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Measuring the extent to which educational marital homophily differs in twoconsecutive generations is challenging when the educational distributions ofmarriageable men and women are also generation-specific. We propose a set ofcriteria that indicators may have to satisfy to be considered as suitablemeasures of homophily. One of our analytical criteria is on the robustness tothe number of educational categories. Another analytical criterion defined byus is on the association between intergenerational mobility and homophily. Athird criterion is empirical and concerns the identified historical trend ofhomophily, a comprehensive aspect of inequality, in the US between 1960 and2015. While the ordinal Liu--Lu-indicator and the cardinal indicatorconstructed with the Naszodi--Mendonca method satisfy all three criteria, mostindices commonly applied in the literature do not. Our analysis sheds light onthe link between the violation of certain criteria and the sensitivity of thehistorical trend of homophily obtained in the empirical assortative matingliterature.

Historical trend of homophily: U-shaped or not U-shaped? Or, how would  you set a criterion to decide which criterion is better to choose a  criterion?