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) synthesize the post-2020 DiD methodological literature and recommend reporting multiple heterogeneity-robust estimators for exactly this reason. Baker, Larcker & Wang (2022) 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) 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). 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). 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). 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) era increasingly report BJS as the primary estimate with the other three as robustness (Baker et al., 2022).

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). The 74 clusters in our panel comfortably exceed the rule-of-thumb 40-cluster minimum for cluster-robust asymptotics to be well- behaved.