Why Donor Eligibility Is a Design Decision
In synthetic control, the counterfactual for a treated unit is constructed from units that did not receive the intervention. Those units are not interchangeable merely because they were untreated in a formal sense. A candidate donor may have experienced spillovers from the intervention, another major policy change, or a different institutional process that makes its outcomes a poor guide to the treated unit’s untreated path. A defensible donor pool therefore requires substantive eligibility rules, not just a list of available comparison units.
This tutorial concerns which units should be allowed to contribute to the comparison set and why. It does not determine the weights or the pre-intervention predictors used to construct a particular synthetic control. Those are subsequent design and estimation choices. The aim here is to establish a pool whose members could plausibly inform the treated unit’s outcome in the absence of treatment.
A candidate’s eligibility is distinct from whether it will ultimately receive positive weight. An eligible donor may contribute little or nothing to a final synthetic control. Conversely, a unit should not be kept in the pool merely because it seems useful for matching if its outcomes are affected by the intervention or by a competing event. The exclusion decision should be justified before looking at post-intervention outcomes in a way that would favor a desired result.
Core Eligibility Questions
Start from the substantive intervention and the structure of the setting. For each candidate unit, ask whether it was treated, whether treatment could reach it indirectly, whether it experienced another event that changes the relevant outcome, and whether its institutions and outcome-generating process are sufficiently comparable. A documented rule applied consistently is more defensible than exclusions chosen after examining which set gives the preferred estimate.
A unit that received the intervention cannot represent the treated unit’s no-intervention outcome unless the design explicitly addresses its treatment status. Record when and how treatment began, including phased or partial implementation.
Consider whether the policy, program, or behavioral response can affect nominally untreated units through migration, trade, shared services, information, or advance responses. Exclude or otherwise address units with material exposure.
Check for other interventions or shocks near the intervention date that affect a candidate’s outcome but not the treated unit in the same way. A coincident event can make its post-period outcome an unsuitable comparison.
Ask whether differences in institutions, population, measurement, or outcome-generating processes make the candidate an implausible stand-in, even if it is untreated and unexposed.
State the information used, the cutoff or criterion applied, and the units excluded. Prefer reasons grounded in institutional knowledge or pre-intervention facts over decisions motivated by post-intervention fit.
These checks connect to the identification assumptions for synthetic control: the constructed comparison must represent the treated unit’s outcome path under no treatment. In particular, interference matters. If treatment changes donor outcomes, the observed donor outcomes are not clean observations of their no-treatment paths. A donor pool cannot repair a violation simply by containing many units.
Worked Eligibility Decisions
Worked Example: Screening a Regional Donor List
Suppose a hypothetical city introduces a transit subsidy in 2022. The outcome is annual public-transit trips per resident, and researchers identify 12 candidate cities that were initially considered untreated. Before examining their post-2022 outcomes, they establish the following facts: two cities adopted the same subsidy in 2022; one neighboring city shares a transit network with the treated city and is expected to receive increased service use because of the subsidy; one city changed its trip-counting system in 2022; and the remaining eight cities had no known exposure or concurrent measurement change.
Apply the eligibility rule in sequence. The two cities that adopted the subsidy are directly treated, so they are excluded. The neighboring city is indirectly exposed through the shared network, so it is excluded if that exposure could materially change its trips. The city with the changed counting system is excluded because its measured outcome is no longer comparable across the intervention date. Thus:
Eight candidates remain eligible under the stated facts. This arithmetic counts units; it does not establish that the eight are all suitable in every other respect. Researchers must still consider whether those cities have sufficiently comparable institutions and outcome-generating processes. The conclusion is conditional on the documented exposure and measurement facts, not on whether excluding a particular city improves a later estimate.
Worked Example: Quantifying Contamination in an Illustrative Comparison
Consider a hypothetical comparison with three candidate donors. Suppose, only to illustrate contamination, that their untreated outcomes in a post-intervention year would each be 100 trips per resident. The intervention indirectly increases trips in donor A by 4 trips per resident, while donors B and C are unexposed. Assume an illustrative synthetic combination assigns shares \(0.50\), \(0.30\), and \(0.20\) to A, B, and C, respectively. These shares are hypothetical and are not being estimated here.
The synthetic combination of donors’ untreated outcomes would be:
With donor A’s indirect increase, its observed outcome is 104 rather than 100. The comparison made from the observed donor outcomes is therefore:
The contaminated comparison is 2 trips per resident higher than the corresponding combination of untreated outcomes:
Thus, even though only one donor is exposed, its influence can shift the counterfactual comparison. In this illustration, if the treated unit’s outcome is compared with the contaminated value, the estimated treated-minus-comparison gap is 2 trips per resident smaller than it would be using the uncontaminated comparison. The direction and magnitude depend on the exposure effect and the donor’s contribution; contamination does not always bias a contrast in the same direction. The defensible response is to assess exposure substantively and exclude or otherwise explicitly address a materially contaminated donor, rather than assuming its untreated label is sufficient.
