As the Earth warms, carbon sinks on land and in the ocean will weaken, thereby increasing the rate of warming. Although natural mechanisms contributing to this positive climate-carbon feedback have been evaluated using Earth system models, analogous feedbacks involving human activities have not been systematically quantified. Here we conceptualize and estimate the magnitude of several economic mechanisms that generate a carbon-climate feedback, using the Kaya identity to separate a net economic feedback into components associated with population, GDP, heating and cooling, and the carbon intensity of energy production and transportation. We find that climate-driven decreases in economic activity (GDP) may in turn decrease human energy use and thus fossil fuel CO2 emissions. In a high radiative forcing scenario, such decreases in economic activity reduce fossil fuel emissions by 13% this century, lowering atmospheric CO2 by over 100 ppm in 2100. The natural carbon-climate feedback, in contrast, increases atmospheric CO2 over this period by a similar amount, and thus, the net effect including both feedbacks is nearly zero. Our work highlights the importance of improving the representation of climate-economic feedbacks in scenarios of future change. Although the effects of climate warming on the economy may offset weakening land and ocean carbon sinks, a loss of economic productivity will have high societal costs, potentially increasing wealth inequity and limiting resources available for effective adaptation.