Difference-in-Differences Methods

Professor: Pedro H. C. Sant’Anna
Email: psantanna@microsoft.com


Difference-in-Differences (DiD) methods are widely used to answer what-if type of questions in economics, political science, and many other social and medical sciences. These methods are also very popular in industry, where causal inference plays a prominent role. Although very popular, the last few years have seen a booming of new papers on DiD and related designs, making it challenging to keep up with rapidly evolving best practices. The main goal of this course is to provide a fast-track towards these best practices.


1. Introduction to DiD and an overview of Causal Inference

We will discuss DiD popularity by briefly highlighting several applications in different fields. We will also lay down the potential outcome framework that will serve as the foundation for all our discussions. More specifically, we will:

  • Highlight DiD popularity in different fields.
  • Introduce the potential outcome framework and how we use it to embrace treatment effect heterogeneity.
  • Discuss the challenges to conduct causal inference with observational data, and how DiD methods address these.

2. Classical 2×2 DiD Setup

We do a deep-dive into the classical two-periods and two-groups DiD setup, paying particular attention to the commonly used assumptions to justify its reliability. In this section of the course, we will discuss:

  • The role of identifying assumptions: no anticipation and parallel trends.
  • Estimation of average treatment effects using simple comparison of means and regressions.
  • When parallel trends assumption is sensitive to functional form restrictions.

3. 2×2 DiD setups with covariates

In many situations researchers wish to leverage available information about observed characteristics in DiD setups. Here, we will describe how you can reliably do this. We will discuss the following topics:

  • Allowing for covariate-specific trends.
  • Pitfalls of some two-way fixed-effects linear regression specifications.
  • Estimating treatment effects using the
    • outcome-regression approach.
    • inverse probability weighting approach.
    • doubly robust approach.
  • How to use machine learning procedures to do DiD (very brief)

4. DiD with variation in treatment timing

It is not uncommon to have units being exposed to treatment at different points in time. How do DiD procedures perform in these more challenging setups? Does the choice of estimation method matter? How so? The recent DiD literature has provided many insights in these cases, and we will cover a good chunk of that, particularly in the case with staggered treatment adoption. Our discussion topics include:

  • What are the causal parameters of interest?
  • What type of parallel trends are we willing to impose?
  • Pitfalls of two-way fixed effects linear regression specifications.
  • Recovering meaningful causal parameters.
  • Highlighting treatment effect dynamics via event-studies.
  • Highlighting other sources of treatment effect heterogeneity.

Practical Exercises

We hope to cover not only the theory but also how the difference DiD methods are used in practice. To achieve this, we will also provide empirical exercises. We will provide both R and Stata codes, though in the lecture we will probably favor the R implementations.

Selected References

Abadie, Alberto. 2005. Semiparametric Difference-in-Difference Estimators. Review of Economic Studies. Available at https://academic.oup.com/restud/article-abstract/72/1/1/1581053

Callaway, Brantly and Pedro H. C. Sant’Anna. 2021. Difference-in-Differences with Multiple Time Periods. Journal of Econometrics. Available at https://doi.org/10.1016/j.jeconom.2020.12.001

Goodman-Bacon, Andrew. 2021. Difference-in-differences with variation in treatment timing. Journal of Econometrics. Available at https://www.sciencedirect.com/science/article/abs/pii/S0304407621001445

Roth, Jonathan, Pedro H. C. Sant’Anna, Alyssa, Bilinski and John Poe. 2022. What’s Trending in Difference-in-Differences? A Synthesis of the Recent Econometrics Literature. Journal of Econometrics (conditionally accepted), available at https://psantanna.com/files/RSBP_DiD_Review.pdf

Roth, Jonathan and Pedro H. C. Sant’Anna. 2022. When Is Parallel Trends Sensitive to Functional Form? Econometrica (Forthcoming). Available at https://psantanna.com/files/Roth_SantAnna_ECMA2022.pdf

Sant’Anna, Pedro H. C. and Jun Zhao. 2020. Doubly Robust Difference-in-Differences Estimators. Journal of Econometrics. Available at https://www.sciencedirect.com/science/article/pii/S0304407620301901 

Note: Additional references for the topics will be assigned throughout the course.