  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.
