The synthetic control method estimates the effect of an intervention on a single treated unit (a region, a country, a store) by building a weighted blend of untreated units that matches the treated unit’s history before the intervention, then reading the effect as the gap between the real unit and its synthetic twin afterwards. The weights are non-negative and add up to one, so the synthetic control is literally “34 percent of this region, 28 percent of that one and 38 percent of a third”, which makes it unusually easy to explain to a stakeholder.
Marketers mostly meet synthetic control through geo testing, because it’s the engine inside Meta’s GeoLift package, and through Google’s CausalImpact, which solves a closely related problem with a Bayesian time-series model. It’s the natural step up from difference in differences when your treated region doesn’t trend like any single comparison region, which in my experience is most of the time for the regions people actually want to test in. The widget below fits the weights in your browser, so you can watch the method work before trusting it with a real test.
Where the synthetic control method came from
The method was introduced by Alberto Abadie and Javier Gardeazabal in 2003, to estimate the economic cost of terrorism in the Basque Country by comparing it with a weighted combination of other Spanish regions. Abadie, Alexis Diamond and Jens Hainmueller then formalised it in a 2010 paper in the Journal of the American Statistical Association, estimating the effect of California’s 1988 tobacco control program (Proposition 99) on cigarette sales against a synthetic California built from other states. That paper also introduced the placebo-based inference that most practitioners still use, and Abadie’s 2021 review in the Journal of Economic Literature is the best practical guide to when the method is and isn’t appropriate.
The problem those papers solved is the same one a marketer faces with a regional test. You have one treated unit (or a handful), a long pre-period, and a pool of untreated units, none of which is a perfect match on its own. Difference in differences would average the pool equally and hope the trends line up; synthetic control lets the data choose which units to lean on.
How the weights are chosen
Write the treated unit’s outcome in pre-period week as and donor ‘s outcome as . The basic synthetic control picks weights to make the weighted donors track the treated unit as closely as possible over the pre-period weeks, subject to two constraints:
The constraints are what make it a synthetic control rather than just a regression. Non-negative weights that sum to one mean the synthetic unit is an interpolation of real units, never an extrapolation, so you can’t get a good fit by adding three times one region and subtracting twice another. They also tend to produce sparse answers, with most donors getting zero weight, which is easier to sanity check. The full method also matches on covariates and pre-period summaries with a second layer of importance weights; the version here fits on the outcome series alone, which is also how GeoLift works unless you add covariates. After launch, the synthetic line is a genuine out-of-sample forecast of what the treated unit would have done, because nothing after the pre-period went into choosing the weights.
The widget fits the weights by accelerated projected gradient descent (take a step downhill on the squared error, then project back onto the set of non-negative weights that sum to one), which is a few lines of code and converges in milliseconds for eight donors. Donor regions tend to move together, which makes the problem badly conditioned, so whatever solver you use, check that the pre-period fit is as good as it should be before you read the result. Try turning the noise up: the pre-period fit degrades, the weights spread across more donors, and the post-period estimate wanders further from the truth. Then add the equal-weight average, which is the counterfactual a simple DiD would use. Because the donors have different trends, the equal-weight version usually drifts away from the treated region after launch and gets the lift wrong, which is the whole case for choosing weights.
Is the lift real? Placebo tests and pre-period fit
With one treated unit you can’t compute a standard error in the usual way, so Abadie and colleagues proposed placebo tests instead. Pretend each donor was the treated unit, build a synthetic control for it from the remaining donors, and look at the gap it shows after the launch date (when nothing actually happened to it). If the real treated unit’s gap is more extreme than nearly all the placebos, the effect is unlikely to be the kind of noise you’d see anyway. Comparing the ratio of post-period to pre-period error (RMSPE, root mean squared prediction error) rather than the raw gap stops a poorly fitted placebo from looking dramatic. The widget’s gray lines are those placebos.
