used by the ONDH for its surveys in the rural areas was specifically designed to provide a valid counterfactual. This was done by sampling communities (households and children) that had only slightly different poverty rates. In this manner, they can be expected to be otherwise similar _except_ for the fact that those with poverty rates above 30 percent were treated with the INDH program. Exploiting this counterfactual as well as the panel nature of the data, we use a variety of models to estimate a robust range of potential INDH impacts on economic outcomes and ECD.

# _4.2 Regression Models_

The first method we use is regression on the impact evaluation panel data to compare outcomes in INDH and non-INDH communities just above and below the 30 percent poverty cutoff for participation while controlling for the poverty rate. We also estimate quantile (median) regression models in case the impact on the median is different from that on the mean and to control for outliers. Several early childhood outcome variables are captured by looking at whether there is access to certain services. These are binary variables, such as whether or not a child attends pre-primary education. To study the impact of the INDH on such variables, discrete choice models (logistic regressions) are used.

# _4.3 Regression Discontinuity Design_

The impact evaluation leverages the fact that the sample was designed to undertake RDD. The basic idea of RDD is that treatment status, _Wi_ , is determined, either entirely or in part, by some ‘forcing variable,’ _Xi_ (in our case, the poverty rate), being on one side or the other of a treatment threshold (in our case, a commune level poverty rate of 30 percent from the 2004 poverty map) (Imbens & Lemieux, 2008). For lower poverty rates than the critical threshold of 30 percent, communes are not treated, while for higher poverty rates they are. The difference or jump in an outcome, _Yi_ , at the treatment threshold can be attributed to the program, assuming a ‘smooth’ (continuous) relationship between the outcome variable and the forcing variable in the absence of the program. For example, we expect that household incomes tend to be lower in rural communes where poverty rates tend to be higher. If the program did not exist, this relationship should be continuous, whatever the value of the poverty rate in 2004. Now, we know that once the 2004 poverty rate reaches 30 percent, the status of the commune changes from untreated to treated. If, on the basis of these observations, we record a ‘jump’ in the outcome variable at the level of this threshold (and if there is no other program which uses this same threshold as a selection criterion), we may interpret the size of this jump as the effect of INDH treatment.

Statistical methods must be used to estimate the relationship between the forcing variable and the different outcome variables and to determine whether or not any jump can be considered statistically significant. For this reason, in practice, the RDD method consists of performing a regression of the outcome variable on the effect of the program and on a function (whether linear or not, parametric or not) of the selection variable on which the participation threshold is identified. The regression models discussed above are essentially an RDD model with the assumption of a linear relationship between the poverty rate and outcomes. What we present as the regression discontinuity results below allow for a more flexible functional form, using local linear regressions based on kernel-weighting.<sup>15</sup> Although the RDD method is not—in econometric terms—fundamentally an experimental

> 15 Estimates are implemented using the program ‘rd’ version 2.8 in STATA 12 (Nichols, 2007).

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