  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.
