Correcting for endogeneity in models with bunching

SUMMARY

Note that, for any variable V, E[rC,Z̃ (X) · L(E[V |X ⇤, Z̃]|X ⇤, Z̃)]=Z̃ E[rC,Z̃ (X) · E[L(E[V |X ⇤, Z̃]|X ⇤, Z̃)|X, Z̃]]=0. The authors can write Z̃ BZ̃= E[rC,Z̃ (X) · rX ⇤,Z̃ (E["|X ⇤, Z̃])] Z̃ E[rC,Z̃ (X)2 ] E[rC,Z̃ (X) · rX ⇤,Z̃ (E[Z|X ⇤, Z̃])]0 ( Z̃ ⇡ ) E[rC,Z̃ (X)2 ] Z̃ Z̃ Because Z̃ has a constant term, E[rC,Z̃ (X)]=0. The authors can thus write ⇣ ⌘ ⇣ ⌘ Cov rC,Z̃ (X), rX ⇤,Z̃ (E["|X . . .

 



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