Square-root nuclear norm penalized estimator for panel data models with approximately low-rank unobserved heterogeneity

Jad Beyhum; Eric Gautier

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arXiv · 1904.09192

Square-root nuclear norm penalized estimator for panel data models with approximately low-rank unobserved heterogeneity

Jad Beyhum·Eric Gautier

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Abstract

This paper considers a nuclear norm penalized estimator for panel data models with interactive effects. The low-rank interactive effects can be an approximate model and the rank of the best approximation unknown and grow with sample size. The estimator is solution of a well-structured convex optimization problem and can be solved in polynomial-time. We derive rates of convergence, study the low-rank properties of the estimator, estimation of the rank and of annihilator matrices when the number of time periods grows with the sample size. Two-stage estimators can be asymptotically normal. None of the procedures require knowledge of the variance of the errors.

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BibTeX RIS

Jad Beyhum, Eric Gautier. 2019-04-19. Square-root nuclear norm penalized estimator for panel data models with approximately low-rank unobserved heterogeneity. https://arxiv.org/abs/1904.09192

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