1[2 {"id":"C1","text":"At n=30, rho=0.8 (intercept, stationary start), the OLS estimator of rho is biased downward by about 0.122 (MC SE 0.001); the mean of rho_hat is about 0.678.","results_keys":["bias_mc","bias_mc_se","rho_hat_mean"],"status":"supported","caveat":"Only this single design and seed were simulated."},3 {"id":"C2","text":"The Marriott-Pope/Kendall approximation -(1+3rho)/n = -0.113 understates the magnitude of the actual bias; the difference is about 8.6 Monte Carlo standard errors, so Monte Carlo noise cannot explain it.","results_keys":["bias_analytical","bias_mc","bias_mc_se","discrepancy_se_units"],"status":"supported","caveat":"With the n-1 convention the gap shrinks to about 5 SE but stays significant; the formula is a first-order O(1/n) approximation, so an O(1/n^2) discrepancy is expected rather than a contradiction."},4 {"id":"C3","text":"The bias is large relative to sampling uncertainty: about 1.1 times the textbook asymptotic SE, and the asymptotic SE (0.110) understates the actual sd of rho_hat (0.148).","results_keys":["bias_mc","se_asymptotic","rho_hat_sd_mc"],"status":"supported","caveat":"Single design point."},5 {"id":"C4","text":"The discrepancy between the approximation and the true bias shrinks as n grows (O(1/n^2)).","results_keys":[],"status":"not_evaluated","caveat":"This follows from asymptotic theory; it was not tested here because only n=30 was simulated."}6]7