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Report n° 7: The Stern review

Calculating the "permanent cost" of climate change

For each scenario calculation is as follows :

  • sum of utilities of consumption flows between 2005 and 2200; the following fact is taken into consideration: if Peter is richer than Pedro, one extra euro on his bank account increases his well-being less than the same euro in Pedro's pocket.
  • decreasing weight assigned to each of the utilities as time elapses; it is the pure present preference rate (pppr).
  • determination of the equivalent per capita consumption in 2000 which, allocated the same growth rate, would produce the same aggregate utility as the previous calculation.

The starting point is a damage-free base scenario (here, 1.3% on average over two centuries, the solid curve). In scenarios with damage, income growth is lower (dotted curve).
An equivalent scenario is created (dashed curve) in which income increases at the same rate as in the damage-free scenario, and which produces a utility equivalent to the scenario with damage. The difference in the 2005 income between the scenarios with and without damage provides the so-called permanent cost of climate change.

Stern justifies his choice with ethical considerations on the rights of future generations :
In 2100 they represent 0.82 times the 2005 generation as opposed to 0.13 with r=2%.
The realism and the ethical nature of such a low ppp are somewhat questionable: in a growth model, such an interest shown in the future leads to recommending high immediate savings rates, in other words sacrifices for present generations for the sake of "a non rosy future".
We should recall that in the fifties it was to avoid being tempted to impose too large immediate sacrifices for the sake of "a rosy future" (the scenery was dominated at the time by debates on the primitive accumulation patterns of real socialism) that economists (Koopmans) adopted ppps of 1% to 3%.

The debate is partly ill-founded since it can be considered that a very low ppp merely offsets the biases relating to the tools used and to the limitations of state of the art economic analysis in the field :

  • absence of the environment in the utility function: the function (U(C)) cannot clarify the choice between passing on to our descendants more consumption capacity or a better quality of the environment in order to help them. If our descendants are richer, the marginal utility of their consumption will be lower and they will attach greater relative value to the quality of the environment. Suppose, by way of illustration, that our descendants can only live in the Nordic area because the rest of the planet has become uninhabitable. We would have deprived them of access to a whole natural environment, in spite of the fact that they would have considered it of great value.
    To take into account a preference for a stable climate (or a reluctance for a Faustian wager with the planet) the environment should have been included in the utility function.

  • inadequate consideration of risk-aversion: Stern uses a Monte-Carlo draw of multiple scenarios and calculates the mathematical expectation of losses. Since the marginal utility of income decreases, a scenario which provides for an income of 100 (following severe climate damage) weighs more, in such a calculation, than a scenario with an income of 110.
    However, it does not allow comparison of a low risk 100 scenario with a scenario featuring an average of 120 but a huge uncertainty regarding climate risk. Normally, at this stage, another function should be introduced allowing a comparison of more or less risky draws (the so-called Von Neumann - Morgenstern function); its curvature z would display risk-aversion.
    It is usually higher than one (2 for Gollier 2007) which increases the current value of risks.
    But at present there is no simple way of including such a function in a model that can be calculated on a minimum empirical basis, nor is it possible to proceed as if it were sufficient to simply increase the value of h . Doing so would result in a higher discount rate which would reduce the value of future risks. We can only take note of the limitations of current economic analyses in one important aspect: clearly, the same loss of economic value will have a greater impact on the well-being of an Indian than of a European. However, Europeans are richer and are more adverse to climate risk, so that one can state from experience without the slightest cynicism that certain "accidents" affecting some hundred of them can have a greater media and political (and therefore economic) impact than if the same accidents affected twenty times as many "poor" people.

  • underestimation of the value of the risk of "disasters": the distribution of Monte-Carlo draws displays ex ante probabilities of rare but disastrous events; since such events are very rare, they count for little in the calculation of the mathematical expectation of damage.
    In this, Weitzman's criticism is relevant when explaining that standard treatment (normal law) is inappropriate for phenomena with infinite variance. Monte-Carlo draws underestimate the probability of disastrous events and the actual distribution of risk may display "thick tails" instead of dropping to zero as is the case for rare major risks used by most analysts.