Synthetic Control Method & Placebo Checks

The Synthetic Control Method (SCM, Abadie et al.) & Placebo Permutation Inference constructs data-driven synthetic counterfactuals for causal policy evaluation when an intervention impacts strictly a single aggregate unit (e.g. a single country, state, or key city) where no single natural control exists; Core algorithm: finding non-negative convex weights $W^* = [w_2, \dots, w_{J+1}]^T$ (constrained by $w_j \ge 0, \sum w_j = 1$) over a donor pool of untreated units minimizing pre-treatment predictor distance; the estimated post-treatment causal effect equals the observed trajectory minus the synthetic clone: $\hat{\tau}_{1t} = Y_{1t} - \sum_{j=2}^{J+1} w_j^* Y_{jt}$; Statistical significance is established via Placebo Tests in space (iteratively assigning pseudo-treatments across all donor units to compute empirical RMSPE distribution ratios).

Single-market regional policy rollouts (e.g. piloting dynamic commissions in one metropolitan region) and macroeconomic regulatory impact studies.

Classical DiD fails when no single control unit shares parallel pre-trends with a unique mega-city; SCM constructs a mathematically optimal weighted synthetic counterfactual.

Formulate the constrained convex quadratic optimization problem minimizing pre-intervention predictor distance subject to $w_j \ge 0, \sum w_j = 1$?

Explain how in-space placebo iterations across all donor units construct empirical Post/Pre-RMSPE ratios to compute exact permutation $p$-values?

Why does re-running SCM on an artificial pre-intervention placebo date evaluate model specification validity?

Explain Synthetic Difference-in-Differences (SDID) combining both unit weights and time weights to handle fixed level offsets?

How does economic spillover between donor units and treated units contaminate the synthetic counterfactual, and how to filter donor pools?