Causal Inference and Observational Studies
Causality beyond regression
Potential outcomes framework
For each unit, let and denote potential outcomes under treatment and control. The causal effect is defined as , though only one of these outcomes is observed for any unit.
Fundamental problem of causal inference
Causal effects are not directly observed for individuals because treatment and control outcomes cannot be observed simultaneously for the same unit.
What is the key challenge in causal inference?
The fundamental problem is that each unit reveals only one of its potential outcomes.
Correct answer: Observing both potential outcomes for every unit
What is confounding?
Confounders can bias naive comparisons unless adjusted for through design or analysis.
Correct answer: A situation where treatment assignment and outcome are both associated with a third variable.
Identification strategies
Randomized experiments, matching, regression adjustment, inverse probability weighting, instrumental variables, and difference-in-differences are common strategies for identifying causal effects under explicit assumptions.
Randomization mainly helps by
Random assignment balances observed and unobserved confounders on average.
Correct answer: Balancing confounders in expectation
What does an instrumental variable need to do in principle?
Valid instruments satisfy relevance and exclusion-type conditions.
Correct answer: It must affect treatment but influence the outcome only through treatment and not through direct confounding paths.
Associational vs causal questions
Associational
- Concerned with dependence
- Can often be answered with prediction or regression
- Does not require intervention logic
Causal
- Concerned with intervention effects
- Requires assumptions for identification
- Often needs experimental or quasi-experimental design