expectations - Class Notes for Econometrics Expectation of...

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Class Notes for Econometrics Expectation of Ordinary Least Squares under the Gauss Markov assumptions Jean Eid Assume that the following hold MLR1 Linearity in the parameter MLR2 Independence of the error term u and random sampling MLR3 No perfect Collinearity MLR3 Zero conditional mean Expectation of the OLS Estimates You need to go and work through the lecture notes for the derivation of OLS. I will be using some algebraic results from these notes in here but will not derive To simplify matters, let us suppose that we are estimating the following model y i = β o + β 1 x i + u i (1) Also assume that MLR2 to MLR4 above hold. From the previous lecture notes we know what the OLS estimates of β 0 and β 1 are. ˆ β 0 = y - ˆ β 1 x ˆ β 1 = N X i =1 y i ( x i - x ) N X i =1 ( x i - x ) 2 One property that we would like the estimator to have is to be unbiassed. This means that we expect the estimator to give us the correct value of the parameters. To have this property we need to check 1
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the expectation of ˆ β 0 and ˆ
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