Individual responses to a treatment D=0,1 differ, depending on covariates X. Averaging such a heterogeneous effect is usually done with the density of X, but the average with `overlap weight (OW)' is done "surreptitiously" with X controlled, where OW is the normalized version of PS×(1-PS) with...

In some surveys, the survey interview dates are scattered over many months. If a treatment unrelated to the survey purpose takes place during the survey period, then randomized data can obtain because individuals interviewed before and after the treatment timing are homogeneous. This happened in...

Given a binary treatment D, a response Y and covariates X, often X interacts with D in an unknown way to make the treatment effect heterogeneous. If D is exogenous, there are various semi-parametric approaches (matching, inverse probability weighting, etc.) to estimate a weighted average of the...