Agent-based Integrated Assessment Models: Alternative Foundations to the
Environment-Energy-Economics Nexus

Karl Naumann-Woleske (0000-0001-8182-9256)
Chair of EconophysiX and Complex Systems, Laboratoire d’Hydrodynamique, CNRS,
Ecole Polytechynique, Institut Polytechnique de Paris, 91120 Palaiseau, France

<EMAIL_ADDRESS>
Abstract

Climate change is a major global challenge today. To assess how policies may
lead to mitigation, economists have developed Integrated Assessment Models,
however, most of the equilibrium based models have faced heavy critiques.
Agent-based models have recently come to the fore as an alternative
macroeconomic modeling framework. In this paper, four Agent-based Integrated
Assessment Models linking environment, energy and economy are reviewed. These
models have several advantages over existing models in terms of their
heterogeneous agents, the allocation of damages amongst the individual agents,
representation of the financial system, and policy mixes. While Agent-based
Integrated Assessment Models have made strong advances, there are several
avenues into which research should be continued, including incorporation of
natural resources and spatial dynamics, closer analysis of distributional
effects and feedbacks, and multi-sectoral firm network structures.

##  1 Introduction

Anthropogenic climate change is one of the major global challenges we face as
a society today, with widespread environmental, social and economic effects
(IPCC, 2022). To assess the economic impact of climate change and develop
economic policies, economists have developed Integrated Assessment Models
(IAMs) that link economic dynamics with environmental aspects. These models
are central in assessments of climate change mitigation strategies and their
implications (e.g. see IPCC, 2018). However, existing models have been subject
to strong critique. Agent-based Models have recently come to the fore as an
alternative framework for macroeconomic modelling, as well as environment-
energy-economics modeling (Balint et al., 2017; Ciarli and Savona, 2019;
Lamperti, Mandel, et al., 2019). In this paper, I analyze four Agent-based
Integrated Assessment models (ABIAMs) and how they respond to the critiques of
the currently mainstream equilibrium-based IAMs. Previous reviews of the
application of complexity economics and agent-based modeling to climate issues
(e.g. Castro et al., 2020; Balint et al., 2017; Lamperti, Mandel, et al.,
2019) have focused on the general benefits of these approaches, but there has
been no systematic comparison of existing ABIAM models.111Lamperti, Mandel, et
al. (2019) showcased the usefulness of the ABIAM approach by highlighting the
work of Lamperti et al. (2018) and Wolf et al. (2013), but did not compare
models in detail.

For the purposes of this paper, we consider an IAM to be a model with
endogenous and linked climate and economic modules.222This is a rather
restricted definition as there is a wide scope of these models (Krey et al.,
2019). However it is appropriate for this paper, as we are addressing economy-
environment linkages and representations of the economic system here. For this
paper, we consider primarily the cost-benefit type IAMs following the Dynamic
Integrated Climate Economics (DICE) models of Nordhaus (1992) and the process-
driven IAMs used in IPCC (2014, 2018, 2022) The majority of the IAMs meeting
this criteria consider a first-best economic system grounded in equilibrium
(general or partial) and perfect foresight (Forster et al., 2018; Keppo et
al., 2021).333A main source of the critique is centered around the IAMs coming
from the economics literature, and that are based on the work of Nordhaus
(1992). The IPCC review models tend to have a higher degree of complexity and
detail It is these models that have faced strong critique for their grounding
in equilibrium, foresight and optimization by representative agents in the
macroeconomic modules underlying IAM (see Ackerman et al., 2009; Pindyck,
2013, 2017; Stern, 2013, 2016; Weitzman, 2013; Revesz et al., 2014; Farmer et
al., 2015). A recent review by Krey et al. (2019) considers several distinct
areas of critique: (a) the absence of heterogeneity of actors and within
groups of actors, which is key to societal transitions due to social processes
emerging from interactions and coordination (e.g. lifestyle change, political
actions). The absence of heterogeneity also strongly limits the analysis of
distributional effects despite their importance (Diffenbaugh & Burke, 2019).
(b) Technology and its diffusion is misrepresented either by being exogenous,
or, when endogenous, being too optimistic (or pessimistic) in advances and
diffusion (see Mercure et al., 2019; Gambhir et al., 2019). (c) A lacking
representation of the financial system, though it faces large risks (e.g. see
Monasterolo, 2020; Monasterolo et al., 2019) and at the same time may be a
driving force in the green transition (see Campiglio et al., 2018; Caldecott,
2018). (d) Energy-economy feedbacks are not fully represented, with missing
energy system, material and economy linkages (Pauliuk et al., 2017) and an
unrealistic decoupling of economic growth from energy usage or emissions
(Nieto et al., 2020). Adding to this list, IAMs, in particular those based on
Nordhaus (1992), are frequently criticised for their "ad-hoc" (Lamperti et
al., 2018) representation of damages from increases in the temperature anomaly
over pre-industrial levels, thus underestimating the costs of climate change
and the benefits to a low-carbon economy (Stern, 2016; Pindyck, 2017). In
these models, the gradual deterministic reactions to mean surface temperatures
omit the emergence of tipping-points, rare events, increasing variability and
decreasing predictability of climate conditions (Wright & Erickson, 2003).

