1# Contract (P0)2**Question.** In a Gaussian AR(1) y_t = c + rho*y_{t-1} + e_t (c=0 in DGP), how biased is the OLS estimator of rho (regression on constant and y_{t-1}, t=2..n) in finite samples, and how well does the Marriott–Pope/Kendall approximation -(1+3rho)/n describe it at the design (n, rho)?34**Estimands.** (i) bias_analytical = -(1+3rho)/n evaluated at design values (n = series length = 30 as stated in design). (ii) bias_mc = mean(rho_hat) - rho over R replications, with MC SE = sd(rho_hat)/sqrt(R). Also discrepancy in SE units, rho_hat mean/sd, and asymptotic SE sqrt((1-rho^2)/n) as baseline quantity. Meaningful under: Gaussian iid innovations, stationarity (|rho|<1), stationary initial condition, correct OLS with intercept.56**Outputs.** out/results.json (task_id, bias_analytical, bias_mc, bias_mc_se, rho_hat_mean, rho_hat_sd_mc, discrepancy_se_units, se_asymptotic, n_replications, feasibility, feasibility_reason, data_issues, n_input_rows, n_analysed, random_seed); out/report.md (6 sections; must state the nature of the approximation and scope of MC evidence); out/analysis.py (deterministic, data/ only); out/claims.json.78**Information rules.** Use only data/design.csv; follow design exactly (n=30, rho=0.8, sigma=1, intercept, stationary y_1, R=20000, seed 20261029 with numpy default_rng); c=0; fresh series per replication; OLS of y_t on (1,y_{t-1}) for t=2..n.910**Invalidity conditions.** Missing/inconsistent design parameters, |rho|>=1 (no stationary initial distribution), not using the given seed, using a different sample range or omitting the intercept.11