In the file pubexp.dat there are data on public expenditure on education (EE),gross domestic product (GDP), and population (P) for 34 countries in the year 1980. It is hypothesized that per capital expenditure on education is linearly related to per capita GDP. That is,
y =b1+b2x+e
y =EE / P and x =GDP / P
It is suspected that e may be heteroskedastic with a variance related to x .(a) Why might the suspicion about the heteroskedasticity be reasonable?
(b) Estimate the above model using least squares; plot the least squares function
and the residuals. Is there any evidence of heteroskedasticity?
(c) Test for heteroskedasticity using the Goldfeld-Quant test.
(d) Use White’s formula for least squares variance estimates to find some
alternative standard errors and those obtained in part (b) to construct two
alternative 95% confidence intervals for b2 . What can you say about the
confidence interval that ignores the heteroskedasticity?