1. Here we will be using the same dataset from Empirical Exercise 2; the file is included in the Assignments folder for this week. The filename is "gas_expenditure_hw3.gdt". It is already in Gretl format so you simply need to save it to your computer, open Gretl, click file > open data > user file and browse for the file. This file includes the variable that we constructed in the exercise, RealGasCap, real per capita gasoline expenditures. However, notice that I have scaled this variable to be measured in U.S. dollars to make interpretation more straightforward.

Therefore, our variable list is as follows:
Year = Year, 1953-2004
GasExp = total U.S. gasoline expenditure in billions of U.S. dollars
Pop = U.S. total population in thousands
Gasp = Price index for gasoline (in dollars)
Income = Per capita disposable income
PNC = Price index for new cars
PUC = Price index for used cars
PPT= Price index for public transportation
PD = Aggregate price index for consumer durables
PN = Aggregate price index for consumer nondurables
PS = Aggregate price index for consumer services
RealGasCap = real per capita gasoline expenditures (U.S. dollars)

a. Estimate the following log-linear model and display your results.

ln?RealGasCap_t= β₁+β₂ ln ?Income_t+ β₃ ln?Gasp_t+β4 ln?PNC_t+β₅ lnPUC_t + u_t
b. Provide an estimate of the own price elasticity of demand for gasoline. Is it statistically significant? Does it align with economic theory? Give an interpretation of your result.

c. Provide an estimate of the cross-price elasticity of demand for gasoline, both with respect to new cars and with respect to used cars. Are these estimates statistically significant? Do they align with economic theory? Give an interpretation of your result.

d. Provide an estimate of the income elasticity of demand for gasoline. Is it statistically greater than zero? In other words, is gasoline a normal good? Be sure to state your null and alternative hypotheses, your test statistic, your rejection region, and your conclusion. Give an interpretation of your result.

e. Suppose we are interested in whether the demand for gasoline is income inelastic. Construct a test of the hypothesis that the income elasticity is less than or equal to one against the alternative that it is greater than one. Be sure to state your null and alternative hypotheses, your test statistic, your rejection region, and your conclusion.