The Coffeealyzer showed that 25 of the 55 observations in the control group drank coffee. It also showed that all 55 observations in the treatment group drank coffee like they were supposed to!

You discover that most of the coffee drinkers in the control group are working at least two different jobs. Previous research shows that those working more than one job, on average, are less productive at any of their jobs than those only working one job, all else equal.

To deal with the problem you discovered in the experiment, you decide to drop those in the control group that drank coffee from the study. After dropping these observations, the difference in averages will Overestimate the ATT.

Question

The Coffeealyzer showed that 25 of the 55 observations in the control group drank coffee.  It also showed that all 55 observations in the treatment group drank coffee like they were supposed to!

You discover that most of the coffee drinkers in the control group are working at least two different jobs. Previous research shows that those working more than one job, on average, are less productive at any of their jobs than those only working one job, all else equal.

To deal with the problem you discovered in the experiment, you decide to drop those in the control group that drank coffee from the study.  After dropping these observations, the difference in averages will Overestimate the ATT.

BlackTom AI · Accepted Answer

The scenario describes an experiment where the Coffeealyzer shows that every observation in the treatment group drank coffee, while 25 of 55 observations in the control group did. A key issue is that most coffee drinkers in the control group are working at least two jobs, and prior research suggests that those with multiple jobs tend to be less productive on average. The proposed action is to drop the control observations who drank coffee.

Option analysis:
- Underestimate: This choice argues that dropping the control coffee drinkers will cause the estimated ATT to be too small relative to the true ATT. Why that happens: the control group’s average outcome (Y0) will increase when you remove the lower-productivity coffee drinkers, since those removed are the ones associated with lower productivity. With a higher control mean after the drop, the gap between the treated mean (Y1, where everyone drank coffee) and the control mean shrinks. Since ATT is effectively E[Y1 − Y0 | T=1], making Y0 larger reduces the estimated ATT, thus underestimating the true effect. The logic hinges on conditioning on a post-randomization subset that is correlated with the outcome, which introduces selection bias and distorts the comparison.

- If there were other options, we would evaluate them similarly: for any option claiming an overestimate, the rationale would need to show how dropping coffee drinkers would make the treated minus control difference larger than the true ATT, which contradicts the direction described above. Conversely, an option claiming exact estimation would require that the drop not bias the comparison at all, which is unlikely given the systematic association between coffee drinking (in the control group) and productivity.

In summary, removing the lower-productivity control observations (coffee drinkers) raises the control mean, narrows the treatment-control gap, and thus leads to underestimating the true ATT.

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