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This paper is aimed at presenting a new intergenerational mobility index that (a) combines the intergenerational elasticity and the R-squared of the intergenerational regression and (b) enables the expression of the total degree of mobility as the weighted sum of mobility with respect to both parents. As a case study, we apply our proposal to investigate the intergenerational mobility of education in several European countries and its changes across birth cohorts. The results derived from the proposed index indicate that Nordic countries display higher levels of educational mobility than Southern countries, whereas continental countries are in an intermediate position. Moreover, it appears that the degree of mobility increases over time only in those countries with low initial levels and remains stable for the most mobile countries. Finally, for most of the countries the proposed methodology can prove that the degree of educational mobility with respect to each parent tends to converge to the same level over the course of time. [ABSTRACT FROM AUTHOR]