LETTER • OPEN ACCESS You may also like - Health co-benefits of sub-national ABM-IAM: optimal climate policy under bounded renewable energy policy in the US Emil G Dimanchev, Sergey Paltsev, Mei rationality and multiple inequalities Yuan et al. - Economic damages from on-going climate change imply deeper near-term emission To cite this article: Karolina Safarzyska and Jeroen C J M van den Bergh 2022 Environ. Res. Lett. 17 cuts 094022 Anselm Schultes, Franziska Piontek, Bjoern Soergel et al. - The social costs of health- and climate- related on-road vehicle emissions in the continental United States from 2008 to View the article online for updates and enhancements. 2017 Sarah E Zelasky and Jonathan J Buonocore This content was downloaded from IP address 83.43.242.15 on 12/09/2022 at 12:52 Environ. Res. Lett. 17 (2022) 094022 https://doi.org/10.1088/1748-9326/ac8b25 LETTER ABM-IAM: optimal climate policy under bounded rationality OPEN ACCESS and multiple inequalities RECEIVED 10 February 2022 Karolina Safarzyńska1,∗ and Jeroen C J M van den Bergh2,3,4 REVISED 1 16 August 2022 Faculty of Economic Sciences, Warsaw University, Dluga 44/5000-241, Warsaw, Poland 2 Institute of Environmental Science and Technology, Universitat Autònoma de Barcelona, Edifici Z—Campus UAB, 08193 Bellaterra, ACCEPTED FOR PUBLICATION Spain 19 August 2022 3 ICREA, Barcelona, Spain PUBLISHED 4 School of Business and Economics & Institute for Environmental Studies, VU University Amsterdam, Amsterdam, The Netherlands 1 September 2022 ∗ Author to whom any correspondence should be addressed. E-mail: ke.safarzynska@uw.edu.pl Original content from this work may be used Keywords: agent-based modelling, social cost of carbon, climate policy under the terms of the Creative Commons Supplementary material for this article is available online Attribution 4.0 licence. Any further distribution of this work must maintain attribution to Abstract the author(s) and the title of the work, journal Despite considerable concern about potentially inequitable effects of climate policy, models fall citation and DOI. short in assessing their implications for policy design. To address this issue, we develop an agent-based climate-economy model, agent-based modelling-Integrated Assessment Model, as a disaggregated, behavioural approach to integrated climate assessment. It describes networks of heterogeneous consumers, banks, power plants and firms, and is calibrated on patterns of growth and carbon dioxide emissions generated by the DICE model of Nordhaus. Whereas the latter assumes full employment and abstains from a financial sector and inequality considerations, our approach relaxes these restrictions to obtain a more reliable assessment of climate policy impacts. We show that inequalities in labour and capital income serve as essential but overlooked links between climate-change damages and optimal climate policy. Our result show that lower inequalities of labour income increase the social cost of carbon (SCC), while the impact of capital income inequalities on the SCC depends on the share of population receiving capital rents. 1. Introduction of growth and carbon dioxide emissions generated by the well-known DICE (2016) model. We exam- The long-term impacts of climate policies have been ine how inequalities among households affect the studied with Integrated Assessment Models (IAMs) social cost of carbon (SCC). We pay special atten- that capture the co-dynamics of economy and climate tion to two mechanisms overlooked so far in the lit- (Tol 1995, Plambeck and Hope 1996, Nordhaus 2016, erature: (a) unemployment caused by climate change Weyant 2017). IAMs rely on aggregate equations that increases labour income inequalities; and (b) the that describe how accumulation of carbon emis- impact of capital investments and bankruptcies of sions by production activities affects global tem- firms on capital income inequality. We show that perature, which in turn causes economic damages lower inequalities of labour income translate into the that reduce economic growth. Here, we take a dif- larger SCC, whereas the impact of capital income ferent approach by proposing a behavioural, agent- inequalities depends on the share of population based climate-economy model for Disaggregate Cli- receiving capital rents. mate Assessment. Our model, called agent-based The dependence of the optimal carbon tax on modelling-IAM (ABM-IAM), includes a climate cycle inequalities has been studied in three ways: in an and damages, and describes economic growth as intertemporal setting (Anthoff et al 2009, Adler et al driven by interactions between heterogeneous con- 2017); in the context of between-region inequal- sumers, firms, power plants and banks interacting ity, with countries being aggregated into a lim- within networks. The model is calibrated on patterns ited number of regions (Nordhaus and Yang 1996, © 2022 The Author(s). Published by IOP Publishing Ltd Environ. Res. Lett. 17 (2022) 094022 K Safarzyńska and J C J M van den Bergh Nordhaus 2017); and focused on within-region representative agent is optimized over time, an agent- inequalities (Dennig et al 2015, Budolfson et al 2017, based model allows us to explicitly describe indi- Kornerk et al 2021). The former addresses inequal- vidual, heterogeneous consumers. ities between generations, while ignoring inequalit- ABMs have been used to study such varied issues ies within them. Governments may respond to the as pandemics, bubbles in financial markets, social intertemporal inequality by taxing carbon to provide segregation, diffusion of energy technologies, or job better conditions for the future generations. The dis- search and matching in labour markets (Windrum agreement over the value of intertemporal inequality and Birchenhall 1998, 2005, Gaffeo et al 2008, aversion, which measures the concern for the well- Delli Gatti et al 2009, Epstein 2009, Cincotti et al being of future generations, has been at the core of 2010, Neveu 2013, Cardaci and Saraceno 2015, Russo the Stern-Nordhaus debate. The second approach is et al 2016, Rengs et al 2020). Macroeconomic agent- concerned with intragenerational inequity and oper- based models have been developed as a behavioural ates through attaching different weights to regions in alternative to general equilibrium models. Such mod- the social welfare function used for the climate policy els have proved capable of explaining core economic assessment. It has been shown that higher regional phenomena like economic growth, structural change inequality aversion increases the SCC (Anthoff and (creative destruction) and business cycles (e.g. Dosi Emmerling 1996). et al 2010). Because of a more realistic representation The third approach examines how the optimal of agents’ heterogeneity, they have opened up oppor- carbon tax is affected by consumption inequalities tunities to explore distributional issues (Farmer et al within-regions (Dennig et al 2015, Budolfson et al 2015, Arthur 2021). Among others, they have shown 2017, Kornek et al 2021). The study by Denning that securitization and the emergence of complex fin- et al (2015) propose a Nested Inequalities Climate- ancial products can result in a more unequal and Economy model that includes sub-regional income financially unstable economy (Cardaci and Saraceno quintiles for all of the 12 regions in the Nord- 2015, Russo et al 2016, Botta