Temple
University

Department
of Economics

1. The file FOODUS.TXT contains observations on
food expenditure (y_{t}) income (x_{t}) and number of persons
in each household (n_{t}) from a random sample of 38 households in a
large U.S. city. Food expenditure and income are measured in terms of thousands
of dollars. Consider the statistical model

where the e_{t}
are independent normal random errors with zero mean.

(a)
Estimate the unknown
coefficients in the model.

(b)
Plot the least squares
residuals in (a) against income and against the number of persons. Do these plots suggest heteroscedasticity?

(c)
Use a Godlfeld-Quandt
test to test for heteroscedasticity with the observations ordered by income and
then ordered by number of persons.

(d)
Find generalized
least squares estimates of the above model under the assumption that Compare the estimates with those obtained using least squares. Does correcting for heteroscedasticityappear
to have improved the precision of estimation.

(e)
At the 5% level test
that the model is heteroscedastic using White’s test.

(f)
Test the hypothesis
that the model is a heteroscedastic function of the number of people and income
using the Breusch-Pagan test.

(g)
Estimate the model
under the assumption that the error variance is given by.

Use maximum likelihood to estimate all of the model parameters.