Intergenerational Discounting with Intragenerational Inequality in Consumption and the Environment

Environmental and Resource Economics https://doi.org/10.1007/s10640-018-0282-4 Intergenerational Discounting with Intragenerational Inequality in Consumption and the Environment Rintaro Yamaguchi1 Accepted: 15 August 2018 © The Author(s) 2018 Abstract It is now established that the consumption discount rate is determined by the growth of consumption multiplied by the elasticity of marginal utility, but distributive concerns are rarely reflected in the literature. Assuming a social welfare function with inequality aversion, we consider a consumption discount rate that can be decomposed into the growth effect and the intragenerational distribution effect. The framework is then extended to include population change and inequality in the environment as an amenity in a utility with constant elasticity of substitution. Numerical examples illustrate that distributional effects turn non-negligibly negative, that may reduce consumption discount rate by 1–3% for plausible parameters, once distribution is adjusted for both population and the environment. Keywords Discounting · Income distribution · Intragenerational equity · Climate change 1 Introduction In a cost-benefit analysis of climate change policy, benefits and costs that arise in the future are recalculated in present terms. There is a long history of discussion about this time weighting— or discounting—in the policy and academic arenas, and even more has been written since the publication of the Stern Review (Stern 2006) and related studies (e.g., Nordhaus 2008). This is because climate change policy is a typical textbook example of long-run projects, so that even a minor change in the discount rate could change bottom line net benefits, even under the presence of sound sensitivity analysis. The climate discounting literature rediscovers the well-known Ramsey formula, according to which the consumption discount rate can be decomposed into the pure rate of time preference and the product of the elasticity of marginal utility of consumption and the growth rate of consumption. Choosing the right values, if any, for each parameter or scenario has been shown to be a controversial task involving social agreement on not just facts but also values (Dasgupta 2008; Heal and Millner 2014).1 1 It has been argued recently that uncertainty components imply declining discount rates, either by extended Ramsey formula or by expected net present value approach (Gollier and Weitzman 2010; Traeger 2011b; Gollier 2012). Gollier (2016) contains an account of the development of the literature. B Rintaro Yamaguchi 1 National Institute for Environmental Studies (NIES), 16-2 Onogawa, Tsukuba 305-8506, Japan 123 R. Yamaguchi Most of these studies assume an aggregate world consumption to derive consumptionbased discount rates. However, a salient feature of climate change damage is that it has asymmetric consequences in terms of geography and income groups. Moreover, policies that attempt to address the issue, which are commonly dichotomized between mitigation and adaptation, have differentiated economic impacts on different groups. On the one hand, carbon taxes or emission permits require that emerging as well as developed nations disburse the social cost of carbon, at least in the current policy framework. On the other hand, disaster management, or more generally, adaptation strategies, usually benefit mostly lower income groups in vulnerable nations and islands. The dual practice of mitigation and adaptation would then have mixed effects on intragenerational inequality in the world. In the absence of those measures, it is possible that aggregate consumption continues to grow while income distribution becomes more unbalanced. Put differently, the debate about the temporal substitution of well-being should also take account of how aggregate consumption is divided within each generation (e.g., López 2005).2 Thus, a relevant research question is what the discount rate in an increasingly unequal (or equal) world should look like.3 The importance of equity weighting in climate change discounting has been highlighted already in a welfare-theoretic approach, including Azar and Sterner (1996), Fankhauser et al. (1997), Azar (1999), Pearce (2003), and Anthoff and Tol (2010). Studies considering non-consumption discounting has also become vast. Weikard and Zhu (2005) consider dual discounting for consumption and the environment; Hoel and Sterner (2007) study relative scarcity price of the environment; Kaplow and Weisbach (2011) separate the nexus from consumption to utility and then to social welfare; Traeger (2011a, b) incorporates limited substitutability of the environment. Yamaguchi (2013) considers consumption discount rates of the rich and poor when there are both consumption goods and the environment; however, imagining differentiated discount rates for different income groups yields practical difficulties. We instead focus on a single discount rate with an aggregate consumption numeraire and investigate the consequences of changing intragenerational distribution of consumption. In a recent related literature, Emmerling (2018) and Anthoff and Emmerling (2016) carefully include intragenerational equity in discounting and social cost of carbon, and most notably, investigate their link with the Atkinson measure of inequality. Emmerling et al. (2017) propose focusing on the consumption discounting of the median-income household. Gollier (2015), noting the similarity between inequality and uncertainty, separates initial consumption level inequality and growth rate inequality. He shows an intuitive result by which the expectation of economic convergence raises the discount rate when relative prudence is larger than unity. Fleurbaey and Zuber (2015a), also addressing both inequality and uncertainty, find that extremal returns and the position of the worst-off matter. In an emerging literature of solvable model of climate change and social cost of carbon, Rezai and van der Ploeg (2016) test both one and two for the parameter of intergenerational inequality aversion. In our study, we imagine an instantaneous distribution mechanism that determines mapping of aggregate consumption to individual consumption in each period, given the aggregate consumption growth. Assuming constant relative inequality and risk aversion, we consider the consumption discount rate that is decomposed into the aggregate consumption growth effect and the effect of intragenerational distribution change. Furthermore, we include in 2 Some recent studies focus on how income inequality affects the willingness to pay for the environment (Baumgärtner et al. 2017a; Drupp et al. 2018a). 3 Empirical evidence is still mixed, but Milanovic (2016) finds that emerging “middle class” in Asian countries may have flattened global income distribution. 123 Intergenerational Discounting with Intragenerational… the framework the issues of population change in order to determine the soci (...truncated)