also influence the subsequent growth rate of nutritional outcomes, then the DD estimator is sensitive to the functional form assumption [Heckman 1996, Heckman, Lalonde, Smith 1998, Abadie 2005, Ravallion 2006].<sup>17,18</sup> To address this concern, we combine regression methods (and DD specifically) with a weighting approach following Hirano, Imbens and Ridder (2003), adjusting for differences in covariates by weighting on the inverse of the non-parametric estimate of the estimated propensity score _P_ ( _X_ ) 19. The key identifying assumption of conditional independence can be re-written as: Which now assumes that selection bias is time invariant conditional on those initial conditions ( _X_ ) that affect the assignment of the program to a community. Implementing this method is equivalent to estimating equation (2) using weights 1 _P_<sup>ˆ</sup> ( _X_ ) for participating villages and 1 1( − _P_<sup>ˆ</sup> ( _X_ )) for non-participant ones.

# **5. Results**

# _5.1. The effect of the program on nutritional outcomes_<sup>_20_</sup>

Table 2 presents the results based on the longitudinal sample of communities and estimates of the intention to treat effect of the program availability on a set of nutritional outcomes.<sup>21</sup> The effect of the program, defined as having Seecaline in the community (ITT) can be read as the interaction between program and follow-up survey (difference-in-difference). In the OLS specifications presented in Table 2 the coefficient on the project dummy provides the initial differences at baseline for the various outcomes of interest. Seecaline communities indeed started from lower initial conditions, with 4.6 percentage (pct) point higher incidence of stunting, and 8 points higher underweight incidence at baseline. The initial differences are also reflected in the average weight and height z-scores, with a difference of about 0.2 SD

> 17 Heckman et al (1998) show that methods that combine matching with DD help control for the heterogeneity in initial conditions and contribute to a substantial reduction in the bias.

> 18 Another potential concern invalidating the DD estimator is the possibility that the program is placed based on transitory shocks to communities. From our knowledge of the program assignment, we know that a subset of districts (about 10%) was subsequently added as a response to the occurrence of cyclones and droughts. These shocks however are observed and therefore belong to the list of observable covariates in the analysis.

> 19 Following Rosenbaum and Robin (1983), if treatment and potential outcomes are independent conditional on all covariates, they are also independent conditional on the probability of receiving the program given the covariates _P(X)_ .

> 20 The estimation of propensity score, balancing of differences in the village characteristics and the trimming is described in the appendix along with the results.

> 21 The design of the survey first stratifies the sample on provinces and urban/rural location and then randomly sampled the enumeration areas (EAs) at the village level within these strata. Within each EA households were randomly selected. Therefore all errors are clustered at the village level.

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