# Verification checks (P4)
| check | outcome |
|---|---|
| Clean re-run of out/analysis.py (deleted results.json/exclusions.csv) gives byte-identical results.json | PASS |
| Manual NW SE equals statsmodels HAC (use_correction=False) to 1e-10 (assert in script) | PASS |
| Memo's iid numbers reproduced (alpha 2.0925, beta 0.1017, se 0.0448, t 2.27, p 0.0238) | PASS |
| CI contains beta_hat; half-width/se_hac = 1.95996 | PASS |
| se_iid > 0, se_hac > 0; se_hac > se_iid (expected with positively autocorrelated x and u) | PASS |
| t_hac = beta_hat/se_hac | PASS |
| p_hac > 0.05 consistent with CI containing 0 | PASS |
| n_raw 400 − removed 0 = n_analysed 400 | PASS |
| Conclusion robust to bandwidth (lags 5, 8, 12, 24 all p≈0.11–0.12; normal and t(398) references) | PASS |