Causal Analysis Using DAGs: Applications and Limitations

This chapter applies the theory developed in Chap. 4 in various situations. First, an often-discussed example is shown and developed further to illustrate a standard application. The theory is then applied to give a formal treatment to the method of instrumental variables. Also, the method of propensity score-based matching to estimate causal effects from observational data is given a new proof in this framework. The theory may be applied to the handling of data sets showing Simpson’s paradox. The causal structure suggests whether the conditional or marginal conclusions may be seen as relevant when these contradict. The chapter also presents a number of real-life problems where the DAG-based theory of causality, as presented so far, does not provide a useful description. These include causal systems with memory, joint effects when individual effects do not exist, time lag in effects, cyclic causality, and limitations of learning the behavior of the causal system through interventions.