AN-020: Goodman-Bacon TWFE decomposition

Intuition (plain-language)

Goodman-Bacon shows which comparisons a TWFE coefficient is actually built from. Here 100% of the weight sits on the clean treated-vs-never-treated comparison, with zero on the 'forbidden' already-treated comparisons. The single-cohort design is identification-clean, and the heterogeneous-timing concern simply does not bite.

Question

The two-way fixed-effects DiD coefficient is a weighted average of all 2×2 comparisons implicit in the panel. When some controls are already-treated before the treatment cohort, the TWFE coefficient can include "forbidden" comparisons that contaminate the estimate (Goodman-Bacon 2021). The Callaway-Sant'Anna and Sun-Abraham corrections in AN-018 reproduce the DDR — but is that because the TWFE was clean to begin with, or because the corrections happen to give similar magnitudes? The Goodman-Bacon decomposition answers this directly.

Design

• Sample: BEC parquet cache, 18-month window; aggregated to codigogrupo × month to manage panel size.
• Specification: bacondecomp::bacon(y ~ treat, id_var = id_grp, time_var = data_oc_numb) on a balanced group × month panel where treat = 1 if codigogrupo == "65" AND month ≥ 698 (March 2018).
• Decomposition components:
• Treated vs Untreated — the clean 2×2 comparison between group 65 and the never-treated 76 groups. Desired estimate.
• Within — time-only variation absorbed by group FE; trivial.
• Treated vs Already-treated — would be the forbidden comparison if some controls had been treated earlier than group 65. In our setting this cannot arise: no group within the 18-month window switches regime before March 2018.
• Outcomes: log prices, log firms, log bids, distance (km).

Results

Per-outcome decomposition (table tab_bacon.tex):

Outcome	Comparison type	Weight	Weighted avg. estimate
Log prices	Treated vs Untreated	1.000	0.370
Log firms	Treated vs Untreated	1.000	−0.041
Log bids	Treated vs Untreated	1.000	0.037
Distance	Treated vs Untreated	1.000	−37.99

Zero weight on any other comparison type. The decomposition collapses to the clean 2×2 in every outcome.

Output: output/tables/tab_bacon.tex, output/tables/diag_bacon.txt.

Interpretation

The TWFE DDR is identification-equivalent to the clean 2×2. In a single-cohort design with never-treated controls, the Goodman-Bacon decomposition cannot produce forbidden treated-vs-already-treated comparisons because there is no variation in treatment timing among the controls. All weight falls on the clean Treated-vs-Untreated 2×2. This is the strongest possible structural answer to the heterogeneous-timing-bias concern raised by CS2021 and Sun-Abraham: the bias does not exist here by construction.

Reading vs CS2021 + Sun-Abraham convergence. AN-018 shows the three estimators converge on direction and (for SA) on magnitude. This AN supplements that by showing the convergence is not coincidence: the DDR was a clean estimator on this design, the modern corrections do not change what they do not need to change.

The 0.370 magnitude is the group-month aggregate, not the item-level DDR. Goodman-Bacon at the group-month panel aggregates item-level effects via group means; the magnitude differs from the item-level DDR (0.113 after sign-flip) but the decomposition property (weight = 1 on clean 2×2) is what this analysis identifies.

Confidence: green. This is the rare AN that earns green within the project. The Goodman-Bacon decomposition is structural — the weight = 1.000 result is a mathematical property of the design (single cohort, never-treated controls), not an empirical estimate that could be noisy. There is no within-project replication to do; the result is what it is.

Follow-ups

• AN-018 (CS2021 + Sun-Abraham) is the complementary check that the magnitudes survive when the contamination — even if formally absent — is corrected for explicitly.
• The result also serves H:price-discipline-loss by ruling out heterogeneous-timing as a confound on the price coefficient.