I got the two-group two-period setup fine, that part is pretty standard.
Start by clearly defining the two-period two-group DiD estimator, emphasizing the parallel trends assumption and the regression formulation. Then extend to staggered adoption by introducing time and cohort fixed effects, and discuss modern estimators that address negative weighting issues. Use a concrete EU region rollout example to illustrate.
Pro tip: Mention that with staggered adoption, the standard two-way fixed effects (TWFE) estimator can be biased due to heterogeneous treatment effects, and reference recent advances like Callaway & Sant'Anna (2021) or Sun & Abraham (2021) to show depth.
Explain the setup: two groups (treated and control) and two periods (pre and post). The estimator is the difference in average outcomes between treated and control groups, before and after treatment.
Highlight the parallel trends assumption: absent treatment, the average outcomes of the two groups would have followed parallel paths. Show the regression: Y = α + β*Treated + γ*Post + δ*(Treated*Post) + ε, where δ is the DiD estimate.
Describe the setting: units adopt treatment at different times (staggered). Introduce the two-way fixed effects (TWFE) regression: Y_it = α_i + λ_t + δ*D_it + ε_it, where D_it is an indicator for treatment status.
Explain that TWFE can produce biased estimates when treatment effects are heterogeneous over time or across cohorts, due to 'forbidden comparisons' between already-treated and later-treated units.
Mention alternative estimators like Callaway & Sant'Anna (2021), Sun & Abraham (2021), or Borusyak et al. (2021) that correct for these issues, and recommend using them in practice.
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This is the part I was most nervous about and weirdly it went okay.
Start by defining the two-way fixed effects (TWFE) estimator and its implicit assumption of homogeneous treatment effects. Then explain how staggered adoption and heterogeneous effects cause already-treated units to serve as controls, leading to negative weights. Conclude with the consequences for ATT estimation and mention robust alternatives.
Pro tip: Emphasize that the negative weights problem is not just a technical curiosity but can reverse the sign of the estimated effect, making TWFE unreliable for policy evaluation. Mention that modern estimators like Callaway & Sant'Anna (2021) or Sun & Abraham (2021) explicitly address this by using not-yet-treated or never-treated units as controls.
Explain that TWFE is a regression with unit and time fixed effects, commonly used for difference-in-differences (DiD) with staggered treatment adoption. Its goal is to estimate the average treatment effect on the treated (ATT).
TWFE assumes treatment effects are constant across units and time. When this holds, the estimator is unbiased. But with heterogeneous effects, the estimator becomes a weighted average of all possible 2x2 DiD comparisons, some with negative weights.
With staggered adoption, already-treated units are used as controls for later-treated units. If treatment effects grow over time, the difference between later-treated and already-treated units can be negative, leading to negative weights. These negative weights can bias the ATT estimate, even reversing its sign.
Provide a simple example: two groups, one treated early with increasing effects, one treated later. The TWFE estimate may understate or even show a negative effect because the early-treated group's outcome is subtracted from the later-treated group's outcome.
Mention that to avoid negative weights, one can use estimators like Callaway & Sant'Anna (2021), Sun & Abraham (2021), or Borusyak et al. (2021) that explicitly model group-time ATTs and use only not-yet-treated or never-treated units as controls.
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Went with the cohort-by-cohort approach, basically aggregating treatment effects within adoption cohorts and then averaging.
Start by defining the causal estimand for staggered adoption, such as the group-time average treatment effect on the treated (ATT(g,t)) or a summary like the overall ATT. Then propose a robust estimator like Callaway & Sant'Anna (2021) or Sun & Abraham (2021) that avoids the pitfalls of TWFE, and outline an event study with pre-trend tests using leads and lags.
Pro tip: Emphasize that you would check for heterogeneous treatment effects and avoid using TWFE due to negative weighting issues; this shows you're up-to-date with modern econometrics and practical about implementation.
Clearly state the causal parameter of interest, e.g., ATT(g,t) for each adoption cohort g and time t, or a weighted average like the overall ATT. Explain why this estimand is relevant for the business question.
