Panel Data Quantile Regression for Treatment Effect Models

Abstract

In this study, we develop a novel estimation method for quantile treatment effects (QTE) under rank invariance and rank stationarity assumptions. Ishihara (2020) explores identification of the nonseparable panel data model under these assumptions and proposes a parametric estimation based on the minimum distance method. However, when the dimensionality of the covariates is large, the minimum distance estimation using this process is computationally demanding. To overcome this problem, we propose a two-step estimation method based on the quantile regression and minimum distance methods. We then show the uniform asymptotic properties of our estimator and the validity of the nonparametric bootstrap. The Monte Carlo studies indicate that our estimator performs well in finite samples. Finally, we present two empirical illustrations, to estimate the distributional effects of insurance provision on household production and TV watching on child cognitive development.

Keywords:

• Panel data
• Quantile regression
• Treatment effect

Supplementary Materials

Supplementary materials provide the two datasets and R codes.

Acknowledgments

I would like to thank the editor, associate editor, and anonymous referees for their careful reading and comments. I would also like to thank Hidehiko Ichimura, Hiroyuki Kasahara, Masayuki Sawada, Katsumi Shimotsu, and the seminar participants at the University of Tokyo, Kobe University, and Tohoku University.

Additional information

Funding

This research was supported by a Grant-in-Aid for JSPS Fellows (20J00900) from the JSPS.