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# 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
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