Department of Econometrics and Business Statistics
ETF2100/5910 Introductory Econometrics
Assignment 3, Semester 1, 2017
Worth 10% of Final Mark
Due 4pm Wednesday 24 May 2017
(Hand in to Duangkamon’s mailbox – Building H Level 5)
Total marks 80.
Question 1
(35 marks)
A sample of 200 households was taken to investigate how far Australian households tend to
travel when they take a vacation. Measuring distance in kilometres per year (kms), consider the
following model
kmsi  1  2incomei  3agei  4kidsi  ei
where
income
age
average age of adult members of the household,
kids
number of children in household
annual household income in $000’s
(a)
Use the data in the file vacation.xlsx to estimate the model by the method of least
squares (OLS). Report the results in the standard format and discuss your results.
Construct a 95% interval estimate for the effect of one more child on kms traveled,
holding the two other variables constant.
(10 marks)
(b)
Plot the least squares residuals versus income and age. Do you observe any patterns
that suggest heteroscedasticity is present?
(5 marks)
(c)
Estimate the model by least squares (OLS) using heteroscedasticity robust standard
errors. Report the results in the standard format and discuss your results. Construct a
95% interval estimate for the effect of one more child on kms traveled, holding the two
other variables constant. How does this interval estimate compare to the one in (a)?
(10 marks)
(d)
Obtain GLS estimates assuming i2  2incomei2 . Report the results in the standard
format and discuss your results. Using GLS standard errors, construct a 95% interval
estimate for the effect of one more child on kms traveled, holding the two other variables
constant. How does this interval estimate compare to the ones in (a) and (c)?
(10 marks)
Question 2
(45 marks)
The file br2.xlsx contains data on 1080 houses sold in Baton Rouge, Louisiana during mid
2005. The data are on the selling price (price), the size of the house in square feet (sqft), the
age of the house in years (age), whether the house is on a waterfront (waterfront=1,0) and if it
is of a traditional style (traditional =1,0). Consider the following relationship
ln  pricei   1  2 ln  sqfti   3agei  4 agei2  5 waterfronti  6traditionali  ei
(2.1)
(a)
What signs would you expect for 3 and 4 ? Is it possible that at some point an old
house will become “historic” with age increasing its value? Explain why. (4 marks)
(b)
Find least squares estimates of (2.1) and save the residuals.
Report the estimated results in the usual way. Briefly comment on the estimated
coefficients in terms of expected signs and significance.
(7 marks)
(c)
Find the age at which age begins to have a positive effect on the house price. Construct
a 95% interval estimate for the effect of age on ln  price  using your estimate of the
age at which age begins to have a positive effect on price.
(8 marks)
(b)
Plot the lease squares residuals again age. Is there any visual evidence of
heteroscedasticity?
(4 marks)
(e)
Use the “White test” for heteroscedasticity with the candidate variables age2 ,
waterfront, and traditional. Define the variance function, the hypotheses to be tested
and the test statistics.
(6 marks)
(f)
Assume i2  2 exp 2agei2  3waterfronti  4traditionali . Explain how you
would modify equation (2.1) to correct for the problem of heteroscedasticity. Obtain
the GLS estimates of the model in (2.1). Report results in the usual way. (10 marks)
(g)
Construct a 95% interval estimate for the effect of age on ln  price  using the age at
which age begins to have a positive effect on price (found in part c). How does the
interval compare to the one in (c)?
(6 marks)