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Regularized Quantile Regression with Interactive Fixed Effects

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Document pages: 61 pages

Abstract: This paper studies large $N$ and large $T$ conditional quantile panel datamodels with interactive fixed effects. We propose a nuclear norm penalizedestimator of the coefficients on the covariates and the low-rank matrix formedby the fixed effects. The estimator solves a convex minimization problem, notrequiring pre-estimation of the (number of the) fixed effects. It also allowsthe number of covariates to grow slowly with $N$ and $T$. We derive an errorbound on the estimator that holds uniformly in quantile level. The order of thebound implies uniform consistency of the estimator and is nearly optimal forthe low-rank component. Given the error bound, we also propose a consistentestimator of the number of fixed effects at any quantile level. To derive theerror bound, we develop new theoretical arguments under primitive assumptionsand new results on random matrices that may be of independent interest. Wedemonstrate the performance of the estimator via Monte Carlo simulations.

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