in the outcome variables, notably in enrollment rates. About half of the communities in the sample present average enrollment rates for the pre-treatment period above 1. A substantial number of communities with average enrollment rate above one could arise if mean coverage is close to 1 and there is some noise in this measure because the ratio is constructed from two different data sets. However, the fact that the average rate across communities is above 1 at certain ages does suggest that there is some over-reporting of students enrolled or under-reporting of the number of children in the communities in the sample. If measurement error in these variables is classical and uncorrelated with the introduction of pre-primaries, it will only reduce precision. However, this assumption cannot be tested. Hence, we verify if we can replicate the main results by focusing on those communities that in the pre-treatment period had average enrollment below 1. Results, presented in columns (7) and (8), once again indicate no effects on enrollment rates, but point to positive and significant impacts on adequate progression rates.<sup>14</sup> Finally, in constructing the main sample for the analysis, we selected communities that did not have a neighboring community within a 0.5 kilometers radius from its center. The motivation for this restriction was to reduce the possibility of spill-over effects that may introduce biases in the estimation. For example, if children in comparison communities attended the newly constructed pre-primary in a beneficiary community this would induce a downward bias in our estimates. Similarly, if the opening of a pre-primary in a community induces changes in the composition of children attending the primary school in that community (because children in neighboring communities start attending there), this will also bias our estimates.

We consider that setting the described minimum-distance restriction could be sufficient to reduce the possibility of spill-over effects in this context based on the following reasons. To start with, it has been recognized that parents usually desire to have their young children attending educational centers located close from home (e.g. see Paes de Barros et al., 2011 for evidence on Brazil). Consistent with this view, 97% of children ages 4 to 6 years old attending a pre-primary in rural Guatemala walk 30 minutes or less to attend an educational center (Living Standards Measurement Survey, 2006). Moreover, the reluctance of parents to have their children attending pre-primaries outside their communities may be heightened in this context due to cultural factors related to a strong

> 14One additional concern is the possibility that a community that does not have a public pre-primary might have a private one (this could attenuate our estimates). As mentioned above, we have data on private pre-primaries and their exact location for 2005 but not for prior years. Consequently, we cannot assess whether the expansion in public pre-primaries affected the supply of private pre-primaries in our sample. Still, we believe that it is unlikely that private supply will play a relevant role in this context because of the overall little demand for private pre-primaries in rural Guatemala. This is well exemplified in the fact that only 1.2% of communities in the comparison group and 0.8% of treatment communities had a private pre-primary in 2005.

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