Derive and validate DID for staggered rollout
Overview
This question evaluates a data scientist's competency in causal inference and panel-data methods—specifically Difference-in-Differences with staggered adoption, treatment-effect identification, event-study analysis, and robust inference when randomized designs are infeasible—and is commonly asked to assess reasoning about bias sources, heterogeneous timing, and assumption-driven diagnostics in policy evaluation. Category: Statistics & Math; level of abstraction: both conceptual understanding and practical application, since it probes estimand definition and limitations (including biases from two-way fixed effects and weighting), choice of appropriate estimators and diagnostics, inference decisions (clustered standard errors and small-cluster methods), and clear presentation of ATT and uncertainty to stakeholders; English summary.
Causal Effect of a Staggered Adoption Policy Across EU Regions
You cannot randomize. An intervention is rolled out at different dates across EU regions, observed over multiple time periods.
Answer the following:
(a) Write the two-period, two-group Difference-in-Differences (DiD) estimator and then generalize to multiple periods with staggered adoption.
(b) Explain why two-way fixed effects (TWFE) regressions can yield biased average treatment effect on the treated (ATT) under heterogeneous treatment timing or effects, including the role of negative weights.
(c) Propose a correct estimator suitable for staggered adoption (for example, Sun–Abraham or Callaway–Sant'Anna). Define the target estimand, outline an event-study specification that identifies dynamic effects, and describe how you would test for pre-trends.
(d) Describe identification assumptions (parallel trends, no anticipation), diagnostics (placebos, lead and lag checks), standard error choices (cluster-robust by region, wild bootstrap for few clusters), and how you would handle treatment reversal or partial adoption. Conclude with how you would present the ATT and its uncertainty to executives.
Solution
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