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# Checks (P4)

check outcome
Clean re-run (delete results.json, rerun) gives byte-identical file PASS
CI [beta_ci_low, beta_ci_high] contains beta_hat PASS
se_iid > 0, se_hac > 0 PASS
CI symmetric around beta_hat (beta ± 1.96 se_hac) PASS
t_hac == beta_hat / se_hac PASS
p_hac < 0.05 iff CI excludes 0 (both false) PASS
n_analysed (400) = n_raw (400) − removed (0); matches exclusions.csv PASS
se_hac > se_iid, as expected with positively autocorrelated x and u (ratio 1.457; rough AR(1) approximation sqrt((1+0.40)/(1-0.40)) ≈ 1.53) PASS
rho_resid (0.609) roughly consistent with the stated ~0.7 PASS (somewhat below 0.7; OLS residual autocorrelation is biased downward in finite samples)
Memo numbers (2.0925, 0.1017, 0.0448, 2.27, 0.0238) reproduced to stated rounding PASS
Verdict robust across bandwidths 4–24 (p from 0.114 to 0.123) PASS
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