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10490 2023 June 2023 Climate Damages in Convergence-Consistent Growth Projections Tony Harding, Juan Moreno-Cruz, Martin Quaas, Wilfried Rickels, Sjak Smulders Impressum CESifo Working Papers ISSN 2364-1428 electronic version Publisher and distributor Munich Society for the Promotion of Economic Research - CESifo GmbH The international platform of Ludwigs-Maximilians University’s Center for Economic Studies and the ifo Institute Poschingerstr. 5, 81679 Munich, Germany Telephone 49 089 2180-2740, Telefax 49 089 2180-17845, email officecesifo.de Editor Clemens Fuest https//www.cesifo.org/en/wp An electronic version of the paper may be downloaded · from the SSRN website www.SSRN.com · from the RePEc website www.RePEc.org · from the CESifo website https//www.cesifo.org/en/wp CESifo Working Paper No. 10490 Climate Damages in Convergence-Consistent Growth Projections Abstract Projections of climate change damages based on climate-econometric estimates suggest that, without mitigation, global warming could reduce average global incomes by over 20 towards the end of the century Burke et al., 2015. This figure significantly surpasses climate damages in Integrated Assessment Models IAMs. For example, global climate damages obtained with the seminal DICE model are just a 7 reduction in output Nordhaus, 2018. Here, we show that the discrepancy between the projections can be resolved by accounting for growth convergence in a climate-econometric approach that is consistent with the macroeconomic models underlying most IAMs. By re-estimating the global non-linear relationship between temperature and country-level economic growth, our convergence-consistent projections reveal that under an unmitigated warming scenario, global climate damages amount to 6. JEL-Codes O400, O440, Q540, Q550, Q560. Keywords climate change, economics growth, convergence, integrated assessment models. Tony Harding Harvard University, Cambridge / MA / USA tonyhardinghks.harvard.edu Juan Moreno-Cruz University of Waterloo / ON / Canada juan.moreno-cruzuwaterloo.ca Martin Quaas German Centre for Integrative Biodiversity Research iDiv Halle-Jena-Leipzig / Germany martin.quaasidiv.de Wilfried Rickels Kiel Institute for the World Economy IfW Kiel / Germany wilfried.rickelsifw-kiel.de Sjak Smulders Tilburg University / The Netherlands J.A.Smuldersuvt.nl We thank Reyer Gerlagh and Mauricio Rodriguez Acosta for their comments and feedback. 1 Introduction Estimating the future economic consequences of climate change is crucial for developing ecient climate policies. Integrated Assessment Models IAMs serve as a standard tool for formulating ecient climate policy pathways by weighing the costs of climate policies against the costs of climate damages. For instance, the United States Interagency Working Group on the Social Cost of Greenhouse Gases IWG, 2021 employs three peer-reviewed IAMs to calculate the social cost of three greenhouse gases GHGs. These estimates are then applied in regulatory impact analyses to inform optimal emissions abatement strategies Aldy et al., 2021. IAMs typically incorporate neo-classical growth models, utilizing the best available data from physical and economic sciences to establish relationships between economic production, climate change, climate policy costs, and climate change’s impacts on economic activity. These models employ a neoclassical production function characterized by exogenous technical change and diminishing returns of capital. The rate of technical change pins down the long-run growth rate of income, which is independent of productivity levels or investment rates. As climate change reduces aggregate productivity, the average and marginal productivity of capital subsequently declines. This leads to lower investment and a lower future capital stock. Because of diminishing returns to capital, the endogenous reduction in the future capital stock causes the average productivity of capital to converge back to old levels. As a result, output levels are permanently lower compared to a scenario without climate change, but the growth rate is only temporarily lower, converging back to the old level in the long run. Only steady productivity growth through ongoing technical progress can drive long-run capital and output growth. 