Defining, identifying, and estimating causal effects with the potential outcomes framework: a review for education research

Causal inference involves determining whether a treatment (e.g., an education program) causes a change in outcomes (e.g., academic achievement). It is well-known that causal effects are more challenging to estimate than associations. Over the past 50 years, the potential outcomes framework has become one of the most widely used approaches for defining, identifying, and estimating causal effects. In this paper, we review the potential outcomes framework with a focus on potential outcomes notation to define individual and average causal effects. We then show how three canonical assumptions, Unconfoundedness, Positivity, and Consistency, may be used to identify average causal effects. The identification results motivate methods for estimating causal effects in practice, which include model-based estimators, such as regression, inverse probability weighting, and doubly robust estimation, and procedures that target covariate balance, such as matching and stratification. Examples and discussion are grounded in the context of a running example of a study aimed at assessing the causal effect of receipt of special education services on 5th grade mathematics achievement in school-aged children. Practical considerations for education research are discussed.