This paper studies a linear and additively separable model for multidimensional panel data of three or more dimensions with unobserved interactive fixed effects. Two approaches are considered to account for these unobserved interactive fixed-effects when estimating coefficients on the observed covariates. First, the model is embedded within the standard two-dimensional panel framework and restrictions are derived under which the factor structure methods in Bai (2009) lead to consistent estimation of model parameters, but at potentially slow rates of convergence. The second approach utilises popular machine learning techniques to develop group fixed-effects and kernel weighted fixed-effects that are more robust to the multidimensional nature of the problem and can achieve the parametric rate of consistency under certain conditions. Theoretical results and simulations show the benefit of standard two-dimensional panel methods when the structure of the interactive fixed-effect term is known, but also highlight how the group fixed-effects and kernel methods perform well without knowledge of this structure. The methods are implemented to estimate the demand elasticity for beer under a handful of models for demand.

翻译：本文研究了一种适用于三维及以上多维面板数据的线性可加分离模型，该模型包含未观测的交互固定效应。在估计观测协变量系数时，本文考虑了两种处理未观测交互固定效应的方法。第一种方法将模型嵌入标准二维面板框架，并推导出在满足特定约束条件时，Bai(2009)提出的因子结构方法能够实现模型参数的一致估计（但收敛速度可能较慢）。第二种方法利用流行的机器学习技术，构建了群组固定效应和核加权固定效应，这些方法对多维问题的鲁棒性更强，且在一定条件下能够达到参数收敛速度。理论结果与模拟实验表明，当交互固定效应项结构已知时，标准二维面板方法具有优势；同时，群组固定效应与核方法在未知结构情况下仍能表现良好。本文以啤酒需求弹性估计为例，在多种需求模型下对所述方法进行了实证应用。