1 IAMs have been developed since the late 1980s. In the meantime, climate change has continued to progress in the real world, with observable impacts on economies worldwide. Recent climate-econometric approaches leverage this data to empirically estimate climate change damage functions and project future climate change damages e.g., Burke et al., 2015, 2018. However, these approaches do not directly apply the neoclassical growth model of IAMs to the data and, specically, they do not account for the convergence eects inherent in neoclassical growth models. With the muted convergence eects in these projections, climate change has persistent dierential eects on income across counties and leads to a strong divergence in economic incomes across countries, resulting in pronounced winners and losers. This paper presents a climate-econometric approach that enhances the empirical estimation and projections of climate change’s macroeconomic impacts, aligning them more closely with the theoretical models underpinning IAMs and the methods employed in the broader empirical growth literature Barro and Sala-i Martin, 1992; Temple, 1999; Johnson and Papageorgiou, 2020. By adopting the foundational 1 Some recent IAMs consider that climate change could have a lasting eect on economic growth, such as through alterations in innovation rates e.g., Gerlagh, 2023. In this paper, our primary focus is on generating empirical estimates of climate impacts that align with the underlying economic theory of the most prevalent IAMs. In the conclusion, we discuss the possibility of future work to explore estimates consistent with more recent IAM model frameworks. 2Solow-Swan macroeconomic growth model, we derive a convergence-consistent equation for estimating the impacts of climate indicators{temperature and precipitation{on economic growth rates, using country- level data. Subsequently, we apply our empirical estimates to project economic damages from climate change throughout the 21st century under the widely-used high-emissions scenario RCP8.5. We conrm previous evidence for a non-linear eect of temperature on economic output levels. How- ever, unlike previous studies, we do not nd evidence of enduring impacts on economic growth. When projecting economic damages from climate changes, we rather observe that incorporating convergence eects considerably diminishes climate damages. Whereas prior estimates indicate that climate change will reduce global average incomes by approximately 20, our central specication indicates a reduction in global average incomes close to 6. This reconciles the discrepancies in climate damages between the climate-econometric approach and the IAM literature. Moreover, accounting for convergence con- siderably narrows the range of country-level economic growth rates projected for the end of the century, indicating that climate change has less of an impact on inter-country income inequality than previously found. This paper adds to the growing body of literature on empirically-based estimates of climate’s impact on economic growth using climate-econometric methods Dell et al., 2014. Specically, it addresses a crucial open question concerning whether climate change aects income levels or rather income growth rates Burke et al., 2015; Kalkuhl and Wenz, 2020; Newell et al., 2021. Most closely related to this paper is Dell et al., 2012, who estimate the eect of temperature and precipitation on economic growth and nd that rising temperatures reduce economic growth in poorer countries. Our study builds on this paper by considering non-linear eects of temperature and precipitation on economic growth and applying the resulting estimates to projections of climate damages. Including non-linear eects of climate variables, we cannot conrm the previous evidence for a persistent growth eect. Additionally, we emphasize the importance of accounting for convergence eects when applying estimates in projections. In Section 2, we build on a concise neo-classical growth model and derive an empirical model, factoring in convergence, to estimate the macroeconomic climate damages. In Section 3, we detail the data utilized in the empirical estimation process. In Section 4, we present our ndings. Finally, in Section 5, we draw our conclusions. 2 Estimating growth eects with convergence 2.1 Neoclassical macroeconomic growth and convergence The Solow-Swan model relates aggregate output to labor and capital inputs through a constant-returns- to-scale Cobb-Douglas technology. In the long-run, the model nds that the economy under consideration 3reaches a steady-state where per-capita output is described by 2 yt ln Y t Lt lnA0 gt 1 lns 1 lnn g 1 where yt is the natural logarithm of per-capita output in year t, Yt Lt is the per-capita output, s is the savings rate,n is population growth,g is labor-productivity growth, is the production elasticity of capital, and is the capital depreciation rate. The term A0 represents all exogenous, non-economic, sources of productivity. Already Mankiw et al. 1992, p. 5 emphasizes that \the A0 term reects not just technology but resource endowments, climate, institutions.