Do international large-scale assessments influence education policy? How? Through scripts, lessons, or incentives? For some, they all produce similar outcomes. For others, different assessment data, shaped by different designs, and mediated by international organizations' (IOs) policy directives, prompt different policy decisions. For some, participation in these assessments may be linked to lower repetition rates, as per the policy scripts hypothesis inspired by world society theory. For others, assessments' comparison strategies (age vs. grade) influence repetition in participating countries, according to policy lessons or incentives hypotheses, respectively inspired by educational effectiveness research and the sociology of quantification, and particularly the notion of retroaction. Fixed-effects panel regression models of eighteen Latin American countries (1992-2017) show that participation in assessments is associated with changing repetition rates in primary and secondary, while controlling for other factors. The findings show statistically significant differences between some assessment types. The conclusions spur new questions, delineating a future agenda.