Econ 399 Chapter2c - 2.5 Variances of the OLS Estimators-We...

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

View Full Document Right Arrow Icon
2.5 Variances of the OLS Estimators -We have proven that the sampling distribution of OLS estimates (B 0 hat and B 1 hat) are centered around the true value -How FAR are they distributed around the true values? -The best estimator will be most narrowly distributed around the true values -To determine the best estimator, we must calculate OLS variance or standard deviation -recall that standard deviation is the square root of the variance.
Image of page 1

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

View Full Document Right Arrow Icon
Gauss-Markov Assumption SLR.5 (Homoskedasticity) The error u has the same variance given any value of the explanatory variable. In other words, 2 x) | ar(u V
Image of page 2
Gauss-Markov Assumption SLR.5 (Homoskedasticity) -While variance can be calculated via assumptions SLR.1 to SLR.4, this is very complicated -The traditional simplifying assumption is homoskedasticity, or that the unobservable error, u, has a CONSTANT VARIANCE -Note that SLR.5 has no impact on unbiasness -SLR.5 simply simplifies variance calculations and gives OLS certain efficiency properties
Image of page 3

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

View Full Document Right Arrow Icon
Gauss-Markov Assumption SLR.5 (Homoskedasticity) -While assuming x and u are independent will also simplify matters, independence is too strong an assumption -Note that: ) | ( E 0 ) | ( E )] | ( [ ) | ( x) | ar(u 2 2 2 2 2 x u x u x u E x u E V
Image of page 4
Gauss-Markov Assumption SLR.5 (Homoskedasticity) -if the variance is constant given x, it is always constant -Therefore: ) ( ) ( E 2 2 u Var u 2 is also called the ERROR VARIANCE or DISTURBANCE VARIANCE
Image of page 5

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

View Full Document Right Arrow Icon
Gauss-Markov Assumption SLR.5 (Homoskedasticity) -SLR.4 and SLR.5 can be rewritten as conditions of y (using the fact we expect the error to be zero and y only varies due to the error) (2.56) ) | ( (2.55) ) | ( 2 1 0 x y Var x x y E
Image of page 6
Heteroskedastistic Example Consider the following model: (ie) u 065 . 0 130 i i i income weight -here it is assumed that weight is a function of income -SLR.5 requires that:
Image of page 7

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

View Full Document Right Arrow Icon
Image of page 8
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    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.

    Student Picture

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

  • Left Quote Icon

    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.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    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.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern