Nuclear norm regularized estimation of panel regression models

Hyungsik Moon () and Martin Weidner

No CWP14/19, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies

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 fi rst 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 de fined as minimizers of a convex objective function. In addition, the nuclear norm penalization helps to resolve a potential identifi cation 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 nite 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.

Keywords: Interactive Fixed Effects; Factor Models; Nuclear Norm Regularization; Convex Optimization; Iterative Estimation (search for similar items in EconPapers)
Date: 2019-04-03
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Citations: View citations in EconPapers (18)

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Related works:
Working Paper: Nuclear Norm Regularized Estimation of Panel Regression Models (2023)
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