C9D2 - w u U p w + + + = 3 2 1 2 2 2 2 3 2 1 1 1 - + + + +...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: w u U p w + + + = 3 2 1 2 2 2 2 3 2 1 1 1 - + + + + = w p u u U p w p u u U p 2 2 3 2 1 1 2 2 ) 1 ( + + + + =- w p u U u w w + + + + + = 3 2 1 2 1 ) ( w p u u U w + + + + =- 2 3 1 2 1 2 2 ) 1 ( p w u u U p p + + + + + = ) ( 3 2 1 2 1 p u w p + + = 2 1 2 2 2 3 1 2 1 1 - + + + + = w p u u U w 1 INSTRUMENTAL VARIABLE ESTIMATION OF SIMULTANEOUS EQUATIONS In the previous sequence it was asserted that the reduced form equations have two important roles. One is that they reveal violations of Assumption B.7, that the disturbance term be distributed independently of the explanatory variable(s). w u U p w + + + = 3 2 1 2 2 2 2 3 2 1 1 1 - + + + + = w p u u U p w p u u U p 2 2 3 2 1 1 2 2 ) 1 ( + + + + =- w p u U u w w + + + + + = 3 2 1 2 1 ) ( w p u u U w + + + + =- 2 3 1 2 1 2 2 ) 1 ( p w u u U p p + + + + + = ) ( 3 2 1 2 1 p u w p + + = 2 1 2 2 2 3 1 2 1 1 - + + + + = w p u u U w INSTRUMENTAL VARIABLE ESTIMATION OF SIMULTANEOUS EQUATIONS 2 Here the reduced form equation for w reveals that u p is a determinant of it, so we would obtain inconsistent estimates if we used OLS to fit the structural equation for p . We would have a parallel problem if we used OLS to fit the structural equation for w . w u U p w + + + = 3 2 1 2 2 2 2 3 2 1 1 1 - + + + + = w p u u U p w p u u U p 2 2 3 2 1 1 2 2 ) 1 ( + + + + =- w p u U u w w + + + + + = 3 2 1 2 1 ) ( w p u u U w + + + + =- 2 3 1 2 1 2 2 ) 1 ( p w u u U p p + + + + + = ) ( 3 2 1 2 1 p u w p + + = 2 1 2 2 2 3 1 2 1 1 - + + + + = w p u u U w INSTRUMENTAL VARIABLE ESTIMATION OF SIMULTANEOUS EQUATIONS 3 However the reduced form equation for w also provides a solution to the problem. U is a determinant of w , and by virtue of being exogenous, it is distributed independently of u p . Further, it is not an explanatory variable in its own right. 4 INSTRUMENTAL VARIABLE ESTIMATION OF SIMULTANEOUS EQUATIONS ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ---- + =--- +-- =-- + +- + +- =---- = w w U U u u U U w w U U u u w w U U w w U U u w u w U U w w U U p p U U b i i p pi i i i p pi i i i i p pi i i i i i i 2 2 2 1 2 1 IV 2 ] [ ] [ ] [ w u U p w + + + = 3 2 1 p u w p + + = 2 1 Thus it satisfies the three requirements for acting as an instrument for w and we will obtain a consistent estimate of 2 if we use the IV estimator shown. 5 INSTRUMENTAL VARIABLE ESTIMATION OF SIMULTANEOUS EQUATIONS ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ---- + =--- +-- =-- + +- + +- =----...
View Full Document

This note was uploaded on 05/26/2010 for the course ECON 301 taught by Professor Öcal during the Spring '10 term at Middle East Technical University.

Page1 / 39

C9D2 - w u U p w + + + = 3 2 1 2 2 2 2 3 2 1 1 1 - + + + +...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online