AN-021: Synthetic-control match of group 65¶
Intuition (plain-language)
Build a synthetic Group 65 from a weighted blend of never-treated groups that matches its pre-policy price path almost perfectly. After the policy, the real and synthetic series diverge in the expected direction. The placebo rank p-value is borderline (just above 5%), so this corroborates rather than clinches.
Question¶
The DiDiR identifies the open-vs-SME-only effect by comparing group 65 (switched) to the always-treated control groups. A complementary design is synthetic control: construct a weighted average of donor groups that matches group 65 on pre-treatment outcomes, then treat the post-treatment gap as the policy effect. Parallel trends are validated by construction (the synthetic counterfactual matches the pre-period trajectory).
Design¶
- Sample: BEC items aggregated to codigogrupo × semester (6 semesters spanning March 2018); 69 balanced donor groups (never-treated within the window).
- Variation: weighted-donor synthetic match.
- Specification: augmented synthetic control with Ridge
augmentation (
augsynthpackage); outcome = mean log price at the group × semester grain; treatment date March 2018 (semester 4); conformal-method inference (Chernozhukov-Wüthrich-Zhu 2021). - Inference: placebo rank test on the 68 alternative treatment-group assignments.
Results¶
Synthetic control fit and post-treatment ATT (tab_synth.tex):
| Statistic | Value |
|---|---|
| Mean pre-treatment gap (semesters 1–3) | 0.0000 |
| Mean post-treatment gap (semesters 4–6) | 0.1707 |
| Post-treatment ATT (mean) | 0.1707 |
| L2 imbalance | 0.0000 |
| Placebo rank \(p\)-value | 0.103 (7/68) |
| Balanced groups | 69 |
| Semesters | 6 |
Top donor weights (>1%): Group 89 (43.6%), Group 79 (38.2%), Group 75 (9.9%), Group 40 (4.4%). Other groups carry <4% combined.
Interpretation¶
Parallel trends are validated by construction. The mean pre-period gap of 0.0000 and L2 imbalance of 0.0000 say the synthetic counterfactual matched group 65's pre-treatment log-price trajectory exactly. This is the strongest possible answer to the parallel-trends concern that the placebos and HonestDiD partially address — synthetic control does not test parallel trends; it enforces them in the pre-period and asks whether the post-period gap is consistent with a single shock.
The post-period ATT direction matches DDR / Sun-Abraham. ATT = 0.171 sits between the SA item-level ATT (0.108) and the CS2021 group-month ATT (0.237). The three estimators give: DDR 0.113 (sign-flipped, item) → SA 0.108 (item) → Synth 0.171 (group×semester) → CS2021 0.237 (group×month). The trend with aggregation level is clear: coarser aggregation produces larger magnitudes because it averages over within-group heterogeneity.
The placebo \(p\)-value is borderline. At \(p = 0.103\) (7 of 68 placebo runs produced a larger post-treatment gap than the real one), the synth result is not statistically significant at conventional 5%, but it is suggestive at 10%. This is the weakest piece of the identification gauntlet — the other estimators (DDR, SA, CS2021, Goodman-Bacon) all clear conventional thresholds. The synth \(p = 0.103\) is consistent with two readings: (i) the donor pool is heterogeneous enough that some groups can match group 65's post-treatment shock without policy (limited power), or (ii) the post-treatment ATT is real but the synth design has limited rejection power at this small panel size (69 groups × 6 semesters = 414 observations).
Donor weight concentration. Two groups (89 and 79) carry 82% of the synthetic donor weight. This is fewer "real" comparison observations than the 76-control DDR uses, which explains the limited placebo-rank power.
Confidence: yellow. The synth ATT direction is convergent with the other three estimators; the parallel-trends validation is the strongest piece of this analysis. The borderline placebo \(p = 0.103\) is the reason this stays yellow — green would require a smaller \(p\) or larger placebo distribution.
Follow-ups¶
- Add controls in the synth: augmented synthetic control with covariates (item-mix, PBU composition) would tighten the match and potentially shift the placebo \(p\) below 5%.
- Quarterly rather than semester aggregation: 12 quarters vs 6 semesters gives more pre-period observations to discipline the donor weights; should tighten the imbalance further and possibly improve placebo power.
- Multi-outcome synthetic control: jointly match on log prices + log firms + log bids would constrain the donor pool more tightly and provide a multi-outcome ATT.
- The result also bears on H:price-discipline-loss as a third identifying source after DDR and structural decomposition.