ECON
Econ 399 Chapter3e

# Econ 399 Chapter3e - 3.4 The Components of the OLS...

• Notes
• 28

This preview shows pages 1–8. Sign up to view the full content.

3.4 The Components of the OLS Variances: Multicollinearity We see in (3.51) that the variance of B j hat depends on three factors: σ 2 , SST j and R j 2 : 1)The error variance, σ 2 Larger error variance = Larger OLS variance -more “noise” in the equation makes it more difficult to accurately estimate partial effects of the variables -one can reduce the error variance by adding (valid) variables to the equation

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

3.4 The Components of the OLS Variances: Multicollinearity 2) The Total Sample Variation in x j , SST j Larger x j variance – Smaller OLS j variance -increasing sample size keeps increasing SST j since 2 ) ( j ij j x x SST -This still assumes that we have a random sample
3.4 The Components of the OLS Variances: Multicollinearity 3) Linear relationships among x variables: R j 2 Larger correlation in x’s – Bigger OLS j variance -R j 2 is the most difficult component to understand - R j 2 differs from the typical R 2 in that it measures the goodness of fit of: ik k i i ij x x x x ... ˆ 2 2 1 1 0 -Where x j itself is not considered an explanatory variable

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

3.4 The Components of the OLS Variances: Multicollinearity 3) Linear relationships among x variables: R j 2 -In general, R j 2 is the total variation in x j that is explained by the other independent variables -If R j 2 =1, MLR.3 (and OLS) fails due to perfect multicollinearity (x j is a perfect linear combination of the other x’s) Note that: 2 j R as ) ˆ ( j Var -High (but not perfect) correlation between independent variables is MULTICOLLINEARITY
3.4 Multicollinearity -Note that an R j 2 close to 1 DOES NOT violate MLR. 3 -unfortunately, the “problem” of multicollinearity is hard to define -No R j 2 is accepted as being too high -A high R j 2 can always be offset by a high SST j or a low σ 2 -Ultimately, how big is B j hat relative to its standard error?

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

3.4 Multicollinearity -Ceteris Paribus, it is best to have little correlation between x j and all other independent variables -Dropping independent variables will reduce multicollinearity -But if these variables are valid, we have created bias -Multicollinearity can always be fought by collecting more data -Sometimes multicollinearity is due to over specifying independent variables:
3.4 Multicollinearity Example -In a study of heart disease, our economic model is: Heart disease=f(fast food, junk food, other)

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

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