Causal Inference Basics
Estimating the effect of an action from data requires assumptions that go beyond the data; making them explicit is the whole discipline.
The Fundamental Problem
Causal inference asks: what would happen if we intervened? The difficulty, sometimes called the fundamental problem of causal inference, is that for any unit we observe only one outcome, the one that occurred, never the counterfactual of what would have happened under a different action. Estimating causal effects means reconstructing that missing counterfactual from assumptions.
The Gold Standard and Its Substitutes
A randomized controlled trial assigns the action at random, which on average balances all confounders, seen and unseen, so a difference in outcomes can be attributed to the action. When randomization is impossible, observational methods try to approximate it by adjusting for confounders, but only for the confounders they can measure and model.
Common Approaches
- Adjustment or stratification: compare like with like on measured confounders.
- Instrumental variables: use a factor that affects the action but not the outcome directly.
- Difference-in-differences: use trends in a comparison group to net out shared shocks.
- Regression discontinuity: exploit a sharp threshold in how the action is assigned.
Assumptions Are Everything
Every observational method rests on assumptions that cannot be verified from the data alone, chiefly that all relevant confounders are accounted for. A causal estimate is only as credible as those assumptions, so honest work states them plainly and tests sensitivity to their violation, rather than presenting a number as if the data spoke for themselves.
Structure Before Estimation
Modern causal inference often begins by drawing the assumed causal structure explicitly, as a graph of what affects what, which makes clear what must be adjusted for and what must not. Deciding the causal structure is a modeling act; the estimation that follows only executes it.