Causal Inference in a 2² Factorial Design Using Generalized Propensity Score

Abstract:

When estimating causal effects, typically one binary treatment is evaluated at a time. This thesis aims to extend the causal inference framework using the potential outcomes scheme to a situation in which it is of interest to simultaneously estimate the causal effects of two treatments, as well as their interaction effect. The model proposed is a 2² factorial model, where two methods have been used to estimate the generalized propensity score to assure unconfoundedness of the estimators. Of main focus is the inverse probability weighting estimator (IPW) and the doubly robust estimator (DR) for causal effects. Also, an estimator based on linear regression is included. A Monte Carlo simulation study is performed to evaluate the proposed estimators under both constant and variable treatment effects. Furthermore, an application on an empirical study is conducted. The empirical application is an assessment of the causal effects of two social factors (parents’ educational background and students’ Swedish background) on averages grades for ninth graders in Swedish compulsory schools. The data are from 2012 and are measured on school level. The results show that the IPW and DR estimators produces unbiased estimates for both constant and variable treatment effects, while the estimator based on linear regression is biased when treatment effects vary.