Optimal Carbon Taxes with Non-Constant Time Preference

The paper derives an explicit formula for the near-term carbon price in a dynamic stochastic general equilibrium climate model in which agents employ arbitrary non-constant time preference rates. The paper uses a simplified version of the model in Golosov et al. (2011), though we argue that the added assumptions are unlikely to matter for our conclusions. The formula is derived first under the assumption that the initial decision-maker has a commitment device, then solving for the unique subgame perfect equilibrium. Somewhat remarkably, the near-term carbon price is the same in both cases. We further show that the near-term carbon price remains unchanged for all potential beliefs about the time preference structure of future generations. It follows that concerns about time inconsistency can be safely ignored when applying the derived formula. The carbon price is the same as the Pigouvian tax in the equilibrium with commitment, and it is bigger than the Pigouvian tax in the equilibrium without commitment provided damages are sufficiently persistent. The formula reduces to the carbon price formula in Golosov et al. (2011) when discounting is constant, and it reduces to the carbon price formula in Gerlagh and Liski (2012) when discounting is quasi-hyperbolic.