A First Course in Causal Inference

Preface

Part 1: Introduction

1. Correlation, Association, and the Yule-Simpson Paradox

2. Potential Outcomes

Part 2: Randomized experiments

3. The Completely Randomized Experiment and the Fisher Randomization Test

4. Neymanian Repeated Sampling Inference in Completely Randomized Experiments

5. Stratification and Post-Stratification in Randomized Experiments

6. Rerandomization and Regression Adjustment

7. Matched-Pairs Experiment

8. Unification of the Fisherian and Neymanian Inferences in Randomized Experiments

9. Bridging Finite and Super Population Causal Inference

Part 3: Observational studies

10. Observational Studies, Selection Bias, and Nonparametric Identification of Causal Effects

11. The Central Role of the Propensity Score in Observational Studies for Causal Effects

12. The Doubly Robust or the Augmented Inverse Propensity Score Weighting Estimator for the Average Causal Effect

13. The Average Causal Effect on the Treated Units and Other Estimands

14. Using the Propensity Score in Regressions for Causal Effects

15. Matching in Observational Studies

Part 4: Difficulties and challenges of observational studies

16. Difficulties of Unconfoundedness in Observational Studies for Causal Effects

17. E-Value: Evidence for Causation in Observational Studies with Unmeasured Confounding

18. Sensitivity Analysis for the Average Causal Effect with Unmeasured Confounding

19. Rosenbaum-Style p-Values for Matched Observational Studies with Unmeasured Confounding

20. Overlap in Observational Studies: Difficulties and Opportunities

Part 5: Instrumental variables

21. An Experimental Perspective of the Instrumental Variable

22. Disentangle Mixture Distributions and Instrumental Variable Inequalities

23. An Econometric Perspective of the Instrumental Variable

24. Application of the Instrumental Variable Method: Fuzzy Regression Discontinuity

25. Application of the Instrumental Variable Method: Mendelian Randomization

Part 6: Causal Mechanisms with Post-Treatment Variables

26. Principal Stratification

27. Mediation Analysis: Natural Direct and Indirect Effects

28. Controlled Direct Effect

29. Time-Varying Treatment and Confounding

Part 7: Appendices

A. Probability and Statistics

B. Linear and Logistic Regressions

C. Some Useful Lemmas for Simple Random Sampling From a Finite Population