Linear Multidimensional Regression with Interactive Fixed-Effects

This paper studies a linear and additively separable regression model for multidimensional panel data of three or more dimensions with unobserved interactive fixed effects. The main estimator follows a double debias approach, and requires two preliminary steps to control unobserved heterogeneity. 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 step develops a weighted fixed-effects method that is robust to the multidimensional nature of the problem and achieves the parametric rate of consistency. This second step is combined with a double debias procedure for asymptotically normal slope estimates. The methods are implemented to estimate the demand elasticity for beer.