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The synthetic control method tries to offer a more systematic way to assign weights to the control group. It typically uses a relatively long time series of the outcome prior to the intervention and estimates weights in such a way that the control group mirrors the treatment group as closely as possible. In particular, assume we have ''J'' observations over ''T'' time periods where the relevant treatment occurs at time
<math>T_{0}</math> where <math>T_{0}<T.</math> Let <math>\alpha_{it}=Y_{it}-Y^N_{it},</math> where <math>Y^N_{it}</math> the outcome in absence of the treatment, be the treatment effect for unit '''''i''''' at time '''''t'''''. Without loss of generality, if unit 1 receives the relevant treatment, only <math>Y^N_{1t}</math>is not observed for <math>t>T_{0}</math> and we aim to estimate <math>(\alpha_{1T_{0}+1
<math>Y^N_{it}=\delta_{t}+\theta_{t}Z_{i}+\lambda_{t}\mu_{i}+\varepsilon_{it}</math> and assuming there exist some optimal weights <math>w_2, \ldots, w_J</math> such that <math>Y_{1t} = \Sigma^J_{j=2} w_{j}Y_{jt}</math> for <math>t\leqslant T_{0}</math>, the synthetic controls approach suggests using these weights to estimate the counterfactual <math>Y^N_{1t}=\Sigma^J_{j=2}w_{j}Y_{jt}</math> for <math>t>T_{0}</math>. So under some regularity conditions, such weights would provide estimators for the treatment effects of interest. In essence, the method uses the idea of matching and using the training data pre-intervention to set up the weights and hence a relevant control post-intervention.<ref>{{cite journal |last=Abadie |first=A. |authorlink=Alberto Abadie |first2=A. |last2=Diamond |first3= J. |last3=Hainmüller |year=2010 |title=Synthetic Control Methods for Comparative Case Studies: Estimating the Effect of California's Tobacco Control Program |journal=[[Journal of the American Statistical Association]] |volume=105 |issue=490 |pages=493–505 |doi=10.1198/jasa.2009.ap08746 }}</ref>
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