Program
6th Summer School in Advanced Economics
“Modern Causal Inference: Bridging Theory and Practice”
Jeffrey M. Wooldridge
Walter Adams Distinguished Professor of Economics
Michigan State University
Pedro H. C. Sant’Anna
Associate Professor of Economics
Emory University
June 22–27, 2025
Spetses Island, Greece
Difference-in-Differences methods were examined, including recent advances designed to accommodate more complex treatment scenarios. Synthetic-control methods were also covered as an important approach for comparative case studies and policy evaluation.
Finally, the programme introduced machine-learning methods in econometrics, providing practical approaches for working with large datasets and combining traditional econometric techniques with modern data-analysis tools.
Course format
The Summer School consisted of both theoretical sessions, in the form of lectures, and practical sessions. The practical sessions took place in a computer laboratory. The objective was to familiarize participants with the theory and application of modern econometric evaluation techniques through guided laboratory sessions.
Participants had the opportunity to replicate published studies, learn the methods, and apply econometric techniques in Stata to conduct their own research. In this way, they acquired modern Stata skills and applied them to their respective fields of interest.
Course description
This course covered causal inference for cross-sectional and panel data using the potential-outcomes framework. It considered a variety of settings, including unconfoundedness or selection on observables, local treatment effects in the presence of endogeneity, and Difference-in-Differences.
The course also examined several estimation strategies, including regression adjustment, inverse-probability weighting, and doubly robust methods. These discussions provided the foundation for understanding how advances in machine learning can be used to conduct causal inference.
A common theme throughout the course was the explicit recognition of treatment-effect heterogeneity and the use of estimation strategies targeting well-defined causal parameters. This approach avoids many of the difficulties associated with reverse-engineering a plausible causal interpretation for misspecified regression coefficients.
The course began with the identification of key treatment-effect parameters under unconfoundedness. It then considered regression adjustment, inverse-probability weighting, normalized weights, doubly robust combinations of these methods, matching, and more recent covariate-balancing approaches to propensity-score estimation.
The programme subsequently examined the identification of the Local Average Treatment Effect and the Local Average Treatment Effect on the Treated, including recent doubly robust methods that incorporate covariates into the instrument propensity score. Control-function methods were also discussed as a way to allow for treatment-effect heterogeneity when functional forms are imposed on conditional-mean functions.
Once the foundations of these estimation strategies had been established, the course explored how recent advances in machine learning can support more flexible estimation of treatment-effect parameters under both unconfoundedness and local-treatment-effect frameworks. Methods included LASSO, Random Forests, Boosting, and cross-fitting.
The course then turned to Difference-in-Differences methods for panel data, beginning with the two-period setting. Regression-based, propensity-score, and doubly robust estimators for the Average Treatment Effect on the Treated were discussed, together with methods for testing and adjusting for possible violations of parallel trends.
For staggered interventions, the course examined methods that allow treatment effects to vary by treatment cohort and calendar time. It also discussed the incorporation of covariates, the construction of event-study estimates and plots, and the relationship among recent staggered Difference-in-Differences estimators.
Finally, the programme considered limitations of conventional event-study tests for parallel trends, sensitivity analysis under relaxations of parallel trends, and alternative methods that may be appropriate when parallel trends is not plausible.
Recommended background
Participants were expected to have a good working knowledge of ordinary least-squares estimation, fixed-effects estimation, and basic nonlinear models such as logit, probit, and exponential conditional-mean models. Relevant background is provided in J. M. Wooldridge, Introductory Econometrics: A Modern Approach, 7th edition, Cengage, 2020.
Course Outline and Schedule
Sunday, June 22, 2025
Arrival of participants, registration, and welcome reception at 19:00 at the Anargyrios and Korgialenios School of Spetses Foundation.
Anargyrios and Korgialenios School of Spetses Foundation
Instructors: Pedro H. C. Sant’Anna, Emory University, and Jeffrey M. Wooldridge, Michigan State University.
