This paper highlights the importance of finding all roots for the Continuously Updating Generalized Method of Moments (CU-GMM) estimator and Likelihood Ratio (LR)-based tests. Traditional numerical optimization methods often fail to locate global minima due to the non-convexity of objective functions, leading to inaccurate estimates and tests. The leading example is the Instrumental Variables model. Numerical comparisons show that our method outperforms traditional techniques, especially with many weak instruments. (Joint work with Whitney Newey (MIT) and Mahrad Sharifvaghefi (University of Pittsburgh))