et al 2021). haus’s Regional Integrated Climate-Economy (RICE) ABMs allow for modelling bounded rational- model5 . Total consumption in each region is disag- ity and social interactions, unlike existing climate- gregated into consumption quantiles. Subsequently, economy models which rely on the assumption of the fraction of consumption lost due to climate representative agents and assume full rationality. change in each quantile is computed. The authors Recently, the impact of different types of bounded compare the consequences of distributing the damage rationality on the SCC has received some attention inversely, uniformly and proportionally inversely to in the context of computable general equilibrium income across regions. Regions differ in terms of the (CGE) modelling (Howarth 2006, Gerlagh and Liski total factor productivities. As a result, the way dam- 2017, 2018, Chan 2020). However, the ability of such ages are distributed (between regions) affects growth models to study social networks in combination with in each region, and subsequently optimal climate bounded rationality is limited. While representing an policy. The authors show that in case damages fall rel- improvement over traditional approaches, such mod- atively more on the poor consumers, who are dispro- els are unable to fully capture relevant behavioural portionally represented in the low-income regions, responses to climate policies, for two reasons. First, consumption of the poorest regions declines. As a behavioural utility functions often complicate analyt- result, the SCC comes out higher compared to other ical solutions or make models so non-linear that an damage distributions. equilibrium may not exist or not be found. As a result, All three above approaches ignore the impact of few realistic behaviours have been examined in the inequalities between households on the SCC as their context of macroeconomic modelling, despite their analyses are conducted at a supranational level of relevance for climate policy as indicated by empirical aggregation. It has, nevertheless, been suggested that studies. Second, these traditional approaches assume the impact of such inequalities on the SCC may be representative agents, thus ignoring diversity of beha- substantial (Kornek et al 2021). To our knowledge, viours within a population of heterogeneous agents, we present the first agent-based model to study this such as consisting of consumer classes, as well as pref- question. We use the technique of agent-based model- erence change due to agents’ interactions (network ling (ABM) as it is better suitable than representative- effect). Agent-based models can overcome both these agent models to study the distributional impacts of shortcomings. climate change than conventional IAMs or dynamic Only few macroeconomic agent-based models stochastic general equilibrium models (Farmer et al account for the energy sector (Castro et al 2020, 2015, Stern 2016, Arthur 2021). Instead of relying Hafner et al 2020). Even fewer account for com- on aggregate equations, where consumption of a plex interlinkages between energy, financial sector and climate change (e.g. Gerst et al 2013, Ponta et al 5 Nordhaus considers 12 regions: US, EU, China, Russia, Japan, 2018, Lamperti et al 2019, Czupryna et al 2020). The Latin America, Indie, Middle East, Africa, Eurasia, OHI (other study by Lamperti et al (2019) extends the model by high-income countries), and others. Dosi et al (2010) with a climate cycle to examine the 2 Environ. Res. Lett. 17 (2022) 094022 K Safarzyńska and J C J M van den Bergh public cost of bailout, i.e. rescuing insolvent banks. expand production. Instead of a single aggregate In their model, climatic shocks reduce the productiv- consumer, we model a population of consumers ity or capital stock of individual firms. Another recent described by individual heuristics, who spend labour study by Rengs et al (2020) develops a model that or/and capital income on consumption. Labour includes different classes of households and two types income inequalities arise as firms can layout work- of innovations aimed at improving either the carbon ers if they experience a decline in demand. This way or labour intensity of production. The results show we allow for unemployment, which is absent in the that a supply-oriented subsidy for green innovation DICE model. The assumption of full employment has can substantially reduce carbon dioxide emissions been criticized as unrealistic and blurring an accur- without causing negative effects on employment. ate assessment of the distributional impacts of climate In this paper, we build upon a previous model change (Taylor et al 2016). Capital income inequal- that captured complex interactions between the ity depend on the rate of investments in capital by real economy and electricity and financial markets heterogeneous firms. Differential saving rates from (Safarzynska and van den Bergh 2017a, 2017b). This capital and labour income have been argued to be a allows to address multiple inequalities. We extend our major driver of inequality (Piketty 2014, Milanovic model with a carbon cycle consistent with Nordhaus’s 2016, Ranaldi and Milanovic 2020, Botta et al 2021), DICE approach to examine how these inequalities but this effect has been ignored in the climate policy affect the SCC compared with the results of DICE assessment. All in all, in our model, labour and capital (Nordhaus 2014). The choice of the DICE model is income inequalities depend on interactions of hetero- motivated by the fact that it often constitutes the geneous consumers and firms. The discussed mech- baseline to which other authors compare their results anisms are a source of non-linear dynamics, and can- in the literature. Moreover, analytical formulas of the not be studied with highly aggregated models. SCC have been derived for the DICE model, which The agent-based technique allows us to study sys- we employ in our model. To our knowledge, we offer tematically how the distribution of climate damages, the first agent-based model to study distributional wealth and capital income among heterogeneous con- impacts of carbon taxes. Existing climate-economy sumers affects optimal climate policy. We find that ABMs, such as reported in Lamperti et al (2019) or both wealth and capital income heterogeneity reduce Gerst et al (2013), do not consider individual con- the SCC compared with the egalitarian economy. sumers but instead assume aggregate demand, which Capital income allows consumers to smooth their means they cannot address this issue. An exception is consumption in case climate change pushes them into Czupryna et al (2020) who consider individual con- unemployment, and may mitigate this effect depend- sumers allocating their budget among various goods ing on the distribution of capital rents in the eco- from distinct sectors. The model describes agricul- nomy. In our model, consumers differ with respect tural, labour and natural disaster damages. However, to taste: poorer households attach a higher weight to it has not been used to study climate policies or their products’ cheapness, while richer to their qualities. distributional consequences. Either type purchases different goods produced with It is worth noting that the DICE model has been heterogeneous techniques that differ with respect criticized on various grounds (Farmer et al 