# Linear Multidimensional Regression with Interactive Fixed-Effects

arXiv: https://arxiv.org/abs/2209.11691 · HTML: https://mlsanity.com/paper/2209.11691/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 31 references that are in the map.
- First posted on arXiv 23 Sep 2022.

## Builds on (most cited first, 1 of 1)

- [Introduction to Tensor Decompositions and their Applications in Machine Learning](https://mlsanity.com/paper/1711.10781/) (2017)

## Abstract (arXiv)

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.