Linear Multidimensional Regression with Interactive Fixed-Effects
This provides a method for econometricians and statisticians dealing with complex panel data, though it appears incremental as it builds on existing factor model techniques.
The paper tackles the problem of estimating linear models with multidimensional panel data and unobserved interactive fixed-effects by developing a Neyman-orthogonal estimator that achieves parametric consistency and asymptotic normality, as demonstrated in an application estimating beer demand elasticity.
This paper studies a linear model for multidimensional panel data of three or more dimensions with unobserved interactive fixed-effects. The main estimator uses a Neyman-orthogonal approach, and requires two preliminary steps. First, the model is embedded within a two-dimensional panel framework where factor model methods in Bai (2009) lead to consistent, but slowly converging, estimates. The second step develops a weighted-within transformation that is robust to multidimensional interactive fixed-effects and achieves the parametric rate of consistency. The estimator is shown to be asymptotically normal. The methods are implemented to estimate the demand elasticity for beer.