[Solved] Economics7103 HW3

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

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.

1. Suppose that for a home i, you think the underlying relationship between electricity use and predictor variables is y_i = e^diz_ieⁱ where e is Eulers number or the base of the natural logarithm, d_i is a binary variable equal to one if home i received the retrofit program, z_i is a vector of the other control variables, _i is unobserved error, and {,,} are parameters to estimate.

(a) Show that ln(y_i) = + ln()d_i + ln(z_i) + _i (b) What is the intuitive interpretation of ?

• Show that . What is the intuitive interpretation of ?
• Show that . What is the intuitive interpretation of when z_i 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 z_i 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.