Assessing Deprivation with an Ordinal Variable : Theory and Application to Sanitation Deprivation in Bangladesh

The challenges associated with poverty measurement with a cardinal variable have received due attention during the last four decades, but there is a dearth of literature studying how to meaningfully assess poverty with an ordinal variable. This paper first proposes a class of simple, intuitive and policy-relevant poverty measures for ordinal variables. These measures are sensitive to depth of deprivations, unlike the headcount ratio. Moreover, under appropriate restrictions, the measures ensure that priority is given to the poorest among the poor while targeting, monitoring and evaluating poverty alleviation programs. To assess the robustness of poverty comparisons to alternative choices of parameters, various stochastic dominance tests are developed (some of which are themselves novel contributions to the stochastic dominance literature). The empirical illustration documenting changes in sanitation deprivation in Bangladesh showcases the measures' ability to identify instances in which overall sanitation deprivation improved while leaving the poorest behind