For seven countries, the hypothesis of equal coefficients across the entire range of quantiles cannot be rejected when using the logistic estimator, meaning that, a rise in the share of workers with upper-secondary or post-secondary non-tertiary degrees does not alter the distribution of earnings. The regressions that make use of the logistic estimator in the second step of the UQRs can, however, not confirm this finding, potentially related to the small share of individuals with a PhD in the working population. The only exception is Portugal where this factor contributes to reduce the inequality gap uis-a-vis the United States.