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# Checks (P4)

check outcome
Clean re-run (deleted outputs, re-ran analysis.py) gives byte-identical results.json (sha256) PASS
n_analysed (400) = n_input_rows (400) − exclusions (0) PASS
se_iid > 0, se_hac > 0 PASS
se_hac > se_iid (expected with positively autocorrelated x and u) PASS (0.0654 vs 0.0448)
t_hac = beta_hat / se_hac PASS
CI contains beta_hat PASS
p_hac > 0.05 consistent with CI covering 0 PASS
Memo numbers reproduced (2.0925, 0.1017, 0.0448, 2.27, 0.0238) by our naive baseline PASS
Bandwidth sensitivity (lags 1–24): p > 0.05 for every lag ≥ 1 PASS (p range 0.079–0.125; only lags=0, i.e. White HC, gives p=0.038)
rho_resid ≈ 0.61, consistent in sign/magnitude with stated DGP ρ≈0.7 (finite-sample downward bias) PASS
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