Question10 In an instrumental variables (IV) regression, the [math] requires that:Select one alternative: a) The instrument is uncorrelated with the structural error term b) The instrument is highly correlated with the endogenous regressor c) The instrument affects the dependent variable directly d) The instrument explains at least 10 % of the variation in the endogenous variable ResetMaximum marks: 0.5 Flag question undefined

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BlackTom AI · Accepted Answer

We begin by restating the question and options to ensure clarity about what is being evaluated in an instrumental variables (IV) regression.
Question: In an instrumental variables (IV) regression, the [math] requires that:
Options:
- a) The instrument is uncorrelated with the structural error term
- b) The instrument is highly correlated with the endogenous regressor
- c) The instrument affects the dependent variable directly
- d) The instrument explains at least 10 % of the variation in the endogenous variable

Option a: The instrument is uncorrelated with the structural error term. In IV theory, the key exogeneity (or validity) condition is that the instrument must be uncorrelated with the structural error term (the error term in the equation of interest). If this assumption fails, the instrument is endogenous and IV estimates will be biased and inconsistent. This is a fundamental requirement for a valid instrument, ensuring that the instrument affects the dependent variable only through the endogenous regressor.

Option b: The instrument is highly correlated with the endogenous regressor. While a strong correlation between the instrument and the endogenous regressor is desirable (to avoid weak instrument problems), it is not the defining requirement of IV validity. A strong instrument helps with identification and reduces variance, but if it is correlated with the error term, the instrument is invalid. Therefore, high relevance alone is not sufficient for validity.

Option c: The instrument affects the dependent variable directly. This would violate the exclusion restriction, which states that the instrument should influence the dependent variable only through the endogenous regressor (no direct effect on the outcome). If the instrument has a direct effect, the exclusion condition is breached, leading to biased IV estimates.

Option d: The instrument explains at least 10 % of the variation in the endogenous variable. The notion of a fixed threshold (e.g., 10%) is not a universal requirement for IV validity. While explained variation (or strength) matters in practice to avoid weak instruments, there is no standard cutoff that guarantees validity. The critical requirements are exogeneity (uncorrelated with the error term) and relevance (correlated with the endogenous regressor), not a specific percentage of explained variation.

In sum, Option a correctly identifies the core exogeneity condition essential for a valid instrument in IV estimation, whereas options b, c, and d describe other considerations or misstatements that do not establish the fundamental validity of an instrument. The emphasis on exogeneity in option a distinguishes it as the central requirement for IV consistency, while the other statements either describe desirable but not sufficient conditions (b), violate the exclusion restriction (c), or refer to a non-binding heuristic (d).

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