The recent focus on 'pro-poor growth' led also to an intense debate on how exactly to define and to measure pro-poor growth. However, all suggested measures, irrespective whether they use the absolute or the relative definition of pro-poor growth have in common that they are based on the anonymity axiom, i.e. they do not distinguish between changes in horizontal and vertical inequality. That means usual assessments of pro-poor growth look at distributional changes over time and ignore how specific groups or households moved. Such a perspective may provide a very incomplete picture given that the common objective of most studies investigating the pro-poorness of growth is to test whether specific policy reforms where beneficial to the initially poor or not. Using panel data from Indonesia and Peru, this paper analyzes and illustrates empirically the implications of removing the anonymity axiom from measurements of pro-poor growth. It is shown that postulating anonymity, when assessing pro-poor growth can lead to misleading conclusions on how a specific policy affected the incomes of the initially poor. For both countries, the analysis shows substantial convergence to the mean, which is, at least for the case of Indonesia, robust to measurement error in the expenditure data.