3 Consistency and positivity
3.1 Asking good causal questions
Sep 12. Slides. After class, read Hernán and Robins 2020 Chapter 3. Optionally, read Hernán 2016.
Good causal questions are structured so that credibility is strong for two key assumptions: positivity and consistency.
- Positivity. Every population subgroup receives every treatment value with non-zero probability
- Consistency. Potential outcomes \(Y^A\) are well-defined and linked to observable data
After class, you will be ready for a discussion in lab related to a common violation of the consistency assumption when one unit’s treatment affects another unit’s outcome.
3.2 Lab: Interference
Sep 13 Slides.
When defining causal effects, we often discuss the outcome \(Y^a\) that a person would realize if they were exposed to treatment value \(a\). But definitions become harder if there exists interference: the outcome of unit \(i\) depends on the treatment assigned to unit \(j\). This discussion will focus on understanding interference and why we need to update our potential outcomes notation if interference is present.