Nonlinear panel data estimation via quantile regressions

We introduce a class of quantile regression estimators for short panels. Our framework covers static and dynamic autoregressive models, models with general predetermined regressors, and models with multiple individual effects. We use quantile regression as a flexible tool to model the relationships between outcomes, covariates, and heterogeneity. We develop an iterative simulation-based approach for estimation, which exploits the computational simplicity of ordinary quantile regression in each iteration step. Finally, an application to measure the effect of smoking during pregnancy on children’s birthweights completes the paper.