Social welfare functions in optimizing climate-economy models: A critical review

Social welfare functions (SWFs) are used in welfare-maximizing climate-economy models as objective functions to identify ‘optimal’ climate policies, to quantitatively compare alternative policies, and to characterize the costs of achieving alternative normative constraints. This paper reviews the main SWFs that have been applied in climate policy analyses according to the welfare maximization paradigm. We find that some of them are internally inconsistent (e.g., they lead to the summation of dimensionless and dimensional parameters) and/or produce counterintuitive rankings (e.g., they assign higher welfare to a low-growth than to a high-growth consumption path). We further find that determining the present value of future economic output or consumption paths is closely linked to the index number problem, which implies that no ‘correct’ calculation method exists. Different calculation methods applied in the past may lead to cost estimates of climate policy targets that differ by several orders of magnitude. Even the internally consistent SWFs are generally inconsistent with each other as they aggregate differently across time, population groups, and possible states of the world. We apply these theoretical findings to provide recommendations for the consistent use of SWFs in climate policy analyses according to the welfare maximization paradigm, and to review the application of SWFs in recent climate policy analyses. We find that some results of these analyses are artifacts caused by the inappropriate choice of SWFs. In summary, our findings indicate that the specification and combination of SWFs in climate policy analyses require considerably more caution than has been exercised in the past.