Propose a robust estimator such as Callaway & Sant'Anna's group-time ATT or Sun & Abraham's interaction-weighted estimator. Explain how it addresses staggered adoption issues like heterogeneous effects and negative weighting.
Describe constructing an event study by estimating dynamic treatment effects relative to adoption time, including leads and lags. Use the chosen estimator to plot coefficients and confidence intervals.
Explain how to test for parallel pre-trends by examining the significance of pre-treatment coefficients (leads). Discuss joint tests and visual inspection, and what to do if pre-trends are violated.
Discuss how to interpret the results, including heterogeneity across groups and time. Mention robustness checks like placebo tests and sensitivity analyses.
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Structure your answer around the four sub-questions, starting with the core DiD assumptions (parallel trends, no anticipation, correct functional form), then move to diagnostics (event study, placebo tests), inference with few clusters (wild cluster bootstrap, randomization inference), and finally handling treatment reversal or partial adoption (staggered DiD, Sun & Abraham, Callaway & Sant'Anna). Emphasize practical trade-offs and how you would communicate uncertainty to stakeholders.
Pro tip: Acknowledge that in industry settings, perfect parallel trends is rare; instead, focus on robustness checks and sensitivity analysis (e.g., Rambachan & Roth) to quantify how much violation would change conclusions. Also, mention that with few clusters, standard errors can be misleading, so you should pre-specify the inference method and run simulations to validate it.
Clearly list the assumptions: parallel trends (in absence of treatment, treated and control groups would have followed parallel outcome trends), no anticipation (treatment timing is exogenous and not anticipated), and stable composition (no spillovers or compositional changes). Also mention that the treatment effect is homogeneous or that you use methods robust to heterogeneity.
Describe diagnostic tools: event study plots to check pre-trends, placebo tests (e.g., fake treatment dates or outcomes), and sensitivity analysis (e.g., Rambachan & Roth bounds). Discuss how to interpret pre-trends and what to do if they fail (e.g., add covariates, use synthetic control, or abandon DiD).
Explain that with few clusters (e.g., <50), cluster-robust standard errors can be downward biased. Recommend wild cluster bootstrap (Cameron, Gelbach, & Miller) or randomization inference (Fisher randomization test). Mention that you would also check sensitivity to the number of clusters and possibly use bias-corrected methods.
For treatment reversal (units switching in and out of treatment), use methods like de Chaisemartin & D'Haultfœuille or Callaway & Sant'Anna that allow for multiple treatment periods and reversals. For partial adoption (staggered adoption), avoid TWFE with heterogeneous effects; instead use group-time average treatment effects (Callaway & Sant'Anna) or Sun & Abraham interaction-weighted estimator.
Summarize how you would choose among methods based on data structure, assumptions, and business context. Emphasize that you would present results with uncertainty intervals and sensitivity analyses to stakeholders, and possibly run simulations to validate the chosen approach.
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Honestly the easiest part of the whole interview after everything that came before.
Focus on translating the ATT estimate and its uncertainty into business impact and decision-making terms, avoiding statistical jargon. Use a clear narrative that connects the estimate to expected outcomes and the uncertainty to risk, enabling executives to make informed choices.
Pro tip: Frame uncertainty as a range of possible outcomes with associated probabilities, and always tie it back to the cost of being wrong versus the cost of inaction. This shows you understand executive priorities and risk tolerance.
Begin by restating the business problem the ATT estimate addresses, so executives understand the context and why it matters.
Translate the ATT into a concrete metric executives care about, such as incremental revenue, user growth, or cost savings, using simple language.
Describe the uncertainty using a confidence interval or a range of plausible values, and explain what it means in terms of best-case and worst-case scenarios.
Discuss how the estimate and its uncertainty inform the decision at hand, including the potential risks and rewards of different actions.
Provide a clear recommendation based on the analysis, and suggest next steps such as further testing or monitoring to reduce uncertainty.
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