Does synthetic mean the donor data are invented?

No; it means their weighted combination is constructed.

Does the method require parallel trends in the same way as basic difference-in-differences?

It uses a different comparison construction, but still needs assumptions supporting the untreated counterfactual.

AI Glossary / Statistics and probability / Intermediate

Synthetic control method

Definition

The synthetic control method estimates an intervention's effect by comparing a treated unit with a weighted combination of untreated units chosen to resemble it before the intervention. The resulting synthetic control supplies an estimated counterfactual outcome path: what might have happened to the treated unit without the intervention, under the method's assumptions.

What it means

A single comparison location may differ too much from the treated location to be credible. A combination of several untreated locations can sometimes match its previous outcomes and characteristics more closely.
The word synthetic refers to this constructed comparison, not to fabricated observations. The underlying donor outcomes are real measurements. The central challenge is whether their weighted combination remains a defensible comparison after treatment, not merely whether the software can produce weights.

How it works

Define the treated unit, intervention date, outcome, and relevant follow-up period. The classic setting involves an intervention affecting one aggregate unit, such as a region or branch, observed over several periods alongside potential controls.
Select a donor pool of comparable units not exposed to the intervention or related spillovers. Donors affected by the same policy, customer migration, or competitive response may no longer represent untreated outcomes.
Use pre-intervention outcomes and relevant predictors to choose weights. In the classic formulation, weights are nonnegative and sum to one, making the synthetic unit a convex combination of donors. Extensions may use different constraints and need separate interpretation.
Assess whether the treated unit can be reproduced reasonably well using available donors. If its pre-intervention characteristics lie far outside their range, a conventional synthetic control may fit poorly. Strong constraints promote transparency but do not manufacture comparability.
Keep post-intervention outcomes out of the process used to tune the pre-intervention match. Choosing specifications because they create the desired effect after treatment undermines the design. Pre-intervention validation periods can help assess predictive fit.
Apply the selected weights to donor outcomes after the intervention. Subtract the synthetic outcome from the treated outcome at each time. The sign and scale of this gap should be interpreted using the outcome definition.
A causal interpretation requires that the synthetic path adequately represents the treated unit's untreated trajectory. Anticipation, spillovers, a treated-unit-specific shock, changing measurement, or unstable relationships can undermine that interpretation even with an attractive pre-period fit.
Use diagnostic and sensitivity exercises. Placebo interventions in untreated units, false intervention dates, and leave-one-donor-out checks can reveal fragility. Such exercises need thoughtful interpretation, especially when placebo units have very different pre-treatment fit.
Inference is not automatically an ordinary randomized-experiment test. The study's assignment process, donor selection, number of units, and model assumptions determine what uncertainty claims are justified. Report effect trajectories and design evidence together.

Three practical examples

Retail evaluation: compare a branch introducing an AI scheduling system with a weighted combination of unaffected branches.
Public policy: estimate a regional intervention's impact using comparable untreated regions.
Service operations: study a site-level workflow change when a randomized rollout is unavailable and suitable historical comparisons exist.

Think of it this way

Think of blending several comparison sites to create one that followed the treated site's earlier path. The blend is useful only if it remains a plausible picture of the path the treated site would have followed without the change.

Worked example

Consider an original toy example with three pre-intervention periods. The treated unit's outcomes are 100, 110, and 120. Donor A records 80, 90, and 100; donor B records 130, 140, and 150.
A weight of 0.60 on A and 0.40 on B reproduces the treated pre-period values exactly: 0.60 times 80 + 0.40 times 130 = 100, with corresponding results of 110 and 120 in the next periods. The weights are nonnegative and sum to one.
In the first post-intervention period, donor A records 110 and donor B records 160. The synthetic outcome is 0.60 times 110 + 0.40 times 160 = 130. If the treated outcome is 145, the estimated treatment gap is 145 - 130 = 15 outcome units.
That gap is a causal estimate only if the synthetic counterfactual is credible. Exact matching over three toy periods does not rule out a separate shock affecting the treated unit, nor does it establish that the relationship will persist.

Illustrative case study

Fictional case: Harbor Stores introduces AI-assisted staffing at one location. Analysts build a synthetic comparison from unaffected stores with comparable pre-launch patterns. A post-launch improvement appears, but a new transport link also opens near the treated store. The team investigates this competing explanation and checks sensitivity to donor choices. It reports the estimated gap with the limitation that the staffing change may not be the only cause, rather than attributing the full difference to the AI system automatically.

Common misconceptions and mistakes

Do not equate a close pre-period fit with guaranteed causal validity. Donor units must be evaluated for spillovers and concurrent changes. A synthetic control is not simply an unweighted average unless the chosen weights happen to be equal. Selecting donors after seeing favorable treatment gaps invites bias. A placebo ranking is not automatically an exact randomized p-value in an observational study.

Business use

Use synthetic controls for carefully scoped evaluations when an intervention affects a small number of aggregate units and suitable untreated histories exist. Publish the donor weights, pre-period fit, outcome definition, and sensitivity results. The method is strongest when its comparison can be explained and scrutinized, rather than treated as a black-box causal score.

Check your understanding

What are the donor weights in the example?

Answer: 0.60 and 0.40.

What is the post-period synthetic outcome?

Answer: 130.

Does the 15-unit gap alone prove an effect?

Answer: No; counterfactual assumptions and competing explanations matter.

Related terms

Causal inference
Spillover (experiment)
Treatment effect
Counterfactual
donor pool
comparative case study
difference-in-differences
spillover
placebo test

Learn next

Study pre-treatment fit diagnostics and donor selection, then compare classic synthetic control with augmented and generalized variants. Examine how their assumptions and extrapolation differ.

Sources

Abadie, Using Synthetic Controls: Feasibility, Data Requirements, and Methodological Aspects: https://economics.mit.edu/sites/default/files/publications/jel.20191450.pdf Abadie and Vives-i-Bastida, Synthetic Controls in Action: https://arxiv.org/abs/2203.06279 The two-donor example is original.

Previous: Synthetic aperture Next: Synthetic data