Previous quantitative assessments of likely impacts of recent reforms of the Common Agricultural Policy (in particular the Agenda 2000) differ across empirical studies. Differences are mainly due to the ways the policy instruments are taken into account (explicit modeling or implicit modeling i.e. using ad-valorem equivalents). The aim of this paper is to assess empirically the impacts of recent reforms of the Common Agricultural Policy and the consequences of the Mid-Term proposals on world cereals markets. We develop an econometric, dynamic, multi-product, partial equilibrium commodity model that focuses on arable crops. Major exporters and major importers are modeled separately, other countries being included in a "rest of the world" category. For the countries or regions explicitly integrated the model estimates supply, demand and trade. The model we develop has two important features: i) the parameters estimated in the behavioral equations (supply and demand) satisfy regularity conditions and ii) the agricultural policy instruments (in particular CAP instruments) are modeled in an explicit way. In the empirical section, attention focuses on the world cereals market. We provide a market outlook through the year 2009 for three different scenarios: baseline projections and two scenarios based on different assumptions regarding the evolution of the Common Agricultural Policy (the Mid-Term Review scenario and the decoupling scenario). Estimated effects of the mid-term scenario on EU crop prices depend on the relationship between EU and world market prices.