Testing Gollier and Weitzman’s Solution of the “Weitzman-Gollier Puzzle”

Szekeres, Szabolcs (2016): Testing Gollier and Weitzman’s Solution of the “Weitzman-Gollier Puzzle”.

Abstract

Despite the fact that the “Weitzman-Gollier Puzzle” arose in the context of risk neutrality, Gollier and Weitzman (2009) claimed to have solved the puzzle by showing that, in case of risk aversion, discounting and compounding approaches yield the same result, and that these can be expressed in ways that are morphologically similar to the conflicting formulations of the original risk neutral model. This paper replicates their analysis with a simple numerical example and shows that the equality of results obtained is due to discount and compound factors being each other’s reciprocals in the risk averse model, while the inequality of the puzzle is due to this condition not being met in the risk neutral case. Their claim to have solved the puzzle is not sustained. It is shown that the source of the puzzle is Weitzman’s incorrect specification of the present value factor and that, correcting for this, the right conclusion under his assumptions is that certainty equivalent discount rates are growing functions of time. Gollier and Weitzman (2009) also claimed that “the ‘effective’ discount rate must decline over time toward its lowest possible value.” This paper finds that when long term market yields are a growing function of time, it makes no sense to invest in projects of similar risk but lesser yield, irrespective of one’s degree of risk aversion.

• Item Type: MPRA Paper
• Language: English
• Keywords: Discounting, uncertainty, "Weitzman-Gollier Puzzle"
• Subjects: D - Microeconomics > D6 - Welfare Economics > D61 - Allocative Efficiency ; Cost-Benefit Analysis; H - Public Economics > H4 - Publicly Provided Goods > H43 - Project Evaluation ; Social Discount Rate

References

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Gollier, Christian (2009), “Expected Net Present Value, Expected Net Future Value, and the Ramsey Rule.” CESifo Working Paper No. 2643, May 2009.

Gollier, Christian and Martin L. Weitzman. 2009. “How Should the Distant Future Be Discounted When Discount Rates are Uncertain?” TSE working paper series 09-107.

Samuelson, Paul A. and William D. Nordhaus (1992), Economics, 14th Edition, New York: McGraw-Hill, Inc.

Szekeres, Szabolcs (2015a), “Governments Should Not Use Declining Discount Rates in Project Analysis.” Working Paper. MPRA Paper No. 63438. http://mpra.ub.uni-muenchen.de/63438/

Szekeres, Szabolcs (2015b) “The Mechanics of the Weitzman-Gollier Puzzles.” Working Paper. MPRA Paper No. 64286, http://mpra.ub.uni-muenchen.de/64286/

Weitzman, Martin L. 1998, “Why the far distant future should be discounted at its lowest possible rate,” Journal of Environmental Management, Volume 36.