# Appendix A — Method-choice rationale Why four difference-in-differences estimators, what each buys, what each cannot see, and why BJS sits at the top of the headline column. ## Why four estimators at all Under homogeneous treatment effects and a single-cohort design, all four of our estimators (TWFE, CS, SA, BJS) converge to the same number. A staggered rollout with heterogeneous effects — which is what NYC's containerization policy actually delivered — drives a wedge between them. The four estimators therefore function as an internal consistency check: sign agreement across the four is evidence that the direction of the effect is robust to methodological choice; disagreement in magnitude is evidence of treatment-effect heterogeneity that the analyst should decompose rather than average. [Roth, Sant'Anna, Bilinski & Callaway (2023)](../../MANUSCRIPT.md#ref-roth2023) synthesize the post-2020 DiD methodological literature and recommend reporting multiple heterogeneity-robust estimators for exactly this reason. [Baker, Larcker & Wang (2022)](../../MANUSCRIPT.md#ref-bakerlarcker2022) survey empirical finance applications and find that TWFE estimates can be sign-flipped relative to the heterogeneity-robust triple in up to 25% of published staggered-DiD papers; reporting the triple alongside TWFE is the cheapest defense against that failure mode. ## Estimator-by-estimator ### 1. Two-way fixed effects (TWFE) The canonical DiD specification: $$ Y_{it} = \alpha_i + \gamma_t + \beta \cdot D_{it} + \varepsilon_{it} $$ where $D_{it} = 1$ if unit $i$ is treated at time $t$. Under treatment-effect heterogeneity with staggered adoption, [Goodman-Bacon (2021)](../../MANUSCRIPT.md#ref-goodmanbacon2021) shows that $\hat\beta$ is a *weighted average* of 2×2 DiD comparisons, and the weights can be negative when already-treated units serve as controls for later-treated units with different ATTs. In pathological cases the estimator can flip sign. **Role in this paper**: baseline specification + cross-check. If TWFE and the heterogeneity-robust estimators agree on sign, the pathology is not binding; if they disagree we trust the robust triple. ### 2. Callaway-Sant'Anna (CS) Proposed by [Callaway & Sant'Anna (2021)](../../MANUSCRIPT.md#ref-callaway2021). Estimates group-time ATT(g,t) — a separate average treatment effect for each treatment cohort at each relative-time post-treatment — and aggregates them with user-chosen weights ("simple" = equal weights; "event study" = weight by relative time). CS can use "not-yet-treated" units as controls for each cohort, which is why we pass `control_group="not_yet_treated"` in notebook 03 and construct the 15-unit never-treated pool as a fallback. **Role**: the *conservative* heterogeneity-robust estimator. CS's simple aggregation pulls toward later-cohort / short-horizon ATTs, which in our panel means it down-weights the pilot (long post- window, larger effect accumulates) relative to the citywide cohort (short post-window, effect still building). This is why CS's point estimate ($-4.87$) is the smallest in magnitude. ### 3. Sun-Abraham (SA) Proposed by [Sun & Abraham (2021)](../../MANUSCRIPT.md#ref-sun2021). Parameterizes the event study directly with cohort × relative-time interaction dummies — effectively a fully-saturated event study that lets each cohort's pattern of leads and lags differ. The aggregate ATT is a weighted sum of cohort-specific coefficients using sample-size weights. **Role**: the *event-study-native* heterogeneity-robust estimator. SA is the closest methodological cousin of our figure-2 event study plot. Its point estimate ($-12.85$) is on the larger-magnitude side of the range because the sample-weighted aggregation gives the pilot cohort (9 CDs × 33 post-months) substantial weight despite its smaller individual effect. ### 4. Borusyak-Jaravel-Spiess (BJS) Proposed by [Borusyak, Jaravel & Spiess (2022)](../../MANUSCRIPT.md#ref-borusyak2022). A matrix-imputation estimator: fit the TWFE model on never-treated and not-yet-treated observations only, use it to impute counterfactual outcomes for treated observations, and report the average imputation residual as the ATT. Asymptotically efficient under cohort homogeneity; still unbiased under heterogeneity. **Role**: the *efficient* heterogeneity-robust estimator, and our headline. BJS's standard error ($0.70$) is 2.5× tighter than CS's ($2.01$) and 4× tighter than SA's ($2.81$) in our panel, which is why we quote BJS's $[-13.28, -10.53]$ CI as the leading number. The efficiency gain comes from pooling the never-treated and not-yet-treated counterfactual information rather than using only never-treated. ## How the cross-estimator spread should be read Under cohort homogeneity the four estimators coincide (up to efficiency); our observed spread — CS at $-4.87$, TWFE at $-10.27$, BJS at $-11.90$, SA at $-12.85$ — therefore **is** the empirical signature of cohort heterogeneity. The §4.4 per-cohort decomposition isolates the source: pilot ATT is $-5.72$, citywide ATT is $-12.22$, and the four pooled estimators weight those two cohorts differently. CS pulls toward the citywide cohort's earlier post-window (smaller accumulated effect); BJS and SA pull toward the treated-units-weighted average; TWFE pulls somewhere in the middle because its Goodman-Bacon decomposition contains a mix. The headline should be read as "the pooled effect is approximately $-12$, the heterogeneity between cohorts is real, and the policy stakeholder should consume §4.4 alongside the headline rather than stop at the abstract." A single-number summary is a genuine disservice to the user of this research. ## Why the headline is BJS, not TWFE Four criteria drove the choice: 1. **Efficiency** — BJS has by far the smallest standard error in our panel ($SE = 0.70$), which translates into the tightest confidence interval for the pooled ATT. 2. **Cohort robustness** — BJS is unbiased under treatment-effect heterogeneity, unlike TWFE. 3. **Interpretability** — the BJS point estimate is an imputation-based counterfactual residual, which maps directly onto the layman reading "how many complaints would have happened without the policy." 4. **Convention** — recent applied DiD papers in the post-[Goodman-Bacon (2021)](../../MANUSCRIPT.md#ref-goodmanbacon2021) era increasingly report BJS as the primary estimate with the other three as robustness [(Baker et al., 2022)](../../MANUSCRIPT.md#ref-bakerlarcker2022). We note TWFE and CS as robustness checks in the main body and report SA in the cross-estimator table but do not lead with any of them. ## Clustered inference All four estimators use cluster-robust standard errors clustered on `unit_id` (community district). The cluster choice is driven by the panel's autocorrelation structure: observations within a community district across months are highly correlated (persistent rat-ecology, persistent DSNY enforcement capacity, persistent reporting propensity). Clustering on the treated unit is the standard prescription [(Abadie et al., 2017)](../../MANUSCRIPT.md). The 74 clusters in our panel comfortably exceed the rule-of-thumb 40-cluster minimum for cluster-robust asymptotics to be well- behaved.