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Causal Inference with Linear Regression: A Modern Approach (Part I)

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A Crash Course on The Basics of Causal Inference

  • Introduction
  • Slides
  • How to Use This Course
  • Course Guidelines
  • What is Causal Inference and why do we need it?
  • Individual Treatment Efffect
  • (Conditional) Average Treatment Effect
  • The do-operator
  • Ignorability
  • Conditional Ignorability & The Adjustment Formula
  • Causal Graphs
  • Graph Patterns
  • Blocking Paths
  • Backdoor Adjustment
  • Double-headed arrows & The do-operator in Causal Graphs
  • Coding Example: Generating Data
  • Coding Example: Observational & Experimental study (no adjustment)
  • Coding Example: Observational study (with adjustment)
  • Extending to Continuous Treatments
  • Recap
  • Theoretical Questions
  • Coding Exercise
  • Resources

The Mechanics of Linear Regression

  • Introduction
  • Slides
  • Prerequisites
  • Linear Regression
  • Closed-Form Solution
  • OLS Residuals
  • From Population to Sample
  • The CEF
  • CEF Properties
  • Linear Regression as CEF Approximator
  • Closed-Form Formula Revisited
  • FWL & The Regression Anatomy Formula
  • Changing Slope Coefficients Part I
  • Changing Slope Coefficients Part II
  • Recap
  • Theoretical Questions
  • Coding Exercise
  • Resources

When Linear Regression Coefficients Reflect Causal Effects

  • Introduction
  • Slides
  • Recap Causality Basics
  • Total, Direct & Indirect Effects
  • Structural Causal Models
  • Linear SCMs & The do-operator
  • The Meaning of Structural Parameters Part I
  • The Meaning of Structural Parameters Part II
  • Linear Structural Equation vs Linear Regression Equation
  • Identifying Structural Coefficients for All Variables Part I
  • Identifying Structural Coefficients for All Variables Part II
  • Coding Example: Independent Structural Errors
  • Coding Example: Dependent Structural Errors
  • Linear Regression: From Searching for The ‘"True Model’ to Control Tool
  • The Single-Door Criterion
  • Coding Example: Single-Door Criterion
  • Total Effects In Terms of Structural Parameters
  • The Back-Door Criterion
  • Coding Example: Back-Door Criterion
  • Helping Out The Fitness Team
  • On The Nuisance of Control Variables
  • Econometrics & Causality
  • Recap
  • Theoretical Questions
  • DAGitty
  • Coding Exercise
  • Resources

Robustness Tests & Sensitivity Analysis

  • Introduction
  • Slides
  • What Are Robustness Tests?
  • Detecting Omitted Variable Bias Part I
  • Coding Example
  • Detecting Omitted Variable Bias Part II
  • Coding Example
  • What Is Sensitivity Analysis?
  • The Real-World Example
  • The Traditional OVB Framework
  • Applying The Traditional OVB Formula
  • (Partial) R-Squared
  • A Partial R-Squared Reparametrization of the OVB Formula
  • Applying The Reparametrized OVB Formula
  • Bounding The Strength of An Omitted Confounder
  • Applying The Bounding Procedure
  • Extreme Scenario Analysis
  • Applying Extreme Scenario Analysis
  • Summary Metrics
  • Applying Summary Metrics
  • Extending With Inference & Multiple Omitted Confounders
  • The Package: PySensemakr
  • Recap
  • Theoretical Questions
  • Coding Exercise
  • Resources

Part 2 & Recommendations

  • Part 2 & Recommendations
  • Reading List & Sources
  • Feedback and Reviews