Question: Take the model Y X0e with E[Xe] 0 and parameter of interest R0 with R k 1. Let b be the

Take the model Y Æ X0¯Åe with E[Xe] Æ 0 and parameter of interest µ Æ R0¯ with R k £1.

Let b¯ be the least squares estimator and bV b¯ its variance estimator.

(a) Write down b C, the 95% asymptotic confidence interval for µ, in terms of b¯, bV b¯, R, and z Æ 1.96 (the 97.5% quantile of N(0,1)).

(b) Show that the decision “Reject H0 if µ0 Ý b C” is an asymptotic 5% test of H0 : µ Æ µ0.

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