In an effort to reduce gasoline consumption and curb carbon emissions, policymakers have proposed raising gasoline taxes. In the Journal of Applied Econometrics (Vol. 26, 2011), a group of economists investigated the effect of a gasoline tax on gas consumption. The researchers used least squares regression to model gasoline consumption in month t (Yt) as a function of the average inflation-adjusted after-tax price of gasoline in month t (Xt) and dummy variables for months.
a. Write a model for Yt as a function of Xt that proposes a linear relationship between gasoline consumption and after-tax gasoline price.
b. Add dummy variables for months to the model, part a. Use December as the base level.
c. What statistical test would you conduct to determine whether mean gasoline consumption varies from month to month? Give the null hypothesis for the test.
d. Assume that monthly data from January 2002 to March 2012 (n = 123 months) were used to fit the model, part b. In terms of the β's of the model, what is the forecast of gasoline consumption in January 2017?