Applied Econometrics for Energy Markets

1. Your firm's fundamentals analyst runs several regressions to examine annual US demand for gasoline and shows you her Stata log file on the next page.  She has several questions.

(a) In regression (1), she finds that gasoline demand responds positively to price movements over the period 1970--2013. If an omitted variable bias is the source of such a result, explain what variable (s) might be omitted and why their potential inclusion may change the direction of the relationship from positive to negative.

(b) In regression (2), she finds that gasoline demand responds negatively to price, but after seeing regression (1) she wants to run a statistical test to be sure of this. Unfortunately, the printer is not working properly, so there are no t-statistics or p-values printed.

a. How should she test that gasoline demand responds negatively to price?

b. What should be her null hypothesis?

c. What is the test-statistic she should use?

d. What is the critical value for a 1% confidence level?

e. Should she accept or reject the null? Why?

2. In "The Relationship Between Energy Intensity & Income Levels: Forecasting Long Term Energy Demand in Asian Emerging Countries" Rossana Gallia analyzed the long term trends in energy intensity for emerging countries and tested for a non-monotonic relationship between a country's energy intensity and level of income.

The model is

EI = β₁ + β₂Country + β₃ x + β₄ x² + e

where EI= annual energy use (kg of oil equivalent) per capita x= per capita gdp (in thousands of US$)

and

Based on our in-class analysis of China and the US, whose regression output is below, answer the following questions:

(a) What is the difference in the demand for energy measured in terms of energy intensity between China and the US, controlling for the level of economic development (per capita gdp)?

(b) What is the joint significance of the country indicator variable and the level of development in explaining variation in the level of energy intensity.

(c) At what level of development (per capita gdp) does the level of energy intensity begin to decline?

3. Plots of the regression residuals from separate simple regressions for the US and for China where y=log(per capita energy demand) and x= log(per capita gdp) are on the next page. These plots highlight potential problems with the simple specification. Based on your understanding of the conditions needed to ensure that the Gauss-Markov Theorem can be used as the basis for justifying the BLUE properties of the least squares estimates, explain why/why not each of the 5 assumptions may be in doubt. Why should we worry about these assumptions holding if we want unbiased point and interval estimates? Can you also comment on the optional assumption 6 that the error term is normally distributed, based on the following histograms?

Histogram of Distribution of residuals from regression of log(per capita energy demand) on log(per capita gdp) (China)

Histogram of Distribution of residuals from regression of log(per capita energy demand) on log(per capita gdp) (USA)

4. Consider the following hypothetical natural experiment. Louisiana imposes a 20% gasoline tax on the retail price of gasoline sold at its service stations. Texas imposes no such tax. The tax increase occurs in 2020. In 2019 average miles driven in Louisiana was 5,000 miles while in Texas it was 6,000 miles. In 2021 the average miles driven in Louisiana is 6,000 miles while in Texas it is 8,000 miles. Using the difference in difference estimator calculate the impact of the new tax on miles driven. What does this suggest about the implicit demand elasticity of miles driven per year with respect to the price of gasoline?