🤖 AI Summary
This paper addresses identification and estimation challenges in interactive fixed-effects panel regressions arising from low-rank covariates and unknown factor dimensions. We propose two convex optimization estimators based on nuclear-norm (trace-norm) regularization and minimization. Unlike conventional non-convex least squares methods—which suffer from local optima and require pre-specified factor numbers—our approach guarantees global optimality, automatically accommodates low-rank structure, and handles unknown factor dimensions. By employing iterative weighted least squares, we construct a convex algorithm asymptotically equivalent to the LS estimators of Bai (2009) and Moon–Weidner (2017). We establish consistency and asymptotic efficiency of the estimators, while significantly reducing computational complexity. Empirically, the method robustly avoids local optima. This work constitutes the first systematic application of nuclear-norm convex optimization to interactive-effect panel estimation, achieving both statistical efficiency and computational feasibility.
📝 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.