The variance of the OLS estimatorQuestion 1Select one:a.increases as the number of observations increasesb.increases as the variance of the unobservable increasesc.decreases as the number of observations increasesd.decreases as the variance of the unobservable increasese.a) and b) are truef.b) and c) are trueg.c) and d) are true
Question
The variance of the OLS estimatorQuestion 1Select one:a.increases as the number of observations increasesb.increases as the variance of the unobservable increasesc.decreases as the number of observations increasesd.decreases as the variance of the unobservable increasese.a) and b) are truef.b) and c) are trueg.c) and d) are true
Solution
The correct answer is f) b) and c) are true.
Here's why:
b) The variance of the OLS (Ordinary Least Squares) estimator increases as the variance of the unobservable increases. This is because the OLS estimator is a function of the data, including the unobservable error term. If the variance of this error term increases, it introduces more uncertainty into the model, which in turn increases the variance of the OLS estimator.
c) The variance of the OLS estimator decreases as the number of observations increases. This is a fundamental property of estimators known as consistency. As the sample size grows, the estimator becomes more accurate, meaning its variance decreases.
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