When Is Neyman-Orthogonal Inference Feasible? Existence and Relevance

Neyman-orthogonal moments underpin debiased and double machine learning, yet their existence and informativeness are typically presumed. We ask three questions: when do nontrivial orthogonal moments exist, which target directions contain first-order information, and does a proposed moment detect all such directions? Restricted local overidentification characterizes existence under attainability. Effective Fisher information determines relevance; its rank counts informative target directions. A rank sandwich combines moment Jacobians with target changes offset by nuisance perturbations, distinguishing information missed by a moment from information absent from the experiment. In sample selection without covariate exclusions, this yields identification-robust inference under rank deficiency. In latent-variable models, the informative target space is an RKHS. For Gaussian repeated measurements, additional measurements enlarge the class of smoothed distributional targets that are regularly learnable, while CDFs, quantiles, and threshold-policy functionals remain uninformative at the parametric rate for every finite number of measurements.