Dynamic Quantile Panel Data Models with Interactive Eects

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We propose a simple two-step procedure for estimating the dynamic quantile panel data model with unobserved interactive effects. To account for the endogeneity induced by correlation between factors and lagged dependent variable/regressors, we first estimate factors consistently via an iterative principal component analysis. In the second step, we run a quantile regression for the augmented model with estimated factors and estimate the slope parameters. In particular, we adopt a smoothed quantile regression analysis where the quantile loss function is smoothed to have well-defined derivatives. The proposed two-step estimator is consistent and asymptotically normally distributed, but subject to asymptotic bias due to the incidental parameters. We then apply the split-panel jackknife approach to correct the bias. Monte Carlo simulations confirm that our proposed estimator has good finite sample performance. Finally, we demonstrate the usefulness of our proposed approach with an application to the analysis of bilateral trade for 380 country pairs over 59 years.