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.dta 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 cluster group and (2) indicator variables for observations within each treated cluster group. Regress the attend outcome variable on these indicators. b. Plot the coefficients on the direct treatment effects (y-axis) against the fraction treated (x-axis). How do the direct treatment effects vary with the fraction treated? c. Plot the coefficients on the indirect treatment effects (y-axis) against the fraction treated (x-axis). How do the indirect treatment effects vary with the fraction treated? Overall, what do you conclude about possible peer effects or spillovers from the treatment?
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