2015). to labour and energy intensities. As a result, the Especially the dynamics of the climate system have way how damages are distributed among consumers been discussed as inconsistent with the current sci- affects demand for different products, and in turn entific knowledge. Subsequently, many efforts have input use. been undertaken to improve the model so as to obtain Our study relates also to the large literature on more precise estimates of the SCC (Hansel et al 2020, the distributional impacts of carbon taxes. The idea Dietz et al 2021). We do not intend to contribute to is that once the optimal climate policy is determ- the discussion over the precise value of an optimal ined with highly aggregated models, distributional carbon tax, but instead want to examine in which dir- effects of climate policy can be assessed independ- ection the SCC will change due to economic inequal- ently, for instance, using static multi-sector CGE ities. In the DICE model, total growth and global models or micro-simulation models that make the carbon dioxide emissions determine the value of the use of microeconomic databases containing data on SCC. For this reason, we calibrate the model to gen- individual households (e.g. Poterba 1989, Pearson erate patterns of macroeconomic variables as in the and Smith 1991, Hamilton and Cameron 1994, DICE model and examine how introducing different Metcalf 2008, Rausch et al 2011, Beck et al 2015). types of inequalities—of capital and labour income For instance, Hallegate and Rozenberg (2017) exam- and climate damages—influence aggregate patterns. ine how changes in wages or labour productivities Our model differs in several respects from the under different climate scenarios affect consumption DICE model: for each aggregate equation, we model a inequalities, using micro-simulations of 1.4 million network of heterogeneous agents in different markets households in 92 countries. However, their approach instead. For instance, capital accumulation follows does not account for the policy response to changes from decisions of firms who decide whether to in consumption inequalities, as we do. Moreover, 3 Environ. Res. Lett. 17 (2022) 094022 K Safarzyńska and J C J M van den Bergh existing studies of the distributional impacts of car- station are made. The emissions from the elec- bon taxes ignore capital income and unemployment tricity sector affect changes in the current stock effects of climate change. We find that the carbon of atmospheric carbon. Changes in the current tax is effective in reducing consumption, income stock of carbon affect the global mean temperat- and wealth inequalities over time. The precise effects ure above the pre-industrial level, which in turn depend on the relationship between the damage and determine the total damage in the economy, as capital income distributions. discussed in section 2.3. The remainder of the paper is organized as fol- (d) Total demand for labour in all sectors determines lows. In section 2, we provide an overview of the wages in the economy. Consumers receive labour model. Section 3 summarizes the results from model income and a share of capital rents. Consumers simulations. Section 4 concludes and discusses policy decide how much of their wealth and income implications. to spent on consumption in each round. This allows us to examine how differential spend- 2. ABM-IAM ing from capital and labour income affects con- sumption inequalities that are directly linked Our model includes heterogeneous consumers, who with emissions. make decisions on how much to spend on con- (e) Damages are distributed among individual con- sumption and which products to buy; heterogeneous sumers, reducing their budgets according to firms, which offer products that differ with respect a parameterized damage distribution function, to quality as well as price, and compete through modified from Dennig et al (2015). We compare reducing costs of production by engaging in innov- three distributions of damages, namely propor- ation activities; and heterogeneous banks and power tional, uniform, and inversely proportional to plants producing energy technologies. supplement- consumers’ wealth (see section 2.2). Differential ary tables ST1-4 summarize all parameters and vari- impact of damages on households can be inter- ables that describe these agents. A full model descrip- preted as damages affecting labour productiv- tion is provided in supplementary material 2 (SM2), ity or causing damage to property of agents, with its schematic presentation depicted in figure 1. which may vary with households and geograph- In sections 2.1–2.3, we summarize modifications to ical location. a model in Safarzynska and van den Bergh (2017a, (f) Banks pay interest rates on deposits of con- 2017b), which we introduce to study multiple dimen- sumers and firms and collect loan repayments sions of inequalities and their impacts on climate which are due. A bank goes bankrupt if either policies. The model is combined with the climate its equity or its reserves become negative. The cycle from the DICE model. The DICE model is also model is stock-flow consistent, which implies used for the calibration of macroeconomic variables. that all monetary flows are balanced each period. Altogether, this results in the ABM-IAM model. If a bank has no sufficient liquidity to offer loans, The sequence of events in the model is as follows: it asks other banks at the interbank lending mar- ket for a loan. Money supply (M1) is composed (a) On the market for final products, firms offer of bank money and loans to producers in differ- products which vary in terms of quality and ent sectors. price. They employ inputs in production and invest in capital expansion; if needed, they ask 2.1. Consumption and saving decisions a bank for a loan to cover costs of inputs. If a In the model, consumption-decisions are determined new firm tries to enter the market it can receive in two steps. In the first step, consumers decide how a start-up loan from a bank. much of their wealth and income to spent on con- (b) Firms set the production level for next period sumption in the current period. The basic idea is that as a weighted average of past sales and produc- there is a target wealth-to-permanent-income ratio, tion. They set prices to cover the cost of inputs which a consumer would like to attain over time and capital expansion. A mark-up is imposed (Carroll 2017). The budget determines how many on the price, which depends on firm’s market products a consumer can afford to buy in the second share. Prices depend also on labour and energy step. Consumers’ budget bit , i.e. how much she spends productivities, which change due to R&D invest- in time t change according to: bit = µI *pLit + µW Dit − ments by individual firms. Firms do not anti- dit Dt , where µI and µW are the shares of income cipate policy changes, but adapt to them. For pLit and bank deposit Dit (i.e. wealth) spent on con- instance, a carbon tax increases the price of sumption, respectively. Although shares are the same energy, and thus the probability of firms invest- across consumers, consumers differ with respect to ing in energy- efficiency improvements. wealth. As a result, more affluent consumers have (c) Electricity producers generate electricity using larger budgets and buy more products. The diver- distinct energy sources. If an old power