Worked Example: A Broad Pool With Poor Structural Comparability
Suppose a hypothetical treated province is an urban region where hospitals are funded through a unified public system. Its 10 untreated candidate provinces include six with similar public financing and four where most hospitals are privately funded and access is organized through a different system. Assume the intervention changes access to publicly funded hospital care. Before treatment, the two groups have comparable population sizes, but the private-system provinces have different rules governing admission and reporting.
A purely numerical screening rule would retain all 10 candidates. A structural rule based on the intervention’s mechanism would instead flag the four private-system provinces: even if they are untreated, the policy could affect their outcome through a different institutional pathway, and their outcome-generating processes may not be comparable. Under this rule, the pool has six candidates, and the retained share of the original list is:
So 60% of the original candidates remain. That percentage is descriptive, not a measure of validity. If the six retained provinces are too few or too unlike the treated province on other important features, the reduced pool may still be inadequate. The relevant conclusion is that the original pool mixes units governed by materially different systems, and that difference needs to be addressed openly. The rule should not be relaxed simply to increase the candidate count unless there is a substantive reason those provinces can still represent the treated province’s untreated outcome.
Why Pool Composition Affects the Counterfactual
Donor-pool composition limits what a synthetic counterfactual can plausibly represent. If all eligible donors share an important feature absent in the treated unit, their combination may be unable to reflect the treated unit’s institutional setting. If the pool contains units with substantially different outcome processes, a numerical combination may fit some observed features while combining units that do not form a credible comparison in the relevant setting. More candidates are not automatically better, and a small pool is not automatically more credible.
There is also a practical tension. Excluding contaminated or structurally unsuitable units protects the comparison from known threats, but an aggressively narrow pool may leave too little relevant variation among eligible units. In that case, a synthetic counterfactual may depend heavily on a small number of unusual candidates or may fail to resemble the treated unit before treatment. That is a warning about the design’s support, not a reason to include clearly invalid donors. The appropriate response is to report the limitation and reconsider whether the design has a credible comparison set.
A short justification should make clear why included units are eligible and why important exclusions were made. It should identify the intervention’s reach, the timing of other changes, and the relevant institutional distinctions. Where classification is uncertain, describe the uncertainty and examine whether the substantive conclusion depends on the rule. Do not silently treat uncertain units as clean controls.
A Justification for Excluding Contaminated Donors
The concern can be expressed directly. Let \(Y_{jt}(0)\) denote donor \(j\)’s outcome in period \(t\) without the intervention of interest. Let \(\delta_{jt}\) be the effect on that donor of direct or indirect exposure, so its observed outcome is \(Y_{jt}(0)+\delta_{jt}\). For an illustrative weighted comparison with shares \(w_j\), where \(w_j \geq 0\) and the shares sum to one, the observed donor combination differs from the no-exposure combination by:
The equality follows by distributing each \(w_j\) across the two terms and canceling the shared untreated-outcome terms. If every included donor is unexposed, then \(\delta_{jt}=0\) for each donor and the difference is zero. If some donor is exposed, its contribution depends on both its exposure effect and its share. This argument does not claim that donor exclusion alone guarantees identification; it shows why a pool containing contaminated units can shift the comparison even when the treated unit and the estimation procedure are otherwise unchanged.
Common Mistakes
- Equating “untreated” with “unaffected.” A region may not adopt a policy but can still be affected through spillovers, shared markets, or anticipation. Check exposure, not only formal treatment status.
- Keeping every available unit to enlarge the pool. A larger pool is not automatically more informative. Exclude units whose treatment status, measurement, or institutional structure makes them unsuitable, and state when the remaining pool is limited.
- Choosing exclusions to improve post-treatment results. Removing a donor because it makes the estimated effect look inconvenient makes the design difficult to defend. Base eligibility on pre-specified or clearly documented substantive criteria.
- Confusing eligibility with final weight. A candidate can be eligible and receive no weight later. Eligibility asks whether a unit may credibly be considered, not whether it must contribute.
- Treating a good pre-intervention match as proof of comparability. Similar observed outcomes do not rule out different institutions, concurrent events, or spillovers. Those issues require substantive assessment as well.
Check Your Understanding
Answer each question by stating the design reasoning, not just the label.
- A candidate region did not adopt a policy, but many residents commute to the treated region and the policy changes cross-region service use. What exposure question should be resolved before including it?
- Why is a donor’s eligibility conceptually different from receiving a positive weight in the final synthetic control?
- A donor changes its outcome measurement system in the intervention year. Explain why this can undermine its eligibility even if the region is untreated.
- What is the difference between a small donor pool that is substantively appropriate and a large pool that includes structurally incomparable units?
- In the contamination derivation, what does \(\sum_{j \in \mathcal{J}} w_j\delta_{jt}\) represent, and under what condition is it zero?