Inference for Inverse Stochastic Dominance

This note presents an innovative inference procedure for assessing if a pair of distributions can be ordered according to inverse stochastic dominance (ISD). At order 1 and 2, ISD coincides respectively with rank and generalized Lorenz dominance and it selects the preferred distribution by all social evaluation functions that are monotonic and display inequality aversion. At orders higher than the second, ISD is associated with dominance for classes of linear rank dependent evaluation functions. This paper focuses on the class of conditional single parameters Gini social evaluation functions and illustrates that these functions can be linearly decomposed into their empirically tractable influence functions. This approach gives estimators for ISD that are asymptotically normal with a variancecovariance structure which is robust to non-simple randomization sampling schemes, a common case in many surveys used in applied distribution analysis. One of these surveys, the French Labor Force Survey, is selected to test the robustness of Equality of Opportunity evaluations in France through ISD comparisons at order 3. The ISD tests proposed in this paper are operationalized through the user-written “isdtest” Stata routine.