Question: Suppose you have two independent samples each with n observations which satisfy the models Y1 X0 11e1 with E[X1e1] 0 and Y2

Suppose you have two independent samples each with n observations which satisfy the models Y1 Æ X0 1¯1Åe1 with E[X1e1] Æ 0 and Y2 Æ X0 2¯2Åe2 with E[X2e2] Æ 0 where ¯1 and ¯2 are both k£1.

You estimate ¯1 and ¯2 by OLS on each sample, with consistent asymptotic covariance matrix estimators bV ¯1 and bV ¯2 . Consider efficient minimum distance estimation under the restriction ¯1 Æ ¯2.

(a) Find the estimator e¯ of ¯ Æ ¯1 Æ ¯2.

(b) Find the asymptotic distribution of e¯.

(c) How would you approach the problem if the sample sizes are different, say n1 and n2?

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