Bayesian Two-Stage Robust Causal Modeling with Instrumental Variables using Student's t Distributions

Abstract

In causal inference research, the issue of the treatment endogeneity is commonly addressed using the two-stage least squares (2SLS)modelingwith instrumental variables (IVs),where the local average treatment effect (LATE) is the causal effect of interest. Because practical data are usually heavy tailed or contain outliers, using traditional 2SLSmodeling based on normality assumptions may result in inefficient or even biased LATE estimate. This study proposes four types of Bayesian two-stage robust causalmodels with IVs tomodel normal and nonnormal data, and evaluates the performance of the four types of models with IVs. TheMonte Carlo simulation results show that the Bayesian two-stage robust causalmodel- ing produces reliable parameter estimates and model fits. Particularly, in different types of the two-stage robustmodels with IVs, the models that take outliers into consideration and use Student’s t distributions in the second stage to model heavy-tailed data or data containing outliers provide more accurate and efficient LATE estimates and better model fits than other distribution models when data are contaminated. The preferred models are recommended to be adopted in general in the two-stage causalmodeling with IVs