Monday, June 23, 2025
Tuesday, June 24, 2025
Wednesday, June 25, 2025
Thursday, June 26, 2025
Friday, June 27, 2025
Daily Content
Day 1
Potential outcomes and parameters of interest. Randomization. Unconfoundedness and overlap. Identification. Regression adjustment, inverse-probability weighting, normalized weights, covariate-balancing propensity-score estimation, matching, and doubly robust estimators. Improved efficiency under randomized controlled trials and multiple treatments.
Day 2
Potential treatment status. Constant-effect models. Compliers and defiers. One-sided non-compliance. Identification of LATE and LATT. Incorporating covariates into LATE and LATT estimation. Control-function methods.
Day 3
Introduction to causal machine learning. The importance of doubly robust procedures. LASSO, Random Forests, Boosting, cross-fitting, and heterogeneous-treatment-effect estimation. Two-period Difference-in-Differences, no anticipation, parallel trends, covariate adjustment, general common timing, heterogeneous effects, and functional form.
Day 4
Staggered interventions. Parameters of interest and parallel trends. Shortcomings of constant-effect models. Regression-based methods, imputation, the Callaway and Sant’Anna long-difference approach, doubly robust estimators, and efficiency gains from exploiting additional pretreatment information.
Day 5
Event-study methods and testing for pretrends. Estimation with heterogeneous trends. Sensitivity analysis for violations of parallel trends. Unconfoundedness conditional on pretreatment outcomes. Synthetic control and Synthetic Difference-in-Differences.
Reading List
General Background Reading
de Chaisemartin, C. and X. D’Haultfœuille (2023), “Two-Way Fixed Effects and Differences-in-Differences with Heterogeneous Treatment Effects: A Survey,” Econometrics Journal 26, C1–C30.
Imbens, G. W. and J. M. Wooldridge (2009), “Recent Developments in the Econometrics of Program Evaluation,” Journal of Economic Literature.
Roth, J., P. H. C. Sant’Anna, A. Bilinski, and J. Poe (2023), “What’s Trending in Difference-in-Differences? A Synthesis of the Recent Econometrics Literature,” Journal of Econometrics 235, 2218–2244.
Day 1
Angrist, J. D. and J.-S. Pischke (2009), Mostly Harmless Econometrics. Princeton University Press, Chapters 1–3.
Cunningham, S. (2021), Causal Inference: The Mixtape. Yale University Press, Chapter 4.
Graham, B., C. Pinto, and D. Egel (2012), “Inverse Probability Tilting for Moment Condition Models with Missing Data,” Review of Economic Studies 79, 1053–1079.
Graham, B., C. Pinto, and D. Egel (2016), “Efficient Estimation of Data Combination Models by the Method of Auxiliary-to-Study Tilting,” Journal of Business & Economic Statistics 34, 288–301.
Hahn, J. (1998), “On the Role of the Propensity Score in Efficient Semiparametric Estimation of Average Treatment Effects,” Econometrica 66, 315–331.
Imai, K. and M. Ratkovic (2014), “Covariate Balancing Propensity Score,” Journal of the Royal Statistical Society: Series B 76, 243–263.
Imbens, G. W. and D. B. Rubin (2015), Causal Inference for Statistics, Social, and Behavioral Sciences. Cambridge University Press, Chapters 1–7 and 12–13.
Negi, A. and J. M. Wooldridge (2021), “Revisiting Regression Adjustment in Experiments with Heterogeneous Treatment Effects,” Econometric Reviews 40, 504–534.
Słoczyński, T. (2022), “Interpreting Estimands When Treatment Effects Are Heterogeneous: Smaller Groups Get Larger Weights,” Review of Economics and Statistics 104, 501–509.
Słoczyński, T., S. D. Uysal, and J. M. Wooldridge (2023), “Covariate Balancing and the Equivalence of Weighting and Doubly Robust Estimators of Average Treatment Effects,” working paper. View paper
Wooldridge, J. M. (2010), Econometric Analysis of Cross Section and Panel Data, MIT Press, Chapter 21.
