The design question
Original fictional balanced panel:2 treated and 2 comparison units; pre 2, pre 1 and post. All treated units adopt after pre 1, controls never adopt. Target is post-period ATT under the stated assumptions. No staggered adoption, general two-way-fixed-effect estimator or event-study regression is implemented.
Group-period means
Every unit has all 3 observations; the two units per group receive equal weight. Use these means to calculate treated before-after, post-only group gap, DiD and pre-period gap change.
group | pre2 | pre1 | post
treated | 12 | 14 | 21
control | 10 | 12 | 15Your attempt
State the untreated parallel-trend assumption, no anticipation, no spillovers and stable measurement/cohort assumptions. Which missing counterfactual does DiD impute? Does a zero pre gap change prove the required post counterfactual?
Worked solution
Treated before-after is 21−14=7; post-only gap 21−15=6. DiD=(21−14)−(15−12)=4. Pre gap change=(14−12)−(12−10)=0. Under the identifying assumptions, the comparison trend 3 supplies the missing untreated treated-group change; without those assumptions 4 is only a descriptive contrast.
Do not overread a pre-check
The parallel-trends assumption concerns the treated group’s UNOBSERVED untreated post trajectory relative to controls. Similar pre paths support discussion but cannot prove that missing path; a low-power nonsignificant pre-test would not prove it either. A treated-only campaign beginning at adoption can bias the post contrast even after equal pre trends.
Sensitivity exercise
Let delta be the extra untreated treated-group trend from pre 1 to post, above the control trend. Adjusted effect=observed DiD−delta. Evaluate assumed delta 0,1,2,4 and explain the sign. These values are assumptions, not estimated confounding, confidence bounds or probabilities.
Sensitivity solution
Adjusted effects are 4,3,2,0. If the treated group would have increased 4 more than controls without treatment, the entire observed contrast could be explained by that differential trend. The fixture does not tell you which delta is plausible. Seek contextual evidence rather than selecting an assumption because it preserves a preferred sign.
Review and explain
Score 0–2 for ATT/timing, arithmetic, assumption clarity, pre-check limits and sensitivity interpretation. Reject missing/duplicate unit-periods or changing group in this balanced-panel exercise. Four units do not justify treating all 12 panel rows as independent observations; no significance or standard-error claim is supplied.
Authoritative reference
World Bank, Impact Evaluation in Practice resources. Read the difference-in-differences discussion and identifying assumptions. The Elm panel and exercises are original. Next: Elm 4.
Try the activity before reading its reference. Keep your sources, commands and assumptions with your work. Companion activities are unsaved self-practice and do not award a certificate or change lesson progress.