drafts are done. going to convert to docx and share

analysis/draft.md

@@ -57,32 +57,24 @@ $$
 Y_{dt} = \alpha_d + \beta_1 \mathrm{YearNum}_t + \beta_2 \mathrm{Post2019}_t + \beta_3 \mathrm{PostTrend}_t + \varepsilon_{dt}
 $$
 
-Where $(PostTrend_t = \max(0, t-2018))$. This distinguishes an immediate post-2019 level shift $(\beta_2)$ from a post-policy slope change $(\beta_3)$.
+Where $PostTrend_t = \max(0, t-2018)$. This distinguishes an immediate post-2019 level shift $\beta_2$ from a post-policy slope change $\beta_3$.
 This follows interrupted time-series logic for a common policy shock, separating immediate and gradual responses (Biglan, Ary, & Wagenaar, 2000; Bernal, Cummins, & Gasparrini, 2017; Linden, 2015).
 
 ### Model 2: District heterogeneity (H2)
 
-$$
-Y_{dt} = \alpha_d + \gamma_t + \sum_{d} \theta_d \bigl(\mathrm{District}_d \times \mathrm{Post2019}_t\bigr) + \varepsilon_{dt}
-$$
+Model 2 estimates district-specific post-policy effects by interacting district indicators with the post-2019 period and including year fixed effects. This yields district-level post coefficients and a joint heterogeneity test. In the current run, the omnibus test of district-by-post terms is not statistically significant (Wald chi-square = 0.670, p=0.4130), so H2 evidence is interpreted primarily from the pattern and magnitude of district-specific estimates rather than a single global rejection.
 
-This yields district-specific post-policy effects and a joint heterogeneity test. In the current run, the omnibus test of district-by-post terms is not statistically significant (Wald chi-square = 0.670, p=0.4130), so H2 evidence is interpreted primarily from the pattern and magnitude of district-specific estimates rather than a single global rejection.
 Because all districts are exposed in the same year, this is not a staggered-adoption DiD problem. Still, recent DiD work highlights that pooled average effects can mask meaningful treatment-effect heterogeneity, so we estimate district-specific post effects directly rather than rely on a single pooled interaction (de Chaisemartin & D'Haultfœuille, 2020; Goodman-Bacon, 2021; Sun & Abraham, 2021).
 
 ### Model 3: Offshore moderation (H5)
 
-$$
-Y_{dt} = \alpha_d + \gamma_t + \sum_{d} \theta_d \bigl(\mathrm{District}_d \times \mathrm{Post2019}_t\bigr) + \phi\bigl(\mathrm{Post2019}_t \times \mathrm{Offshore}_d\bigr) + \varepsilon_{dt}
-$$
-
-Where `Offshore_d = 1` for districts 02/03/04.
-This specification tests whether offshore-regulating districts differ systematically from other districts after controlling for district-specific post-policy shifts.
+Model 3 adds an offshore-by-post interaction term to Model 2 to test whether offshore-regulating districts differ systematically from other districts after conditioning on district-specific post-policy shifts.
 
 ### Spatial diagnostic (H4)
 
 After estimating district treatment effects, we test for global spatial autocorrelation using permutation-based Moran's I (Anselin, 1995). The statistic is computed from a manually specified district contiguity matrix and evaluated with randomization inference (5,000 permutations), assessing whether high- and low-response districts are geographically clustered in ways consistent with diffusion or regional administrative spillovers.
 
-All models use district-clustered standard errors.
+All models use district-clustered standard errors. Full formal equations and notation are reported in the appendix.
 
 ## Results
 
@@ -99,8 +91,8 @@ Figure 1 visualizes these system-level changes across the regulatory pipeline. T
 
 **Model 1 (timing outcome):**
 
-- Immediate post-2019 level shift: **0.1514**, p=0.3294.
-- Post-2019 slope shift: **-0.3603**, p=0.0010.
+- Immediate post-2019 level shift: 0.1514, p=0.3294.
+- Post-2019 slope shift: -0.3603, p=0.0010.
 
 Interpretation: no statistically significant immediate level break in 2019, but a significant post-policy acceleration trend in enforcement timing.
 
@@ -160,9 +152,9 @@ The map indicates that large positive and negative effects coexist across region
 
 In the conditional heterogeneity model (Model 3):
 
-- Offshore-by-post-policy differential = **0.3819**, p<0.001.
+- Offshore-by-post-policy differential = 0.3819, p<0.001.
 
-This estimand is the average post-2019 offshore differential conditional on district-specific post-policy effects. Because the outcome is logged enforcement delay, the coefficient implies an approximate $(e^{0.3819}-1 \approx 46.5\%)$ relative increase in time-to-enforcement for offshore-regulating districts, holding the rest of the specification constant. Read jointly with the annual offshore differential results (Table C3 in the appendix), this pooled estimate should be interpreted as an average over uneven yearly effects, with the strongest divergences concentrated in 2023-2024. Substantively, H5 is supported as a structured heterogeneity result within the all-district analysis, but it should not be interpreted as isolating a single offshore causal mechanism, given that offshore jurisdiction is concentrated in districts 02/03/04.
+This estimand is the average post-2019 offshore differential conditional on district-specific post-policy effects. Because the outcome is logged enforcement delay, the coefficient implies an approximate $e^{0.3819}-1 \approx 46.5\%$ relative increase in time-to-enforcement for offshore-regulating districts, holding the rest of the specification constant. Read jointly with the annual offshore differential results (Table C3 in the appendix), this pooled estimate should be interpreted as an average over uneven yearly effects, with the strongest divergences concentrated in 2023-2024. Substantively, H5 is supported as a structured heterogeneity result within the all-district analysis, but it should not be interpreted as isolating a single offshore causal mechanism, given that offshore jurisdiction is concentrated in districts 02/03/04.
 
 ### H3: Structural moderators
 
@@ -204,7 +196,7 @@ Table 3 summarizes why structural accounts are only partially successful in this
 
 Moran’s I on district effects:
 
-- \(I = -0.0493\), permutation p=0.8550.
+- $I = -0.0493$, permutation p=0.8550.
 
 No evidence of statistically significant global spatial autocorrelation.
 In this run, the spatial evidence is inferential (permutation Moran’s I) rather than model-based spatial plotting; Figure 4 provides the relevant geographic context for district-level effect dispersion.
@@ -234,7 +226,7 @@ In this run, the spatial evidence is inferential (permutation Moran’s I) rathe
 - Linear interrupted model: post-trend -67.0420 days (p=0.0100).
 - Winsorized interrupted model: post-trend -0.3147 (p=0.0016).
 
-Across variants, the post-policy **slope** result is more stable than the immediate **level** effect.
+Across variants, the post-policy slope result is more stable than the immediate level effect.
 
 **Table 4. Robustness summary (interrupted panel framework)**