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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The question asks about the main issue with weak instruments in IV/2SLS estimation. 
Option 1: 'IV/2SLS estimates remain unbiased but become very inefficient.' While weak instruments do reduce precision, the core problem is not merely inefficiency; in finite samples bias and invalid inference occur, so this statement is incomplete. 
Option 2: 'IV/2SLS estimates become inconsistent even in large samples.' This would imply a fundamental failure of consistency in the population limit, which is not the standard diagnosis for weak instruments; with weak instruments the bias is severe in finite samples, but consistency can be recovered as sample size grows when instruments are valid, though the distribution is nonstandard. 
Option 3: 'IV/2SLS estimates can be severely biased in finite samples, and standard errors/inference become unreliable.' This captures the classic problem: weak correlation between instruments and endogenous regressor leads to substantial finite-sample bias and distorted standard errors, making tests unreliable. It reflects the practical concern researchers face when instruments are weak. 
Option 4: 'IV/2SLS requires using robust standard errors, which OLS does not.' This mixes a remedy with a mischaracterization; robust standard errors are a general tool for heteroskedasticity or inference concerns, not a defining feature of weak instruments, and OLS can also use robust SEs. The statement misstates the core issue and overgeneralizes the guidance. 
In summary, the third option precisely identifies the central problem associated with weak instruments: large finite-sample bias and unreliable inference due to weak instrument strength, whereas the other options describe inaccuracies or misinterpretations of the issue.

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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