Why Move the Intervention Date?
A synthetic control is built to approximate the treated unit’s untreated trajectory. Its post-intervention gap is informative only if the synthetic comparison is credible. One way to probe that credibility is to ask what the same procedure would have shown if the intervention had supposedly occurred earlier, when the treated unit had not yet received it. This is an in-time placebo: a fictitious intervention date placed inside the actual pre-intervention period.
The central diagnostic question is whether a synthetic control, estimated using only data available before the fictitious date, produces a substantial gap afterward. A gap that appears well before the real intervention may signal that the model is unstable or that the treated unit and its synthetic comparison were already diverging. If the gap appears only close to the actual intervention, anticipation is another possible explanation: behavior or outcomes may have responded before the formal treatment date.
The superscript \((p)\) emphasizes that the synthetic control may need to be refitted for each placebo date. In particular, neither post-placebo outcomes nor predictors measured after \(T_p\) should be used to choose that date’s weights. Using future information would let the model see the very period it is supposed to predict, making the diagnostic misleading.
A useful summary for a selected evaluation window \(P_p\), consisting of periods after \(T_p\) and before \(T_0\), is the average placebo gap:
The summary’s sign and size should be reported in the outcome’s units. The time pattern matters as well: a single large gap, a gradual drift, and a persistent level shift can have the same average while raising different diagnostic concerns.
Designing an In-Time Placebo
The actual treatment date, the candidate placebo date, the fitting window, and the evaluation window should be specified clearly. A valid design uses pre-placebo data to construct the comparison and reserves later pre-intervention periods to assess its predictive performance. If the placebo date is near \(T_0\), its evaluation window may be short; that limitation should be stated rather than concealed by choosing a longer window that includes post-treatment outcomes.
For a clean comparison across candidate dates, keep the donor pool, outcome definition, predictor strategy, and fitting rules consistent where possible. Re-estimate weights using only information available at each candidate date. Some predictors may not be measured annually, but they must still be chosen and measured without relying on post-placebo information. A change in weights is expected when the fitting period changes; the diagnostic is about how the resulting synthetic comparison predicts later untreated outcomes.
Place \(T_p\) within the actual pre-intervention period. Decide in advance which later pre-intervention periods will be used to inspect the gap.
Use only the specified pre-placebo outcomes and predictors to construct the synthetic control at \(T_p\). Do not use post-\(T_p\) information to tune the fit.
For each evaluation period, subtract the synthetic outcome from the treated outcome. Report the sequence, its units, and any chosen summary.
Consider whether the pattern points to instability, pre-existing divergence, or a response that may have begun in anticipation of the actual intervention.
Worked Examples
Worked Example: A Placebo Gap Before the Intervention
Suppose a hypothetical region adopts a program in 2020. Researchers choose 2016 as a fictitious date. They fit weights using outcome data from 2012–2015 only. The following table gives the treated and synthetic outcomes in index points.
| Year | Treated outcome | Synthetic outcome | Gap |
|---|---|---|---|
| 2012 | 100 | 99 | 1 |
| 2013 | 104 | 103 | 1 |
| 2014 | 108 | 107 | 1 |
| 2015 | 112 | 111 | 1 |
| 2017 | 117 | 112 | 5 |
| 2018 | 121 | 116 | 5 |
| 2019 | 126 | 120 | 6 |
For 2017–2019, the gaps are \(117-112=5\), \(121-116=5\), and \(126-120=6\) index points. Their average is
The synthetic control tracked the treated unit closely during the fitting period, but the treated outcome subsequently exceeded the synthetic outcome before the 2020 intervention. This is a warning: the eventual post-2020 gap cannot be interpreted without considering this pre-intervention divergence. The placebo result does not establish why the gap arose. It could reflect an unstable comparison, an unmodeled change, or another difference between the treated unit and its synthetic control.
Worked Example: Comparing Several Fictitious Dates
In a second hypothetical analysis, researchers fit a separate synthetic control at each of three fictitious dates. For each date, the table reports the post-placebo gaps, in units of annual hospital visits per 1,000 residents, over the listed periods before the actual intervention. These are results from separate refits, not a single sequence assumed to be shared by all dates.
| Placebo date | Evaluation-period gaps | Average gap |
|---|---|---|
| 2014 | 2015–2019: 0, 1, 1, 2, 2 | \((0+1+1+2+2)/5=1.2\) |
| 2016 | 2017–2019: 1, 2, 2 | \((1+2+2)/3\approx1.667\) |
| 2018 | 2019: 2 | \(2/1=2\) |
The averages increase across these rows, but they do not by themselves show that the synthetic control becomes less accurate over time. The evaluation windows differ in length, and each date has a different fitting period and refitted weights. The entries suggest a pattern worth investigating: later pre-intervention observations tend to lie above their corresponding synthetic predictions. Researchers should inspect the gap sequences, confirm the fitting rules were applied consistently, and consider whether a substantive pre-intervention change occurred. A rising pattern is a diagnostic clue, not a treatment-effect estimate.
