Published 22 June 2026

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This paper proposes inference methods for structural parameters in instrumental variable regression models that are robust to many and arbitrarily weak instruments and many included exogenous regressors. This setting is practically important to accommodate fixed effect dummies and saturated specifications to identify the local average treatment effect, for example. We propose the cross-fitted Lagrange multiplier and Anderson-Rubin statistics and study their asymptotic properties under mild regularity conditions. We consider both homogeneous and heterogeneous treatment effects. Simulation results endorse desirable finite sample performances of the proposed methods.