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 may, however, not suffice when the nuisance parameters are very imprecisely estimated. Leading examples where this is the case 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. Combining these equations with sample splitting yields higher-order bias-corrected estimators of target parameters. In an empirical application we apply our method to a fixed-effect model of team production and obtain estimates of complementarity in production and impacts of counterfactual re-allocations.

翻译：在存在附带参数的情况下，对目标参数进行推断的一种常用方法是构建与附带参数正交的估计方程，即其期望一阶导数为零。然而，当附带参数的估计非常不精确时，这种一阶正交化可能并不足够。面板数据和网络数据模型中的固定效应模型是这种情况的主要例子。在本文中，我们展示了在条件似然设定下，如何构建与任意选定阶数正交的估计方程。将这些方程与样本分割相结合，可以得到目标参数的高阶偏差校正估计量。在一项实证应用中，我们将该方法应用于团队生产的固定效应模型，并获得了生产中互补性的估计以及反事实重新分配的影响。