Bonhomme, Stéphane, Jochmans, Koen and Weidner, Martin (2026) Orthogonal Moments in Likelihood Models. TSE Working Paper, n. 26-1774, Toulouse

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Abstract

Many models, such as fixed-effect models for panel or network data, are hard to
estimate because they feature nuisance parameters that are both numerous and
estimated imprecisely. This, in general, causes an incidental-parameter problem
in the estimator of the parameters of interest. The problem can be alleviated
by working with an estimating equation whose expectation is insensitive to
the value of the nuisance parameters. We discuss and contrast three notions
of insensitivity, also called orthogonality, in the context of likelihood models:
Neyman orthogonality, Neyman orthogonality to order q, and full orthogonality.
Orthogonal moments are obtained by projecting the estimating equation on
nested subspaces, which are spanned by, respectively, the scores of the nuisance
parameters, the first q derivatives of the likelihood ratio with respect to the
nuisance parameters, and all likelihood ratios of the model. We give explicit
constructions in binary-choice, count-data, and nonlinear regression models.