Robust Bayesian Estimation in Causal Two-Stage Least Squares Modeling with Instrumental Variables

Abstract

In causal randomized experiments or psychological trials, the two-stage least squares (2SLS) model with instrument variables (IVs) is a widely used approach to address the issue of treatment endogeneity. The IVs are used to estimate a part of the causal effect whose estimation is not affected by the violation of the linearity assumption in the causal model, and the causal effect of interest in the 2SLS model becomes the local average treatment effect (LATE). Because practical data usually violate the normality assumption, the LATE estimate from the traditional normal-distribution-based method may be inefficient or even biased. This study proposes a robust Bayesian estimation method using Student’s t distributions to model data with heavy tails or containing outliers and compares the performance of the proposed robust method to that of the traditional normal-distribution-based method. A Monte Carlo simulation study is conducted and shows that the proposed robust method outperforms the traditional method when data are contaminated. The robust method provides more accurate and efficient LATE estimates and better model fits and thus is recommended to be used in general in the 2SLS modeling with IVs.