Wednesday, October 8, 2014

Slow steam, fat tails and a dismal theorem

Paul Krugman's column the other day, invoking William Nordhaus's "demolition" of the forecasting model in The Limits to Growth, got me wondering about how well Nordhaus's indictment has stood up over the years. So I started poking around in the archives.

Twenty years after publication of Limits to Growth, the research team reconvened in 1992 for Beyond the Limits an  update of the earlier analysis. Nordhaus, too, followed up his earlier "blistering" review with a critique of the second version. This second review was more conciliatory, albeit still critical of the Limits to Growth and Beyond the Limits assumptions and conclusions:
While the LTG school argued that economic decline was inevitable and economists argued that the LTG argument was fallacious, the argument is ultimately an empirical matter. Put differently, critics would have gone too far had they claimed that the postulated pessimistic scenario could not hold.
Instead of simply "demolishing" the LTG model, in his second review, Nordhaus responded with his own simple model, using more a conventional generalized Cobb-Douglas production function.
Like LTG models, the general model given in the last section shows the tendency toward economic decline. In addition, there are no less than four conditions, each of which is satisfied in the LTG model, that will lead to ultimate economic stagnation, decline, or collapse...  
[However]...the entire argument can be reversed with a simple change in the specification of the model; more precisely, I will introduce technological change into the production structure and assume that the Cobb-Douglas production function accurately represents the technological possibilities for substitution.
"Ultimately, then," Nordhaus concluded his discussion of simple growth models,
...the debate about future of economic growth is an empirical one, and resolving the debate will require analysts to examine fundamental structural parameters of the economy... How large are the drags from natural resources and land? What is the quantitative relationship between technological change and the resource-land drag? How does human population growth behave as incomes rise? How much substitution is possible between labor and capital on the one hand, and scarce natural resources, land, and pollution abatement on the other? These are empirical questions that cannot be settled solely by theorizing.
One of the discussants for Nordhaus's 1992 Brookings paper was Martin Weitzman, who described it as "an outstanding paper." that "represents the economic state of the art, circa 1992, in dealing seriously and honestly with the major limits-to-growth arguments." One could almost imagine hearing the scalpel being quietly honed as Weitzman administered that subtle anesthesia.

Fast forward another two decades and it is Nordhaus's turn to comment on a paper by Weitzman, "On modeling and interpreting the economics of catastrophic climate change."
In an important paper, Weitzman (2009) has proposed what he calls a dismal theorem. He summarizes the theorem as follows: "[T]he catastrophe-insurance aspect of such a fat-tailed unlimited-exposure situation, which can never be fully learned away, can dominate the social-discounting aspect, the pure-risk aspect, and the consumption-smoothing aspect." The general idea is that under limited conditions concerning the structure of uncertainty and societal preferences, the expected loss from certain risks such as climate change is infinite and that standard economic analysis cannot be applied.
Nordhaus concluded his discussion of Weitzman's theorem on a somber and humble note:
In many cases, the data speak softly or not at all about the likelihood of extreme events. This means that reasonable people may have quite different views about the likelihood of extreme events, such as the catastrophic outcomes of climate change, and that there are no data to adjudicate such disputes. This humbling thought applies more broadly, however, as there are indeed deep uncertainties about virtually every issue that humanity faces, and the only way these uncertainties can be resolved is through continued careful consideration and analysis of all data and theories.
The word "growth" doesn't appear in Nordhaus's 16-page commentary. Pascal's wager, anyone?

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