Wooldridge PPT ch15

# R 2 from regressing x on z since r 2 1 iv standard

This preview shows pages 7–14. Sign up to view the full content.

R 2 from regressing x on z Since R 2 < 1, IV standard errors are larger However, IV is consistent, while OLS is inconsistent, when Cov( x,u ) ≠ 0 The stronger the correlation between z and x , the smaller the IV standard errors

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

View Full Document
Fall 2008 under Econometrics Prof. Keunkwan Ryu 8 The Effect of Poor Instruments What if our assumption that Cov( z,u ) = 0 is false? The IV estimator will be inconsistent, too Can compare asymptotic bias in OLS and IV Prefer IV if Corr( z,u )/Corr( z,x ) < Corr( x,u ) x u x u u x Corr x z Corr u z Corr σ σ β β σ σ β β + = + = ) , ( ~ plim : OLS ) , ( ) , ( ˆ plim : IV 1 1 1 1
Fall 2008 under Econometrics Prof. Keunkwan Ryu 9 IV Estimation in the Multiple Regression Case IV estimation can be extended to the multiple regression case Call the model we are interested in estimating the structural model Our problem is that one or more of the variables are endogenous We need an instrument for each endogenous variable

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

View Full Document
Fall 2008 under Econometrics Prof. Keunkwan Ryu 10 Multiple Regression IV (cont) Write the structural model as y 1 = β 0 + β 1 y 2 + β 2 z 1 + u 1 , where y 2 is endogenous and z 1 is exogenous Let z 2 be the instrument, so Cov( z 2 ,u 1 ) = 0 and y 2 = π 0 + π 1 z 1 + π 2 z 2 + v 2 , where π 2 ≠ 0 This reduced form equation regresses the endogenous variable on all exogenous ones
Fall 2008 under Econometrics Prof. Keunkwan Ryu 11 [Eg 15.4] Using College Proxy as an IV for Education

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

View Full Document
Fall 2008 under Econometrics Prof. Keunkwan Ryu 12 Two Stage Least Squares (2SLS) It’s possible to have multiple instruments Consider our original structural model, and let y 2 = π 0 + π 1 z 1 + π 2 z 2 + π 3 z 3 + v 2 Here we’re assuming that both z 2 and z 3 are valid instruments – they do not appear in the structural model and are uncorrelated with the structural error term, u 1
Fall 2008 under Econometrics Prof. Keunkwan Ryu 13 Best Instrument Could use either z 2 or z 3 as an instrument The best instrument is a linear combination of all of the exogenous variables, y 2 * = π 0 + π 1 z 1 + π 2 z 2 +

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