Causal Inference in Python

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• Preface
  • Prerequisites
  • Outline
  • Conventions Used in This Book
  • Using Code Examples
  • OReilly Online Learning
  • How to Contact Us
  • Acknowledgments
• I. Fundamentals
• 1. Introduction to Causal Inference
  • What Is Causal Inference?
  • Why We Do Causal Inference
  • Machine Learning and Causal Inference
  • Association and Causation
    • The Treatment and the Outcome
    • The Fundamental Problem of Causal Inference
    • Causal Models
    • Interventions
    • Individual Treatment Effect
    • Potential Outcomes
    • Consistency and Stable Unit Treatment Values
    • Causal Quantities of Interest
    • Causal Quantities: An Example
  • Bias
    • The Bias Equation
    • A Visual Guide to Bias
  • Identifying the Treatment Effect
    • The Independence Assumption
    • Identification with Randomization
  • Key Ideas
• 2. Randomized Experiments and Stats Review
  • Brute-Force Independence with Randomization
  • An A/B Testing Example
  • The Ideal Experiment
  • The Most Dangerous Equation
  • The Standard Error of Our Estimates
  • Confidence Intervals
  • Hypothesis Testing
    • Null Hypothesis
    • Test Statistic
  • p-values
  • Power
  • Sample Size Calculation
  • Key Ideas
• 3. Graphical Causal Models
  • Thinking About Causality
    • Visualizing Causal Relationships
    • Are Consultants Worth It?
  • Crash Course in Graphical Models
    • Chains
    • Forks
    • Immorality or Collider
    • The Flow of Association Cheat Sheet
    • Querying a Graph in Python
  • Identification Revisited
  • CIA and the Adjustment Formula
  • Positivity Assumption
  • An Identification Example with Data
  • Confounding Bias
    • Surrogate Confounding
    • Randomization Revisited
  • Selection Bias
    • Conditioning on a Collider
    • Adjusting for Selection Bias
    • Conditioning on a Mediator
  • Key Ideas
• II. Adjusting for Bias
• 4. The Unreasonable Effectiveness of Linear Regression
  • All You Need Is Linear Regression
    • Why We Need Models
    • Regression in A/B Tests
    • Adjusting with Regression
  • Regression Theory
    • Single Variable Linear Regression
    • Multivariate Linear Regression
  • Frisch-Waugh-Lovell Theorem and Orthogonalization
    • Debiasing Step
    • Denoising Step
    • Standard Error of the Regression Estimator
    • Final Outcome Model
    • FWL Summary
  • Regression as an Outcome Model
  • Positivity and Extrapolation
  • Nonlinearities in Linear Regression
    • Linearizing the Treatment
    • Nonlinear FWL and Debiasing
  • Regression for Dummies
    • Conditionally Random Experiments
    • Dummy Variables
    • Saturated Regression Model
    • Regression as Variance Weighted Average
    • De-Meaning and Fixed Effects
  • Omitted Variable Bias: Confounding Through the Lens of Regression
  • Neutral Controls
    • Noise Inducing Control
    • Feature Selection: A Bias-Variance Trade-Off
  • Key Ideas
• 5. Propensity Score
  • The Impact of Management Training
  • Adjusting with Regression
  • Propensity Score
    • Propensity Score Estimation
    • Propensity Score and Orthogonalization
    • Propensity Score Matching
    • Inverse Propensity Weighting
    • Variance of IPW
    • Stabilized Propensity Weights
    • Pseudo-Populations
    • Selection Bias
    • Bias-Variance Trade-Off
    • Positivity
  • Design- Versus Model-Based Identification
  • Doubly Robust Estimation
    • Treatment Is Easy to Model
    • Outcome Is Easy to Model
  • Generalized Propensity Score for Continuous Treatment
  • Key Ideas
• III. Effect Heterogeneity and Personalization
• 6. Effect Heterogeneity
  • From ATE to CATE
  • Why Prediction Is Not the Answer
  • CATE with Regression
  • Evaluating CATE Predictions
  • Effect by Model Quantile
  • Cumulative Effect
  • Cumulative Gain
  • Target Transformation
  • When Prediction Models Are Good for Effect Ordering
    • Marginal Decreasing Returns
    • Binary Outcomes
  • CATE for Decision Making
  • Key Ideas
• 7. Metalearners
  • Metalearners for Discrete Treatments
    • T-Learner
    • X-Learner
  • Metalearners for Continuous Treatments
    • S-Learner
    • Double/Debiased Machine Learning
      • Double-ML for CATE estimation
      • Visual intuition for Double-ML
  • Key Ideas
• IV. Panel Data
• 8. Difference-in-Differences
  • Panel Data
  • Canonical Difference-in-Differences
    • Diff-in-Diff with Outcome Growth
    • Diff-in-Diff with OLS
    • Diff-in-Diff with Fixed Effects
    • Multiple Time Periods
    • Inference
  • Identification Assumptions
    • Parallel Trends
    • No Anticipation Assumption and SUTVA
    • Strict Exogeneity
    • No Time Varying Confounders
    • No Feedback
    • No Carryover and No Lagged Dependent Variable
  • Effect Dynamics over Time
  • Diff-in-Diff with Covariates
  • Doubly Robust Diff-in-Diff
    • Propensity Score Model
    • Delta Outcome Model
    • All Together Now
  • Staggered Adoption
    • Heterogeneous Effect over Time
    • Covariates
  • Key Ideas
• 9. Synthetic Control
  • Online Marketing Dataset
  • Matrix Representation
  • Synthetic Control as Horizontal Regression
  • Canonical Synthetic Control
  • Synthetic Control with Covariants
  • Debiasing Synthetic Control
  • Inference
  • Synthetic Difference-in-Differences
    • DID Refresher
    • Synthetic Controls Revisited
    • Estimating Time Weights
    • Synthetic Control and DID
  • Key Ideas
• V. Alternative Experimental Designs
• 10. Geo and Switchback Experiments
  • Geo-Experiments
  • Synthetic Control Design
    • Trying a Random Set of Treated Units
    • Random Search
  • Switchback Experiment
    • Potential Outcomes of Sequences
    • Estimating the Order of Carryover Effect
    • Design-Based Estimation
    • Optimal Switchback Design
    • Robust Variance
  • Key Ideas
• 11. Noncompliance and Instruments
  • Noncompliance
  • Extending Potential Outcomes
  • Instrument Identification Assumptions
  • First Stage
  • Reduced Form
  • Two-Stage Least Squares
  • Standard Error
  • Additional Controls and Instruments
    • 2SLS by Hand
    • Matrix Implementation
  • Discontinuity Design
    • Discontinuity Design Assumptions
    • Intention to Treat Effect
    • The IV Estimate
    • Bunching
  • Key Ideas
• 12. Next Steps
  • Causal Discovery
  • Sequential Decision Making
  • Causal Reinforcement Learning
  • Causal Forecasting
  • Domain Adaptation
  • Closing Thoughts
• Index

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