We generalize the synthetic control method to a multiple-outcome framework, where the time dimension is supplemented with the extra dimension of related outcomes. As a result, the synthetic control method can be credibly used even if only a small number of pretreatment periods are available, provided that the unit of interest can be closely approximated by the synthetic control in terms of the observed predictors and the multiple related outcomes before the treatment. Given the (close to) perfect pretreatment fit, we show that the bound on the bias of the multiple-outcome synthetic control estimator is of a smaller stochastic order than that of the single-outcome synthetic control estimator. To illustrate our method, we estimate the effects of non-pharmaceutical interventions (NPIs) on various outcomes in Sweden in the first 3 quarters of 2020. Our results suggest that if Sweden had implemented stricter NPIs like the other European countries by March, then there would have been about 70% fewer cumulative COVID-19 infection cases and deaths by July, and 20% fewer deaths from all causes in early May, whereas the impacts of the NPIs were relatively mild on the labor market and economic outcomes.

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