What effect is estimated from the execution of IPW?
When running IPW in R, I know that you specify the formula for the weight itself, i.e.:
(treatment / propensity) + ((1 - treatment) / (1 - propensity))
To my knowledge, this weight helps generate the ATE.
My question is this, is the ATE what you ideally should be estimating when using IPW? This might seem like a simple question since most of the implementations of IPW I have seen estimate the ATE. However, I am slightly confused by the wording of a 2008 Paper which uses matching to estimate the causal effect of UN peacekeeping operations on peace in which the authors claim:
"By necessity we estimate the average treatment effect on the treated (ATT). That is, we answer the question: how well did the United Nations do in the range of cases where it actually intervened and, if the United Nations were to intervene in a similar case, how well would we expect it to perform? We cannot tell how well the United Nations would have done had it intervened in a type of situation where it has never intervened (typically called the average treatment effect on the control or ATC). We do not have treated cases to match to all of our control cases and so we cannot answer that question. Like drugs and surgical procedures, United Nations interventions are designed for certain cases and not for others."
I know that the authors here are not using IPW, however, I thought the point of IPW was to balance the data set to account for specified confounders that create an imbalance with respect towards treatment propensity in the first place.
According to a response on this Stack Overflow post, the ATE and ATT are the same when "the baseline of the treatment group equals the baseline of the control group [and] the treatment effect on the treated group equals the treatment effect on the control group". We cannot necessarily know this with observational data, but I thought, in balancing the data set, we can get closer to meeting these assumptions so that we can estimate ATE.
I very well may be mistaken here as I am still trying to wrap my head around when different treatment effects are appropriate. My fundamental area of confusion is the degree to which IPW allows one (if it does at all) to estimate the ATE with observational data due to its ability to balance the data set.