Synthetic Control Method: Why average pre-treatment controls? The help file of the `synth' package in Stata states that they average the value of each matching variables across the whole pre-treatment period. Why not match on the value of X in each pre-treatment period?

Complementary to Marti's answer (+1): when we have multiple matching variables it becomes increasingly harder to find a single match/near-neighbour that is satisfactory. By "averaging" we get a synthetic match that is optimal based on our selected metric. Of course, if we could find a control instance that directly matches our treated instance perfectly in all the matching pre-treatment variables we should use it! :)
