# Can I test whether there is a group of observations in a dataset having a treatment effect in the opposite direction with respect to the ATE?

Suppose that I'm looking for the effect of a shock (for example, a natural disaster, or the current Covid pandemic) on given outcomes, where each observation corresponds to a different person. I expect of course that the situation will, on average, get worse. But I'm curious to see whether this holds for everyone, or there are some people who are better off after the shock. Of course, if I already had an idea of whom could be to benefit from the shock, I could test it.

For example, in the case of Covid, I could think that in general people have gotten poorer, but some people working on specific sectors (for example, online marketing) have gotten richer. In that case, if the variable "employment sector" were available, I could test such hypothesis.

But suppose that, instead, I suspect that some people may be better off after the shock, but I don't have a clue of whom they might be. Can I test whether such subgroup exists? Of course there will be someone who will have better outcomes, but this may be due to chance. Are there explorative techniques to test whether there is a subgroup of people improving due to the shock, without knowning which this subgroup could be? This question also encompasses another one: can I test for heterogeneity, if I don't know which the source of heterogeneity could be?

• This seems to be called unit-treatment interaction. See statmodeling.stat.columbia.edu/2006/06/16/treatment_inter and use internet search! See also stats.stackexchange.com/questions/434928/… – kjetil b halvorsen Nov 16 '20 at 17:30
• Thanks for pointing me to that question. The 1st paper mentioned there states that, if the variance is higher in the treatment group, it could be due to the variance of the treatment effect across people. In a pre-post setting, if we assume that the effect is additive and, in absence of the shock, the variance remains equal, it should remain so also in the case where the treatment has the same effect for everyone. It makes sense, at least if we remain away from extreme values (as we approach the minimum or maximum, impossibility to get higher or lower treatment effects should limit variance) – Federico Tedeschi Nov 17 '20 at 11:37