Simply comparing the treated unit to the untreated unit in the post-treatment period would underestimate the true treatment effect.

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BlackTom AI · Accepted Answer

The statement asserts that a naive comparison between the treated unit and the untreated unit in the post-treatment period would understate the true treatment effect.

First, consider what the treatment effect is: it is the difference between what happened to the treated unit and what would have happened to it if it had not been treated (its counterfactual). Simply comparing post-treatment outcomes across treated and untreated groups uses the untreated group's actual post-treatment values as the counterfactual for the treated group, which may be biased if the untreated group does not perfectly mirror the treated group’s potential trajectory had there been no treatment.

Second, in many DID or pre/post settings, the untreated group serves as a proxy for the counterfactual only if the two groups would have followed parallel trends in the absence of treatment. If there are pre-existing differences or divergent trends, the untreated post-treatment outcome may not accurately reflect the untreated potential outcome for the treated unit, leading to bias. Depending on the direction of these differences, a simple post-treatment comparison can either understate or overstate the true effect. In the provided figure, note how the treated (blue) and untreated (red) lines move over time; the raw post-treatment gap does not perfectly capture the full impact the treatment would have had on the treated unit absent treatment.

Third, the core intuition behind why the simple post-treatment comparison underestimates is that it ignores the counterfactual path the treated unit would have taken without treatment. If the treated unit was on a different trajectory prior to treatment, projecting that trajectory forward using the untreated’s post-treatment values will generally fail to capture the full effect, especially if the treatment causes the treated unit to deviate more strongly than the untreated group does afterward.

Finally, this reasoning highlights why more robust approaches (like difference-in-differences or synthetic control methods) use the untreated group to approximate the counterfactual only under plausible assumptions about parallel trends and pre-treatment fit. Therefore, the statement that a straightforward post-treatment comparison would underestimate the true treatment effect aligns with concepts about counterfactual accuracy and potential biases in naive comparisons.

FA25_QTM_110_1 Quiz #8: Difference in Differences

Simply comparing the treated unit to the untreated unit in the post-treatment period would underestimate the true treatment effect.

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