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“Growth, inequality and poverty: looking beyond averages.”

Existing program evaluation approaches The fundamental problem of program evaluation is that we cannot observe a person i’s outcomes in two states: treatment and non-treatment. Let x be the outcome of interest and subscripts T and C denote treatment and non-treatment, respectively. In our application below this will be a malnutrition indicator for children, but x could equally be income, consumption, mortality or any other welfare indicator or any other continuous measure relevant for program evaluation. We would like to evaluate the program impact βi i iT iC β = − x x (1) but cannot because we only observe either xiT or xiC but not the corresponding counterfactual. One standard way to overcome this problem is to look at differences across people rather than the unobservable differences for i over states. When treatment assignment is randomized then the distribution of the outcome variable should be the same for the subpopulation that benefited from a program (the ‘treatment group’) and those that did not participate in the program (the ‘control group’). We can then look at single differences to compare the difference in outcomes. In the case of means, the average program impact β is equal to E Ex Ex [β ] = − [ T C ] [ ] (2) When the assignment of treatment has been non-random and treatment and control groups differ systematically the estimated E[β] is biased. Instead, we can then test for a treatment effect by comparing differences over time between treatment and control groups. If we have repeated observations over time at t and t-1 for each i the average treatment effect β can be estimated through differences-in-differences (DD) E Ex x Ex x [β ] Tt Tt , ,1− − Ct Ct , ,1 = −− −       (3) The key shortcoming of any of the existing approaches to program evaluation is that they are limited to focusing on the impact of an intervention on a particular moment of the distribution, typically the mean. To look beyond the average treatment effect we need a different evaluation method. This article proposes one such method based on stochastic dominance.