This paper exploits data from the Survey of Adult Skills (PIAAC) to shed light on the link between measured cognitive skills (proficiency), (formal) educational attainment and labour market outcomes. After presenting descriptive statistics on the degree of dispersion in the distributions of proficiency and wages, the paper shows that the cross-country correlation between these two dimensions of inequality is very low and, if anything, negative. As a next step, the paper provides estimates of the impact of both proficiency and formal education at different parts of the distribution of earnings. Formal education is found to have a larger impact on inequality, given that returns to education are in general much higher at the top than at the bottom of the distribution. The profile of returns to proficiency, by contrary, is much flatter. This is consistent with the idea that PIAAC measures rather general skills, while at the top end of the distribution the labour market rewards specialised knowledge that is necessarily acquired through tertiary and graduate education. Finally, a decomposition exercise shows that composition effects are able to explain a very limited amount of the observed cross-country differences in wage inequality. This suggests that economic institutions, by shaping the way personal characteristics are rewarded in the labour market, are the main determinants of wage inequality.