After reviewing the simulation performance of general-to-specific automatic regression-model selection, as embodied in PcGets, we show how model selection can be non-distortionary: approximately unbiased ‘selection estimates’ are derived, with reported standard errors close to the sampling standard deviations of the estimated DGP parameters, and a near-unbiased goodness-of-fit measure. The handling of theory-based restrictions, non-stationarity and problems posed by collinear data are conside...