Assessing the Treatment Effect on the Causal Models via Parametric Approaches with Applications to the Study of English Educational Effect in Japan

Observational studies are widely used to evaluate the effect of treatment when it is not feasible to conduct controlled experiment. This article considers the use of parametric analyses for estimating the causal treatment effect. The proposed approach is an alternative to the widely used stratification estimator as well as Robins' double robust estimator both of which are consistent under the key assumption of strong ignorability. To relax the assumption of strong ignorability, we instead impose fully parametric structures on the causal models to identify the causal treatment effect. The proposed parametric framework provides a likelihood ratio test for checking the assumption of strong ignorability. Simulations are conducted to investigate the performance of the proposed estimator as well as the power of the likelihood ratio test. We demonstrate how the proposed method can be used for data from an observational study for measuring English educational effect on Japanese elementary school students.