A researcher uses synthetic control to evaluate a minimum wage increase in one state. The synthetic control tracks the treated state's pre-intervention employment trend almost exactly over 12 years. After the wage increase, employment runs 3 percentage points below the synthetic control. Placebo tests on each donor state produce gaps of 0.2–0.8 percentage points. What should the researcher conclude?
AThe result is statistically significant at p < 0.05 by standard regression criteria
BThe estimate is implausibly large and likely reflects overfitting to the pre-intervention period
CThe post-intervention gap is large relative to placebo estimates, providing evidence that the policy had a real effect
DThe result is inconclusive because only one state was treated, making any inference impossible
In synthetic control, inference is done via permutation tests: applying the method to each untreated donor unit reveals the distribution of placebo 'effects.' If the treated state's 3-percentage-point gap far exceeds all placebo gaps (0.2–0.8 pp), that result would be extremely unlikely if the policy had no effect — constituting strong inferential evidence. This is not asymptotic inference; it is a ranking-based permutation test appropriate for a single treated unit. The excellent pre-intervention fit strengthens, not undermines, the estimate's credibility.
Question 2 Multiple Choice
What is the primary advantage synthetic control offers over standard regression-based difference-in-differences when evaluating a policy affecting a single aggregate unit?
ASynthetic control does not require a pre-intervention period, making it usable when historical data is unavailable
BThe counterfactual is explicitly constructed as a weighted combination of donor units, and its pre-intervention fit is directly verifiable, making identification assumptions transparent
CSynthetic control eliminates the need for any control group, relying solely on the treated unit's own time series
DSynthetic control produces smaller standard errors than difference-in-differences by incorporating more comparison units
The defining advantage is transparency: the researcher explicitly constructs the counterfactual (showing which donor units receive which weights) and verifies it by plotting pre-intervention trajectories. If the synthetic control diverges from the treated unit in the pre-period, the counterfactual is not credible — and this failure is immediately visible. In standard regression DiD, the counterfactual is implicit in the regression coefficients, making it much harder to inspect. Synthetic control makes the 'what would have happened without treatment' question concrete and directly checkable.
Question 3 True / False
In synthetic control, inference about whether an observed post-intervention gap is real uses classical standard errors computed from the pre-intervention regression fit.
TTrue
FFalse
Answer: False
Synthetic control uses permutation-based inference (placebo tests), not classical standard errors. Classical asymptotic inference requires a large number of treated units, but synthetic control has only one. Instead, the researcher applies the method to each untreated donor unit, treating each as if it had received the treatment, and observes the distribution of resulting 'effects.' The actual estimated effect is then ranked within this placebo distribution. Standard errors from regression are not appropriate for this single-treated-unit setting and would produce misleading precision.
Question 4 True / False
One weakness of synthetic control is that a poor pre-intervention fit between the treated unit and its synthetic control is hidden from view and can primarily be detected through auxiliary diagnostic tests.
TTrue
FFalse
Answer: False
This is precisely the opposite of the truth — and is one of the method's key strengths. A poor pre-intervention fit is immediately visible when the researcher plots the treated unit's trajectory alongside the synthetic control over the pre-intervention period. If the two series diverge before the treatment, the researcher knows the synthetic control is not a credible counterfactual. This transparency distinguishes synthetic control from regression-based approaches where the counterfactual is implicit. The method cannot hide a bad fit; it displays it prominently.
Question 5 Short Answer
Why is a long pre-intervention period important for synthetic control, and what does it allow you to verify that a short pre-intervention window cannot?
Think about your answer, then reveal below.
Model answer: A long pre-intervention period serves two purposes. First, it provides more data points over which to construct the synthetic control, reducing the risk that the weights are fit to noise rather than stable structural similarities. Second, and more importantly, a long window allows the researcher to verify that the synthetic control tracks the treated unit's trajectory through multiple economic cycles, external shocks, and policy environments — establishing that the match reflects genuine underlying similarity rather than a coincidental alignment on a few recent observations. With a short pre-intervention window, the synthetic control might fit by accident (overfitting), and the researcher cannot tell whether the good fit reflects stable structural comparability or a fragile coincidence that would break down post-intervention.
The pre-intervention fit is the entire basis for trusting the post-intervention counterfactual. A longer validation period makes that trust more credible, because it is much harder for an artificial match to coincidentally track the treated unit through many years of diverse conditions than through just a few years.