Unconditional Quantile Regression for Panel Data with Exogenous or Endogenous Regressors

Unconditional quantile treatment effects are difficult to estimate in the presence of fixed effects. Panel data are frequently used because fixed effects or differences are necessary to identify the parameters of interest. The inclusion of fixed effects or differencing of data, however, redefines the quantiles. This paper introduces a quantile estimator for panel data which conditions on fixed effects for identification but allows the parameters of interest to be interpreted in the same manner as cross-sectional quantile estimates. The quantile treatment effects are unconditional in the fixed effect but identification originates from differences in the covariates or instruments. The fixed effects are never estimated and the estimator is consistent for small T.