The synthetic control method (SCM) allows estimation of the causal effect of an intervention in settings where panel data on just a few treated units and control units are available. We show that the existing SCM as well as its extensions can be easily modified to estimate how much of the "total" effect goes through observed causal channels. The additional assumptions needed are arguably very mild in many settings. Furthermore, in an illustrative empirical application we estimate the effects of adopting the euro on labor productivity in several countries and show that a reduction in the Economic Complexity Index helped to mitigate the negative short run effects of adopting the new currency in some countries and boosted the positive effects in others.As in Abadie et al. (2015) we assume that ∀ t = 1, ..., T − 1, L * also satisfiesTo easy the notation the subscript t is dropped from the weights. Following Abadie et al.(2010), consider a generic vector of weights W = (w n+1 , ..., w J ) such that w j ≥ 0 for all j = n + 1, ..., J and w n+1 + ... + w J = 1. With these weights (and considering the factor model introduced in the text) the synthetic value of Y 01 1t is given byThe difference between the real potential outcome and the synthetic one is thenLet Y P i be the ((T − 1) × 1) vector with tth element equal to Y it , P i the ((T − 1) × 1) vector with tth element equal to it , η P the ((T − 1) × r) matrix with tth row equal to η t and λ P the ((T − 1) × F ) matrix with tth row equal to λ t . Moreover, let ϕ P (0) be the ((T − 1) × 1) vector with tth element equal to ϕ t (0) and M P i (0) the ((T − 1) × 1) vector with tth element equal to M it (0). We can now write
24Note that we have M P 1t (0) as t < T . It is easy to see that:Similar to Abadie et al. (2010) assume thatAssumption 1 is equivalent to assume no perfect-collinearity among unobserved common factors and implies that (λ P λ P ) −1 exists. We can then multiply both sides of A.2 by (λ P λ P ) −1 λ P to getSubstituting in A.1 and considering a generic post-intervention period t ≥ T , we have