Question

Explain the consequence of using homoskedasticity-only standard errors when in fact the errors are heteroskedastic for each of the following:

a) The OLS estimators of  β₀and β₁
b) Hypothesis tests for β₁
c) A 95% confidence interval for β₁

Thanks

Answer 1

1

In the presence of heteroskedasticity, OLS estimators of β₀ and β₁ will remain unbiased and consistent, but these two estimators will no longer BLUE (i.e. Best Linear Unbiased Estimators), because of the reason that due to the presence of heteroskedasticity these estimates become inefficient as variance is not consistent now.

2

Because of the inconsistency of the variance co-variance matrix the estimated regression coefficient and slope become insignificant, therefore t-statistic become insignificant here Hypothesis testing of β1becomes insignificant.

3

In the presence of heteroskedasticity the estimate for the variance of the OLS estimates will become inaccurate and consequently it will affect the 95% confidence interval. But there is no certainty that confidence interval will increase or decrease. So in general, these incorrect confidence intervals can be wider or narrower with respect to the ideal 95% confidence interval.