The Role of Propensity Score Structure in Asymptotic Efficiency of Estimated Conditional Quantile Treatment Effect

TL;DR

This paper investigates how the structure of propensity scores influences the asymptotic efficiency of estimated conditional quantile treatment effects, comparing parametric, nonparametric, and semiparametric methods through theory, simulations, and real data.

Contribution

It systematically analyzes the impact of propensity score structure on estimator efficiency and highlights the advantages of semiparametric estimation in practical scenarios.

Findings

Propensity score structure significantly affects estimator efficiency.

Semiparametric methods often outperform parametric and nonparametric approaches.

Simulation and real data studies support the theoretical insights.

Abstract

When a strict subset of covariates are given, we propose conditional quantile treatment effect to capture the heterogeneity of treatment effects via the quantile sheet that is the function of the given covariates and quantile. We focus on deriving the asymptotic normality of probability score-based estimators under parametric, nonparametric and semiparametric structure. We make a systematic study on the estimation efficiency to check the importance of propensity score structure and the essential differences from the unconditional counterparts. The derived unique properties can answer: what is the general ranking of these estimators? how does the affiliation of the given covariates to the set of covariates of the propensity score affect the efficiency? how does the convergence rate of the estimated propensity score affect the efficiency? and why would semiparametric estimation be worth of recommendation in practice? We also give a brief discussion on the extension of the methods to handle large-dimensional scenarios and on the estimation for the asymptotic variances. The simulation studies are conducted to examine the performances of these estimators. A real data example is analyzed for illustration and some new findings are acquired.