A number of chronic poverty measures are now empirically applied to quantify the prevalence and intensity of chronic poverty, vis‐à‐vis transient experiences, using panel data. Welfare trajectories over time are assessed in order to identify the chronically poor and distinguish them from the non‐poor, or the transiently poor, and assess the extent and intensity of intertemporal poverty. We examine the implications of measurement error in the welfare outcome for some popular discontinuous chronic poverty measures, and propose corrections to these measures that seeks to minimize the consequences of measurement error. The approach is based on a novel criterion for the identification of chronic poverty that draws on fuzzy set theory. We illustrate the empirical relevance of the approach with a panel dataset from rural Ethiopia and some simulations.