Abstract: Many econometric models feature nuisance parameters. These may be difficult to estimate, for example because their dimension is large relative to the sample size, thereby complicating our ability to perform inference on parameters of interest. We consider conditional likelihood problems and propose a scheme to orthogonalize moment conditions such that all their derivatives with respect to the nuisance parameters to a given order have zero mean. When combined with sample splitting this yields estimating equations that enjoy robustness to estimation error in the nuisance parameters to that order. This strategy generalises (first-order) Neyman orthogonality to higher order. We illustrate its use on fixed-effect models for N-by-T panel data. There, orthogonalization to first order is insufficient to deal with the 1/T incidental-parameter bias. On the other hand, orthogonalization to second-order yields estimators whose bias is of order 1/T^2 and are, therefore, correctly centered under rectangular-array asymptotics. More generally, a q-th order orthogonalised score equation yields an estimator with bias of order 1/T^q. A second application is to models for network data. As an illustration we consider the estimation of production functions for team output. We document complementarities between scientific authors from a data set on academic research output.
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