Verification checks (P4)
- Determinism: re-ran out/analysis.py; out/results.json byte-identical (cmp) — PASS.
- Independent re-implementation (raw numpy OLS + hand-coded Bartlett NW with L=4, no small-sample correction): beta, alpha, se_iid, se_hac, R², mean growth agree to <1e-14 — PASS.
- n_analysed = 240; first_quarter 1960Q1, last_quarter 2019Q4 — PASS.
- Exclusion ledger: 319 quarters − 79 − 0 = 240 = n_analysed — PASS.
- SEs positive (se_iid 0.0200, se_hac 0.0358) — PASS. CI [-0.326, -0.186] contains beta_hat -0.256 and is symmetric — PASS.
- okun_negative_5pct consistent: beta<0 and |t_hac|=7.14>1.96 (CI excludes 0) — PASS.
- Magnitude vs baseline: HAC SE ≈1.8× iid SE, consistent with positive residual autocorrelation (ACF lag1 0.39, lag2 0.29); beta ≈ −0.26 is negative and of a plausible order of magnitude for a quarterly-difference Okun regression (no external reference values used) — PASS.
- Bandwidth sensitivity: se_hac over lags 0–12 ranges 0.029–0.037; conclusion unchanged for all — PASS.
- Identity check: alpha_hat + beta_hat*mean_growth = mean_du (0.1844 − 0.2558·0.7535 = −0.0083) — PASS.
- Information rule: only quarters 1959Q4–2019Q4 enter the computation (enforced via window slicing) — PASS.