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Nuclear Norm Regularized Estimation of Panel Regression Models

Hyungsik Roger Moon, Martin Weidner

arXiv 25 Oct 2018 · Econometrics · publishedJournal of Econometrics (2026) · 47 citations (OpenAlex)

arXiv:1810.10987 · PDF · DOI · OpenAlex · Extracted main text

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.

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59
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distinct cited
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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Bai (2009) Panel data models with interactive fixed effects1.000104100%
2Moon and Weidner (2015) Linear Regression for Panel With Unknown Number of Factors as Interactive Fixed Effects1.00053100%
3Moon and Weidner (2017) Dynamic linear panel regression models with interactive fixed effects0.95315687%
4Belloni, Chen, Madrid Padilla, and Wang (2023) High-dimensional latent panel quantile regression with an application to asset pricing0.8435460%
5Feng (2024) Nuclear norm regularized quantile regression with interactive fixed effects0.8435460%
6Wang, Su, and Zhang (2022) Low-rank panel quantile regression: Estimation and inference0.7373367%
7Bai and Ng (2002) Determining the Number of Factors in Approximate Factor Models0.73732100%
8Gobillon and Magnac (2016) Regional policy evaluation: Interactive fixed effects and synthetic controls0.73732100%
9Chernozhukov, Hansen, Liao, and Zhu (2023) Inference for Low-Rank Models0.73732100%
10Recht, Fazel, and Parrilo (2010) Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization0.6444250%

Showing the top 10 of 59 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Inference in Unbalanced Panel Data Models with Interactive Fixed Effects1.00084
2Spectral and Post-Spectral Estimators for Grouped Panel Data Models1.00073
30.5cmLow-Rank Estimation of Nonlinear Panel Data Models0.94163
4Tractable Estimation of Nonlinear Panels with Interactive Fixed Effects0.874182
5Regularized Quantile Regression with Interactive Fixed Effects0.81142
6A Simple and Computationally Trivial Estimator for Grouped Fixed Effects Models0.652121
7Detecting Latent Communities in Network Formation Models0.64441
8Threshold Regression in Heterogeneous Panel Data with Interactive Fixed Effects0.64422
9Robust Estimation and Inference in Panels with Interactive Fixed Effects0.51122
10Causal Models for Longitudinal and Panel Data: A Survey0.51121