![propensity score matching using xlstat propensity score matching using xlstat](https://cdn.xlstat.com/media/post/0001/01/thumb_788_post_large.jpeg)
With a correctly modeled propensity score and exact matching on the propensity score, the treatment effect estimate for 1:1 PS matching will be unbiased. If the effect of treatment is the same for everyone, then this quantity is equal to the average treatment effect in the population (ATE). PS matching can really only be used to estimate the average treatment effect on the treated (ATT). For now we'll assume 1:1 matching without replacement and without a caliper. Variations include how many control units to match, whether they should be matched with or without replacement, whether a caliper should be used, etc. PS matching involves estimating a PS for each unit (usually using logistic regression), then, for each treated unit, finding one or more control units with a similar PS, and discarding the unmatched control units. We have to assume there is some functional relationship, so that in theory we could model the outcome "correctly" as a function of treatment and the propensity score. One important concept to know is the relationship between the PS and the outcome. I'll only talk about PS matching and regression on the PS. They vary mostly in their empirically untestable assumptions and on their empirical performance. Each method has its strengths and weaknesses. There have been systematic studies on the relative performance of these methods, but new variations of them always come out and it's not always immediately clear whether the new methods will adhere to the hierarchy of methods commonly assumed. These are PS matching, PS weighting, PS subclassification, and regression on the PS. There are four common ways of using propensity scores (PS) to reduce confounding and arrive at an unbiased estimate of a causal effect.