Integrated assessment models (IAMs) are valuable tools that consider the interactions between socioeconomic systems and the climate system. Decision-makers and policy analysts employ IAMs to calculate the marginalized monetary cost of climate damages resulting from an incremental emission of a greenhouse gas. Used within the context of regulating anthropogenic methane emissions, this metric is called the social cost of methane (SC-CH$_4$). Because several key IAMs used for social cost estimation contain a simplified model structure that prevents the endogenous modeling of non-CO$_2$ greenhouse gases, very few estimates of the SC-CH$_4$ exist. For this reason, IAMs should be updated to better represent methane cycle dynamics that are consistent with comprehensive Earth System Models. We include feedbacks of climate change on the methane cycle to estimate the SC-CH$_4$. Our expected value for the SC-CH$_4$ is $1163/t-CH$_4$ under a constant 3.0% discount rate. This represents a 44% increase relative to a mean estimate without feedbacks on the methane cycle.
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