Kasy (2014) considers a triangular system of equations characterized by the following assumptions:
Under these assumptions, the following definitions are introduced:
It is claimed in the statement and proof of Kasy (2014),, theorem 1, that under these assumptions:
P(Y≤y|X=x,Z=z)=P(Yx≤y|X=x,Z=z)=P(Yx≤y|Zx=z,Z=z)=P(Yx≤y|Zx=z).
This assertion is wrong, the following theorem 1 states a corrected version. For theorem 1 to hold, we need to additionally impose the following regularity conditions.
The second part of assumption 5
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