We propose the double robust Lagrange multiplier (DRLM) statistic for testing hypotheses specified on the minimizer of the population continuous updating objective function. The (bounding) χ2 limiting distribution of the DRLM statistic is robust to both misspecification and weak identification,...

Long-run restrictions are a very popular method for identifying structural vector autoregressions, but they suffer from weak identification when the data is very persistent, i.e., when the highest autoregressive roots are near unity. Near unit roots introduce additional nuisance parameters and...