plant gence in the number of products bought by the richest becomes an obsolete, investments in a new power and poorest consumers is weakened by the fact that 4 Environ. Res. Lett. 17 (2022) 094022 K Safarzyńska and J C J M van den Bergh Figure 1. Schematic presentation of the model. Note: Elements in light colour are new compared to the earlier version of the model. rich consumers choose better quality and hence more where parameter αi captures i’s inclination towards expensive products. the product quality; α is the network elasticity, where Wealth of each consumer i changes over time: mjt is firm j’s market share. The network elasticity each period, she receives wage (if employed), and in measures the tendency of consumers to follow choices addition a share of energy and capital rents (µsi ). of others. In model simulations, we distribute values Formally, the deposits of consumer i (Dit ) changes of the inclination towards the product quality (αi ) in according to: Dit = Dit−1 ∗ (1 + rc ) + pLit + µsi ∗ at − a way that consumers with more wealth (deposits) at Cit , where rc is an interest rate paid on deposits; time 0 are assigned a higher value of this parameter. pLit is wage; and Cit is consumption at time t. Para- This implies that wealthier individuals are more ori- meter µsi defines the share of energy and capital rents ented towards product quality. (at ), which a consumer is entitled to. Rents are com- puted as spendings by firms on inputs, which are 2.2. The climate cycle not produced in the model, to ensure that the model On the electricity market, three energy technolo- is stock-flow consistent. For instance, consumption- gies compete for adoption: gas, coal and renewable good firms pay the energy costs to energy firms, but energy. Electricity production by each power plant expenses on fuels by the latter constitute dividends. is described by a Cobb–Douglass function, which On the other hand, expenses by consumption-good accounts for substitution of fuel, labour and capital firms on capital (which is not produced in the model) in electricity generation. Productivities of incumbent constitute capital rents, which are distributed among plants can change over time due to innovation and consumers. learning-by-doing. Output decisions by each plant In the second step, each consumer decides which are modelled as Cournot competition. In particular, product to buy by comparing product qualities, prices power plants decide simultaneously how much elec- and adoption rates. In the model, consumers buy tricity to sell on the spot market. If an incumbent products that yield them the highest utility. If such plant leaves the market, investments are made in new products are out of stock, a consumer chooses prob- installed capacity. The decision about the size of and abilistically among available products in the market. fuel type embodied in a new power plant are based The probability ρijt that a consumer buys product j K∗log(uijt ) on the discounted value of investments. Each fuel j e is equal to: ρijt = ∑ K∗log(uijt) , where uijt captures util- is characterized by its emission intensity εj . The total je emissions from the energy sector are equal to: Ft = ity derived by consumers from purchasing design j, ∑∑ while K captures the strength of market competition. i j qijt εj , where qijt is electricity produced by plant The utility evaluated by consumer i from adopting i embodying technology j. good j depends on the product quality xjt , its price The climate module follows Nordhaus’s pjt (cheapness), and the number of other consumers (2017) approach. Changes in the current stock of i αi −0.5 who bought the product mjt : uijt = xα jt pjt mα jt , atmospheric carbon (Ėt ) depend on the existing stock 5 Environ. Res. Lett. 17 (2022) 094022 K Safarzyńska and J C J M van den Bergh EP +ET −E t correspond to damage being proportional, independ- of carbon Et , as well as past emissions: Ėt = t T lag t , P where Et is the permanent stock of carbon (GtC) that ent, and inversely proportional to wealth. If ξ = 1, the stays in the atmosphere for thousands of years; ETt rich are affected the most by climate change, while is the transient part of the stock (GtC), with Tlag ξ = −1 implies that damages reduce the budgets of describing how long it takes for the mean global less affluent consumers relatively more. The value of ξ temperature to adjust to an increase in the stock affects only the distribution, and not the total amount of atmospheric carbon. The permanent stock of of damage. To illustrate how the distribution of climate dam- carbon changes over time according to: ĖPt = φ1 Ft , ages affects consumers’ budgets consider a simple while the transient stock of carbon changes follows: population composed of just two consumers. Of ĖTt = −φETt + φ2 (1 − φ1 )Ft . Thus, the current stock these, one is rich and the other poor: the budget of of atmospheric carbon depends on a share of carbon the rich consumer equals to 8.5, while of the poor emitted into the atmosphere staying there forever 4.5 in the absence of climate change damages. If the (φL ), a share (1−φ0 ) of emissions exiting the atmo- economy suffers total damage equal to 5 and ζ = 1, sphere immediately, and the part that decays at a the budget of the rich is reduced to 4.75, while of the geometric rate φ. poor to 3.35. If instead ζ = −1, the rich consumer can The stock of carbon Et affects the global mean spend 7.25 on consumption, while the poor one suf- temperature above the pre-industrial level Tt accord- fers disproportionally large reduction in her budget, ln Et ing to: Tt = ω ln 2Ẽ , where Ẽ is the pre-industrial stock which becomes 0.75, which would result in larger of atmospheric carbon, while ω is the climate sensitiv- consumption inequalities. These effects are static. In ity parameter describing the raise in temperature due the model, many differentiated products compete for to doubling of the carbon stock. adoption by heterogeneous consumers. We examine long-term effects using model simulations. 2.3. Climate damages In the baseline model, to which we will refer as the An increase in the global temperature reduces output model with rational consumers, we assume no net- according to the damage function (Nordhaus 1994, work effect in consumption, while we allow for unem- Nordhaus 2017): Dt = 1+ζ11 Tt ζ2 , where ζ1 captures the ployment. We relax these assumptions in scenarios 4 reductions in total output. Following Dennig et al and 5 described below. In addition, we examine the (2015), we disaggregate total damage among con- impact of heterogeneous wealth and rents on the SCC sumers. As consumption is equal to the fraction of in the following scenarios: output ct = (1 − st ) Yt , where st is the saving rate and Scenario 1: Just economy Yt total output, both approaches are equivalent in In our model simulations, the wealth of consumers terms of generating the same amount of damage. We changes over time: each period, consumers receive a refrain from considering damages to capital or labour wage (if employed), interest on deposits, and a share productivity of individual firms, which has been done of capital rents (µsi ). In the ‘just economy’ scenario, elsewhere (e.g. Lamperti et al 2019). This is motivated all consumers acquire an equal share of rents, cap- by the fact that our model excludes catastrophic dam- tured through µsi = 1/nc , where nc