Causal Diagram

A causal diagram (DAG) is a graph of arrows representing causal relationships between variables: an arrow $X \to Y$ means $X$ has a direct causal effect on $Y$. Drawing the DAG before writing a regression is the single most useful disciplining device in applied work — it forces you to commit to which variables are confounders (must control), which are pure outcome causes (include for precision), and which are mediators or colliders (do not control).

When to use

Build the DAG whenever you face a causal question. It tells you (i) what to control for (Omitted Variable Bias arises from any uncontrolled backdoor path with arrows into both treatment and outcome), (ii) what to not control for (a collider or post-treatment mediator), and (iii) when an instrument is needed (when no set of observable controls closes every backdoor). The seatbelt-law PS_4 illustrates the A/B/C taxonomy: A = confounders (must include), B = pure outcome causes (include for precision), C = unrelated or post-treatment (exclude).