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
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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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.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Bai (2009) Panel data models with interactive fixed effects | 1.000 | 10 | 4 | 100% |
| 2 | Moon and Weidner (2015) Linear Regression for Panel With Unknown Number of Factors as Interactive Fixed Effects | 1.000 | 5 | 3 | 100% |
| 3 | Moon and Weidner (2017) Dynamic linear panel regression models with interactive fixed effects | 0.953 | 15 | 6 | 87% |
| 4 | Belloni, Chen, Madrid Padilla, and Wang (2023) High-dimensional latent panel quantile regression with an application to asset pricing | 0.843 | 5 | 4 | 60% |
| 5 | Feng (2024) Nuclear norm regularized quantile regression with interactive fixed effects | 0.843 | 5 | 4 | 60% |
| 6 | Wang, Su, and Zhang (2022) Low-rank panel quantile regression: Estimation and inference | 0.737 | 3 | 3 | 67% |
| 7 | Bai and Ng (2002) Determining the Number of Factors in Approximate Factor Models | 0.737 | 3 | 2 | 100% |
| 8 | Gobillon and Magnac (2016) Regional policy evaluation: Interactive fixed effects and synthetic controls | 0.737 | 3 | 2 | 100% |
| 9 | Chernozhukov, Hansen, Liao, and Zhu (2023) Inference for Low-Rank Models | 0.737 | 3 | 2 | 100% |
| 10 | Recht, Fazel, and Parrilo (2010) Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization | 0.644 | 4 | 2 | 50% |
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