SMU SOE Economics Lecture Series (Nov 22, 2023, 10am-11.30am): Quantile Regression with Group-level Treatments

Quantile Regression with Group-level Treatments

To study the distributional effects of group level treatments, Angrist and Lang (2004) applied quantile regression with group level regressors, and Chetverikov et al. (2016) proposed a grouped instrumental variables quantile regression estimator, a quantile extension of the Hausman and Taylor’s (1981) instrumental variables estimator for panel data. However, the analyses of distributional effects of group level treatments in Angrist and Lang (2004) and Chetverikov et al. (2016) are incomplete and their models are quite restrictive, and they only allow for heterogenous distributional effects of group-level treatments that corresponds to individual-level unobserved characteristics, but not group-level unobserved characteristics. In other words, Angrist and Lang (2004) and Chetverikov et al. (2016) allow for within group hetergeneous distributional treatment effects, but not between group heterogeneous distributional treatment effects. In this article, we provide a comprehensive analysis by proposing a quantile regression model that allows for heterogenous distributional effects of group level treatments associated with both individual level and group level unobserved characteristics, corresponding to within-group and between-group distributional effects. We propose two step quantile regression and instrumental variables quantile regression estimators, depending on whether the group level treatments are correlated with the group level unobserved characteristics. Large sample properties are presented and simulation results indicate our estimators perform well in finite samples.

Please view the paper here.