Causal Catalog

Assumptions

Consistency

Definition	The observed outcome \(Y\) for a unit is the same as the potential outcome \(Y(T=t)\) for that unit under the treatment that was actually observed \(T=t\).
Mathematical definition	\(Y = Y(T)\) For binary treatment, that means: \(Y = Y(1) \text{ if } T=1\) \(Y = Y(0) \text{ if } T=0\)
Intuition/Examples	Expired aspirin (Lecture 2, slide 31) High or low energy dog (Neal reading, p14)

Exchangeability

Definition	The distribution of \(Y(0)\) and \(Y(1)\) for the \(T=1\) and \(T=0\) groups are the same. Also known as ignorability.
Mathematical definition	\(Y(0), Y(1) \perp T\)
Intuition/Examples	Caffeine and exam performance brainstorm

Study Designs

Randomized Experiments

Assumptions needed	Consistency No interference
Assumptions ensured	Exchangeability
Causal quantities identified	Average treatment effect (ATE)

Pros/cons

Advantages	Disadvantages
To be added after our brainstorming!