Justify synthetic control and handle inference
Overview
This question evaluates understanding of synthetic control methodology, causal identification assumptions, estimation and regularization choices, inference techniques for pointwise and cumulative effects, and diagnostic checks for panel time-series interventions.
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Oct 13, 2025, 9:49 PM
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Synthetic Control: Assumptions, Estimation, Inference, and Diagnostics
Context
You are estimating the causal effect of an intervention on a single treated unit using time-series data and a donor pool of untreated units. Synthetic Control (SCM) constructs a weighted combination of donors to approximate the treated unit’s counterfactual path in the absence of treatment. Answer the following, focusing on identification, estimation choices, inference, and practical diagnostics.
Task
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Identification assumptions and how violations bias estimates
- Convex-hull or linear-span requirement (overlap).
- No interference/spillovers between treated and donor units.
- Stability of relationships over time (factor-loadings/predictor relationships).
- Reliance on strong pre-period fit to proxy unobserved confounders.
- Variable and lag selection without post-treatment leakage; how to regularize with high-dimensional predictors.
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Inference strategy
- Construct pointwise and cumulative treatment effects.
- Use in-space and in-time placebos (MSPE ratio) to obtain p-values.
- Build uncertainty bands and explain why naive bootstrapping can fail.
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Diagnostics and fixes when assumptions are strained
- Poor pre-period fit, structural breaks, seasonality mismatches, staggered adoption, carryover effects, reversion to the mean, donor dominance.
- Tools such as leave-one-out tests, retuning windows, augmented/ridge/Lasso variants, or switching to ITS/DID if needed.
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