Causal Inference Basics

因果推断基础入门

Demo Author

Demo Institution

2026-02-16

Introduction

What is Causal Inference?

Definition: Causal inference is process of drawing conclusions about causal relationships based on observed data (Angrist and Pischke 2009).

Key Question: What would have happened to Y if we had changed X by one unit, while holding everything else constant?

Why Causal Inference Matters

  • Policy Evaluation: Understanding the effect of interventions
  • Scientific Discovery: Identifying causal mechanisms
  • Decision Making: Making informed choices under uncertainty

Example: Does taking a drug actually cure a disease, or is it just correlation?

Core Concepts

Potential Outcomes Framework

Let \(Y_{1i}\) and \(Y_{0i}\) denote potential outcomes for unit \(i\):

\[ \begin{align*} Y_{1i} &= \text{Outcome if treated} \\ Y_{0i} &= \text{Outcome if not treated} \end{align*} \]

The causal effect for unit \(i\) is:

\[ \tau_i = Y_{1i} - Y_{0i} \]

Problem: We can only observe one of these for each unit!

Average Treatment Effect (ATE)

The average causal effect across the population:

\[ \text{ATE} = \mathbb{E}[Y_{1i} - Y_{0i}] \]

Fundamental Problem of Causal Inference:

We cannot observe \(Y_{1i}\) and \(Y_{0i}\) simultaneously for the same unit \(i\).

References

References

Angrist and Pischke (2009)

Imbens (2004)

Thank You

Thank You!

Questions?

Questions?

.center[ Questions?]

Demo Lecture

Angrist, Joshua D., and Jörn-Steffen Pischke. 2009. Mostly Harmless Econometrics: An Empiricist’s Companion. Princeton, NJ: Princeton University Press.
Imbens, Guido W. 2004. “Nonparametric Estimation of Average Treatment Effects Under Exogeneity: A Review.” Review of Economics and Statistics 86 (1): 4–29.