Variable Selection in Causal Inference using a Simultaneous Penalization Method

In the causal adjustment setting, variable selection techniques based only on the outcome or only on the treatment allocation model can result in the omission of confounders and hence may lead to bias, or the inclusion of spurious variables and hence cause variance inflation, in estimation of the treatment effect. We propose a variable selection method using a penalized objective function that is based on both the outcome and treatment assignment models. The proposed method facilitates confounder selection in high-dimensional settings. We show that under some mild conditions our method attains the oracle property. The selected variables are used to form a doubly robust regression estimator of the treatment effect. Using the proposed method we analyze a set of data on economic growth and study the effect of life expectancy as a measure of population health on the average growth rate of gross domestic product per capita.