Suppose you have a model: Y = X + where the observations are iid but & is

Suppose you have a model: Y = Xβ + ε

 

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€ where the observations are iid but & is potentially correlated with X. Suppose there is an instrumental variable Z that satisfies E(e|Z) = 0 and E(X₁Z₁) 0. However, you only observe a noisy measure of Z: Z* = Z+u Analyze whether By that that uses Z* as the instrument is consistent for 3. What assumptions are required for consistency? € where the observations are iid but & is potentially correlated with X. Suppose there is an instrumental variable Z that satisfies E(e|Z) = 0 and E(X₁Z₁) 0. However, you only observe a noisy measure of Z: Z* = Z+u Analyze whether By that that uses Z* as the instrument is consistent for 3. What assumptions are required for consistency?

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