We introduce a framework for developing efficient and interpretable climate emulators (CEs) for economic models of climate change. The paper makes two main contributions. First, we propose a general framework for constructing carbon-cycle emulators (CCEs) for macroeconomic models. The framework is implemented as a generalized linear multi-reservoir (box) model that conserves key physical quantities and can be customized for specific applications. We consider three versions of the CCE, which we evaluate within a simple representative agent economic model: (i) a three-box setting comparable to DICE-2016, (ii) a four-box extension, and (iii) a four-box version that explicitly captures land-use change. While the three-box model reproduces benchmark results well and the fourth reservoir adds little, incorporating the impact of land-use change on the carbon storage capacity of the terrestrial biosphere substantially alters atmospheric carbon stocks, temperature trajectories, and the optimal mitigation path. Second, we investigate pattern-scaling techniques that transform global-mean temperature projections from CEs into spatially heterogeneous warming fields. We show how regional baseline climates, non-uniform warming, and the associated uncertainties propagate into economic damages.