OPTIMAL MEDIAN UNBIASED ESTIMATION OF COEFFICIENTS ON HIGHLY PERSISTENT REGRESSORS

This paper derives an optimal estimator for the slope coefficient on highly persistent and predetermined regressors in an otherwise standard linear re- gression. Optimality pertains to the class of procedures that are median unbiased irrespectively of the degree of persistence. It holds for a wide class of monotone loss functions. The optimality statement generalizes to confidence sets. The estimator, which is based on inversion of the Jansson-Moreira (2004) statistic, dominates cur- rently available alternatives in terms of expected square losses across the domain of near nonstationarity. In the empirical application we document encouraging perfor- mance of the proposed estimator for forecasting asset returns.