arXiv:2605.10842v3 Announce Type: replace-cross Abstract: We construct moment functions that are Neyman-orthogonal to a chosen order in moment-condition models that involve finite-dimensional nuisance parameters. These moment functions reduce sensitivity to estimation error in the nuisance parameters and, as such, offer a unified and tractable route to higher-order debiasing in a wide range of econometric models. The number of additional nuisance parameters required by our construction, beyond those already present in the original moment conditions, is independent of the order of orthogonalization and can be reduced to a single scalar if desired.