Finite-Sample Inference for Persistent Dynamic Panels Under Cross-Sectional Dependence: Driscoll–Kraay Theory, Simulation, and a Policy Application

Common interventions in persistent dynamic panels pose an inferential problem because dynamic estimator bias and covariance calibration affect the same coefficient. This paper examines that interaction through a closed-form intervention projection for nested steps; exact oracle Bartlett covariance benchmarks; and simulations calibrated to 137 firms, 168 weeks, persistence of 0.991678, and observed cross-sectional dependence. The analytical calculations connect the intervention coefficient to persistence estimation and distinguish outcome persistence from aggregated score dependence. In the calibrated single-step design at bandwidth four, the nominal 95% intervals give raw coverage of 74.57%, feasible recentred coverage of 85.68%, and oracle score recentred coverage of 89.35%. In paired simulations with four fitted indicators, the bias is 6.2% of the true shift with only the focal step active and near zero when a small earlier shift is also active, although the persistence bias is nearly unchanged. Persistence alone, therefore, does not determine the bias in the intervention coefficient. The empirical illustration uses a panel interrupted time series for Saudi Arabia’s QFI Amendment 2. The contemporaneous conditional level shift in total foreign ownership is 0.024238 percentage points, and the first-difference event pulse is 0.022962. The mean recursive forecast gap over weeks 121 to 129 is 0.06972 percentage points.