− ∑ w j y j 2 ,
where wj are nonnegative weights that add up to one. How to choose the weights to best estimate the intervention effect? ∙ ADH propose choosing the weights so as to minimize the distance between y11, x1 and
∑ J1 j 2
wj yj1, xj, say. That is, functions of the
pre-treatment outcomes and the predictors of post-treatment outcomes. ∙ ADH propose permutation methods for inference, which require estimating a placebo treatment effect for each region, using the same synthetic control method as for the region that underwent the intervention.