计量经济学导论第四版英文完整教学课件.ppt

Economics 20 - Prof. Anderson * Assumptions for Unbiasedness Still assume a model that is linear in parameters: yt = b0 + b1xt1 + . . .+ bkxtk + ut Still need to make a zero conditional mean assumption: E(ut|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 Economics 20 - Prof. Anderson * 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(ut|xt) = 0 This assumption would imply the x’s are contemporaneously exogenous Contemporaneous exogeneity will only be sufficient in large samples Economics 20 - Prof. Anderson * 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 ui is independent Our strict exogeneity assumption takes care of it in this case Economics 20 - Prof. Anderson * 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 Economics 20 - Prof. Anderson * Variances of OLS Estimators Just as in the cross-section case, we need to add an assumption of homoskedasticity in order to be able to derive variances Now we assume Var(ut|X) = Var(ut) = s2 Thus, the error variance is independent of all the x’s, and it is constant over time We also need the assumption of no serial correlation: Corr(ut,us| X)=0 for t ? s Economics 20 - Prof. Anderson * OLS Variances (continued) Under these 5 assumptions, the OLS variances in the time-series case are the same as in the cross-section case. Also, The estimator of s2 is the same OL