We compare the economic and econometric assumptions of two contemporary procedures for the estimation of markups, the stochastic frontier approach (SFA) and the production function approach (PFA), and apply them to EU food retailing over the period 2010–2018. Although, the estimates of the underlying technology of the two methods are similar, our results suggest that the PFA leads to significantly larger markups, yielding approximated excess consumer expenditures 58.14%–313.33% larger than predicted by the SFA. In addition, the correlation of markups between the two methods is low. This can have implications for the consistency of policy recommendations based on the SFA and the PFA as they yield different outcomes with respect to the state of competition in a market. Last, we find a link between market concentration and markups for the PFA pointing towards adverse effects of further concentration on consumer welfare, whereas our results show no evidence for a relationship between SFA markups and market concentration. [EconLit Citations: D22, D43, L11, L13, L81, Q18]