Higher-Order Neyman Orthogonality in Moment-Condition Models

2026-05-11

AI Summary

This study addresses the bias arising from estimation errors in nuisance parameters within parametric moment condition models. To mitigate this issue, the paper proposes a high-order debiasing method that constructs moment functions exhibiting Neyman orthogonality of a specified order with respect to the nuisance parameters, thereby substantially reducing the sensitivity of the estimator to such errors. The approach is both unified and computationally tractable, with a key innovation being that the number of additional nuisance parameters required for orthogonality does not grow with the order of orthogonality—indeed, it can be reduced to a single scalar. Theoretical analysis and empirical evidence demonstrate that this method effectively diminishes estimation bias and significantly enhances robustness and precision across a broad class of econometric models.

Abstract

We construct moment functions that are Neyman-orthogonal to a chosen order in parametric moment condition models. These moment functions reduce sensitivity to nuisance estimation error 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.

Problem

• Neyman orthogonality
• moment-condition models
• nuisance estimation error
• higher-order debiasing
• econometric models

Innovation

• Higher-Order Orthogonality
• Neyman Orthogonality
• Moment-Condition Models
• Debiasing
• Nuisance Parameters