Anticipation, Instability, and Falsification
An in-time placebo can help separate several explanations, but it cannot identify them on its own. To make the logic explicit, write the observed outcome for the treated unit as its outcome without the intervention plus any intervention-related effect:
Here \(Y_{1t}(0)\) is the outcome that would be observed without the intervention, and \(\tau_t\) is the effect at time \(t\). Before the intervention, \(\tau_t\) is often assumed to be zero. But if units respond to an announced or expected intervention before its formal start, \(\tau_t\) may be nonzero before \(T_0\). Let \(\delta_t=Y_{1t}(0)-\widehat{Y}_{1t}^{SC}\) denote the error in using the synthetic outcome to represent the untreated outcome. Then the observed gap satisfies
This decomposition gives the diagnostic its limits. Far before treatment, a nonzero gap is evidence that the fitted synthetic comparison does not predict the treated unit well in that period, but it does not reveal the cause. Near treatment, a gap may also include anticipation if the intervention already affects outcomes. A placebo date does not make the untreated counterfactual observable, so it cannot separate \(\tau_t\) from \(\delta_t\) by itself.
Worked Example: A Gap Near an Announced Intervention
Suppose a hypothetical city’s program formally begins in 2021, but its announcement occurs in late 2019. Researchers choose 2019 as a placebo date, fit the synthetic control using data through 2018, and inspect 2019–2020. The gaps are 0 visits per 1,000 residents in 2019 and 7 in 2020. The average is
The isolated 2020 gap is temporally consistent with anticipation if residents or providers could respond to the announced program before implementation. It is not proof of anticipation: a change unique to the city, a poor synthetic fit, or another coincident event could also produce the gap. The researchers should document the announcement and response timeline, inspect fit and outcome patterns, and describe the 2020 result as a pre-intervention discrepancy unless the design supports a stronger interpretation.
In-time placebos are also useful as a falsification check. If the analysis would claim a large effect after the real intervention but produces similarly large gaps at many earlier dates, that pattern weakens the argument that the post-intervention gap is uniquely attributable to the intervention. Conversely, small earlier gaps are reassuring about predictive performance in those periods, but they do not prove the required assumptions hold after the intervention.
Do not treat the collection of placebo dates as automatically supplying a randomization test or a conventional p-value. Calendar dates are generally not exchangeable: outcomes may be serially correlated, the dates may have different fitting and evaluation windows, and the intervention date is not randomly assigned among them. A numeric proportion of placebo gaps more extreme than the real-date gap is not, without an appropriate inferential design, a probability that the null hypothesis is true or a calibrated p-value.
Common Pitfalls and Reporting
- Fitting with future information. Using outcomes after \(T_p\) to select weights makes the placebo forecast use information it should not have. Fit each placebo using only its designated pre-placebo data.
- Calling every early gap anticipation. Anticipation requires a plausible pathway and timing for effects before the formal start. A gap alone also reflects error in the synthetic comparison.
- Ignoring the gap sequence. A mean can hide whether the gap is a one-period spike, a gradual drift, or a sustained difference. Show or describe the sequence as well as any summary.
- Comparing unlike windows as if they were identical tests. Placebo dates may have different numbers of evaluation periods and different fits. Explain these differences and avoid treating their averages as directly comparable without qualification.
- Calling a diagnostic proof. No apparent placebo effect does not establish that the synthetic control is valid for the post-intervention period. It only indicates that the chosen procedure did not produce a concerning gap in the examined pre-intervention windows.
A concise report names each placebo date, states which periods were used to fit and evaluate the synthetic control, gives the gaps in outcome units, and explains how the observed pattern affects interpretation of the main analysis. The most defensible conclusion is calibrated: the placebo checks may reveal pre-existing divergence, lend support to predictive stability over the tested windows, or raise a plausible anticipation concern, but they do not settle these issues independently.
Check Your Understanding
Answer each question using the definitions and diagnostics above.
- Why must the synthetic control for a fictitious date be fitted without outcomes measured after that date?
- A placebo analysis gives gaps of \(-2\), \(0\), and \(4\) outcome units over three evaluation periods. Calculate the average gap and state what additional information is needed to interpret it.
- How can a gap before the formal start date be consistent with anticipation, and why does it not prove anticipation?
- Why is the fraction of in-time placebo gaps more extreme than the actual-date gap not automatically a p-value?
- What conclusion is justified if several tested pre-intervention windows show small gaps? What conclusion is not justified?