Zixi Zhou

Estimating a unit coordinate from the same history used to evaluate an orthogonal panel score can create a drift of order $T^{-1}$. This drift can shift the $\sqrt{NT}$ limit when $N/T$ converges to a positive constant. In a partially linear model, we separate derivative–influence covariance, score curvature, and propagation of first-step bias. The last component vanishes as the nuisance sieve grows, while the other two may reinforce or cancel. We estimate the drift from the full unit history and construct valid standard errors under independent units, deterministic quasi-uniform coordinates, finite-range dependence, and tensor-product B-splines. Separate results cover sample means and regular smooth scalar moment coordinates. For a sample mean and a fixed sieve, buffered splitting removes covariance but retains curvature; an equal split doubles its leading coefficient. Simulations show cancellation of substantial bias components and improved coverage after correction.