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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. The second approach considers group fixed-effects and kernel methods that are more robust to the multidimensional nature of the problem. 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.
