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

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.