1[2 {"id":"C1","text":"The OLS estimator of rho is downward biased at n=30, rho=0.8: Monte Carlo bias about -0.124 (MC SE 0.001), mean rho_hat about 0.676.","results_keys":["bias_mc","bias_mc_se","rho_hat_mean"],"status":"supported","caveat":"Single design point; Monte Carlo estimate."},3 {"id":"C2","text":"The Marriott-Pope/Kendall approximation -(1+3rho)/n gives -0.113 and understates the Monte Carlo bias by about 8%, a discrepancy of about -9.9 Monte Carlo standard errors.","results_keys":["bias_analytical","bias_mc","discrepancy_se_units"],"status":"supported","caveat":"Uses n=30 (series length); with n-1=29 the gap is about -6.1 SE (diagnostics only)."},4 {"id":"C3","text":"The discrepancy is consistent with the formula being a first-order O(1/n) asymptotic approximation whose neglected O(n^-2) terms are non-negligible at small n and rho near 1; it does not show the formula is wrong.","results_keys":["bias_analytical","bias_mc","discrepancy_se_units"],"status":"supported","caveat":"Interpretation rests on known asymptotic theory; the MC only evaluates one design and cannot verify the rate."},5 {"id":"C4","text":"The actual sampling sd of rho_hat (about 0.149) exceeds the textbook asymptotic SE sqrt((1-rho^2)/n) (about 0.110).","results_keys":["rho_hat_sd_mc","se_asymptotic"],"status":"supported","caveat":"Single design point."}6]7