fifth-graders in the affected schools did not achieve basic levels of learning in math and reading, respectively.<sup>19</sup> School shutdowns can increase learning gaps between low and top performers if their impacts are more detrimental for low performers.<sup>20</sup> To investigate whether the impacts of the school shutdowns are more pronounced at the lower tail of the learning distribution, we estimate quantile treatment effects using the Athey and Imbens (2006) changes-in-changes (CiC) estimator.<sup>21</sup> Figure 2 shows that the negative effects of the school’s shutdown were stronger in math, and potentially stronger in the lower tail of the test score distribution, as suggested by the inter-quantile difference between the lower and top deciles estimates in math.

Figure 2: Distributional impacts of the school shutdowns, fifth-grade (2007-2009) <!-- Start of picture text --> Extended winter break 95% CI Extended winter break 95% CI<br>2.0 2.0<br>0.0<br>0.0<br>-2.0<br>-2.0<br>-4.0<br>-4.0<br>-6.0<br>-6.0<br>-8.0<br>-10.0 -8.0<br>10 20 30 40 50 60 70 80 90 10 20 30 40 50 60 70 80 90<br>Percentiles of test score distribution Percentiles of test score distribution<br>(a) Math, TD (b) Reading, TD<br>, SAEB scale γ , SAEB scale γ<br><!-- End of picture text --> Note: The authors’ estimate is based on data from _Prova Brasil_ , Census of Education, and IBGE. 95% Confidence Interval. Math performance on a scale from 0 to 350 (SAEB scale). reading performance on a scale from 0 to 325 (SAEB scale). Figures (a) and (c) show the estimates for the TD. Figures (b) and (d) show the estimates for DiD. All regressions are weighted by fifth-grade enrollment at the school level. Standard errors clustered at the municipality level. The controls are municipal fixed effects, students’, teachers’, schools’, and principals’ characteristics, the percentage of teachers that work in a state and a locally-managed school at the same time, and the percentage of teachers that work in a state-managed school that implemented the managerial practices intervention. The triple difference specifications also include schools’ fixed effects. All triple DiD estimates exclude state-managed schools in which the state government implemented managerial practices intervention. We perform the estimates using the _cic_ (changes in changes) Stata command.

The more detrimental effects in the state-managed network might indicate that locally-managed

> 19The share of students with insufficient performance in 2007 considers all state and locally managed schools affected by the shutdowns.

> 20We also assess the effects of the school shutdowns on grade promotion, retention, and dropout. DiD estimates indicate a small increase in promotion rates and a decrease in school retention and dropout rates in locallymanaged schools. Triple difference estimates point to nil effects on those outcomes in state-managed schools (Table A.14).

> 21We use the command _cic_ in Stata to perform the estimation. This command allows the estimation of the confidence intervals with bootstrapped standard errors. However, it does not perform the _Wild Bootstrap_ to adjust the standard errors when the number of clusters is relatively small.

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