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Evaluating social programs with endogenous program placement and selection of the treated.

The difference in interpretation between SD results on levels and changes is also relevant as we move from first to higher order stochastic dominance. The smallest welfare changes appear at the lower end of the domain regardless of the welfare level. Hence, the conventional poverty analysis attributes of second and third order dominance, namely equality preference and transfer sensitivity, no longer apply in the same way as for the analysis of levels. First order SD tests sensibly check for differences in distributions of changes between intervention and control sublocations. Second order SD tests assess the extent to which one distribution’s changes in MUAC Z-score summary statistics are concentrated at the lower end of the distribution of changes. Third order SD tests, however, are not really meaningful. The lower end of this distribution, that is, the most negative changes in nutritional status, do not necessarily represent the most malnourished sublocations and it would make little sense to give additional weight to the lower end of the distribution, which is what third order SD testing would do. We therefore suggest applying SD test on changes data only up to order s=2. Methodologically, changes in these MUAC Z-score summary statistics are analogous to changes in incomes. Hence, we can draw on the literature on economic mobility. However, in this literature the term ‘economic mobility’ is implicitly or explicitly defined in at least six different ways (Fields 2001; Fields 2007). The mobility definition that is most appropriate for analyzing MUAC Z-score changes is that of directional MUAC movement2 , as we want to capture both the magnitude and the direction of MUAC Z-score changes over time, and capture them in absolute, not relative terms, that is, irrespective of what happened to other changes in MUAC Z-scores of other locations.