Our study contributes to a deeper understanding of the phenomenon of research engagement and productivity of academics, particularly those from developing country contexts that are currently not well-represented in the literature. Thirty-seven Romanian public universities grouped into three categories: research-intensive, teaching and research, and teaching, were analyzed using canonical multivariate methods based on their institutional and bibliometric data for a period spanning between 2012 and 2020. We found that the most important predictor for research productivity is the university category, associated with prestige. The institutional public budget has no significant impact on faculty research productivity; the amount and the impact of research are related to who is financed and not how much money from institutional financing is received. The teaching workload has a negative influence on research results, while the PhD students, analyzed separately, proved to be a significant predictor of all the scientific output indicators when considered as an absolute number. During the study period, there was a significant shift in the publication output from quantity (number of articles) towards quality-articles in highly cited journals, and this trend accelerated in the last two years. The process of universities' classification using research output is verified and tested, proving that it is an ongoing, highly variable process with continuously shifting demands. Although our research findings are specific to the Romanian context, many of them may contribute to a better understanding of the institutional drivers of research productivity and can be replicated in other contexts.