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Synthetic Control Method
Causal inference technique constructing a weighted control group by combining multiple untreated units to create a plausible counterfactual for the treated unit.
Synthetic Weighting
Mathematical process of assigning optimal weights to control units to minimize pre-treatment differences with the treated unit based on predetermined covariates.
Causal Treatment Effect
Estimation of the differential impact of a policy intervention by comparing the post-treatment evolution of the treated unit to its synthetic counterfactual.
Synthetic Counterfactual
Artificial reconstruction of the hypothetical evolution of the treated unit in the absence of intervention, based on a linear combination of control units.
Calibration Period
Pre-intervention time window used to determine optimal weights by minimizing the gap between the treated unit and its synthetic control group.
Donor Matrix
Structured set of candidate control units serving as the basis for constructing the weighted synthetic control based on their pre-treatment similarity.
Optimized Loss Function
Mathematical criterion minimizing weighted distances between pre-treatment characteristics of the treated unit and the linear combination of controls.
Optimal Weight Vector
Mathematical solution ensuring weights sum to unity and are non-negative, forming a convex interpolation of control units.
Synthetic Placebo Test
Empirical validation applying the methodology to untreated units to evaluate the distribution of treatment effects under the null hypothesis.
Synthetic Parallelism Assumption
Postulate that the synthetic control follows the same trajectory as the treated unit in the absence of intervention, justifying causal estimation.
Convex Interpolation
Mathematical constraint requiring non-negative weights summing to one, ensuring the synthetic control remains within the convex hull of observed data.
Synthetic Gap
Temporal difference between observed values of the treated unit and values predicted by its synthetic control after intervention.
Comparison Matrix
Two-dimensional structure organizing pre-treatment similarities between treated units and synthetic control candidates for optimization.
Fit Quality Score
Quantitative metric evaluating the accuracy of pre-treatment reconstruction of the synthetic control compared to the actual treated unit.
Weight Stability
Sensitivity analysis examining the variation of estimated effects when optimal weights are slightly perturbed within the convex neighborhood.
Period Aggregation
Method combining treatment effects across multiple post-intervention periods to estimate a more robust overall average causal effect.