What is the primary problem associated with using "weak instruments" (instruments that have low correlation with the endogenous variable) in IV/2SLS estimation?

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Question: What is the primary problem associated with using "weak instruments" (instruments that have low correlation with the endogenous variable) in IV/2SLS estimation?
Answer options:
1) IV/2SLS requires using robust standard errors, which OLS does not.
2) IV/2SLS estimates become inconsistent even in large samples.
3) IV/2SLS estimates can be severely biased in finite samples, and standard errors/inference become unreliable.
4) IV/2SLS estimates remain unbiased but become very inefficient.

Option 1: IV/2SLS requires using robust standard errors, which OLS does not.
- Why this is not accurate: The need for robust standard errors is not the core problem caused by weak instruments. Weak instruments primarily affect bias and inference, not solely the necessity of robust standard errors in the general sense. This statement misidentifies the fundamental issue, confusing inference methods with the existence of weak instruments.

Option 2: IV/2SLS estimates become inconsistent even in large samples.
- Why this is not correct: In large samples, IV/2SLS estimates are asymptotically consistent even with weak instruments, provided some conditions hold (though efficiency and finite-sample bias may be problematic). The claim of inconsistency in large samples overstates the problem and ignores the standard asymptotic results. The primary concern is more about finite-sample bias and weak-instrument-robust inference, not asymptotic inconsistency.

Option 3: IV/2SLS estimates can be severely biased in finite samples, and standard errors/inference become unreliable.
- Why this is correct: This captures the central issue with weak instruments. When instruments barely explain the endogenous variation, the 2SLS estimator can be biased and its sampling distribution can be distorted in finite samples, leading to unreliable standard errors and hypothesis tests. Hence inference is severely distorted in finite samples with weak instruments, even though consistency holds asymptotically under certain conditions.

Option 4: IV/2SLS estimates remain unbiased but become very inefficient.
- Why this is not accurate: The claim that estimates remain unbiased under weak instruments is not generally true in finite samples; bias can be substantial. Moreover, while efficiency can deteriorate due to weak instruments compared to using strong instruments, the core, well-documented problem is not simply inefficiency but finite-sample bias and unreliable inference. This statement misses the key finite-sample bias concern and overstates the benign nature of the bias.

In summary, the strongest and most precise characterization of the primary problem with weak instruments in IV/2SLS is that finite-sample bias can be substantial and inference based on standard errors can be unreliable. The other options do not accurately reflect the established issues with weak instruments.

What is the primary problem associated with using "weak instruments" (instruments that have low correlation with the endogenous variable) in IV/2SLS estimation?

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