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Regularized Quantile Regression with Interactive Fixed Effects

Junlong Feng

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Abstract: I consider nuclear norm penalized quantile regression for large $N$ and large $T$ panel data models with interactive fixed effects. The estimator solves a convex minimization problem, not requiring pre-estimation of the (number of the) fixed effects. Uniform rates are obtained for both the slope coefficients and the low-rank common component of the interactive fixed effects. The rate of the latter is nearly optimal. To derive the rates, I show new results that establish uniform bounds of norms of certain random matrices of jump processes. These results may have independent interest. Finally, I conduct Monte Carlo simulations to illustrate the estimator's finite sample performance.

Date: 2019-10, Revised 2020-02
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