Please submit your problem set answers and code via Canvas by 5pm EST on Monday April 3,

2023.

You have graduated from McCourt – congratulations!! Since you took Professor Manoli’s class, you have been hired as a senior executive data analyst. Your first assignment is to analyze data from a randomized experiment that was conducted by your company.

The randomized experiment provided free lunches to randomly selected elementary school        students with the goal of increasing school attendance. The lunches were provided for one         month and attendance was measured over this month. The treatment indicator is equal to 1 if a student was randomly assigned to receive free lunches and 0 otherwise. The attend indicator     captures whether the student attended school for the entire month or not. The randomization  was clustered at the school and grade level (within each elementary school, there are 5 elementary school grades).

Download rct_problem_set.csv and use this data for the following exercises:

1.   Start by regressing the outcome of interest, attend, on the treatment indicator. What are your preliminary results? How does accounting for the clustered randomization    design affect your preliminary results?

2.   Check for balance between the treatment and control observations based on age, gender, math scores and reading scores. Are these observables balanced across the treatment and control groups?

3.   Check if there are observations that are missing outcome data. If there are any, does this attrition appear random or not?

4.   Implement a permutation test to assess the credibility of your estimated treatment        effect. Include a plot of the distribution of estimates from your permutation samples     and mark your estimate based on the actual data in this distribution. What fraction of   estimates from your permutation test have higher estimated treatment effects that the estimate based on the actual data?

5.   Now suppose that you learn that, in addition to being clustered at the school and grade level, you learn that the randomization varied treatment intensity within treatment         clusters. The treatcluster variable captures which school-grades were assigned to             treatment and which were assigned to control. Within the treated clusters, the clusters  were randomly assigned to groups 1, 2, 3, 4 and 5, with the fraction of observations        within these clusters assigned to treatment varying from 20%, 40%, 60%, 80% and 100% respectively.

a.   To test for peer effects from the treatment, create two sets of indicator variables: (1) indicator variables for treatment observations within each treated