Question6 For IV estimation, which condition ensures instrument relevance? Select one alternative: a) [math] b) [math] c) [math] d) [math] ResetMaximum marks: 0.5 Flag question undefined

Question

BlackTom AI · Accepted Answer

We begin by restating the scenario and the options to set the stage for analysis.
Question: For IV estimation, which condition ensures instrument relevance? Select one alternative:
Options:
 a) Corr(Z, Y) = 0
 b) Corr(Z, u) ≠ 0
 c) Var(Z) = 0
 d) Corr(Z, X) ≠ 0

Now, evaluate each option one by one.
Option a: Corr(Z, Y) = 0. This would imply that the instrument Z has no linear association with the dependent variable Y through the outcome equation. However, relevance in IV refers to the instrument’s ability to predict the endogenous regressor X, not directly the outcome Y. So this option misidentifies the relevance condition and is therefore incorrect as the criterion for instrument relevance.

Option b: Corr(Z, u) ≠ 0. Here, u denotes the error term in the outcome equation. If Corr(Z, u) ≠ 0, the instrument is correlated with the error term, which implies endogeneity of the instrument. This violates the exclusion restriction and undermines identification, not a feature that ensures relevance. Thus this is incorrect as a relevance condition and would cause bias, not sufficient relevance.

Option c: Var(Z) = 0. If the variance of the instrument is zero, Z would be a constant, providing no variation to explain X. Such a degenerate instrument cannot be useful for estimation, certainly not a condition for relevance. Therefore, this option is incorrect.

Option d: Corr(Z, X) ≠ 0. This is the standard definition of instrument relevance: the instrument must be correlated with the endogenous regressor X. A nonzero correlation ensures that Z can explain variation in X, allowing the IV estimator to learn about the causal effect of X on Y under the usual assumptions. Thus, this option correctly captures the relevance condition.

In summary, the incorrect options either misunderstand what relevance means (a), express a violation of IV assumptions (b), describe a degenerate instrument (c), or correctly identify the relevance condition (d). The reasoning shows why each alternative fails or succeeds as a description of instrument relevance.

Question6 For IV estimation, which condition ensures instrument relevance? Select one alternative: a) [math] b) [math] c) [math] d) [math] ResetMaximum marks: 0.5 Flag question undefined单项选择题

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