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

Jad Beyhum (1, 2) , Eric Gautier (1, 2)

1 TSE-R - Toulouse School of Economics
2 UT Capitole - Université Toulouse Capitole

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.

Mots clés: panel data; interactive fixed effects; nuclear norm penalization; unknown variance; factor models; flexible unobserved heterogeneity

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Jad Beyhum, Eric Gautier. Square-root nuclear norm penalized estimator for panel data models with approximately low-rank unobserved heterogeneity. 2019. ⟨hal-02102986v1⟩