1[2 {"id":"C1","text":"Over 1960Q1-2019Q4, a one-percentage-point higher quarterly real GDP growth is associated with a ~0.26 pp fall in the unemployment rate; the 95% HAC interval lies below zero (negative_effect).","results_keys":["effect_estimate","effect_ci_low","effect_ci_high","effect_se","hac_lags","conclusion"],"status":"supported","caveat":"Reduced-form association, not a structural causal effect; simultaneity possible."},3 {"id":"C2","text":"Output growth explains a substantial part of quarterly unemployment changes: residual RMSE 0.250 pp vs 0.325 pp for the mean-only baseline.","results_keys":["baseline_metric","model_metric","r_squared"],"status":"supported","caveat":"In-sample fit only."},4 {"id":"C3","text":"The HAC standard error of beta is robust to lag choice (0.029-0.037 for 0-12 lags) and larger than the classical OLS SE.","results_keys":["effect_se_hac_by_lag","effect_se_ols_classical","effect_se"],"status":"supported","caveat":"Fixed-lag grid only; no automatic bandwidth selection."},5 {"id":"C4","text":"The classical Chow test rejects joint equality of (alpha, beta) across 1960Q1-1983Q4 and 1984Q1-2019Q4 at 5% (unstable).","results_keys":["chow_f_stat","chow_p_value","stability_conclusion","chow_df"],"status":"supported","caveat":"Classical test assumes homoskedastic iid errors, which the residual variances contradict; a HAC Wald joint test also rejects (hac_wald_joint_equality_p)."},6 {"id":"C5","text":"The instability is not in the Okun slope: subperiod slopes are nearly equal (-0.259 vs -0.273) and the slope-only HAC test does not reject; the intercept fell (0.254 to 0.152), lowering the growth rate consistent with stable unemployment from ~0.98% to ~0.55% per quarter.","results_keys":["beta_sub1","beta_sub2","hac_wald_slope_equality_p","intercept_sub1","intercept_sub2","hac_wald_intercept_equality_p","growth_for_stable_u_sub1","growth_for_stable_u_sub2","hac_wald_joint_equality_p"],"status":"supported","caveat":"Intercept difference alone is not individually significant (p=0.25); joint rejection reflects correlated estimates."}7]8