“ This standard equation predicts that long-run income levels vary across countries with A0, g, ,s, n, and . However, the prediction for long-run income growth is simply g, independent of all the other determinants. This means that shocks to the economies have no permanent growth eects unless they permanently aect the trend productivity growth rate. If a permanent increase in temperature lowers productivity levels permanently, pre-shock capital stocks can no longer be sustained and investment falls. In the long-run, lower capital stock levels restore pre-shock returns to investment. After this adjustment process, the output levels are permanently lower, but the growth rate is back to the old level. Whenever there is more capital than justied by the productivity levels, the returns to investment are low, and growth is slowed down until the capital stock has adjusted to productivity levels. Only steady productivity growth through ongoing technical progress can drive long-run capital and output growth. In DICE and most other IAMs, it is by assumption that climate impacts productivity levels, but not the long-run trend of technological change. Consequently, the long-run growth rate is not aected by climate. However, the absence of long-run growth eects predicted by neoclassical growth theory can and needs to be empirically tested. This requires a more dynamic approach than Equation 1. The workhorse dynamic equation to estimate the determinants of growth and long-run level of per capita income in country i from time t 1 to t is the ‘convergence equation’ Acemoglu, 2009, Section 3.2 yi;t gi yi;t 1 y i;t 1 2 where yi;t is the natural logarithm of per capita income so that the left-hand side represents per capita income growth, y i;t y i;0 git is the long-run exponential growth path to which actual income yit is converging, and 0 measures the ‘speed of convergence’ Temple, 1999, which is proportional to 1 , i.e. the production elasticity of inputs other than capital in the production function. 3 Decreasing returns to man-made capital imply 1 0. Heregt, , andy i;0 need to be estimated from observable 2 The discrete-time Cobb-Douglas Solow model can be presented by production function Y K AL 1 and capital accu- mulation function K sY K . In Appendix C.1 we show how 1 and 2 can be derived from these two equations. 3 Dening z it y it y it as the deviation of actual income from trend income, we can write 2 as z it 1 z i;t 1 , which shows that z it 0 i.e. y it y it when t1, providedj1 j 1. 4determinants, including climate variables; combined with observed income yi;t they predict the growth process. The model allows for two sources of growth. First,gi captures long-run trend growth and is driven by continuous productivity improvements. Changes in trend growth gi permanently aect income growth. Second, deviations from the trend, yi;t y i;t , temporarily aect growth. This captures convergence growth. A fall in actual income without any corresponding change in trend growth creates temporarily faster growth so that the economy gradually returns to the old growth path. Similarly, an increase in the trend level of income, y i;0 , creates only temporarily faster growth so that the economy converges to income at a higher level but eventually grows at the old-growth rate. This, in turn, suggests two channels by which changes in climate could impact economic growth. If changes in climate aect gi, the long-run growth trend, these changes will have permanent eects on economic growth by changing steady-state growth rates. Impacts on growth rates would be the case if climate changes permanently impacted determinants of long-run economic growth, such as the rate of innovation. If climate changes only impact output levels, such as through a change in productivity, this will only have a transitory eect. In the long-run, convergence pressures will return growth to the steady-state. The pace at which this occurs depends on the speed of convergence, . We analyze these two channels in a manner consistent with theory following the approach of Bond et al. 2010 to estimate both transitory and permanent growth eects of climate. To derive the corresponding empirical model, we rst rewrite Equation 2 as yi;t y i;t 1 X k k x i;t;k it i i;t 3 where measures the speed of convergence, x i;t;k denotes explanatory variables k that may determine growth, it are country-specic time trend functions representing the rates of steady-state growth, i are country-specic intercepts representing initial conditions, and i;t is an error term. For analyzing the determinants of macroeconomic growth, the coecients on x i;t;k are of main interest. This approach has been used to analyze explanatory variables such as population growth, human capital, or invest- ment. Here, our interest is the partial eect of climate, so we use climate variables|temperature and precipitation|as the explanatory variables. Ifj1 j 1, lim t1 it 1it 2i, and explanatory variables x i;t;k { including climate variables { reach steady-state values such that eventually x i;t;k x i;k , then, under this specication, the country- specic per capita income converges to an exponential growth path with growth rate gi 1i Notice,