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Answer: The estimates will converge upon the true values as the sample size, n, increases
**Explanation:** In statistics and econometrics, a consistent estimator has the property that as the sample size increases, the estimates converge in probability to the true population parameter values. This means that with larger sample sizes, the estimator becomes more accurate and approaches the true value. **Why other options are incorrect:** - **Option A**: This describes an **unbiased estimator**, not a consistent one. An unbiased estimator has an expected value equal to the true parameter value, but this doesn't guarantee convergence with increasing sample size. - **Option B**: This is another description of unbiasedness or perhaps efficiency, but consistency specifically requires convergence as sample size increases, not just being "as close as possible" regardless of sample size. - **Option D**: Consistency does not necessarily imply unbiasedness or efficiency. An estimator can be consistent but biased in finite samples (though bias must approach zero as sample size increases). Similarly, consistency doesn't guarantee efficiency (minimum variance among unbiased estimators). **Key distinction:** - **Unbiasedness**: E(θ̂) = θ (on average, equals true value) - **Consistency**: θ̂ → θ as n → ∞ (converges to true value as sample size increases) - **Efficiency**: Minimum variance among unbiased estimators Consistency is an asymptotic property, while unbiasedness is a finite-sample property.
Author: Nikitesh Somanthe
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Under multiple linear regression, if an estimator is said to be consistent, what does this imply?
A
On average, the estimated values of the coefficients will be equal to the true values
B
The coefficient estimates will be as close to their true values as possible, regardless of the sample size
C
The estimates will converge upon the true values as the sample size, n, increases
D
The OLS estimator will also be unbiased and efficient