Discussion Paper

No. 2009-10 | January 14, 2009
On the Relation between Dual-Rate Discounting and Substitutability


To justify substantial emission reductions, recent literature on cost-benefit analysis of climate change suggests discounting environment consumption with an environmental discount rate instead of a consumption discount rate that is usually used in cost-benefit analysis. The present study clarifies that whether or not this dual-rate discounting approach succeeds in justifying substantial emission reductions depends on whether or not environment and goods consumption are substitutes in the Hicks-Allen sense and in the Edgeworth-Pareto sense (substitutes in the Hicks-Allen sense implies the Hicksian goods demand to be increasing in the relative price of environmental goods, while substitutes in the Edgeworth-Pareto sense implies the marginal utility of goods consumption to be decreasing in environment consumption). Moreover, a low intratemporal elasticity of substitution between environment and goods consumption within a period contributes to a low environmental discount rate in comparison to the consumption discount rate, while a low intertemporal elasticity of substitution between composite consumption of different periods contributes to declining discount rates over time.

Paper submitted to the special issue “Discounting the Long-Run Future and Sustainable Development

JEL Classification:

D90, H43, Q28


  • Downloads: 2827


Cite As

Tomas Kögel (2009). On the Relation between Dual-Rate Discounting and Substitutability. Economics Discussion Papers, No 2009-10, Kiel Institute for the World Economy. http://www.economics-ejournal.org/economics/discussionpapers/2009-10

Comments and Questions

Richard Tol - Dual discounting
January 15, 2009 - 14:16

I had hoped that my 2004 paper would be the last on dual discounting. See http://ideas.repec.org/a/eee/ecmode/v21y2004i1p95-98.html

With dual discounting, one uses the discount rate to correct for an incomplete specification of the impact function. This is fine in principle, but would it not be better to correctly specify the ...[more]

... impact function?

Koegel argues that sometimes one does not have the knowledge to completely specify the impact function. In that case, one cannot correctly specify the effective discount rate either.

What follows is nice but irrelevant math.

Tomas Kogel - Author's response to Richard Tol
February 06, 2009 - 16:26

See attached files

Tomas Kogel - Revised paper
February 06, 2009 - 16:29

See revised paper attached

Anonymous - Comment 2
January 15, 2009 - 16:54

The paper surely looks correct and it is definitely interesting. Maybe not fully pathbreaking but one more piece of the puzzle in this area that as a whole is very important: thus the contribution of the paper is potentially significant.

Reyer Gerlagh - Comment 3
January 23, 2009 - 08:32

See attached file

Richard S.J. Tol - Correction on Gerlagh
January 23, 2009 - 12:52

Note that I do not dismiss dual discounting because it is inefficient. I dismiss dual discounting because it is a confusing and unnecessary approximation.

Tomas Kogel - Author's response to Reyer Gerlagh
February 06, 2009 - 16:31

See attached file

Anonymous - Referee Report 4
March 24, 2009 - 09:19

See attached file

Tomas Kögel - Reply to Referee Report 4
May 26, 2009 - 16:00

See attached file