## 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.

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 language | English |
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Publisher | University of Aberdeen |

Pages | 1-39 |

Number of pages | 39 |

Volume | 21 |

Publication status | Published - 29 Oct 2021 |

### Publication series

Name | Discussion Papers in Economics and Finance |
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No. | 6 |

Volume | 21 |

ISSN (Electronic) | 0143-4543 |

### Bibliographical note

Acknowledgments: We would like to thank seminar participants at Heriot-Watt and conference participants at the 9th ECINEQ Meeting for helpful comments and suggestions.## Keywords

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