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Summary2011 - EC 7087 Econometric Theory 2011 A Summary of...

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EC 7087 Econometric Theory, 2011: A Summary of the Course 1. We began by considering the formula for the conditional expectation of a variable y , given the value of an associated variable x , under the as- sumption that these have a bivariate normal distribution. This is a linear function of x . Within the context of a multivariate normal distribution of a vector z = [ y , x ] , we found the expression for E ( y | x ), which we have used at the end of the course in developing linear filters. 2. Next, we considered, in some detail, the classical linear regression model ( y ; Xβ, σ 2 I ). In particular, we derived the formulae for the estimators of the sub vectors β 1 , β 2 within the partitioned version ( y ; X 1 β 1 + X 2 β 2 , σ 2 I ) of this model. It was straightforward to specialise these formulae to en- compass the regression model with an intercept term, and we saw how the slope parameters could be estimated by taking the data in deviation form. We also considered the consequences of omitting some of the vari-
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