Measuring the extent to which such assortative matching diﬀers between two economies is challenging when the marginal distributions of the characteristic along which sorting takes place (e.g. education) also changes for either or both sexes. Drawing from the statistics literature we deﬁne simple conditions that any index has to satisfy to provide a measure of change in sorting that is not distorted by changes in the marginal distributions of the characteristic. While most indices used in the literature satisfy these conditions, one of them – the likelihood ratio of Eika et al. (2019) – does not. We attribute their empirical result of declining homogamy at the top of the distribution to the violation of our conditions.
Chiappori, Pierre-André; Costa-Dias, Monica; and Meghir, Costas, "The Measuring of Assortativeness in Marriage: A Comment" (2021). Cowles Foundation Discussion Papers. 2665.