Inference with v estimation o The homoskedasticity assumption in this case is E(l21-)=a2=Var() e As in the ols case, given the asymptotic variance we can estimate the standard error 2 a)=- C nop 2 selB SSTR Economics 20- Prof anderson 6
Economics 20 - Prof. Anderson 6 Inference with IV Estimation The homoskedasticity assumption in this case is E(u 2 |z) = s2 = Var(u) As in the OLS case, given the asymptotic variance, we can estimate the standard error ( ) ( ) 2 , 2 1 2 , 2 2 1 ˆ ˆ ˆ x x z x x z SST R se n Var s b s s b = =
IV versus ols estimation Standard error in iv case differs from ols only in the R2 from regressing x on z o Since R2< 1, Iv standard errors are larger However. iv is consistent. while ols is inconsistent, when Cov(x,u)#0 o The stronger the correlation between z and x. the smaller the iv standard errors Economics 20- Prof anderson 7
Economics 20 - Prof. Anderson 7 IV versus OLS estimation Standard error in IV case differs from OLS only in the R2 from regressing x on z Since R2 < 1, IV standard errors are larger However, IV is consistent, while OLS is inconsistent, when Cov(x,u) ≠ 0 The stronger the correlation between z and x, the smaller the IV standard errors