the first year of the program, every family who is in the CAS database in that year is a potential entrant, and it is labeled as belonging to the 2002 cohort. To define subsequent cohorts, we consider every family in the CAS database in that year, but who has not enrolled in CS in any prior year. Throughout the paper we refer interchangeably to the 2-year impacts as short run effects, the 4-year impacts as medium run effects and the 6-year impacts as long run effects (the latter are referred to in the paper but only presented in the appendix). All models include standard errors clustered at the municipality level (the municipality is measured at the time of eligibility).<sup>24</sup>

**Multiple Hypotheses Testing** In the presentation of our results the stars next to each coefficient indicate whether it is statistically different from zero, after accounting for multiple hypothesis testing using the procedure in algorithms 4.1 and 4.2 of Romano and Wolf (2005). This procedure requires to test at once all the null hypotheses. We test the null hypotheses for short and medium run estimates separately, and the null hypotheses of the different subgroups are tested together, to control for splitting the population into multiple subgroups. In practice, to adjust for multiple hypothesis testing, we estimate for each bootstrap sample the models corresponding to tables 3, 4, 5, 6 and 7. This implies that we test simultaneously 111 hypothesis.<sup>25</sup>

Algorithm 4.2 is a iterative rejection/acceptance procedure, for a fixed level of significance. In the tables presented, the stars are reported for levels of 1%, 5%, and 10%, which means that we apply the algorithm three times, once for each level. The critical values are adjusted for a two sided test. We use 250 bootstrap replications to obtain the adjusted critical values and we account by potential correlation of residuals within municipality using block-bootstrap.

**Robustness Analysis** We perform a battery of checks to assess the validity of our empirical strategy. We start by performing standard balancing checks, by analyzing whether there are any differences between families just above and below the cutoffs in terms of variables measured before 2002.

We show that our results are not driven by the choice of the functional form for _f_ ( _CASimt−k − CASmt−k_ ), nor they are sensitive to trimming the sample around cutoff and the choice of the bandwidth. We have similar results regardless of whether we control for interactive municipality-year effects, or whether we include only additive municipality and year effects, which suggests that municipality specific shocks are not likely to be correlated with how CS is rolled out across years.

> 24Bai, 1997, shows that sampling error in the location of a change point can be ignored in estimation of the magnitude of the break. We rely on this result and do not adjust our standard errors for the estimation of the cutoffs, as Card et al., 2008.

> 25There are 16 outcomes used for placebo estimates for corresponding to the samples of short and medium run; 19 outcomes used for short and medium run estimates; for short and medium run we condition on the fulfilment or not the condition before 2002; and, although not presented, also allow the effects for type of area of residence (rural or urban).

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