Day 2
Abadie, A. (2003), “Semiparametric Instrumental Variable Estimation of Treatment Response Models,” Journal of Econometrics 113, 231–263.
Angrist, J. D. and J.-S. Pischke (2009), Mostly Harmless Econometrics, Chapter 4.
Cunningham, S. (2021), Causal Inference: The Mixtape, Chapter 7.
Imbens, G. W. and J. D. Angrist (1994), “Identification and Estimation of Local Average Treatment Effects,” Econometrica 62, 467–475.
Imbens, G. W. and D. B. Rubin (2015), Causal Inference for Statistics, Social, and Behavioral Sciences, Chapters 23–24.
Frölich, M. (2007), “Nonparametric IV Estimation of Local Average Treatment Effects with Covariates,” Journal of Econometrics 139, 35–75.
Heiler, P. (2022), “Efficient Covariate Balancing for the Local Average Treatment Effect,” Journal of Business & Economic Statistics 40, 1569–1582.
Sant’Anna, P. H. C., X. Song, and Q. Xu (2022), “Covariate Distribution Balance via Propensity Scores,” Journal of Applied Econometrics 37, 1093–1120.
Słoczyński, T., S. D. Uysal, and J. M. Wooldridge (2022), “Doubly Robust Estimation of Local Average Treatment Effects Using Inverse Probability Weighted Regression Adjustment.”
Day 3
Abadie, A. (2005), “Semiparametric Difference-in-Differences Estimators,” Review of Economic Studies 72, 1–19.
Ahrens, A., C. Hansen, M. E. Schaffer, and T. Wiemann (2024), “Model Averaging and Double Machine Learning,” arXiv:2401.01645.
Angrist, J. D. and J.-S. Pischke (2009), Mostly Harmless Econometrics, Chapter 5.
Belloni, A., V. Chernozhukov, and C. Hansen (2014), “Inference on Treatment Effects after Selection among High-Dimensional Controls,” Review of Economic Studies 81, 608–650.
Belloni, A., V. Chernozhukov, I. Fernández-Val, and C. Hansen (2017), “Program Evaluation and Causal Inference with High-Dimensional Data,” Econometrica 85, 233–298.
Chernozhukov, V., D. Chetverikov, M. Demirer, E. Duflo, C. Hansen, W. Newey, and J. Robins (2018), “Double/Debiased Machine Learning for Treatment and Structural Parameters,” Econometrics Journal 21, C1–C68.
Cunningham, S. (2021), Causal Inference: The Mixtape, Chapter 9.
Farrell, M. H. (2015), “Robust Inference on Average Treatment Effects with Possibly More Covariates than Observations,” Journal of Econometrics 189, 1–23.
Heckman, J. J., H. Ichimura, and P. E. Todd (1997), “Matching as an Econometric Evaluation Estimator: Evidence from Evaluating a Job Training Programme,” Review of Economic Studies 64, 605–654.
Lee, S. J. and J. M. Wooldridge (2023), “A Simple Transformation Approach to Difference-in-Differences Estimation for Panel Data,” working paper. View paper
Roth, J. and P. H. C. Sant’Anna (2023), “When Is Parallel Trends Sensitive to Functional Form?” Econometrica 91, 737–747.
Sant’Anna, P. H. C. and J. Zhao (2020), “Doubly Robust Difference-in-Differences Estimators,” Journal of Econometrics 219, 101–122.
Semenova, V. and V. Chernozhukov (2021), “Debiased Machine Learning of Conditional Average Treatment Effects and Other Causal Functions,” Econometrics Journal 24, 264–289.
Tan, Z. (2020), “Model-Assisted Inference for Treatment Effects Using Regularized Calibrated Estimation with High-Dimensional Data,” Annals of Statistics 48, 811–837.
Wager, S. and S. Athey (2018), “Estimation and Inference of Heterogeneous Treatment Effects Using Random Forests,” Journal of the American Statistical Association 113, 1228–1242.
Day 4
Borusyak, K., X. Jaravel, and J. Spiess (2024), “Revisiting Event Study Designs: Robust and Efficient Estimation,” Review of Economic Studies 91, 3253–3285.
