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Column name '1 Proof of Theorem 3 1.1 Average direct e ect on the never-takers In the following, we show that n 1=E[Y1(1;0)Y1(0;0)j=n] =E[Y1Q00(Y0)jD= 1;M= 0]. From (), we obtain the rst ingredient E[Y1(1;0)j=n] =E[Y1jD= 1;M= 0]. Furthermore, from () we have E[Q00(Y0)jD= 1;M= 0] =E[Y1(0;0)jD= 1;M(1) = 0]. Under Assumption 7 and 8, E[Y1(0;0)jD= 1;M(1) = 0]A7=E[Y1(0;0)jD= 1;=n] A8=E[Y1(0;0)j=n]:(1) 1.2 Quantile direct e ect on the never-takers We prove that n 1(q) =F1 Y1(1;0)j=n(q)F1 Y1(0;0)j=...' is too long. It should be less than 500 characters.
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