As Bad as it Gets: How Climate Damage Functions Affect Growth and the Social Cost of Carbon

Environ Resource Econ https://doi.org/10.1007/s10640-018-0219-y As Bad as it Gets: How Climate Damage Functions Affect Growth and the Social Cost of Carbon Lucas Bretschger1 · Aimilia Pattakou1 Accepted: 9 January 2018 © The Author(s) 2018. This article is an open access publication Abstract The paper analyzes the effects of varying climate impacts on the social cost of carbon and economic growth. We use polynomial damage functions in a model of an endogenously growing two-sector economy. The framework includes nonrenewable natural resources which cause greenhouse gas emissions; pollution stock harms capital and reduces economic growth. We find a big effect of the selected damage function on the social cost of carbon and a significant impact on the growth rate. In our calibration a quartic damage function raises the social cost of carbon by more than a factor of ten compared to the linear function. In the social optimum the growth rate remains positive even when the damage function is highly convex. We test the robustness of the results by adding pollution decay, lowering the elasticity of intertemporal substitution, and addressing uncertainty, which does not alter our results. We find that high marginal climate damages require stringent climate policies but do not preclude positive economic growth despite convexity, provided that policies are designed in an efficient manner. Keywords Climate damages · Social cost of carbon · Endogenous growth · Polynomial functions JEL Classification Q43 · O47 · Q56 · O41 1 Introduction 1.1 Climate Impacts There is broad agreement that climate change has widespread effects on the economy and the natural environment. It causes economic damages which worsen with increasing temper- The original article displays figure errors caused by miscommunication during the proofing stage. The original article has been corrected. B 1 Lucas Bretschger Eidgenossische Technische Hochschule Zurich, Zurich, Switzerland 123 L. Bretschger, A. Pattakou atures.1 For a thorough assessment of the consequences and the formulation of appropriate climate policies the determination and the use of an appropriate damage function is indispensable: it lies “at the heart” of the economic analysis of climate change (Farmer et al. 2015, p. 332). Such a function specifies how economic damages change as a function of greenhouse gas concentration in the atmosphere. The present paper thoroughly explores the impact of damage modeling in a theoretical setup of an economy with climate change and endogenous growth. The economic impacts from climate change are difficult to be estimated on a global level (IPCC 2014b). So far, there is no agreement on the form and the parametrization of a general climate damage function. Nordhaus and Boyer (2000, p. 23) state that “estimating the damages from greenhouse warming has proven extremely elusive.” According to Weitzman the literature offers “little guidance on why one specification or another” of a damage function has been selected (Weitzman 2010a). It is thus admitted that a strong empirical basis for the damage functions used in the best-known models is lacking. What is more, climate damages have implausibly small effects on economic growth in most integrated assessment models even under extreme temperature scenarios (Stern 2013; Revesz et al. 2014). The big challenge for formulating a comprehensive climate damage function is to properly aggregate various highly heterogeneous effects. Climate impacts on different regions and ecosystems are provided in IPCC (2014b) and Roson and Sartori (2016).2 Yet, for a global analysis of climate damages, the available data are not sufficiently complete. Bottomup studies may be used to inspire a general formula, but by their nature they are limited in scope. It thus remains unclear which functional form for the damage function is suitable (Moore and Diaz 2015) and where the limitations are to capture “everything by a simple function” (Farmer et al. 2015, p. 332). Damage functions are one of various elements of integrated assessment models which have recently been criticized. Farmer et al. (2015, p. 329) conclude that also the issues of risks, heterogeneity, and technical change are “inadequately addressed” by climate modelers. In all these areas, model specifications strongly affect the results and associated policy recommendations (Revesz et al. 2014). While recent contributions have addressed the additional issues under critique,3 the functional form of the climate damage function has received little attention,4 although its potential impact on optimal policies is substantial and the critique has been especially sharp.5 The present paper shows how important the specifications of the damage functions are in climate economics. We use higher-order polynomial functions up to a cubic and quartic form to assess the impact of climate damages on welfare and growth. In our model, damages affect the capital stock, 1 The effects range from sea level rise, drop in crop yields, and human health to energy demand; in 2017, strong hurricanes have caused immense damage: according to the Economist “Hurricane Harvey already set records as America’s most severe deluge.. The UN reckons that, in the 20 years to 2015, storms and floods caused $1.7trn of destruction; the World Health Organisation estimates that, in real terms, the global cost of hurricane damage is rising by 6% a year. Flood losses in Europe are predicted to increase fivefold by 2050.” Economist (2017, 2 Sept). 2 These authors present estimations of damage functions parameters for 140 countries and regions and for six climate impacts: sea level rise, variation in crop yields, heat effects on labor productivity, human health, tourism and household energy demand showing the heterogeneity of the different damages. 3 Technological change is addressed in Acemoglu et al. (2012), the impact of risk in Bretschger and Vinogradova (2016), the spatial distribution in Brock and Xepapadeas (2017), the time distrubution in Gerlagh and Liski (2017) and Bretschger and Karydas (2017) and the North–South aspects in Bretschger and Suphaphiphat (2014). 4 Notable exceptions are Moore and Diaz (2015) and Van den Bijgaart et al. (2016). 5 In a well-known contribution, Pindyck (2013, p. 860) writes: “the models’ descriptions of the impact of climate change are completely ad hoc, with no theoretical or empirical foundation.” 123 As Bad as it Gets: How Climate Damage Functions… reducing both current income and economic growth; for a long-run ecological phenomenon economic dynamics become crucial. The agreed temperature targets of international climate policy suggest that marginal climate damages become very large or even infinite once the temperature ceiling is reached. Conversely, most economic models use constant or quadratic functions for climate damages so that a specific threshold temperature does not emerge and optimum warming can exceed the ceiling, depend (...truncated)