Abul Naga, R. H., Stapenhurst, C., & Yalonetzky, G. (2024). Inferring inequality: Testing for median-preserving spreads in ordinal data. Econometric Reviews, 1.


The median-preserving spread (MPS) ordering for ordinal variables has become ubiquitous in the inequality literature. We devise statistical tests of the hypothesis that a distribution G is not an MPS of a distribution F. Rejecting this hypothesis enables the conclusion that G is more unequal than F according to the MPS criterion. Monte Carlo simulations and novel graphical techniques show that a simple, asymptotic Z test is sufficient for most applications. We illustrate our tests with two applications: happiness inequality in the US and self-assessed health in Europe.
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