## Answered) The variable x can be written in terms of a dummy instrumental variable z as, = + + where ( | ) = . Find ( | = ). ( | = ) = [( + + ) | = ] = ( | = )...

Having solved A + B, Solve C (Answer to A & B) is attached and to the tutor who answered it *tip this time!

a. The variable x can be written in terms of a dummy instrumental variable z as, = + + where ( | ) = .
Find ( | = ).
( | = ) = [( + + ) | = ]
= ( | = ) + ( | = ) + ( | = )
= + ( | = ) + [ ( | ) = ]
= + () [ ( | = ) = ]
= Find ( | = ).
( | = ) = [( + + ) | = ]
= ( | = ) + ( | = ) + ( | = )
= + ( | = ) + [ ( | ) = ]
= + () [ ( | = ) = ]
= + = ( + ) âˆ’ = ( | = ) âˆ’ ( | = )
b. Consider the simple regression of y on z, = + + From the sample data it was obtained that, Ì…) =
âˆ‘( âˆ’ Ì…)( âˆ’ = ( âˆ’ )(
Ì… âˆ’ Ì… ) âˆ‘( âˆ’ Ì…) =
= ( âˆ’ ) The OLS estimator for the slope of the above simple regression equation of y on z is,
Ì‚ = âˆ‘=( âˆ’ Ì…)( âˆ’ Ì…)
âˆ‘=( âˆ’ Ì…) ( âˆ’ )(
Ì… âˆ’ Ì… )
= (
âˆ’ ) Ì… âˆ’ Ì… )
= (

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This question was answered on: Sep 05, 2019

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