Estimates are also similar if we include neighborhood fixed effects (neighborhoods are defined within municipalities). We estimate the effects separately for the sample of families living in municipalities where the size of the estimate of ψ in equation (2) is high and for those where it is low. Our results are driven by the first set of municipalities. In our main set of estimates we restrict the sample to those families who were present in the CAS system prior to the introduction of CS (in 2000 or 2001).

Finally, our results are robust to alternative methods to obtain the cutoff. In particular, we follow a split-sample approach suggested in Card et al., 2008, to obtain the thresholds.<sup>26</sup> That is, we re-estimated the _effective cutoff_ using a random sample of families in each municipality-year. The _effective cutoff_ for eligibility for each year between 2002 and 2006 and for each municipality is estimated as in equation 2. However, instead of using all families in a given year and municipality with a valid CAS, a random sample of 2/3 of families is used. For each municipality-year the cutoff is similar to that obtained using the whole sample (it is available from the authors). Then, using these thresholds we estimate models 4 and 5, but restricting the sample to those families not used to estimate the municipality-year cutoff relevant to assess the impacts of CS.

Most of these robustness checks are included in Appendix A, but we refer to the most important ones in the main text.<sup>27</sup>

# **4 Data**

Our analysis is based on administrative data: the _CAS Consolidado_ (for 2000-2006), _Ficha de Proteccion Social_ (FPS) (for 2007-2009), and the registers of participants in CS and other welfare programs.

_CAS Consolidado_ covered about one-third of the Chilean population in 2006. The FPS expanded the coverage from 2007 onward, reaching two-thirds of the population in 2009. These records include all families (and their members) applying to any publicly provided social program in Chile. We can link individuals across years through their national ID number (the RUN-Rol Unico Nacional). The data include individuals surveyed between March 1998 and December 2009, covering over 14 million individuals, corresponding to nearly 60 million observations (see more

> 26This split-sample method corrects also inference for estimated cutoffs, which may result from identifying a change point through structural breaks, since the introduction of specification search bias may lead to over reject a break of zero too often.

> 27In Appendix C we adapt the standard RD procedure to a dynamic version similar to Cellini, Ferreira and Rothstein (2010), to allow for the fact that individuals who do not receive CS in a given year may receive it in subsequent years. The gradual rollout of CS means that subsequent program entry by ineligibles can lead to underestimate program impacts, since we assume that the initial group of ineligibles does not receive any additional subsequent treatment beyond what we observe in the first year (defining the cohort). On the other end, if there is additional entry by eligible and if this is not accounted for, our estimates may be too large relatively to true program impacts. Estimates presented in table C.2) in Appendix C are not substantially different from our main results.

16