We focus on human capital measured by education outcomes (skills) and establish the relationship between human capital, R&D investments, and productivity across 12 OECD economies and 17 manufacturing and service industries. Much of the recent literature has relied on school attainment rather than on skills. By making use of data on adult cognitive skills from the Programme for the International Assessment of Adult Competences (PIAAC), we compute a measure of sectoral human capital defined as the average cognitive skills in the workforce of each country-sector combination. Our results show a strong positive relationship between those cognitive skills and the labour productivity in a country-sector combination. The part of the cross-country cross-sector variation in labour productivity that can be explained by human capital is remarkably large when it is measured by the average sectoral skills whereas it appears statistically insignificant in all our specifications when it is measured by the mere sectoral average school attainment. Our results corroborate the positive link between R&D investments and labour productivity, finding elasticities similar to those of previous studies. This evidence calls for a focus on educational outcomes (rather than on mere school attainment) and it suggests that using a measure of average sectoral cognitive skills can represent a major step forward in any kind of future sectoral growth accounting exercise.