Callaway, B. and P. H. C. Sant’Anna (2021), “Difference-in-Differences with Multiple Time Periods,” Journal of Econometrics 225, 200–230.
de Chaisemartin, C. and X. D’Haultfœuille (2020), “Two-Way Fixed Effects Estimators with Heterogeneous Treatment Effects,” American Economic Review 110, 2964–2996.
Goodman-Bacon, A. (2021), “Difference-in-Differences with Variation in Treatment Timing,” Journal of Econometrics 225, 254–277.
Sun, L. and S. Abraham (2021), “Estimating Dynamic Treatment Effects in Event Studies with Heterogeneous Treatment Effects,” Journal of Econometrics 225, 175–199.
Wooldridge, J. M. (2024), “Two-Way Fixed Effects, the Two-Way Mundlak Regression, and Difference-in-Differences Estimators,” working paper. View paper
Day 5
Abadie, A., A. Diamond, and J. Hainmueller (2010), “Synthetic Control Methods for Comparative Case Studies: Estimating the Effect of California’s Tobacco Control Program,” Journal of the American Statistical Association 105, 493–505.
Arkhangelsky, D., S. Athey, D. A. Hirshberg, G. W. Imbens, and S. Wager (2021), “Synthetic Difference-in-Differences,” American Economic Review 111, 4088–4118.
Athey, S., M. Bayati, N. Doudchenko, G. Imbens, and K. Khosravi (2021), “Matrix Completion Methods for Causal Panel Data Models,” Journal of the American Statistical Association 116, 1716–1730.
Ben-Michael, E., A. Feller, and J. Rothstein (2021), “The Augmented Synthetic Control Method,” Journal of the American Statistical Association 116, 1789–1803.
Ben-Michael, E., A. Feller, and J. Rothstein (2022), “Synthetic Controls with Staggered Adoption,” Journal of the Royal Statistical Society: Series B 84, 351–381.
Caetano, C. and B. Callaway (2024), “Difference-in-Differences with Time-Varying Covariates in the Parallel Trends Assumption,” arXiv:2406.15288.
Callaway, B. and P. H. C. Sant’Anna (2021), “Difference-in-Differences with Multiple Time Periods,” Journal of Econometrics 225, 200–230.
Ding, P. and F. Li (2019), “A Bracketing Relationship between Difference-in-Differences and Lagged-Dependent-Variable Adjustment,” Political Analysis 27, 605–615.
Freyaldenhoven, S., C. Hansen, and J. M. Shapiro (2019), “Pre-Event Trends in the Panel Event-Study Design,” American Economic Review 109, 3307–3338.
Gobillon, L. and T. Magnac (2016), “Regional Policy Evaluation: Interactive Fixed Effects and Synthetic Controls,” Review of Economics and Statistics 98, 535–551.
Roth, J. (2022), “Pretest with Caution: Event-Study Estimates after Testing for Parallel Trends,” American Economic Review: Insights 4, 305–322.
Rambachan, A. and J. Roth (2023), “A More Credible Approach to Parallel Trends,” Review of Economic Studies 90, 2555–2591.
Sant’Anna, P. H. C. and Q. Xu (2024), “Difference-in-Differences with Compositional Changes,” arXiv:2304.14256.
Viviano, D. and J. Bradic (2024), “Dynamic Covariate Balancing: Estimating Treatment Effects over Time,” arXiv:2103.01280.
Wooldridge, J. M. (2024), “Two-Way Fixed Effects, the Two-Way Mundlak Regression, and Difference-in-Differences Estimators,” working paper.
Wooldridge, J. M. (2005), “Fixed-Effects and Related Estimators for Correlated Random-Coefficient and Treatment-Effect Panel Data Models,” Review of Economics and Statistics 87, 385–390.
Xu, Y. (2017), “Generalized Synthetic Control Method: Causal Inference with Interactive Fixed Effects Models,” Political Analysis 25, 57–76.
6th Summer School in Advanced Economics
