“Counterfactual” is not a synonym for “control group”

“Counterfactual” is not a synonym for “control group”. In fact, the treatment group’s actual outcomes are used when estimating the control group’s counterfactual outcomes, which is necessary to estimate the average treatment effect on control (ATC) or average treatment effect (ATE) estimands.

An individual’s treatment effect is defined as a within-person difference between the potential outcome following treatment and the potential outcome following control. This individual treatment effect is impossible to measure, since only one potential outcome is realised depending on which group the individual was in. However, various averages of the treatment effects can be estimated.

For ATC, we are interested in estimating averages of these treatment effects for control group participants. We know the control group’s actual outcomes. We also need to answer the counterfactual query:

If individuals in the control group had been assigned treatment, what would their average outcome have been?

To estimate ATC using matching, we need to find a treatment group match for each individual in the control group. Those treatment group matches are used to estimate the control group’s counterfactual outcomes.

For ATE, we are interested in estimating averages of these treatment effects for all participants. This means we need a combination of answers to the following counterfactual queries:

(a) If individuals in the treatment group had been assigned control, what would their average outcome have been?

(b) If individuals in the control group had been assigned treatment, what would their average outcome have been?

To estimate ATE using matching, each treatment individual needs a control group match and each control group individual needs a treatment group match. So, for ATE, both treatment and control groups could be considered counterfactuals, in the sense that they are both used to estimate the other group’s counterfactual outcomes. However, I think it is clearer if we draw a distinction between group (treatment or control) and what we are trying to estimate using data from a group (actual or counterfactual outcomes).

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