import sys
from pathlib import Path
ROOT = next(
p for p in [Path.cwd(), *Path.cwd().parents]
if (p / "scripts/tranche50_report.py").exists()
)
sys.path.insert(0, str(ROOT / "scripts"))
from tranche50_report import reportCoase and Cap-and-Trade: Evidence on the Independence Property from the European Carbon Market
Aleksandar Zaklan (2023) · American Economic Journal: Economic Policy
report("aeraej-38", tranche="tranche100")Aleksandar Zaklan (2023). American Economic Journal: Economic Policy. Table 3.
Source specification
| Source coefficient | Template on source sample | Source N | Template source-sample N |
|---|---|---|---|
| -0.095342 | -0.095342 | 3465 | 3465 |
Source-to-template coefficient difference: 5.33e-15, in original outcome units.
| Role | Column |
|---|---|
| Outcome | ln_emissions |
| Treatment | interact_post_treatment_treated |
| Unit | firm_num |
| Time | year |
| Cluster | firm_num |
No additional covariates beyond fixed effects.
Estimates below divide the outcome by its source-sample standard deviation, 2.29786. Static TWFE is the treatment coefficient. Dynamic TWFE, BJS and Sun–Abraham average supported post-treatment cells by observation count. CS-DID additionally reports an equal-event-time average.
Analysis sample and treatment timing
| Observations | Units | Treated | Control units | Cohorts | Clusters |
|---|---|---|---|---|---|
| 3465 | 385 | 304 | 81 | 1 | 385 |
Adoption is the first observed treated period. Initially treated units and units without an observed minus-one baseline are excluded. Post-adoption untreated rows are excluded for switching policies. The plot shows at most 100 seeded-sample units; estimation uses the full eligible sample. Empty cells remain missing.
y__d: 100 of 385 units shown (seed 20261008). All eligible units enter estimation. Purple: untreated; yellow: treated; white: unobserved.
Estimates
| Estimator | Estimate (SD) | SE | 95% lower | 95% upper | Target | Status |
|---|---|---|---|---|---|---|
| Static TWFE | -0.041492 | 0.017602 | -0.0761 | -0.0068837 | Coefficient | estimated |
| Dynamic TWFE | -0.023165 | 0.017656 | -0.057881 | 0.01155 | Treated cells | estimated |
| BJS / did2s | -0.041492 | 0.017556 | -0.07601 | -0.0069736 | Treated cells | estimated |
| Sun–Abraham | -0.023165 | 0.017656 | -0.057881 | 0.01155 | Treated cells | estimated |
| CS-DID (equal event-time) | -0.023165 | 0.017593 | -0.057646 | 0.011316 | Equal post-event times | estimated |
| CS-DID (treated cells) | -0.023165 | 0.017593 | -0.057646 | 0.011316 | Treated cells | estimated |
| SDID | -0.030647 | nan | nan | nan | Treated cells | estimated |
| Matrix completion | -0.039988 | nan | nan | nan | Treated cells | estimated |
| Horizontal ridge | -0.10085 | nan | nan | nan | Treated cells | estimated |
| Multisynth (cohort-averaged) | -0.023904 | nan | nan | nan | Treated cells | estimated |
| Multisynth (individual) | 0.022376 | nan | nan | nan | Treated cells | estimated |
Intervals use the configured clusters and the estimator’s available inference. Hollow points have no computed interval; no new refit-bootstrap batch is run.
Event studies
Cohort homogeneity
The imported TestingInEventStudies deviations design tests positive-event-time cohort deviations jointly. This is the homoskedastic nested-model F-test; the estimator confidence intervals above use clustered inference.
**y__d: homogeneity test not identified.** Only one treated cohort remains on the common supported sample.
Fitting settings and checks
| Specification | Estimator | Settings | Pooling |
|---|---|---|---|
| y__d | CS-DID | {“est_method”: “dr”, “control_group”: “notyettreated”, “xformla”: “y ~ 1”, “base_period”: “universal”, “anticipation”: 0, “panel”: true, “allow_unbalanced_panel”: false, “clustervar”: “cluster”, “clusters”: 385, “bstrap”: false, “cband”: false, “aggregate”: “dynamic”, “event_aggregate”: “dynamic”, “balance_e”: null, “post_event_min”: 0, “post_event_max”: 4} | {“parameter”: null, “value”: null, “status”: “not_applicable”, “fit_scope”: “Group-time DIDs; no synthetic-control pooling parameter”} |
| y__d | SDID | {} | {“parameter”: null, “value”: null, “status”: “not_applicable”, “fit_scope”: “Separate adoption-cohort fits”, “within_cohort_target”: “Mean treated outcome history”, “cross_cohort_partial_pooling”: false, “shared_structure”: null, “note”: “Regularization penalties are not partial-pooling parameters.”} |
| y__d | Matrix completion | {“lambda_fraction”: 0.25, “max_iterations”: 1000, “tolerance”: 1e-12} | {“parameter”: null, “value”: null, “status”: “not_applicable”, “fit_scope”: “Joint untreated-cell fit”, “within_cohort_target”: null, “cross_cohort_partial_pooling”: false, “shared_structure”: “Low-rank matrix and unit/time effects”, “note”: “Regularization penalties are not partial-pooling parameters.”} |
| y__d | Horizontal ridge | {“penalty”: 1.0} | {“parameter”: null, “value”: null, “status”: “not_applicable”, “fit_scope”: “Separate adoption-cohort fits”, “within_cohort_target”: “Mean treated outcome history”, “cross_cohort_partial_pooling”: false, “shared_structure”: null, “note”: “Regularization penalties are not partial-pooling parameters.”} |
| y__d | Multisynth (cohort-averaged) | {“nu”: 1, “nu_selection”: “Package data-derived default”, “lambda”: 0, “fixedeff”: true, “scm”: true, “time_cohort”: true, “n_leads”: 5, “n_lags”: 4, “eps_abs”: 1e-06, “eps_rel”: 1e-06, “V”: “Identity (package default)”, “matrix_assembly”: “Unmodified package default”} | {“parameter”: “nu”, “value”: 1, “status”: “used”, “fit_scope”: “Joint optimization of 1 cohort fits”, “cross_cohort_partial_pooling”: true, “note”: “nu=0 weights separate cohort imbalance only; nu=1 weights pooled imbalance only. One shared nu, not a cohort-specific tuning parameter.”} |
| y__d | Multisynth (individual) | {“nu”: 0.427701208572024, “nu_selection”: “Package data-derived default”, “lambda”: 0, “fixedeff”: true, “scm”: true, “time_cohort”: false, “n_leads”: 5, “n_lags”: 4, “eps_abs”: 1e-06, “eps_rel”: 1e-06, “V”: “Identity (package default)”, “matrix_assembly”: “Equivalent sparse matrix construction”} | {“parameter”: “nu”, “value”: 0.427701208572024, “status”: “used”, “fit_scope”: “Joint optimization of 304 unit fits”, “cross_cohort_partial_pooling”: true, “note”: “nu=0 weights separate cohort imbalance only; nu=1 weights pooled imbalance only. One shared nu, not a cohort-specific tuning parameter.”} |
{
"did2s_vs_direct_imputation_max_post_difference": 2.7755575615628914e-17,
"package_aggregate_vs_estimable_cell_weights": 0.0
}