Optimal Carbon Taxes with Non-Constant Time Preference

Iverson, Terrence (2012): Optimal Carbon Taxes with Non-Constant Time Preference.

Abstract

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: hyperbolic discounting; time inconsistency; optimal carbon price
• Subjects: Q - Agricultural and Natural Resource Economics ; Environmental and Ecological Economics > Q5 - Environmental Economics

References

Ainslie, G. (1991): "Derivation of `rational' economic behavior from hyperbolic discount curves," The American Economic Review, 334-340.

Azfar, O. (1999): "Rationalizing hyperbolic discounting," Journal of Economic Behavior & Organization, 38, 245-252.

Barro, R. (1999): "Ramsey meets Laibson in the neoclassical growth model," The Quarterly Journal of Economics, 114, 1125-1152.

Beltratti, A., G. Chichilnisky, and G. Heal (1998): "Preservation, uncertain future preferences and irreversibility. In: Sustainability: Dynamics and uncertainty, editors Chichilnisky, G. and Heal, G. and Vercelli, A." Kluwer Academic Publishers.

Brock, W. and L. Mirman (1972): "Optimal economic growth and uncertainty: The discounted case," Journal of Economic Theory, 4, 479-513.

Chichilnisky, G. (1996): "An axiomatic approach to sustainable development," Social choice and welfare, 13, 231-257.

Cropper, M., S. Aydede, and P. Portney (1994): "Preferences for life saving programs:How the public discounts time and age," Journal of Risk and Uncertainty, 8, 243-265.

Fishburn, P. (1970): Utility theory for decision making, Wiley.

Fishburn, P. and A. Rubinstein (1982): "Time preference," International Economic Review, 23, 677-694.

Frederick, S., G. Loewenstein, and T. O'Donoghue (2002): "Time discounting and time preference: A critical review," Journal of Economic Literature, 40, 351-401.

Fujii, T. and L. Karp (2008): "Numerical analysis of non-constant pure rate of time preference: A model of climate policy," Journal of Environmental Economics and Management,56, 83-101.

Gerlagh, R. and M. Liski (2012): "Carbon prices for the next thousand years," CESifo Working Paper Series.

Goldman, S. (1980): "Consistent plans," The Review of Economic Studies, 533-537.

Gollier, C. and R. Zeckhauser (2005): "Aggregation of heterogeneous time preferences," Journal of Political Economy, 113, 878-896.

Golosov, M., J. Hassler, P. Krusell, and A. Tsyvinski (2011): "Optimal taxes on fossil fuel in general equilibrium," NBER Working Paper 17348.

Guo, J., C. Hepburn, R. Tol, and D. Anthoff (2006): "Discounting and the social cost of carbon: a closer look at uncertainty," Environmental Science & Policy, 9, 205-216.

Harris, C. and D. Laibson (2004): "Dynamic choices of hyperbolic consumers," Econometrica, 69, 935{957.

Heal, G. (2005): "Intertemporal welfare economics and the environment," Handbook of Environmental Economics, 3, 1105-1145.

Karp, L. (2005): "Global warming and hyperbolic discounting," Journal of Public Economics, 89, 261-282.

Karp, L. (2007): "Non-constant discounting in continuous time," Journal of Economic Theory, 132, 557-568.

Karp, L. and Y. Tsur (2011): "Time perspective and climate change policy," Journal of Environmental Economics and Management, 62, 1-14.

Kirby, K. and R. Herrnstein (1995): "Preference reversals due to myopic discounting of delayed reward," Psychological Science, 6, 83-89.

Koopmans, T. (1960): "Stationary ordinal utility and impatience," Econometrica, 287-309.

Laibson, D. (1997): "Golden eggs and hyperbolic discounting," The Quarterly Journal of Economics, 112, 443-478.

Ljungqvist, L. and T. Sargent (2004): Recursive macroeconomic theory, MIT Press.

Loewenstein, G. (1987): "Anticipation and the valuation of delayed consumption," The Economic Journal, 666-684.

Mastrandrea, M. and S. Schneider (2001): "Integrated assessment of abrupt climatic changes," Climate Policy, 1, 433-449.

Nordhaus, W. (2011): "The economics of tail events with an application to climate change," Review of Environmental Economics and Policy, 5, 240-257.

Peleg, B. and M. Yaari (1973): "On the existence of a consistent course of action when tastes are changing," The Review of Economic Studies, 391-401.

Phelps, E. and R. Pollak (1968): "On second-best national saving and game-equilibrium growth," The Review of Economic Studies, 35, 185-199.

Pollak, R. (1968): "Consistent planning," The Review of Economic Studies, 35, 201-208.