{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# C9D4 - TWO-STAGE LEAST SQUARES p = 1 2 w u p w = 1 2 p 3U 4...

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

TWO-STAGE LEAST SQUARES w u x U p w + + + + = 4 3 2 1 α α α α 1 In a second variation, we shall consider the model shown above. x is the rate of growth of productivity, assumed to be exogenous. w is now hypothesized to be a function of p , U , and x . For simplicity, p has reverted to being a simple function of w . p u w p + + = 2 1 β β

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

View Full Document
w u x U p w + + + + = 4 3 2 1 α α α α 2 2 2 2 4 2 3 2 1 1 1 β α β β α β α β α β - + + + + + = w p u u x U p 2 2 2 4 3 1 2 1 1 β α α α α β α α - + + + + + = w p u u x U w p u w p + + = 2 1 β β 2 The reduced form equations are now as shown. The equation for w is underidentified because there is no exogenous variable to act as an instrument for p . Both U and x are already in the equation in their own right and are therefore unavailable. TWO-STAGE LEAST SQUARES
w u x U p w + + + + = 4 3 2 1 α α α α 2 2 2 2 4 2 3 2 1 1 1 β α β β α β α β α β - + + + + + = w p u u x U p 2 2 2 4 3 1 2 1 1 β α α α α β α α - + + + + + = w p u u x U w p u w p + + = 2 1 β β 3 However, the equation for p is now overidentified. An equation is said to be overidentified if the number of available instruments exceeds the number of endogenous explanatory variables used as explanatory variables. TWO-STAGE LEAST SQUARES

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

View Full Document
w u x U p w + + + + = 4 3 2 1 α α α α 2 2 2 2 4 2 3 2 1 1 1 β α β β α β α β α β - + + + + + = w p u u x U p 2 2 2 4 3 1 2 1 1 β α α α α β α α - + + + + + = w p u u x U w p u w p + + = 2 1 β β 4 We could use U as an instrument. TWO-STAGE LEAST SQUARES
w u x U p w + + + + = 4 3 2 1 α α α α 2 2 2 2 4 2 3 2 1 1 1 β α β β α β α β α β - + + + + + = w p u u x U p 2 2 2 4 3 1 2 1 1 β α α α α β α α - + + + + + = w p u u x U w p u w p + + = 2 1 β β 5 Equally, we could use x as an instrument. Both estimators are consistent. Hence, in large samples they will yield the same estimate - the true value. But in finite samples they will be different because they have different error components.

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern