The combination of technological unemployment and oversupply of graduates has increased competition in the labour markets. Postgraduates have been noted to hold more than one job and in some cases apply for jobs meant for undergraduates. Could this imply that post graduates have created more overall unemployment than undergraduates have, in the Ugandan labour market? This is the novel of this study. This was accomplished by a statistical model that comparatively analysed the bi-causal effect of postgraduates on unemployment; versus effect of undergraduates on unemployment. As such, the study utilised Uganda's secondary data from 1991 to 2017, and employed the Vector Error Correction (VECM) model. The results of the study showed the existence of a long run impact of both the postgraduates and undergraduates on overall unemployment, but an insignificant impact in the short run. The postgraduates had a greater impact on unemployment in the long run, than the undergraduates. The study therefore reveals an affirmative answer to the aforementioned question.