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Narrative research is in vogue in the social sciences. A current debate in philosophy of economics concerns the role of storytelling in economic modelling, and a growing research programme in policy studies investigates the influence of stories on policy outcomes. These two streams of research have yet to be connected in an investigation of how scientific models, in addition to delivering numerical results, also shape policy through the stories that are told with them. This article addresses that gap, arguing that stories produced with integrated assessment models of global climate change are particular types of policy narratives. An analytical framework for studying their composition and content is suggested. The narrative analysis of modelled stories illuminates some of the models' underpinning values and beliefs. These values and beliefs influence the normative, policy-relevant conclusions generated with the models. For illustration, the framework is applied to the analysis of two variations of the Dynamic Integrated Climate Economy model that are used to tell different stories about climate justice and climate policy. Key policy insights IAMs consist of mathematical structures and the stories told by manipulating these structures. There is an intricate but not fully deterministic relationship between IAM structures and stories. Examining both these elements contributes to our understanding of the models' role in climate governance. Appreciation of modelled stories may facilitate more effective use of IAMs in the policy process. [ABSTRACT FROM AUTHOR]