A Neyman-Orthogonalization Approach to the Incidental Parameter Problem

TL;DR

This paper introduces a higher-order orthogonalization method for inference in models with nuisance parameters, improving robustness when nuisance parameters are poorly estimated, especially in fixed-effects models.

Contribution

It develops a novel approach to construct estimating equations orthogonal to nuisance parameters to any order, enhancing inference accuracy in complex models.

Findings

Method successfully applied to a fixed-effect model of team production.

Higher-order orthogonalization reduces bias from nuisance parameters.

Improves inference robustness in models with imprecise nuisance parameter estimates.

Abstract

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.