A Neyman-Orthogonalization Approach to the Incidental Parameter Problem

A popular approach to perform inference on a target parameter in the presence of nuisance parameters is to construct estimating equations that are orthogonal to the nuisance parameters, in the sense that their expected first derivative is zero. Such first-order orthogonalization allows the estimator of the nuisance parameters to converge at a slower-than-parametric rate. It may, however, not suffice when the nuisance parameters are very imprecisely estimated. Leading examples are models for panel and network data that feature fixed effects. In this paper, we show how, in the conditional-likelihood setting, estimating equations can be constructed that are orthogonal to any chosen order $q$, in that their leading $q$ expected derivatives are zero. This yields estimators of target parameters that are unaffected by the presence of nuisance parameters to order $q$. In an empirical illustration, we apply our method to a fixed-effect model of team production.

💡 Research Summary

The paper tackles a fundamental obstacle in modern econometrics: inference on a low‑dimensional target parameter when a large number of nuisance (incidental) parameters are present, as in panel and network models with fixed effects. Classical Neyman‑orthogonalization constructs estimating equations whose first‑order derivative with respect to the nuisance parameters has zero expectation. This first‑order orthogonality guarantees that the nuisance estimators may converge slower than the parametric √n rate, but only if they converge faster than n‑1/4. In many applications, especially when the number of units N is comparable to the time dimension T, the fixed‑effects are estimated at the slower T‑1/2 rate, violating the required condition and leaving a non‑negligible bias.

The authors propose a systematic extension: “q‑th‑order Neyman orthogonalization”. Within a conditional‑likelihood framework, they show how to transform any estimating equation u(z;θ,η) into a new one whose first q derivatives with respect to the nuisance vector η have zero expectation. Formally, for p = 1,…,q, \