Question

A study analyzed the effect of military expenditures (M) and GNP (Y) on aggregate private consumption (C ). The estimated equation is:

SE = (2.73) (0.006) (0.0736)
R²=0.999 n=30
i)If heteroscedasticity is a problem, does it affect the coefficients or their variances? What is the consequence?
ii)Explain how in practice the researcher can test for heteroscedasticity using the white test.

Answer 1

If heteroscedasticity is a problem, it affects the variances of the coefficients. To test for heteroscedasticity using the White test, the researcher needs to follow a series of steps involving estimating the original regression model, obtaining the residuals, and including squared residuals as additional variables.

Step-by-step explanation:

i) If heteroscedasticity is a problem, it affects the variances of the coefficients, not the coefficients themselves. Heteroscedasticity refers to the situation where the error term in a regression model has different variances for different levels of the independent variables. The consequence of heteroscedasticity is that the standard errors and t-statistics of the coefficients may be biased, leading to incorrect hypothesis tests and confidence intervals.

ii) To test for heteroscedasticity using the White test, the researcher needs to perform the following steps:

1. Estimate the original regression model.
2. Obtain the residuals from the regression model.
3. Square the residuals and include them as additional independent variables in the regression model.
4. Estimate the new regression model.
5. Perform a test of significance on the squared residuals. If the squared residuals are significantly related to the independent variables, it indicates the presence of heteroscedasticity.