Background

This section provides theoretical background on the difference-in-differences methodologies implemented in ModernDiD; for practical usage see the User Guide.

• DiD with Multiple Time Periods
  • Why Standard TWFE Regressions Are Problematic
  • Setup and Notation
  • The Group-Time Average Treatment Effect
  • Identifying Assumptions
  • Nonparametric Identification of ATT(g,t)
  • Aggregation of Effects
  • Inference and Pre-Treatment Testing
• Doubly Robust DiD
  • Setup and Notation
  • Identification
  • Individual OR and IPW Approaches
  • Doubly Robust Estimands
  • Semiparametric Efficiency Bounds
  • Improved Doubly Robust Estimators
• Triple Difference-in-Differences
  • When Triple DiD is Appropriate
  • Setup and Notation
  • Parameters of Interest
  • Identification Assumptions
  • Why Standard Approaches Fail
  • Identification and Estimation
  • Asymptotic Properties and Inference
  • Event-Study Aggregation
  • Pre-Treatment Testing
• DiD with Continuous Treatments
  • Setup and Notation
  • Potential Outcomes Framework
  • Parameters of Interest
  • Identification Assumptions
  • Identification Results
  • What Does TWFE Estimate with a Continuous Treatment?
  • Estimation Methods
  • Extensions to Staggered Adoption
• DiD with Intertemporal Treatment Effects
  • When Intertemporal Effects Matter
  • Setup and Notation
  • Design Requirements
  • Identifying Assumptions
  • Parameters of Interest
  • Estimation
  • Normalized Effects
  • Cost-Benefit Analysis
  • Pre-Treatment Testing
  • Why Standard Approaches Fail
  • Asymptotic Properties and Inference
  • Extensions
• Dynamic Covariate Balancing DiD
  • Why standard approaches fall short
  • Setup and notation
  • Identifying assumptions
  • Estimation
  • Inference
  • Practical extensions
• Honest DiD Sensitivity Analysis
  • Model Setup and Causal Decomposition
  • Partial Identification and the Restriction Set
  • Restriction Classes
  • Inference Methods
  • Sensitivity Analysis and Breakdown Values
• Extended Two-Way Fixed Effects
  • Why Conventional TWFE Fails
  • Setup and Notation
  • Identifying Assumptions
  • The Conditional Expectation in the Never-Treated State
  • Identification and Imputation
  • The ETWFE Regression
  • Event Study and Pre-Treatment Testing
  • Nonlinear Extensions
  • Aggregation of Cohort-Time Effects
  • Additional Considerations
• Nonparametric Instrumental Variables
  • The NPIV Model
  • Sieve TSLS Estimation
  • Ill-Posedness and Instrument Strength
  • Data-Driven Sieve Dimension Selection
  • Minimax Rate Adaptivity
  • Uniform Confidence Bands
  • Multivariate Basis Construction
  • Extensions

Acknowledgements

The ModernDiD package implements various difference-in-differences methodologies from the econometric literature. We acknowledge the original authors of these methods and the authors of the R packages that inspired this implementation.