Question

In the presence of changing variability, the estimated standard errors of the OLS estimators are inappropriate. What does this imply about using standard testing?

A. We should use F tests only
B. Standard t or F tests are not valid as they are based on these estimated standard errors.
C. Use standard t or F tests
D. We should use standard t tests only

Answer 1

Option B. Standard t or F tests are invalid when there's changing variability in the OLS estimators due to biased standard errors, leading to incorrect conclusions. The Student's t-distribution should be used with small sample sizes and when population standard deviation is unknown.

Step-by-step explanation:

In the presence of changing variability, the estimated standard errors of the OLS estimators are inappropriate. This situation implies that standard t or F tests are not valid as they rely on these estimated standard errors. When the assumption of constant variability is violated, this condition is known as heteroscedasticity, leading to OLS standard errors that are biased and can erroneously suggest statistical significance.

To address this issue, modified procedures like the White standard errors, or using the heteroscedasticity-consistent standard errors, are necessary to obtain valid hypothesis tests. In scenarios with small sample sizes, the Student's t-distribution should be used instead of the normal distribution to calculate the test statistic since it provides a better estimate of the true standard error when population standard deviation (σ) is unknown.