1. a. The following semi logarithmic coffee consumption model is
estimated over time based upon U.S. quarterly data ( = 1991Q1-
2007Q2): = 28.29 − 12.28log + 42.77log + 10.44log
Where: is pounds of coffee consumed per capita; is the price of
coffee in cents per pound; is disposable income per capita in 000’s
U.S. dollars; is the price of tea in cents per pound; and log denotes
natural logarithm. Interpret the parameter estimates.
[20 marks]
b. Changing the functional form to a double logarithmic specification, a
time trend () and quarterly dummy variables are incorporated to
allow for seasonal effects. The quarterly dummy variables are defined
as: 1=1 if quarter 1, otherwise 0; 2=1 if quarter 2, otherwise 0; and
3=1 if quarter 3, otherwise 0.
log = 1.2789 − 0.1647log + 0.5115log + 0.1483log
− 0.0089 − 0.09611 − 0.15702 − 0.00973
Interpret the estimated parameters associated with the time trend and
dummy variables.
[20 marks]
c. Explain why a fourth quarter dummy variable is not introduced into
the model.
[5 marks]
d. The estimated model in part (b) introduces differential intercept
dummies only. What implicit assumption is being made in the model
when using this particular specification?
[10 marks]
e. Rewrite the model in (b) to allow for differential own price elasticity
seasonal effects and explain in detail how you would test the null
hypothesis that the price of coffee has constant price elasticity across
quarters.
[45 marks]