10 Potential outcomes framework

 

This chapter covers

  • Explaining potential outcomes and their assumptions
  • Understanding the relationship between potential outcomes and DAGs
  • Using potential outcomes in the adjustment formula and instrumental variables

There are two main frameworks in causal inference: one based on graphs (DAGs) and another called potential outcomes (POs), also known as the Rubin causal model. These two frameworks are valid and consistent, allowing you to choose the one that suits your situation. We’ve spent parts 1 and 2 of the book on DAGs, and now, in part 3, we will get a taste of POs.

You may be wondering, why bother learning a new framework now? There are three reasons:

  • A significant amount of literature is written using the PO framework, especially in econometrics, biostatistics, and epidemiology. So, if you come across it, understanding POs is essential.
  • The PO notation operates at an individual level, making it more convenient for managing individual effects. Moreover, it is well-suited for dealing with counterfactuals, as expressing them in “do” notation can be cumbersome.
  • Looking at the same concepts from a different perspective will help you assimilate the content covered so far.

We will begin the chapter by introducing PO notation and explaining how to define the average treatment effect (ATE) using this new notation. Additionally, we will outline the fundamental assumptions required for the proper use of POs.

10.1 What is a potential outcome?

10.1.1 Individual outcomes

10.1.2 Population outcomes

10.1.3 Causal effects

10.1.4 PO assumptions

10.2 How do POs relate to DAGs?

10.2.1 The first law of causal inference

10.2.2 Expressing PO assumptions with DAGs

10.2.3 Counterfactuals

10.3 Adjustment formula with potential outcomes

10.4 IVs with potential outcomes

10.5 Chapter quiz

Summary