Linear Multidimensional Regression with Interactive Fixed-Effects
Econometrics
2026-03-06 v7 Machine Learning
Methodology
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.
Keywords
Cite
@article{arxiv.2209.11691,
title = {Linear Multidimensional Regression with Interactive Fixed-Effects},
author = {Hugo Freeman},
journal= {arXiv preprint arXiv:2209.11691},
year = {2026}
}