Positive assortative matching refers to the tendency of individuals with similar char-acteristics to form partnerships. Measuring the extent to which assortative matching differs between two economies is challenging when the marginal distributions of the characteristic along which sorting takes place (e.g., education) change for either or both sexes. We show how the use of different measures can generate different conclusions. We provide axiomatic characterization for measures such as the odds ratio, normalized trace, and likelihood ratio, and provide a structural economic interpretation of the odds ratio. We then use our approach to consider how marital sorting by education changed between the 1950s and the 1970s cohort, for which both educational attainment and returns in the labor market changed substantially.
We investigate the role of training in reducing the gender wage gap using the British Household Panel Survey. On the basis of a life-cycle model and using tax and welfare benefit reforms as a source of exogenous variation, we evaluate the role of formal training and experience in defining the evolution of wages and employment careers, conditional on education. Training is potentially important in compensating for the effects of children, especially for women who left education after completing high school, but does not fundamentally change the wage gap resulting from labor market interruptions following child birth.