While the European Union's Everything But Arms (EBA) agreement has granted unlimited preferential access to the European market for the least developed countries (LDCs) since 2001, the sugar sector has been exempted for the first years. Only from 2009 on, the LDCs were entitled to export an unlimited amount of sugar to the EU, receiving the intervention price. The expected increase in sugar imports led the EU to substantially reduce the intervention price, besides other measures. This caused a disadvantage for countries which had been granted preferential access to the European market already: the African, Caribbean, and Pacific (ACP) countries. Our paper quantifies this erosion of preferences, employing a gravity framework. In terms of methodology we are addressing two fundamental problems well known in the gravity literature. The occurrence of excess zeros in the dependent variable of such disaggregated data is tackled with the employment of the scale‐independent negative binomial quasi generalised pseudo maximum likelihood estimator. The problem of identification is addressed by modelling the policy change with the continuous preference margin instead of using dummy variables. We find that preference erosion did occur. The ACP countries were indeed negatively affected by the consequences following the introduction of the EBA.