Cheering Up the Dismal Theorem
The Weitzman Dismal Theorem (DT) suggests agents today should be willing to pay an unbounded amount to insure against fat-tailed risks of catastrophes such as climate change. The DT has been criticized for its assumption that marginal utility (MU) goes to negative infinite faster than the rate at which the probability of catastrophe goes to zero, and for the absence of learning and optimal policy. Also, it has been pointed out that if transfers to future generations are non-infinitesimal, the insurance pricing kernel must be bounded from above, making the DT rather irrelevant in practice. Herein I present a more basic criticism of the DT having to do with its mathematical derivation. The structure of the model requires use of ln(C) as an approximate measure of the change in consumption in order to introduce an ex term and thereby put the pricing kernel into the form of a moment generating function. But ln(C) is an inaccurate approximation in the model’s own context. Use of the exact measure completely changes the pricing model such that the resulting insurance contract is plausibly small, and cannot be unbounded regardless of the distribution of the assumed climate sensitivity. .
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