Nuclear Norm Regularized Estimation of Panel Regression Models

TL;DR

This paper introduces two convex nuclear norm regularization methods for estimating panel regression models with interactive fixed effects, offering computational advantages and addressing identification issues.

Contribution

The paper proposes novel convex nuclear norm based estimators for panel models with interactive fixed effects, improving computational efficiency and resolving identification problems.

Findings

Establishes consistency of the proposed estimators.

Provides methods to approximate least squares estimators using convex optimization.

Demonstrates computational advantages over traditional LS estimators.

Abstract

In this paper we investigate panel regression models with interactive fixed effects. We propose two new estimation methods that are based on minimizing convex objective functions. The first method minimizes the sum of squared residuals with a nuclear (trace) norm regularization. The second method minimizes the nuclear norm of the residuals. We establish the consistency of the two resulting estimators. Those estimators have a very important computational advantage compared to the existing least squares (LS) estimator, in that they are defined as minimizers of a convex objective function. In addition, the nuclear norm penalization helps to resolve a potential identification problem for interactive fixed effect models, in particular when the regressors are low-rank and the number of the factors is unknown. We also show how to construct estimators that are asymptotically equivalent to the least squares (LS) estimator in Bai (2009) and Moon and Weidner (2017) by using our nuclear norm regularized or minimized estimators as initial values for a finite number of LS minimizing iteration steps. This iteration avoids any non-convex minimization, while the original LS estimation problem is generally non-convex, and can have multiple local minima.