1[2 {"id":"C1","text":"The two-way fixed-effects slope of y on x is about 0.604.","results_keys":["beta_fe","beta_fe_within_check"],"status":"supported","caveat":"Within association; causal reading requires strict exogeneity."},3 {"id":"C2","text":"The pooled OLS slope (about 1.268) is roughly twice the FE slope, consistent with fixed effects correlated with x.","results_keys":["beta_pooled","beta_fe"],"status":"supported","caveat":"Does not identify whether firm or year effects drive the gap."},4 {"id":"C3","text":"Firm-clustered SE (0.0450) exceeds the conventional SE (0.0326) by a factor of about 1.38.","results_keys":["se_cluster","se_conventional","se_ratio_cluster_to_conventional"],"status":"supported","caveat":"Clustered SE value depends ~4.5% on degrees-of-freedom convention."},5 {"id":"C4","text":"The 95% cluster-robust confidence interval for beta is [0.515, 0.694], excluding zero.","results_keys":["beta_ci_low","beta_ci_high","ci_critical_value_t"],"status":"supported","caveat":"t(G-1) critical value; asymptotic in number of clusters (G=100)."},6 {"id":"C5","text":"The panel is balanced (100 firms x 12 years) with no exclusions; all 1200 rows analysed.","results_keys":["n_firms","n_years","n_analysed","n_input_rows","data_issues","panel_balanced"],"status":"supported","caveat":""}7]8