Linear Multidimensional Regression with Interactive Fixed-Effects

TL;DR

This paper introduces a new estimator for linear models with multidimensional panel data that accounts for unobserved interactive fixed-effects, achieving fast convergence and asymptotic normality.

Contribution

It develops a Neyman-orthogonal estimator with a two-step procedure that effectively handles multidimensional interactive fixed-effects in panel data models.

Findings

Estimator is asymptotically normal.

Achieves parametric rate of consistency.

Successfully applied to estimate beer demand elasticity.

Abstract

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.