates from something like a bivariate probit will be similar and maybe it isn't worth the trouble.
So I'm wondering: do I need to run something other than TSLS here? And if so, is there an R package for that? Thank you very much.