Econ 399 Chapter2c - 2.5 Variances of the OLS Estimators-We have proven that the sampling distribution of OLS estimates(B hat and B 1 hat are

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Unformatted text preview: 2.5 Variances of the OLS Estimators-We have proven that the sampling distribution of OLS estimates (B 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. 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 σ = V 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 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 ) | ( E )] | ( [ ) | ( x) | ar(u 2 2 2 2 2 x u x u x u E x u E V =- =- = σ Gauss-Markov Assumption SLR.5 (Homoskedasticity)-if the variance is constant given x, it is always constant-Therefore: ) ( ) ( E 2 2 u Var u = = σ- σ 2 is also called the ERROR VARIANCE or DISTURBANCE VARIANCE 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 σ β β = + = x y Var x x y E Heteroskedastistic Example • Consider the following model:...
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This note was uploaded on 03/14/2009 for the course ECON ECON 399 taught by Professor Priemaza during the Spring '09 term at University of Alberta.

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Econ 399 Chapter2c - 2.5 Variances of the OLS Estimators-We have proven that the sampling distribution of OLS estimates(B hat and B 1 hat are

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