Vulnerability Orderings for Expected Poverty Indices

Vulnerability to poverty refers to the risk of an individual or household falling below the poverty line. A partial vulnerability to poverty ordering is defined to indicate when a situation characterized by uncertainty means that people are more vulnerable to poverty than in another situation. The family of expected poverty indices used in this context contains versions under vulnerability of many well‐known poverty indices. The ordering resembles the Hardy et al. result on the Lorenz partial ordering. A separate ordering for the expected income gap ratio is also investigated. First‐order stochastic dominance is used to indicate when the expected value of the censored returns from the states increases.