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Energy and climate policies may have significant economy-wide impacts, which are regularly assessed based on quantitative energy-environment-economy models. These tend to vary in their conclusions on the scale and direction of the likely macroeconomic impacts of a low-carbon transition. This paper traces the characteristic discrepancies in models' outcomes to their origins in different macro-economic theories, most importantly their treatment of technological innovation and finance. We comprehensively analyse the relevant branches of macro-innovation theory and group them into two classes: 'Equilibrium' and 'Non-equilibrium'. While both approaches are rigorous and self-consistent, they frequently yield opposite conclusions for the economic impacts of low-carbon policies. We show that model outcomes are mainly determined by their representations of monetary and finance dimensions, and their interactions with investment, innovation and technological change. Improving these in all modelling approaches is crucial for strengthening the evidence base for policy making and gaining a more consistent picture of the macroeconomic impacts of achieving emissions reductions objectives. The paper contributes towards the ongoing effort of enhancing the transparency and understanding of sophisticated model mechanisms applied to energy and climate policy analysis. It helps tackle the overall 'black box' critique, much-cited in policy circles and elsewhere. Key policy insights Quantitative models commissioned by policy-makers to assess the macroeconomic impacts of climate policy generate contradictory outcomes and interpretations. The source of the differences in model outcomes originates primarily from assumptions on the workings of the financial sector and the nature of money, and of how these interact with processes of low-carbon energy innovation and technological change. Representations of innovation and technological change are incomplete in energy-economy-environment models, leading to limitations in the assessment of the impacts of climate-related policies. All modelling studies should state clearly their underpinning theoretical school and their treatment of finance and innovation. A strong recommendation is given for modellers of energy-economy systems to improve their representations of money and finance. [ABSTRACT FROM AUTHOR]