Applied Causal Inference

Notes & simulations

Causal inference methods — each topic pairs explanation with an interactive simulation you can run in the browser.

Builds on: Statistical Inference

Framework

• Potential Outcomes & ATE — The framework behind all causal questions
• Identification vs Estimation — The distinction that organizes everything
• When ML Helps and When It Doesn’t — The boundary between estimation and identification

Methods

• Selection on Observables — When conditioning on X is enough
• Difference-in-Differences — Parallel trends & treatment effects
• Instrumental Variables — Exogenous variation to isolate causal effects
• Regression Discontinuity — Cutoff rules as natural experiments
• Synthetic Control — Building a counterfactual from weighted donors
• Sample Selection & Heckman — When outcomes are observed only for a non-random subsample

Panel Data

• Fixed vs Random Effects — Within vs between variation, the Hausman test, and when each estimator works

Estimation Tools

Tools that can be paired with different research designs.

• Regression Adjustment — Model the outcome, adjust for confounders
• Matching — Pair treated and control units on covariates
• Inverse Probability Weighting — Reweighting to balance treated and control
• Entropy Balancing — Exact moment balancing without a propensity score model
• Doubly Robust — Combine outcome model + propensity score for double protection
• Double/Debiased ML — Doubly robust + cross-fitting + ML nuisance estimation

Beyond Averages

So far we have focused on average causal effects. But policies often affect individuals differently. This section moves from estimating a single number to estimating a function.

• Heterogeneous Treatment Effects — From \(\tau\) to \(\tau(x)\): why averages can mislead and what CATE is
• Estimating Heterogeneous Effects — Causal forests, meta-learners, and practical cautions