Abstract Since many new generation Earth system models (ESMs) have been suggested to overestimate future global warming, the latest report of the Intergovernmental Panel on Climate Change used the constrained range of global warming instead of that in the raw ensemble. However, it is not clear how the constraints of climate change projections potentially reduce the uncertainty of impact assessments. Here, we show that the climate-related uncertainty of the economic impact of climate change in the world can be constrained. By applying an impact emulator, we estimate the economic impacts in nine sectors based on 67 ESMs’ future climate change projections and find that the impacts in eight sectors are closely related to the recent past trend of global mean temperature, which is the metric used for the constraint of global warming projections. Observational constraints lower the upper bound of the aggregate economic impact simulated by the single emulator from 2.9% to 2.5% of the world gross domestic product (the relative reduction of variance is 31%) under the medium greenhouse gas concentration scenarios. Our results demonstrate how advances in climate science can contribute to reducing climate-related uncertainties in impact assessments, while we do not examine uncertainties of emulators and impact models.