You have access to imaginary data on an energy-efficiency retrofit program in Atlanta kwh.csv (the same as the previous homework) and you are interested in whether the program reduced energy use. In your dataset is the following information: After recruiting the households for the program, you assigned them to
| Variable | Description |
| electricity | kWh of electricity used by the household in the month |
| sqft | Square feet of the home |
| retrofit | = 1 if the home received a retrofit |
| temp | The outdoor average temperature (◦ F) during the month at the home’s location |
Table 1: Variable descriptions for homework 3.
treatment and control groups. Treatment homes received the retrofits on the first of the month and control homes did not have any work done.
- Suppose that for a home i, you think the underlying relationship between electricity use and predictor variables is yi = eαδdiziγeηi where e is Euler’s number or the base of the natural logarithm, di is a binary variable equal to one if home i received the retrofit program, zi is a vector of the other control variables, ηi is unobserved error, and {α,δ,γ} are parameters to estimate.
(a) Show that ln(yi) = α + ln(δ)di + γln(zi) + ηi (b) What is the intuitive interpretation of δ?
- Show that . What is the intuitive interpretation of ?
- Show that . What is the intuitive interpretation of when zi is the size of the home in square feet?
- Estimate the log-transformed equation via ordinary least squares on the transformed parametersusing any algorithm you would like. Save the coefficient estimates and the average marginal effects estimates of zi and and . Bootstrap the 95% confidence intervals of the coefficient estimates and the marginal effects estimates using 1000 sampling replications. Display the results in a table with three columns (one for the variable name, one for the coefficient estimate, and one for the marginal effect estimate). Show the 95% confidence intervals for each estimate under each number.
- Graph the average marginal effects of outdoor temperature and square feet of the home withbands for their confidence intervals so that they are easy to interpret and compare.
