Modified Ramsey discounting for climate change

The Ramsey rule for the consumption rate of discount assumes a transfer of money of a (representative) agent at one point in time to the same agent at another point in time. Climate policy (implicitly) transfers money not just over time but also between agents. I propose three alternative modifications of the Ramsey rule to account for this. Taking the Ramsey rule as given, I derive an intuitively clear but ad hoc modification. Using the assumptions underlying the Ramsey rule, I derive a consistent but more elaborate modification. If the discount rate is differentiated by victim, the consistent modified Ramsey rule is simpler and identical to regional equity weights. I apply the modified Ramsey rules to estimates of the marginal damage costs of carbon dioxide emissions. The results confirm that optimal climate policy has differentiated carbon taxes. Results also show that the standard Ramsey rule drastically underestimates the social cost of carbon.