Causal Inference 因果推論
Released已發布Apply causal inference methods — counterfactual framework, instrumental variables, propensity score matching, and difference-in-differences — to estimate causal effects from observational data. Use this skill when the user needs to determine if X caused Y from non-experimental data, evaluate program/policy impact without a randomized trial, or control for confounders — even if they say 'did this change cause the improvement', 'how do we measure the impact without an experiment', or 'is this correlation or causation'.
統計方法論技能：Causal Inference 分析與應用。
Methodology 方法論
IRON LAW: Correlation Is Not Causation — But Causation Is Estimable
Observational data cannot prove causation through correlation alone.
BUT with the right methodology (matching, IV, DID, RDD), we CAN
estimate causal effects from observational data — IF the assumptions
of each method are satisfied and explicitly tested.
The key question is always: "What would have happened WITHOUT the treatment?"
(the counterfactual)
The Fundamental Problem
We observe: Y_i(treated) — what happened to the treated unit.
We want to know: Y_i(treated) - Y_i(untreated) — the causal effect.
We can never observe: Y_i(untreated) for the same unit at the same time.
All causal inference methods estimate the counterfactual — what would have happened without the treatment.
Method Selection Guide
| Method | When to Use | Key Assumption |
|---|---|---|
| RCT | You can randomize | Random assignment eliminates confounders |
| Propensity Score Matching (PSM) | Treatment is non-random but based on observables | No unobserved confounders (selection on observables) |
| Instrumental Variables (IV) | Unobserved confounders exist but you have an instrument | Instrument affects treatment but not outcome directly |
| Difference-in-Differences (DID) | Policy/event creates natural treatment/control groups | Parallel trends: groups would have trended similarly without treatment |
| Regression Discontinuity (RDD) | Treatment assigned by a cutoff | Observations just above/below cutoff are comparable |
| Synthetic Control | One treated unit, multiple control units (aggregate data) | Synthetic weighted combination matches pre-treatment trends |
Analysis Steps
- Define the causal question: What is the treatment? What is the outcome?
- Identify threats to validity: What confounders could explain the association?
- Choose a method: Based on data structure and available identification strategy
- Check assumptions: Each method has testable and untestable assumptions
- Estimate the effect: Run the analysis
- Sensitivity analysis: How much would results change if assumptions are partially violated?
Output Format輸出格式
# Causal Analysis: {Treatment} → {Outcome}
Gotchas注意事項
- "Controlling for X" doesn't guarantee causation: Adding control variables to a regression reduces SOME confounding but not unobserved confounders. If the treatment wasn't random, OLS with controls is not causal.
- Parallel trends is untestable: For DID, we can check pre-treatment parallel trends but can't prove they would have continued. It's an assumption, not a fact.
- Weak instruments invalidate IV: An instrument that barely affects the treatment produces biased estimates (often worse than OLS). Test instrument strength with the first-stage F-statistic (> 10).
- External validity: Causal effects estimated in one context may not generalize. An effect estimated for users near a cutoff (RDD) may not apply to the full population.
- Causal inference requires domain knowledge: Statistical methods alone can't determine what is a confounder, what is a mediator, or what is a collider. Draw the causal diagram (DAG) first.
References參考資料
- For directed acyclic graphs (DAGs), see
references/causal-dags.md - For DID implementation in Python/R, see
references/did-implementation.md