In propensity score matching, is the estimand to be estimated the ATE or the ATT?

Question

In the propensity score matching literature (Central Role of the Propensity Score by Rubin), the treatment effect estimand is referred to as the "Average Treatment Effect" (ATE). However, in some papers such as this one, the effect estimand from propensity score matching is referred to as the "Average Treatment Effect on Treated" (ATT). This is a bit confusing to me, as I thought it was the ATE that was being estimated. What is the correct estimand?

Answer 1

Which estimand is targeted by matching depends on how the matching is specified. There are specifications that allow you to target the ATE or ATT.

The most common form of matching in some fields, k:1 matching without replacement, can only be used to target the ATT and only when the treated group is smaller than the control group and no caliper is applied. It targets the ATT because the final distribution of covariates in the matched sample resembles that in the treated group. This is described in Rosenbaum & Rubin (1985).

Another matching method is k:1 matching with replacement. This can be used to target either the ATE or ATT and does not require the treated group to be smaller than the control group. This method was described in detail in Abadie & Imbens (2006). To target the ATT, you find control units similar to the treated units, just as you do with matching without replacement. To target the ATE, you find control units similar to the treated units and treated units similar to the control units. This method is less popular in fields outside economics.

Other matching methods can be used to target either estimand. For example, full matching (Stuart & Green, 2008) creates strata of treated and control units such that the full sample is matched. From these strata, matching weights can be computed, and depending on how the matching weights are computed, they can target either the ATE or ATT.

Some matching methods target neither estimand; for example, matching with a caliper targets the average treatment effect in the "overlap", i.e., a subset of the population in which units are approximately equally likely to be treated or not. Any method that drops treated units from the sample is no longer targeting the ATT, even if it would have otherwise. Most methods that target the ATE require no units to be dropped.

To learn more about which methods target which estimand, see Greifer & Stuart (2023).

References

Abadie, A., & Imbens, G. W. (2006). Large Sample Properties of Matching Estimators for Average Treatment Effects. Econometrica, 74(1), 235–267. https://doi.org/10.1111/j.1468-0262.2006.00655.x

Greifer, N., & Stuart, E. A. (2023). Choosing the Causal Estimand for Propensity Score Analysis of Observational Studies (arXiv:2106.10577). arXiv. https://doi.org/10.48550/arXiv.2106.10577

Rosenbaum, P. R., & Rubin, D. B. (1985). Constructing a Control Group Using Multivariate Matched Sampling Methods That Incorporate the Propensity Score. The American Statistician, 39(1), 33–38. JSTOR. https://doi.org/10.2307/2683903

Stuart, E. A., & Green, K. M. (2008). Using full matching to estimate causal effects in nonexperimental studies: Examining the relationship between adolescent marijuana use and adult outcomes. Developmental Psychology, 44(2), 395–406. https://doi.org/10.1037/0012-1649.44.2.395