Unconditional Quantile Regression for Panel Data with Exogenous or Endogenous Regressors

by David Powell

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Stata Code for the QRPD and IV-QRPD Estimators

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Quantile regression allows the impact of the explanatory variables to vary based on a nonseparable disturbance term. Panel data are frequently used in applied research because fixed effects control for unobserved heterogeneity and aid identification. The inclusion of fixed effects or use of a location-shift model in a quantile framework changes the interpretation of the estimates by separating the disturbance and including an additive fixed effect term. This paper introduces a quantile estimator for panel data which uses within-group variation for identification but allows the parameters of interest to be interpreted in the same manner as cross-sectional quantile estimates. The estimator maintains the nonseparable disturbance term. The fixed effects are never estimated or even specified and the estimator is consistent for small T. An IV version is also introduced. The estimation technique is straightforward to implement in standard statistical software. As an application of the estimator, the impact of anticipated income shocks on the distribution of consumption is estimated.

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