Consider the model Y X e E e 0 E Xe 0 with both Y and X scalar Assuming 0 and 0 suppose the parameter of interest is the area under the regression curve (e g consumer surplus), which is A 2 2 Let b (b, b)0 be the least squares estimators of (,)0 so that p n b d N(0,V ) and let bV be a standard estimator for V (a) Given the above, describe an estimator of A (b) Construct an asymptotic 1 confidence interval for A

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Question: Consider the model Y X e E[e] 0 E[Xe] 0 with both Y and X scalar. Assuming 0 and

Consider the model Y Æ ®Å¯X Åe E[e] Æ 0 E[Xe] Æ 0 with both Y and X scalar. Assuming ® È 0 and ¯ Ç 0 suppose the parameter of interest is the area under the regression curve (e.g. consumer surplus), which is A Æ ¡®2/2¯.
Let bµ Æ (b®, b¯)0 be the least squares estimators of µ Æ (®,¯)0 so that p n ¡bµ¡µ
¢
!d N(0,V µ) and let bV µ
be a standard estimator for V µ.

(a) Given the above, describe an estimator of A.

(b) Construct an asymptotic 1¡´ confidence interval for A.

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