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Unformatted text preview: Fall 2008 under Econometrics Prof. Keunkwan Ryu 5 Assumptions for Unbiasedness Still assume a model that is linear in parameters: y t = x t β t + u t Still need to make a zero conditional mean assumption: E( u t  X ) = 0, t = 1, 2, …, n Note that this implies the error term in any given period is uncorrelated with the explanatory variables in all time periods Fall 2008 under Econometrics Prof. Keunkwan Ryu 6 Assumptions (continued) This zero conditional mean assumption implies the x’s are strictly exogenous An alternative assumption, more parallel to the crosssectional case, is E( u t  x t ) = 0 This assumption would imply the x’s are contemporaneously exogenous Contemporaneous exogeneity will only be sufficient in large samples Fall 2008 under Econometrics Prof. Keunkwan Ryu 7 Assumptions (continued) Still need to assume that no x is constant, and that there is no perfect collinearity Note we have skipped the assumption of a random sample The key impact of the random sample assumption is that each u i is independent Our strict exogeneity assumption takes care of it in this case Fall 2008 under Econometrics Prof. Keunkwan Ryu 8 Unbiasedness of OLS Based on these 3 assumptions, when using timeseries data, the OLS estimators are unbiased Thus, just as was the case with cross section data, under the appropriate conditions OLS is unbiased Omitted variable bias can be analyzed in the same manner as in the crosssection case Fall 2008...
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 Fall '10
 H.Bierens
 Econometrics, Regression Analysis, Time series analysis, Prof. Keunkwan Ryu

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