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 formed under which the factor structure methods in Bai (2009) lead to consistent estimation of model parameters, but at slow rates of convergence. The second approach develops a kernel weighted fixed-effects method that is 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 some benefits to standard two-dimensional panel methods when the structure of the interactive fixed-effect term is known, but also highlight how the kernel weighted method performs well without knowledge of this structure. The methods are implemented to estimate the demand elasticity for beer.

翻译：本文研究了一个具有未观测交互固定效应的三维及以上多维面板数据的线性可加可分离模型。在估计观测协变量系数时，考虑了两种处理这些未观测交互固定效应的方法。首先，将模型嵌入标准二维面板框架，并在该框架下构建约束条件，使得Bai（2009）中的因子结构方法能够实现模型参数的一致性估计，但收敛速度较慢。第二种方法开发了一种核加权固定效应方法，该方法对问题的多维性质更具鲁棒性，并在特定条件下能达到参数化的一致性速率。理论结果与模拟实验表明，当交互固定效应项的结构已知时，标准二维面板方法具有一定优势，但同时也凸显了核加权方法在无需知晓该结构的情况下仍能保持良好性能。这些方法被应用于啤酒需求弹性的估计中。