1[2 {"id":"C1","text":"At n=30, rho=0.8 the OLS estimator of rho is substantially downward biased: Monte Carlo bias -0.124 (MC s.e. 0.001), mean rho_hat 0.676.","results_keys":["bias_mc","bias_mc_se","rho_hat_mean"],"status":"supported","caveat":"Single design point and single seed."},3 {"id":"C2","text":"The Marriott-Pope/Kendall approximation -(1+3rho)/n = -0.113 has the correct sign and captures roughly 90% of the bias.","results_keys":["bias_analytical","bias_mc"],"status":"supported","caveat":"Uses n=30 (series length); with n-1=29 the value is -0.117."},4 {"id":"C3","text":"The approximation understates the magnitude of the bias by about 0.010, a discrepancy of about -9.9 Monte Carlo standard errors, which is not attributable to simulation noise and is consistent with omitted O(n^-2) terms.","results_keys":["discrepancy_se_units","bias_mc","bias_analytical","bias_mc_se"],"status":"supported","caveat":"Attribution to O(n^-2) terms is an interpretation; MC at one n cannot verify the rate."},5 {"id":"C4","text":"The bias is of the same order as the sampling uncertainty: it exceeds the textbook asymptotic standard error (0.110), and the MC sd of rho_hat (0.149) is larger than that asymptotic s.e.","results_keys":["bias_mc","se_asymptotic","rho_hat_sd_mc"],"status":"supported","caveat":"Design-specific."},6 {"id":"C5","text":"The first-order formula is accurate in general for other (n, rho) designs.","results_keys":[],"status":"not_evaluated","caveat":"Only one design point was simulated; no evidence on other designs."}7]8