Inferring Inequality: Testing for Median-Preserving Spreads in Ordinal Data

Ramses Abul Naga, Christopher Stapenhurst, Gaston Yalonetzky

Research output: Working paperDiscussion paper

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Abstract

The median-preserving spread (MPS) ordering for ordinal variables (Allison and
Foster, 2004) has become ubiquitous in the inequality literature. However, the literature lacks an explicit frequentist method for inferring whether an ordered multinomial distribution G is more unequal than F according to the MPS criterion. We devise formal statistical tests of the hypothesis that G is not an MPS of F. Rejection of this hypothesis enables the conclusion that G is robustly more unequal than F. Using Monte Carlo simulations and novel graphical techniques, we nd that the choice between Z and Likelihood Ratio test statistics does not have a large impact on the properties of the tests, but that the method of inference does: bootstrap inference has generally better size and power properties than asymptotic inference. We illustrate the usefulness of our tests with three applications: (i) happiness inequality in the United States, (ii) self-assessed health in Europe and (iii) sanitation ladders in Pakistan.
Original languageEnglish
PublisherUniversity of Aberdeen
Pages1-39
Number of pages39
Volume21
Publication statusPublished - 29 Oct 2021

Publication series

NameDiscussion Papers in Economics and Finance
No.6
Volume21
ISSN (Electronic)0143-4543

Keywords

  • inequality measurement
  • hypothesis testing
  • median preserving spread
  • ordinal data

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