Compute the price and income elasticity of gasoline demand

Question

1. Use data in gas.dta. We will conduct an analysis similar to that in the slides during the lecture, but with total gasoline demand in million gallons per month as the explained variable and disposable personal income in billion dollars per year as one of the explanatory variables. Use STATA to estimate the following OLS regression model with dummy variables:

lnQ_ij = β₀ +  β₁.lnP_ij + β₂.lnY_ij + year_j + mon_i + ε_ij.

(a) According to the OLS estimates, what is the impact of rise in gasoline retail price?

(b) Estimate the same model by 2SLS using instrumental variable P_crudeoil. Is there much difference in the estimates and estimation efficiency compared to OLS? Interpret.

2. Consider the same model with month dummies as the one in the slides, but this time use variable for time period instead of year dummies:

lnq_ij = β₀ +  β₁.lnP_ij + β₂.lnY_ij + β₃.period + mon_i + ε_ij.

Let period = t denotes the t^th month in our data e.g. period = 1 denotes the first month, January 1978, and period = 360 denotes the last month, December 2007.

(a) Estimate the price elasticity of gasoline demand by OLS. If the result is not plausible, create and add new explanatory variables such as the square, cube, etc. of period to the model until you get a result with good P-value and R-squared value. Interpret.

(b) Show the residual plot of your regression model.

(c) Compare the residual plot in part (b) with Figure 7 of the slides. Is the model with time period variables a better fit to the data? Explain.

3. Consider the model with price income interaction term:

lnq_ij = β₀ +  β₁.lnP_ij + β₂.lnY_ij + β₃.lnP_ij.lny_ij + year_j + mon_i + ε_ij.

(a) Compute the price and income elasticity of gasoline demand. Interpret the coefficient on the interaction term before fitting a regression model.

(b) Estimate the model by OLS and show the residual plot.

Attachment:- gas_data-2.rar