Question

Answer ALL parts of this question:

(a) What is meant by heteroscedasticity? What are its effects on:

(i) OLS estimators and their variances?

(ii) The validity of t and F tests?

(b) Detail 3 different formal tests for heteroscedasticity, what are the relative

strengths and weaknesses of each?

Answer 1

solution

heteroscedasticity:

it means that the variance of the error term in a regression model does not remain constant between observation

1)the OLS estimators are still unbaised but they are no longer efficient

2 )the estimated standard errors of OLS estimators may be baised the resulting ratios are likely to be baised too. as a result the the usual confidence intervals ,hypothesis testing procedure arelikely to be questionable value.

we describe a 3-step data-analytic process for detecting and managing heteroscedasticity: (a) fitting a model based on theory and saving residuals, (b) the analysis of residuals, and (c) statistical inferences (e.g., hypothesis tests and confidence intervals) involving parameter estimates. (e.g., hypothesis tests and confidence intervals) involving parameter estimates. We also demonstrate this data-analytic process using an illustrative example. Overall, detecting violations of the homoscedasticity assumption and mitigating its biasing effects can strengthen the validity of inferences from behavioral and social science data