I consider estimation of the average treatment effect (ATE), in a population composed of $G$ groups, when one has unbiased and uncorrelated estimators of each group's conditional average treatment effect (CATE). These conditions are met in stratified randomized experiments. I assume that the...

Instrumental variables (IVs) are commonly used to estimate the effects of some treatments. A valid IV should be as good as randomly assigned, it should not have a direct effect on the outcome, and it should not induce any unit to forgo treatment. This last condition, the so-called monotonicity...

In many applications of the differences-in-differences (DID) method, the treatment increases more in the treatment group, but some units are also treated in the control group. In such fuzzy designs, a popular estimator of treatment effects is the DID of the outcome divided by the DID of the...