Question

In the presence of correlated observations, the OLS estimators are unbiased, but their estimated standard errors are inappropriate. Which of the following could happen as a result?

A. The model looks better than it really is with a spuriously high R2
B. The F test may suggest that the predictor variables are individually and jointly significant when this is not true
C. All of the answers are correct
D. The t test may suggest that the predictor variables are individually and jointly significant when this is not true

Answer 1

When OLS estimators are used in the presence of correlated observations, the estimated standard errors can become inappropriate, leading to a spuriously high R-squared, and incorrectly suggesting significance in both F and t tests. Thus, the model looks better than it actually is.

Step-by-step explanation:

In the presence of correlated observations, while ordinary least squares (OLS) estimators remain unbiased for the coefficients, the estimated standard errors can become inappropriate. This inappropriateness of standard errors can lead to several potential issues:

• The value of R2 can appear misleadingly high, suggesting the model explains more variance than it truly does.
• The F test may incorrectly suggest that variables are significant both individually and jointly due to underestimated standard errors.
• The t test might also provide a false indication of significance for the same reasons.

Therefore, the correct answer is C, as all of the statements listed are possible consequences of correlated observations when applying OLS regression.