Quick Guide
Resources
Corrections
Acknowledgements
1
Introduction
1.1
The Case for Causal Models
1.1.1
The Limits to Design-based Inference
1.1.2
Qualitative and Mixed-method Inference
1.1.3
Connecting Theory and Empirics
1.2
Key Contributions
1.3
The Road Ahead
I Foundations
2
Causal Models
2.1
The Counterfactual Model
2.1.1
Potential Outcomes
2.1.2
A Generalization
2.1.3
Summaries of Potential Outcomes
2.2
Causal Models and Directed Acyclic Graphs
2.2.1
The Nodes
2.2.2
The Functions
2.2.3
The Distributions
2.2.4
2.2.4 Conditional Independence
2.3
Graphing Models and Using Graphs
2.3.1
Rules for Graphing Causal Models
2.3.2
Conditional Independence from DAGs
2.3.3
Simplifying Models
2.4
Conclusion
2.5
Chapter Appendix
2.5.1
Steps for Constructing Causal Models
2.5.2
Model Construction in Code
2.5.3
Exercise: Reading Conditional Independence from a Graph
3
Illustrating Causal Models
3.1
Welfare State Reform
3.2
Military Interventions
3.3
Development and Democratization
4
Causal Queries
4.1
Case-Level Causal Effects
4.2
Case-Level Causal Attribution
4.3
Average Causal Effects
4.4
Causal Paths
4.5
Conclusion
4.6
Chapter Appendix
4.6.1
Actual Causes
4.6.2
General Procedure for Mapping Queries to Causal Types
4.6.3
Identifying causal types for queries with
CausalQueries
5
Bayesian Answers
5.1
Bayes Basics
5.1.1
Simple Instances
5.1.2
Bayes’ Rule for Discrete Hypotheses
5.1.3
Continuous Parameters, Vector-valued parameters
5.1.4
The Dirichlet Family
5.1.5
Moments: Mean and Variance
5.1.6
Learning
5.1.7
Bayes Estimation in Practice
5.2
Bayes Applied
5.2.1
Simple Bayesian Process Tracing
5.2.2
A Generalization: Bayesian Inference on Arbitrary Queries
5.3
Features of Bayesian Updating
5.3.1
Priors Matter
5.3.2
Simultaneous, joint updating
5.3.3
Posteriors Are Independent of the Ordering of Data
6
Theories as Causal Models
6.1
Models as
Theories Of
6.1.1
Implications of Structural Causal
6.1.2
Probabilistic Models Implied by Lower Level Probabilistic Models
6.1.3
Models Justified by Theory and Data
6.2
Gains from Theory
6.2.1
Illustration: Gains from a Front-Door Theory
6.2.2
Quantifying gains
6.3
Formal Theories and Causal Models
II Model-Based Causal Inference
7
Process Tracing with Causal Models
7.1
The Intuition
7.2
A Formalization of the General Approach
7.2.1
The Model
7.2.2
Priors
7.2.3
Possible Data Types
7.2.4
Updating on Types Given the Data
7.2.5
Updating on Queries
7.3
Mapping from Models to Classic Qualitative Tests
7.4
Assessing Probative Value from a Graph
7.5
Principles of Learning
7.5.1
A DAG Alone Does Not Guarantee Probative Value for a Single Case
7.5.2
Learning Requires Uncertainty
7.5.3
Population-Level Uncertainty and Case-Level Causal Inference
7.6
Chapter Appendix: Process Tracing with
CausalQueries
7.6.1
Example 1: Simple Model
7.6.2
Example 2: Many Clues
8
Process Tracing Applications
8.1
Inequality and Democratization
8.1.1
The Debate
8.1.2
A Causal Model
8.1.3
Results
8.1.4
Considerations: Theory Dependence
8.2
Institutions and Growth
8.2.1
The Debate
8.2.2
A Causal Model
8.2.3
Results
8.2.4
Considerations: Interactions between Clues
8.3
Appendix: Forming Models in
CausalQueries
9
Integrated Inferences
9.1
From One Unit to Many
9.2
General Procedure
9.2.1
Setup
9.2.2
Inference
9.2.3
Wrinkles
9.3
Payoffs
9.3.1
Mixing Methods
9.3.2
Deriving Probative Value from the Data
9.3.3
Learning without Identification
9.4
Extensions
9.4.1
Beyond Binary Data
9.4.2
Measurement Error
9.4.3
Spillovers
9.5
Chapter Appendix: Mixing Methods with
CausalQueries
9.5.1
An Illustration in Code
9.5.2
Replication of
Chickering and Pearl (1996)
Lipid Analysis.
9.5.3
Probative value arising from correlations in the posterior distribution over parameters
10
Integrated Inferences Applications
10.1
Inequality and Democratization
10.1.1
Data
10.1.2
Case-level queries
10.1.3
Population-Level Queries
10.1.4
Explorations: How Much Do We Get from the Model versus the Data?
10.2
Institutions and Growth
10.2.1
Data
10.2.2
Queries
10.2.3
Explorations: Direct and Indirect Paths from
M
to
Y
10.3
Conclusion
11
Mixing Models
11.1
A Jigsaw Puzzle: Integrating across a Model
11.2
Combining Observational and Experimental Data
11.3
Transportation of Findings across Contexts
11.4
Multilevel Models, Meta-analysis
III Design Choices
12
Clue Selection as a Decision Problem
12.1
A Model-Informed Approach to Clue Selection
12.1.1
Clue Selection with a Simple Example
12.1.2
Dependence on Prior Beliefs
12.1.3
Clue Selection for the Democratization Model
12.2
Dynamic Strategies
12.3
Conclusion
13
Case Selection
13.1
Common Case-Selection Strategies
13.2
No General Rules
13.2.1
Any Cell Might Do
13.2.2
Interest in a Case Might Not Justify Selecting that Case
13.3
General Strategy
13.3.1
Walk through of the General Strategy
13.3.2
Simulation Strategy
13.3.3
Results
13.4
Conclusion
14
Going Wide, Going Deep
14.1
Walk-Through of a Simple Comparison
14.2
Simulation Analysis
14.2.1
Approach
14.2.2
Simulation Results
14.3
Factoring in the Cost of Data
14.4
Conclusion
IV Models in Question
15
Justifying Models
15.1
Justifying probative value
15.1.1
Nothing from Nothing
15.1.2
Justifying the Classic Process-Tracing Tests
15.2
Empirical Discovery of Causal Structure
16
Evaluating Models
16.1
Four Strategies
16.1.1
Check Conditional Independence
16.1.2
Bayesian
p
-Value: Are the Data Unexpected Given Your Model?
16.1.3
Leave-One-Out Likelihoods
16.1.4
Sensitivity
16.2
Evaluating the Democracy-Inequality Model
16.2.1
Check Assumptions of Conditional Independence
16.2.2
Bayesian
p
-Value
16.2.3
Leave-One-Out Likelihoods
16.2.4
Sensitivity to Priors
16.3
Evaluating the Institutions-Growth Model
16.3.1
Check Assumptions of Conditional Independence
16.3.2
Bayesian P-Value
16.3.3
Leave-One-Out (LOO) Cross-validation
16.3.4
Sensitivity to Priors
16.4
Appendix
17
Final Words
17.1
The Benefits
17.2
The Worries
17.3
The Future
V Appendices
18
Glossary
19
Errata and Version History
References
Uses CausalQueries
Integrated Inferences: Causal Models for Qualitative and Mixed-Method Research
Chapter 19
Errata and Version History
2024-01-13
: Typo in caption of Figure
16.6
.
2023-12-20
: Text before Table
11.1
.