This gives you a permutation p-value of the treated unit’s rank divided by the number of units, which has an important consequence for test design: with eight donors, the best possible p-value is one in nine, about 0.11. If your organization insists on 0.05, you need at least 19 donors before the method can even reach that threshold, which is one reason GeoLift’s guidance asks for 20 or more geographic units. The other habit I’d insist on is looking at the pre-period fit before looking at the result. If the synthetic line can’t track the treated unit before launch (a MAPE several times larger than the lift you’re hoping to detect is a bad sign), the post-period gap tells you nothing, and the honest answer is that this region can’t be tested this way.
Augmented synthetic control, and how GeoLift uses it
The weakness of the basic method is that a good pre-period fit isn’t always possible, especially when the treated unit is at the edge of the donor pool (your biggest region, or your fastest-growing one), since a weighted average can’t produce a value bigger than every input. Eli Ben-Michael, Avi Feller and Jesse Rothstein’s augmented synthetic control method (published in JASA in 2021) addresses this by fitting an outcome model, typically ridge regression, to estimate how much bias the imperfect fit leaves, then subtracting it from the synthetic control estimate. The trade-off is that the augmented version can put small negative weights on some donors, so it gives up a little of the “pure interpolation” interpretability in exchange for less bias.
GeoLift’s documentation describes its model as the augmented synthetic control method, and the package installs Ben-Michael’s augsynth R package as a dependency. In practice that means GeoLift is doing what the widget does, with the ridge correction on top, its own inference for confidence intervals, and a market selection routine that runs the method many times on historical data to find test markets that the rest of the pool can reproduce well. If you understand the widget, you understand what GeoLift is checking when it ranks market combinations, and you’re in a much better position to question its output.
CausalImpact: the Bayesian time-series cousin
CausalImpact comes from Kay Brodersen and colleagues at Google, published in the Annals of Applied Statistics in 2015, and it’s the other name you’ll see in this space. Instead of a convex combination of donors, it fits a Bayesian structural time-series model to the treated series, with a local level (and optionally trend and seasonal) component plus the control series as regressors, and forecasts the post-period from that model. The output is a counterfactual with a posterior interval for the cumulative effect, which marketers find easy to read. The original is an R package, and Google also publishes a Python version built on TensorFlow Probability (tfp-causalimpact on pip).
# pip install tfp-causalimpact
import pandas as pd
import causalimpact
df = pd.read_csv("synthetic-control-example.csv") # from the widget above
data = df[["treated", "north", "south", "east", "west", "coast", "valley", "metro", "lakes"]]
# The first column is the outcome; the rest are controls. Rows 0-39 are the pre-period.
impact = causalimpact.fit_causalimpact(data=data, pre_period=[0, 39], post_period=[40, 51])
print(causalimpact.summary(impact, output_format="summary"))The two approaches make different bets. Synthetic control assumes the treated unit is a stable mixture of the donors and gets its credibility from the transparent weights and the placebo test; CausalImpact assumes the regression relationship between the treated series and the controls stays stable, and its intervals depend on the model being right. CausalImpact is also often used with a single control series, or none at all, in which case it’s really a forecast of the treated series from its own history and the result is only as good as that forecast. Both share the same foundation as every incrementality method: the comparison units must not have been affected by the campaign. I’d run both on any important test and treat a disagreement between them as a finding, not an inconvenience.
When to use synthetic control in marketing
Synthetic control fits best when you have one or a few treated regions, a long pre-period, a decent pool of untreated regions, and an outcome you can measure by region every week or day: a TV burst in one region, a new store format in one city, a national launch in one country with others as donors, or a geo holdout of a paid channel. It’s a weaker fit when the treated unit is unlike everything else (your capital city, say), when donors are contaminated by national media or spillover, or when the pre-period contains a structural break like a pricing change. If you can randomize across many regions, a randomized geo experiment with a simpler estimator is often more powerful and easier to defend; the statistical power page has a calculator for that trade-off.
The result should then go somewhere useful. A clean synthetic control estimate of incremental sales and iROAS is exactly the kind of evidence that should calibrate your marketing mix model, and the incrementality testing guide covers how to plan a program of tests around your biggest budget questions. If you’re new to the underlying ideas, the marketing mix modeling guide and the course’s MMM learning path put geo experiments in the context of the full measurement system, and the older geo models brief covers modeling at the regional level.
