What is a single treated unit design?

A single treated unit design has exactly one treated unit and many controls. Examples include a flagship store redesign, a pilot market launch, or a platform entry into a single city. The treated unit is typically unique, so direct matching to a single control unit is implausible.

The estimand is unit-specific

The target is a unit-specific effect for the treated unit $i^*$ in each post-treatment period:

$$ Y_{i^*t}(1)-Y_{i^*t}(0). $$

This is not a population ATT. The estimate has high internal validity for the treated unit, but limited external validity for generalizing beyond it.

Synthetic control: the core tool

Synthetic control builds a weighted combination of control units to match the treated unit’s pre-treatment outcomes. The post-treatment difference between the treated unit and its synthetic counterpart is the causal estimate.

Why this works: if the synthetic control tracks the treated unit closely before treatment, a stable low-rank factor structure implies it should continue to track in the absence of treatment.

Inference via placebo checks

Inference is not based on standard asymptotics. Instead, we use placebo tests:

  • Apply the same synthetic control procedure to each control unit as if it were treated.
  • Compare the treated unit’s estimated effect to the distribution of placebo effects.

This provides a reference distribution for how large an effect could appear by chance under the design.

Synthetic DiD as a hybrid

Synthetic difference-in-differences (SDID) combines the strengths of synthetic control and DiD. It weights both units and time periods, improving pre-treatment fit while still leveraging DiD logic. SDID is especially useful when there are multiple pre- and post-treatment periods and moderate parallel-trends credibility.

Diagnostics that matter most

  • Pre-treatment fit: the treated unit should be well-approximated by the synthetic control.
  • Placebo distributions: the treated effect should stand out relative to controls.
  • Sensitivity to donor pool: check robustness to removing or adding controls.

Takeaway

Single treated unit designs are powerful but narrow. They provide credible, unit-specific causal estimates when synthetic control achieves strong pre-treatment fit, and when placebo tests confirm the effect is unusual relative to controls.

References

  • Shaw, C. (2025). Causal Inference in Marketing: Panel Data and Machine Learning Methods (Community Review Edition), Section 3.2.3.
  • Abadie, A., Diamond, A., and Hainmueller, J. (2010). Synthetic control methods for comparative case studies. Journal of the American Statistical Association.