Wooldridge PPT ch10

# Keunkwan ryu 5 assumptions for unbiasedness still

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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

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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 cross-sectional 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

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Fall 2008 under Econometrics Prof. Keunkwan Ryu 8 Unbiasedness of OLS Based on these 3 assumptions, when using time-series 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 cross-section case
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