is the number ages and tipping points (Dietz et al 2021), to make of consumers. We further assume that all consumers our results comparable with those of the DICE model have the same wealth initially6 . with gradual damages. Scenario 2: Half-just economy Formally, damage Dt is distributed among indi- In ‘half-just’ economy, all consumers acquire an equal vidual consumers, reducing their budgets by dit Dt , share of rents 1/nc —just as in the ‘just’ economy. where dit is the share of damages incurred by con- However, we assume wealth heterogeneity in this sumer i. We modify a parameterized damage dis- scenario. In particular, in the initial round, we dis- tribution function based on Dennig et al (2015) by tribute the total wealth W in the economy as deposits disaggregating damages among individual consumers among consumers according to the gamma distribu- instead of consumption quantiles as has been done tion with mean µg. (⩾1). by the authors. The post-damage consumption of individual i (cit′ ) is equal to: cit′ = cit − nk (1 − Dt )c̄t dit , Scenario 3: Unjust economy where nk is the number of consumers, c̄t is the The ‘unjust’ economy represents a more realistic mean consumption, while dit is the share of dam- scenario, namely with an unequal distribution of ages incurred by consumer i. These shares are calcu- rents and wealth, where rents concentrate in a small lated as follows: dit = kξt qζit , where qit is the share of wealth (deposits) hold by individual i at time t; kξt = 1 ∑ 6 It is important to note that even in the just economy, some ∑ ζ is chosen so as to dit = 1. The equation dit = q i it inequalities unfold over time. For instance, even if all consumers i desire the same cheapest product, they still may buy different kξt qζit captures the relationship between the damage goods, or some consumers may buy no products at all, if the desired and wealth distributions through assuming a wealth product is out of stock. This would result in consumption inequal- elasticity of damages (ξ). Elasticities of 1, 0, and −1 ities to emerge over time. 6 Environ. Res. Lett. 17 (2022) 094022 K Safarzyńska and J C J M van den Bergh fraction (10%) of the consumer population. This is high resource costs and economic instability, includ- motivated by evidence from the U.S., where the top ing due to the invasion of Ukraine by Russia, may 10% of households own 81% of the total value of affect long-run growth projections downwards. those investments (Wolff 2014). A recent analysis Scenario 7: The social cost of carbon indicates that the share of world individuals with pos- We are interested in how equity considerations affect itive capital income rose from 20% to 32% between the optimal carbon tax. To this end, we compare 2000 and 2014 (Ranaldi 2021). We assume rents to be the results from the business-as-usual (BAU) scenario distributed among consumers according to an expo- in the absence of climate policies with the Optimal nential distribution (see figure 3 in SM2). The distri- Scenario (OPT), where the SCC is translated into bution of wealth in the first round of model simula- a carbon tax on electricity. The SCC measures the tions is identical to Scenario 2. net present value of future economic costs arising Scenario 4: Full employment from an additional ton of carbon dioxide emis- The DICE model relies on the assumption of full sions, accounting for the entire path of causes and employment. Instead, in our model, in each time effects between climate cycle and economic damages period, firms revise their demand for labour. We (Nordhaus 2017). We use a tax formula proposed by assume a random allocation of workers to firms. Rezai and van der Ploeg (2016), which is a simpli- ∑ Wages are paid only to nLt = j iLjt workers at time fication of one proposed by Golosov et al (2014): 1 φL (1−φL )φ0 t, where iLjt are workers employed by a firm j. The 1+ρ ( 1− 1 + 1−(1−φ) 1 )Yt . Here γ is a constant 1+ρ 1+ρ total population is constant and equal to nw . In case scale parameter and ρ a parameter capturing time of excess demand for labour (nw < nLt ), nw − nLt of impatience (set to 0.01, following Rezai and van der workers remains unemployed, while others receive Ploeg8 ). We employ this specific formula as it has been pL0 , which can be interpreted as a minimum wage. derived for the climate cycle consistent with the DICE In case of excess demand, the wage increases over model. Accordingly, the optimal carbon tax is pro- n time and it is equal to: pLt = pL0 (1 + Ltn−wnw ), thus it portional to the total output. The tax revenue is dis- depends on the demand and supply for labour. For tributed back to the citizens as a lump-sum equal to the purpose of comparison with the DICE model, we all citizens. The resulting tax is optimal by approx- conduct additional simulations, referred to as the ‘full imation as agent-based models do not allow per- employment’ scenario, where regardless of whether forming an optimization of output since they involve supply or demand is in excess, all workers receive stochastic elements related to innovations and agent wage equal to: pLt = pL0 ( nnwlt ). This means that in case interactions. nw < nLt , the wage is lower than pL0 , while it is higher otherwise. In both ‘full employment’ and ‘unemploy- Scenario 8: Renewable energy ment’ scenarios, total spending on labour income Next, we study the impact of investments in renew- is the same, but scenarios differ in terms of labour able energy on multiple inequalities. In the baseline income distribution. model simulations, an energy owner invests in a new power station when an old plant becomes obsol- Scenario 5: Network effect ete. The size and the type of a new power plant In the baseline model simulations, we assume that are chosen based on the highest discounted value agents are rational by setting the network elasti- of such investments. As a result, combined cycle gas city to 0. We consider an alternative scenario with turbines (CCGTs) power stations dominate the elec- boundedly-rational agents, where the network elasti- tricity market as they are the cheapest to install. In city, i.e. the weight attached to products chosen by the ‘renewables’ scenario, we assume that whenever the others, is strong (α = 0.15). Both types of agents, a power plant becomes obsolete, an owner of energy i.e. boundedly- and fully-rational, spend the same plants decides to invest in a new renewable power fraction of income and wealth on consumption. plant, instead of CCGT, with a probability prenewable Scenario 6: A low-growth scenario equal to 0.5. This may be interpreted as a policy scen- The baseline model was calibrated to replicate pat- ario, where the share of renewable energy in elec- terns of macroeconomic variables between 2010 and tricity production increases over time until reaching 2100 as in the DICE (2016) model (section 3). This on average 50% of electricity production. We con- includes a growth of consumption equal to 1.9%. We sider investments in renewable energy in the pres- introduce an additional scenario, to which we will ence (OPT) and absence (BAU) of the carbon tax. If refer as a low-growth scenario, where the consump- the share of renewable energy in electricity produc- tion growth between 2010 and 2100 is equal to 1.6%. tion reaches 100%, the tax becomes 0 in the OPT This is achieved by setting the annual increase in scenario. total factor productivity (TFP) equal to 0.017 . This scenario is motivated by the fact that current times of 8 In the low-growth scenario, the time impatience parameter is set to 0.0025 so that the value of the SCC is similar between the baseline 7 In the baseline model, this parameter is equal to 0.05. model and the low growth scenario. 