We study the potential impact of introducing performance-based funding systems (PBFS) on national research systems, using information on the number of publications and their scientific impact (citations or publications in top-ranked journals) for 31 countries over the period 1996-2016. The analysis is performed both at the aggregate level and looking separately at each of the six main scientific areas identified according to the Organisation for Economic Co-operation and Development (OECD) classification. On average, PBFS are found to increase the number of publications, though the effect is only temporary and fades after a few years. Looking at the scientific impact, PBFS are found to have a negligible effect on excellence as measured by the share of articles published in the top journals, irrespective of the type of assessment adopted. On the contrary, PBFS have some influence on average research quality, as measured by the number of citations per paper normalised with respect to the field.