How should a government price carbon when it also cares about redistribution? I extend the dynamic Mirrlees model to two goods, one polluting, over a life cycle of privately observed skill shocks. Under weak separability, the dirty good should be taxed at the social cost of carbon (SCC) while labor and savings distortions keep their standard forms. Only non-separability makes it nonlinear, raising it above the SCC when the dirty good is a weaker labor complement. In a US calibration with energy standing in for the dirty good however, a linear carbon tax at the SCC captures 99% of the welfare gain of an optimal nonlinear carbon tax. When labor and capital distortions are fixed at the levels implied by the US tax system, this sufficiency result is overturned as the best linear tax only captures 1.5% of the welfare gain of the best nonlinear carbon tax. Here, a linear tax at an SCC of $190/tCO₂ would be welfare-reducing and the best linear tax would deflate to an equivalent of $47/tCO₂. The numerical results suggest carbon tax revenue should be recycled as a near-uniform lifetime dividend, equivalent to real-world fee-and-dividend designs.

Pollution raises climate risk by shifting the distribution of everyday climate shocks, making extreme weather events more frequent and more intense, and by increasing the probability of an irreversible climate collapse. I study the impact of the first channel on the social cost of carbon, introducing what I call stochastic externalities, in which pollution affects the distribution of random climate damages. Solving the social planner's problem, first in a three-period model and then extending the analysis to an infinite-horizon recursive model, I show that the social cost of carbon gains an additional correction term, equal to the expected marginal damages weighted by the distribution's sensitivity to pollution. This term has closed forms for standard distribution families and nests the standard social cost of carbon. In a DICE-SE model calibrated to 1980-2024 disaster losses, I show that this new channel raises the social cost of carbon by 6.2% in a conservative calibration.

This project applies the fiscal rules and monetary rules methodology to study optimal "climate rules", where decision makers are present-biased and there is a need to balance commitment and flexibility.