7 Environ. Res. Lett. 17 (2022) 094022 K Safarzyńska and J C J M van den Bergh 3. Calibration and results reported in the U.S. for the period 2011–2015. Other parameter values are taken from Safarzynska and van We perform simulations with many heterogeneous den Bergh (2017a). We recalibrated some parameters agents, using the ABM approach. In the supplement- compared to the previous version of the model so that ary materials, we provide some additional analysis simulations generate dynamics of aggregate variables from model simulations, where we doubled the num- consistent with the DICE model. ber of consumers, to show that our results are robust Figure 2 compares dynamics of income, con- to the number of agents9 . We study model dynamics sumption and wealth inequalities in ‘just’, ‘half-just’ between 2015 and 2175. Each period corresponds to and ‘unjust’ economies under different damage dis- one year. For each parameter setting, we report mean tributions. Income and consumption inequalities values over 100 simulations from Monte Carlo exer- are measured through Theil indices, whereas wealth cises conducted with different seeds, motivated by the inequality is calculated as the share of total wealth presence of stochastic factors in our model. Means are by the richest decile of consumers (top 10%). Pat- calculated over the last 50 years, when model dynam- terns depicted in the figure show that climate change ics stabilize, and are summarized in supplementary increases consumption inequalities in all considered tables (ST1-ST6). scenarios with no climate change. We calibrate parameters so that the model under In the ‘unjust’ economy, the trends of all types of full employment in the ‘just economy’ scenario rep- inequalities are upward sloping in line with evidence licates the aggregate patterns of output and con- that inequalities are increasing worldwide (Cingano sumption, the carbon cycle, temperature and dam- 2014). In turn, in the ‘half-just’ economy, wealth ages consistent with the DICE 2016 model between inequalities are reduced over time. Several studies 2015 and 2100. Hence, associated parameter values find that increases in income inequality and con- are taken directly from the DICE model, and are sumption are connected (Krueger and Perri 2006, described in the supplementary table ST5. The value Aguiar and Bils 2015). In addition, evidence indic- of the scaling parameter γ in the SCC comes from ates wealth and income inequalities are positively cor- Golosov et al (2014). Other crucial parameters are related, as labour income is a major source of wealth emissions factors of different energy technologies. We (Berman et al 2016). Wealth inequality exceeds labour set these so that, consistently with the RCP 8.5 scen- income inequality due to rents, dividends or roy- ario, a temperature increase above the pre-industrial alties (Piketty 2014). Our model simulations under level is between 4 ◦ C and 4.5 ◦ C, while cumulat- unequal distribution of wealth and rents replicates ive carbon emissions between 1450 and 800 GtC in these facts. 2100, which corresponds to the medium-high IPCC The upwards sloping trends of inequalities in scenario. the ‘unjust’ economy can be explained by climate Nordhaus calibrates his model, notably TFP, to damages undermining the purchasing power of con- generate a growth rate of consumption per capita sumers, reducing firms’ profits and employment. equal to 1.9%. We achieve the same growth rate This increases income inequalities, and subsequently by setting the increase in TFP equal to 0.05. Other consumption inequalities. In the ‘just’ and ‘half- key parameters determining consumption and out- just’ economies, consumption inequalities increase put dynamics are: the productivity of firms in the less than income. Here, consumers smooth their manufacturing sector A at t = 0; the share of wealth expenditures with wealth. In the ‘unjust’ economy, spend on consumption µW ; and interest rates paid the possibility of smoothing consumption is limited on consumer deposits r c . These are set to 2.5, 2% as most consumers do not acquire rents. and 0.1%, respectively. These values are motivated as follows: the initial TFP was set to 2.5 for total out- 3.1. The impact of multiple inequalities on the put in 2015 to be equal to 75 trillion $. Overall out- social cost of carbon put increases to 300 trillion $ in 2100, which corres- Figure 3 summarizes the main results from our mod- ponds to the SSP3 projection (Leimbach et al 2017). elling exercises. Figure 3(a) compares the SCC in the The marginal propensity to consume out of wealth baseline model with unemployment to the model affects the level of total consumption as well as its with full employment in simulations with rational growth. The larger the value of this parameter is, agents. Figure 3(b) does the same for the models the higher total consumption, production and carbon with rational and boundedly rational agents, in sim- dioxide emissions are. Its value was chosen so that ulations that allow for unemployment. We examine the growth of consumption between 2010 and 2100 if differences in the SCC between distinct dam- is 1.9%. The interest rate on household deposits is set ages, wealth and rents distributions are statistically- equal to 0.1%, motivated by the range 0.1%–0.14% significant. We do this by running non-parametric tests (the Mann–Whitney tests) on the sample of data consisting of results from 100 simulations for each 9 The number of firms is endogenous to model dynamics; therefore initial condition (parameter setting). The results are we have not manipulated this parameter. summarized in the supplementary tables 7–12. 8 Environ. Res. Lett. 17 (2022) 094022 K Safarzyńska and J C J M van den Bergh Figure 2. Dynamics of income, consumption and wealth inequalities (top 10%) in the BAU scenario of the model with rational consumers. Note: Dashed lines correspond to the results from simulations without climate change. All graphs present 5 year averages to weaken the effect of stochastic factors. The initial decrease in consumption and income inequalities is due to firms expanding rapidly their capital in the initial rounds of model simulations. Evidence in supplementary tables 7(a)–(c) indic- thus emissions and the SCC, compared to the situ- ates that differences between models with ‘full ation where unemployment pushes the least affluent employment’ and ‘unemployment’ are insignificant, households into poverty, reducing their demand. regardless of the damage distribution. However, sup- Another mechanism, which explains our results, is plementary table 11(c) indicates that differences in that richer households buy more expensive products the SCC between models with ‘full employment’ and that are often characterised by high mark-ups. These ‘unemployment’ are statistically significant for each have been suggested to be an important driver of damage distribution under the low-growth scenario. labour income inequality, as they decrease the labour Here, unemployment reduces the SCC in the ‘unjust’ share of income (Autor et al 2020). The discussed economy (supplementary tables 5(c) and 6(c))10 . The mechanisms have a stronger impact on the SCC, the negative impact of income inequalities on the SCC is lower economic growth is, as this pushes a larger driven by the difference in tastes among households. share of the population into poverty. In particular, poorer household buy goods produced The main findings from the analysis of our model with more efficient techniques. As a result, if every- with unemployment can be summarized as follows one receives incomes, output growth is higher, and (figure 3(b)). First, the SCC is lower in the ‘unjust’ economy compared to the ‘half-unjust economy’ scenario. The difference in the SCC between both 10 In the ‘just’ and ‘half-just’ economies, the differences in the scenarios is statistically significant for each damage SCC are not statistically significant between simulations with ‘full’ employment and unemployment. Here, smoothing capital with distribution (supplementary table 10(b)). The mean wealth weakens the impact of unemployment on the SCC. results from Monte Carlo exercises indicate that the 9 Environ. Res. Lett. 17 (2022) 094022 K Safarzyńska and J C J M van den Bergh Figure 3. The social cost of carbon under distinct conditions. Note: Mean results from 100 simulations for different initial conditions; the mean SCC is computed over the last 50 years of model simulations. tax drops from on average 234.7 $/ton in the ‘just’ pushing less affluent households (with low or no economy to 212.6 $/ton of carbon in the ‘unequal’ savings) into poverty, making them unable to pur- economy. On the other hand, most differences in the chase consumer products. As a result, the demand SCC between ‘just’ and ‘half-unjust’ economies are by the poorest households in the ‘unjust’ economy insignificant (supplementary table 10(a)), indicating cannot be reduced further by climate change. On that rent inequality has a greater impact on estimates the contrary, climate change reducing budgets of of the SCC than initial wealth heterogeneity. affluent consumers has always a large impact on the Second, in the ‘unjust’ economy, the SCC is sig- total demand, reducing growth and the SCC. In the nificantly larger, when the poor are hurt the most by ‘just’ and ‘half-just’ economies, we observe a sim- climate damages (ξ = −1), compared to other dam- ilar pattern: the SCC is lower for ξ = 1, followed by age distributions (ξ = 0 and ξ = 1) (supplement- ξ = 0, and then ξ = −1. However, the difference ary tables 2(a)–(c) and 8(c)). This can be explained in the SCC between different damages distributions by the fact that over time unemployment unfolds, are not all statistically significant in these scenarios 10 Environ. Res. Lett. 17 (2022) 094022 K Safarzyńska and J C J M van den Bergh Figure 4. Reduction in income, consumption and wealth inequalities due to a carbon tax. Note: The reduction in inequalities is computed as a difference in each inequality between the BAU and OPT scenarios, for rational consumers. In the OPT scenario, tax revenues are distributed as an equal lump-sum transfer to all citizens. as households smooth their consumption with wealth wealth inequalities. These reductions are in general (tables 8(a) and (b)). larger in the ‘unjust’ economy as here the potential Third, for all considered scenarios, the SCC is for them is greater. Here, the tax is more successful in greater in the presence of the network effect com- reducing income and consumption inequalities, the pared to simulations with rational agents. The differ- larger the share of damages fall on the rich. ences in SCCs are statistically significant for all dam- Table 1 presents the results from linear regres- age distributions between scenarios with rational- sions of the logarithm of the SCC on the inequality and boundedly-rational agents (supplementary tables indicators generated by the model simulations. Each 9(a)and (b)). This can be explained by the fact that observation comes from a single simulation run of the rational agents switch to new products easier than model with rational consumers. For every parameter boundedly-rational agents. This results in greater setting, we include 100 observations. In the regres- market competition (lower H-index of market con- sions, we pool data from model simulations from centration) and the lower rate of firms’ bankruptcies three scenarios: ‘just’, ‘half-just’ and ‘unjust’ eco- in the model with rational consumers (see supple- nomy, each run for three damage distributions, which mentary tables 2(a)–(c) and 3(a)–(c)). As a result, results in total in 900 observations. As an explanatory new products, produced with more efficient tech- variable we include consumption, income and wealth niques diffuse on the market, which results in lower inequalities; as well dummies corresponding to dif- emissions, and thus the carbon tax compared to the ferent scenarios: ‘half-just’ and ‘unjust’ economies. In economy with boundedly-rational consumers. Model 3, we add interactions terms between different types of inequalities and such dummies. 3.2. The impact of the SCC on multiple inequalities The results in table 1 support that the ‘unjust’ eco- Figure 4 summarizes the reduction in consumption, nomy results in the lower SCC compared to the ‘just’ income and wealth inequalities in simulations with economy. In favour of this, the dummy correspond- rational consumers. We find that the SCC is suc- ing to the ‘unjust’ economy is positive and signific- cessful in reducing all types of inequalities in the ant in Models 2 and 3. Other results indicate that long run regardless of the distribution of capital larger income inequalities translate into lower val- income, wealth or damages. In the model, firms ues of the SCC. The variable income inequalities has decide whether to invest in improvements in labour a statistically significant impact on the logarithm of or energy productivities depending on the relative the SCC in all models reported in the table. This is prices of both inputs. As a result, the tax induces because labour income is the most important driver substitution of energy for labour, while it shifts R&D of consumption, and thus of production. As a result, activities of firms towards improvements of energy higher employment boosts growth, emissions, and productivities. Overall, the tax reduces unemploy- the SCC. The impact of income inequalities on the ment, which unfolds over time due to climate change SCC is lower in the ‘half-just’ and ‘just’ economies reducing consumers’ budgets. The tax reduces also compared to the ‘unjust’ economy, as indicated by 11 Environ. Res. Lett. 17 (2022) 094022 K Safarzyńska and J C J M van den Bergh Table 1. Regressing the impact of multiple inequalities on the SCC (in logarithm). Variable Model 1 Model 2 Model 3 Consumption Inequalities 0.02 0.03∗ 0.11 (0.02) (0.1) (0.1) Wealth Inequalities −0.07 0.54∗∗ 0.9 (0.05) (0.26) (1.7) Income Inequalities −0.81∗∗∗ −0.80∗∗∗ −0.89∗∗∗ (0.01) (0.01) (0.02) Unjust Economy −0.45∗∗ −2.47∗∗∗ (0.20) (0.39) Half-unjust Economy −0.0.003 −0.56 (0.56) (0.34) Interaction Consumption Inequality and −0.13 Unjust Economy (0.1) Interaction Income Inequality and Unjust 0.39∗∗∗ Economy (0.04) Interaction Wealth Inequality and Unjust 1.79 Economy (1.73) Interaction Consumption Inequality and 0.51∗∗ Half-just economy (0.10) Interaction Income Inequality and Half-just 0.08∗∗ economy (0.03) Interaction Wealth Inequality and Half-just 3.2 economy (2.7) Constant 6.23∗∗∗ 6.15∗∗∗ 6.18∗∗∗ (0.01) (0.04) (0.22) No. obs. 900 900 900 R-squared 0.85 0.87 0.87 Note: Standard errors in brackets; ∗∗∗ indicate significance at 1% level; ∗∗ at 5% level and ∗ at 10% level. positive and significant signs of the interaction terms that of fossil fuel plants. Typically, a single bank between income inequality and the corresponding cannot afford to finance investments in renewable dummy variables. The higher concentration of capital energy alone and hence borrows money at the inter- rents among the smaller share of population is expec- bank lending market. This creates a risk of a cas- ted to reduce growth, and the SCC. However, wealth cade of failures in the financial system if a renew- inequality turned out to have a negative, yet insigni- able power plant goes bankrupt. Following Tedeschi ficant, impact on the SCC only in Model 1, i.e. in the et al (2012), we measure financial stability by the absence of scenario dummies. number of bank bankruptcies. We find that the prob- ability of bank’s bankruptcies is four times higher in the ‘Renewable Energy’ scenario compared to the 3.3. Effectiveness and equity of using carbon-tax baseline model, which constitutes a second mechan- revenues for renewable energy isms through which investments in renewable energy Investments in renewable energy are successful in pre- increase wealth inequalities, compared to economies venting the global temperature from increasing above based on fossil fuel. 3.2 ◦ C by 2100 in the OPT scenario for all damage and capital income distributions (tables 3(a), (b) and 4(a), (b)). In all model simulations, investments in 4. Conclusions renewable energy reduce (labour) income inequalit- ies. In particular, large investments in power plants The debate about climate policies and notably car- act as a demand stimulus, increasing employment bon pricing has been dominated by IAMs. These (Vad Mathiesen et al 2011). However, in the unjust’ assess total macroeconomic costs of climate change economy, investments in renewable energy simul- and policies, without consideration of distribu- taneously increase wealth inequality. This is because tional effects of policies on different income groups rents from energy and capital benefit disproportion- (Kunreuther et al 2014). However, there are con- ally a small group of consumers. This leads to an cerns that the carbon tax may contribute to inequal- increase in consumption inequalities (supplementary ities, which would affect growth and the optimal tables 4(a) and (b)). Rapid investments in renewable tax itself. Previous studies show that inequalities energy come at the cost of systemic risk (Safarzynska within- and between-regions significantly affect the and van den Bergh 2017b, Campiglio et al 2018, SCC. So far, no study has considered wealth inequal- Semieniuk et al 2020), due to the construction of ity at the household level. We developed ABM- renewable power plants being more expensive than IAM, an agent-based climate-economy model with 12 Environ. Res. Lett. 17 (2022) 094022 K Safarzyńska and J C J M van den Bergh households being heterogeneous in income, con- Future studies may consider more realistic estim- sumption and wealth. Results show that considering ates of climate damages, for instance, by includ- capital and labour income inequality alters climate ing the potential effect of tipping points in the policy advice. global coupled climate-biosphere system (e.g. Dietz Our study suggests that wealth and rent inequal- et al 2021), or by broadening the range of dam- ities can have a significant impact on the SCC. Wealth age types covered. In addition, the choice of pro- allows household to smooth their consumption in duction functions specific to particular sectors mer- case of low or no employment. In the long-run, rent its further attention. For example, Saunders (2008) inequality turns out to have a greater impact on shows that some production functions are insuffi- estimates of the SCC than initial wealth heterogen- ciently flexible to capture the impacts of energy- eity. If everyone is entitled to the same share of cap- efficiency improvements. Future research may further ital rents, wealth inequalities decline over time. As try to parameterize household budgets and spend- opposed, rent inequality drives a long-term diver- ing decisions on real data. Moreover, making the gence in wealth. Moreover, if a smaller fraction of the share of wealth spent on consumption endogenous population receives capital income, more consumers to consumers’ wealth would be important to fully are pushed into poverty by climate change than in an capture households’ responses to carbon taxes. To economy with equal rent distribution. This reduces assure that improvements in TFP at the level of the the GDP, emissions and the carbon tax. In addition, whole economy were in line with the DICE model, relaxing the assumption of full employment signi- we omitted the cost of R&D and production of cap- ficantly decreases the SCC compared to the preced- ital. These model simplifications might be relieved by ing estimates—but only in the low-growth scenario further research. Finally, while we calibrated trends under the ‘unjust’ distribution of wealth and capital. in energy prices using historical data, future work Here, unemployment due to climate change pushes might consider making use of forecasts of future the poorest households into poverty, as a result of fuel prices. which they cannot afford purchasing goods. This is likely to cause bankruptcies of some firms, reducing Data availability statement growth, emissions, and thus the SCC. Our study underlines the relevance of behavi- The code is available at https://osf.io/hxksg/, while the oural assumptions of climate-economy models, sug- data that support the findings of this study are avail- gesting more attention needs to be given to these. We able upon request from the authors. compared the results from model simulations with rational and boundedly-rational consumers, keep- Acknowledgments ing aggregate spending constant between both cases, which thus differed only by how consumers arrive at Safarzyńska’s research was supported by the decisions about which products to choose. In simu- National Science Centre of Poland, Grant lations with rational agents, consumers are inclined 2016/21/B/HS4/00647. Van den Bergh was suppor- to buy goods solely based on qualities and prices. ted by an ERC Advanced Grant from the European As opposed, boundedly-rational consumers choose Research Council (ERC) under the European Union’s products based on their quality, price and popular- Horizon 2020 Research and Innovation Programme ity. Our modelling results show that consumer beha- (Grant Agreement No. 741087). viour can have long-term consequences for the eco- nomy. In particular, the model with rational agents is characterised by greater market competition. Here, References new products, which are more labour- and energy- Adler M, Anthoff D, Bosetti V, Garner G, Keller K and Treich N efficient, diffuse easier on the market, mitigating the 2017 Priority for the worse-off and the social cost of carbon impact of climate change on unemployment. Over- Nat. Clim. 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