Double robust inference for continuous updating GMM

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) chi-squared limiting distribution of the DRLM statistic is robust to both misspecification and weak identification, hence its name. The minimizer is the so-called pseudo-true value, which equals the true value of the structural parameter under correct specification. To emphasize its importance for applied work where misspecification and weak identification are common, we use the DRLM test to analyze: the risk premia in Adrian et al. (2014) and He et al.
(2017); the structural parameters in a nonlinear asset pricing model with constant
relative risk aversion.