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Dealing with a Technological Bias: The Difference-in-Difference Approach. (2019). Arkhangelsky, Dmitry.
In: Working Papers.
RePEc:cmf:wpaper:wp2019_1903.

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  6. B Additional identification results Proof of Proposition 3.5: Define λc = Y1(0,c). Let T? be the solution of the following program: T? = arg min T:Y1(0,1)=T#Y1(0,1) E[kY1(0, 2) − T(Y1(0, 2))k2 ] (2.1) By the assumptions the solution exists and is unique (Villani [2008]). For each x ∈ supp{Y1(0,2)} define the curve (displacement interpolation) πt(x) = (1 − t)x + tT? (x). Then it is known that (constant speed) geodesic between λ1 and λ2 is given by t := (πt)#λ2 for t ∈ [0, 1] (see Santambrogio [2015]).
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