DAGs vs. Potential Outcomes

DAGs and Potential Outcomes are two key frameworks for causality. The Potential Outcomes approach asks a 'what if' question, comparing what actually happened (e.g., sales after an ad) to what would have happened without the ad. DAGs are visual maps of all factors and their causal links. The map (DAG) is crucial because it shows you what to account for (like competitor actions) to make a fair 'what if' comparison using Potential Outcomes.

Try this: When facing a causal question, first try to sketch a map of all the influences at play.

Two Lenses for Causality

Think of DAGs and Potential Outcomes as two different but complementary tools for the same job: untangling cause and effect. They aren't rivals; they are partners that help clarify causal questions.

The 'What If' Machine: Potential Outcomes

The Potential Outcomes framework, also known as the Rubin Causal Model, formalizes counterfactual thinking. For any individual (a person, a company, a city), it posits that there are two potential states: the outcome if they receive a 'treatment' (e.g., see an ad) and the outcome if they don't. The causal effect is the difference between these two states. The fundamental problem of causal inference is that we can only ever observe one of these outcomes for any given individual.

The Causal Map: Directed Acyclic Graphs (DAGs)

A DAG is a visual tool for representing your assumptions about how the world works. Each 'node' is a variable (like 'Ad Campaign' or 'Sales'), and each directed arrow represents a causal influence. They are 'acyclic' because a variable can't cause itself through a loop. The power of a DAG is that it forces you to be explicit about the structure of a problem, helping you spot hidden pathways and confounding variables that might mislead you.

How They Work Together

The DAG provides the road map necessary to answer the Potential Outcomes question. For example, in a study on whether a tutoring program improves test scores, a DAG helps you identify that Parental Motivation might affect both whether a child enrolls in tutoring and their Test Scores. This is a confounder. By spotting this on the map, you know you must adjust for it to create a fair comparison between the potential outcome with tutoring and the potential outcome without it.

The Potential Outcomes (Neyman-Rubin) and graphical (Pearl) models developed separately but are now seen as mathematically compatible. Practitioners use both: Potential Outcomes to define the 'what if' question, and DAGs to map the assumptions needed to answer it with data.

• Pearl (2009): Introduced a formal graphical framework using DAGs to represent causal assumptions and provides rules ('do-calculus') for determining if a causal effect is identifiable from data. [1]
• Rubin (1974): Defined the causal effect as the difference between an individual's potential outcomes under treatment versus control, framing causality as a missing data problem. [2]
• Hernán & Robins (2020): Demonstrate how DAGs provide a clear visual language for the independence assumptions required to estimate average causal effects defined within the Potential Outcomes framework. [3]

Neither framework is foolproof. A DAG's validity rests on untestable assumptions about the causal structure; a flawed graph leads to flawed conclusions. The Potential Outcomes model can become unwieldy with complex treatments, multiple versions of a treatment, or interference, where one unit's treatment affects another's outcome (spillover effects).