stat-causal-inference

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Causal Inference

因果推断

Framework

框架

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)

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

核心问题

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.

我们观测到：

Y_i(treated)

—— 接受处理的个体的结果。我们想了解：

Y_i(treated) - Y_i(untreated)

—— 因果效应。我们永远无法观测到：同一个体在同一时间未接受处理时的

Y_i(untreated)

。

所有因果推断方法都是在估计counterfactual（反事实）—— 即未接受处理时会发生什么。

Method Selection Guide

方法选择指南

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

方法	使用场景	核心假设
RCT	可进行随机分配	随机分配可消除混淆变量
Propensity Score Matching (PSM)	处理分配非随机但基于可观测变量	不存在未观测到的混淆变量（基于可观测变量选择）
Instrumental Variables (IV)	存在未观测到的混淆变量但拥有工具变量	工具变量影响处理分配但不直接影响结果
Difference-in-Differences (DID)	政策/事件自然形成处理组/对照组	平行趋势：若无处理，两组趋势将保持一致
Regression Discontinuity (RDD)	处理分配基于阈值	阈值上下的观测对象具有可比性
Synthetic Control	一个处理单元，多个对照单元（聚合数据）	加权合成组合匹配处理前趋势

Analysis Steps

分析步骤

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?

明确因果问题：处理是什么？结果是什么？
识别有效性威胁：哪些混淆变量可以解释关联关系？
选择方法：基于数据结构和可用的识别策略
验证假设：每种方法都有可检验和不可检验的假设
估计效应：运行分析
敏感性分析：若假设部分不成立，结果会有多大变化？

Output Format

输出格式

markdown

undefined

markdown

undefined

Causal Analysis: {Treatment} → {Outcome}

Causal Question

Treatment: {what intervention/event}
Outcome: {what we're measuring}
Counterfactual: {what would have happened without treatment}

Treatment: {what intervention/event}
Outcome: {what we're measuring}
Counterfactual: {what would have happened without treatment}

Identification Strategy

Method: {PSM / IV / DID / RDD / etc.}
Rationale: {why this method fits}
Key assumption: {stated explicitly}
Assumption test: {how we check, or acknowledge if untestable}

Method: {PSM / IV / DID / RDD / etc.}
Rationale: {why this method fits}
Key assumption: {stated explicitly}
Assumption test: {how we check, or acknowledge if untestable}

Results

Estimated causal effect: {magnitude with CI}
Robustness checks: {alternative specifications}

Estimated causal effect: {magnitude with CI}
Robustness checks: {alternative specifications}

Limitations

{What could still invalidate these results}

undefined

{What could still invalidate these results}

undefined

Gotchas

注意事项

"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.

“控制X变量”无法保证因果关系：在回归中添加控制变量可减少部分混淆，但无法消除未观测到的混淆变量。若处理分配非随机，带控制变量的OLS回归不具备因果性。
平行趋势不可检验：对于DID，我们可以检验处理前的平行趋势，但无法证明趋势会持续下去。这是一个假设，而非事实。
弱工具变量会使IV失效：对处理分配影响极小的工具变量会产生有偏估计（通常比OLS更差）。用第一阶段F统计量（> 10）检验工具变量的强度。
外部有效性：在某一情境下估计的因果效应可能无法推广。在阈值附近的用户群体（RDD）中估计的效应可能不适用于全部人群。
因果推断需要领域知识：仅靠统计方法无法确定什么是混淆变量、中介变量或碰撞变量。应先绘制因果图（DAG）。

References

参考资料

For directed acyclic graphs (DAGs), see
```
references/causal-dags.md
```
For DID implementation in Python/R, see
```
references/did-implementation.md
```

关于有向无环图（DAGs），请查看
```
references/causal-dags.md
```
关于在Python/R中实现DID，请查看
```
references/did-implementation.md
```