Improving education in Afghanistan may be key to bringing development and stability to that country. In 2007 , only 37 percent of primary-schoolage children in Afghanistan attended schools, and there was a large gender gap in enrollment (with girls 17 percentage points less likely to attend school). Traditional schools in Afghanistan serve children from numerous villages. Some believe that creating more village-based schools can increase enrollment and students' performance by bringing education closer to home. To assess this belief, researchers Dana Burde and Leigh Linden (2013) conducted a randomized experiment to test the effects of adding village-based schools. For a sample of 12 equal-sized village groups, they randomly selected 5 groups to receive a villagebased school. One of the original village groups could not be surveyed and was dropped, resulting in 11 village groups, with 5 treatment villages in which a new school was built and 6 control villages in which no new school was built.

This question focuses on the treatment effects for the fall 2007 semester, which began after the schools had been provided. There were 1,490 children across the treatment and control villages. Table 10.12 displays the variables in the data set schools_experiment_HW.dta.

(a) What issues are associated with studying the effects of new schools in Afghanistan that are not randomly assigned?

(b) Why is checking balance an important first step in analyzing a randomized experiment?

(c) Did randomization work? Check the balance of the following variables: age of child, girl, number of sheep family owns, length of time family lived in village, farmer, years of education for household head, number of people in household, and distance to nearest school.

(d) We noted that if errors are correlated, the standard OLS estimates for the standard error of \(\hat{\beta}\) are incorrect. In this case, we might expect errors to be correlated within village. That is, knowing the error for one child in a given village may provide some information about the error for another child in the same village. (In Stata, the way to generate standard errors that account for correlated errors within some unit is to use the, cluster (ClusterName) command at the end of Stata's regression command. In this case, the cluster is the village, as indicated with the variable Clustercode.) Redo the balance tests from part (c) with clustered standard errors. Do the coefficients change? Do the standard errors change? Do our conclusions change?

(e) Calculate the effect on fall enrollment of being in a treatment village. Use OLS, and report the fitted value of the school attendance variable for control and treatment villages, respectively.

(f) Calculate the effect on fall enrollment of being in a treatment village, controlling for age of child, sex, number of sheep family owns, length of time family lived in village, farmer, years of education for household head, number of people in household, and distance to nearest school. Use the standard errors that account for within-village correlation of errors. Is the coefficient on treatment substantially different from the bivariate OLS results? Why or why not? Briefly note any control variables that are significantly associated with attending school.

(g) Calculate the effect on fall test scores of being in a treatment village. Use the model that calculates standard errors that account for within-village correlation of errors. Interpret the results.

(h) Calculate the effect on test scores of being in a treatment village, controlling for age of child, sex, number of sheep family owns, length of time family lived in village, farmer, years of education for household head, number of people in household, and distance to nearest school. Use the standard errors that account for withinvillage correlation of errors. Is the coefficient on treatment substantially different from the bivariate OLS results? Why or why not? Briefly note any control variables that are significantly associated with higher test scores.

(i) Compare the sample size for the enrollment and test score data. What concern does this comparison raise?

(j) Assess whether attrition was associated with treatment. Use the standard errors that account for within-village correlation of errors.

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TABLE 10.12 Variables for Afghan School Experiment Variable formal_school testscores treatment age girl sheep duration_village farmer education_head number_ppl_hh Description Enrolled in school Fall test scores (normalized); tests were to be given to all children whether in school or not Assigned to village-based school = 1, otherwise = 0 Age of child Girl = 1, boy=0 Number of sheep owned Duration family has lived in village Farmer 1, otherwise = 0 Years of education of head of household Number of people living in household distance_nearest school Distance to nearest school f07_test_observed Clustercode f07_hh_id Equals 1 if test was observed for fall 2007 and 0 otherwise Village code Household ID