where ��� is the actual batch allocation which takes on the values 1 for batch 3, and 0 for comparison villages. Thus, � indicates baseline ( _t_ = 0) difference between two groups. �� is a child fixed effect. �� is the time dummy for _t_ = 1 or 2, which controls for age and time effects in the model. Thus, the coefficient �� at t = 1 or 2 is the Difference-in-Differences estimator. The model is estimated on the sample of villages that ended up in batch 3 or comparison group based on actual allocation.

# **6.3. Results**

Before reporting IV analysis results, we check the strength of our IVs. Each row in Table A1 reports the first stage regression outcome of a particular group of children at different waves. For example, the first three rows report the first stage regression outcomes of all children at baseline, midline, and endline. We report the estimated coefficients and other statistical outcomes in each column. In the first stage regression, our outcome variable is the actual batch 1 indicator that is 1 for the actual batch 1 and 0 for the actual batch 3. We use two indicator variables for the original batches 2 and 3 as instrumental variables; the original batch 1 is a reference group. We also control for the child and household characteristics that are included in the outcome equation (as reported in Table 3). Across all first stage regression results, it is clear that children in the original batch 2 are less likely to be in the actual batch 1 by about 32 to 49 percentage points. Also, the chance to be in the actual batch 1 is much lower for children in the original batch 3 by about 81 to 85 percentage points. This is as expected based on the implementation process. To measure the strength of two instrumental variables, we report the _F_ -test statistics under the null hypothesis that the coefficients of two instrumental variables are 0. Also, in all first stage regression results, _F_ -test statistics for these two instrumental variables range from 135 to 191, which easily exceed the normal threshold of 10 for a strong IV (Stock, Wright, and Yogo, 2002). Thus, the first stage regression results indicate that our IVs are strong enough to run the second stage regression.

Table 6 presents the IV estimated impact on enrollment and child development outcomes from the second stage regression. There are three regression outcomes at the baseline, midline, and endline surveys. We control for children and their household characteristics as listed in Table 3. Thus, assuming that the randomization of original batches 1, 2 and 3 is valid, the estimated difference in enrollment and child development outcomes between children in batches 1 and 3 yields the unbiased estimate of the impact of the project.<sup>9</sup> Children in batch 1 were more likely to be enrolled in project playgroups than those in batch 3 at all three survey periods; 15.4, 20.6, and 24.5 percentage points higher, respectively. The durations of enrollment in the project playgroups are also longer for children in batch 1 than for those in batch 3 at all three data collection periods; 1.5, 3, and 4.1 months longer, respectively. There is no significant difference in participation rates in non-project services, kindergartens, or primary schools between children living in batch 1 and 3 villages.

> 9 As mentioned earlier, batch 1 villages had implemented the project six months before the baseline survey while batch 3 villages had implemented the project nine months before the midline survey. In Tables A2, we examine the characteristics of children in different batches at baseline. This table presents the statistical tests on children in batches 1 and 3, as well as batch 3 and the comparison group of villages. It shows there are no differences in child backgrounds, not only between children in batches 1 and 3 but also between children in batch 3 and the comparison group of villages. Tests for village level characteristics using data from the PODES 2008 are available in Hasan, Hyson and Chang (eds). 2013. From these various pieces of evidence we are confident that randomization was valid.

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