The accumulation of concerns and critiques suggests that it might be
beneficial to consider alternative frameworks for representing the economy and
the environment-economy feedbacks. Agent-based Integrated Assessment models
aim to provide an alternative methodology for modeling the interactions of the
socioeconomic system with the biosphere. Interest in the application of Agent-
based Modelling to the climate-economy-energy nexus dates back to Moss et al.
(2001); Moss (2002), who argued that it can serve as a well validated
description of social and natural systems. The actual applications of Agent-
based Models to the environment-energy-economy nexus has recently been
reviewed in Balint et al. (2017) and Castro et al. (2020), and includes topics
such as carbon and electricity markets, technology diffusion models, and
coalition formation.

Agent-based Models represent complex adaptive systems (see LeBaron &
Tesfatsion, 2008; Hommes & LeBaron, 2018; Kirman & Gallegati, 2022).
Specifically, they comprise a set of heterogeneous agents that interact, adapt
and evolve over the course of time according to explicit market protocols. The
macro- and meso features of the model are then obtained by aggregation over
the set of all individual agents. The interactions give rise to emergent
phenomena, such as endogenous crises and oscillations, and can serve as tools
to understand out-of-equilibrium dynamics. The agent-based methodology has
already been successfully applied in macroeconomic analysis (see Dawid and
Delli Gatti, 2018, for a detailed review). In relation to the biosphere-
economy interaction, ABIAMs offer several distinct advantages such as the
built in heterogeneity, a more granular endogenous innovation and diffusion
process, a granular representation of the financial system, and agent-specific
damage functions. Their modularity and detail of agent-based models also
allows for a closer interaction with stakeholders, such as policymakers.

The paper proceeds as follows: Section 2 briefly presents the models under
consideration and their macroeconomic backbones, Sections 3 and 4 compare the
energy, resource and climate modules of these ABIAMs. In light of this
structure, in Section 5 I consider the policy studies and recommendations that
these models have been used for. Finally, in Section 6 I consider several next
steps in the ABIAM research stream. Tables A-A in the Appendix give a detailed
comparison of the different models in the spirit of Dawid and Delli Gatti
(2018), with extensions for the energy (Table A) and climate (Table A)
modules. These tables may serve as a reference point for the current state of
the models going forward.

##  2 Agent-based Integrated Assessment Models: Four Candidates

To consider how Agent-based Models may address some of the critiques levied at
Integrated Assessment Models, I consider four ABIAM models: the Dystopian
Schumpeter meets Keynes model (DSK hereafter, Lamperti et al., 2018; Lamperti,
Bosetti, et al., 2019; Lamperti et al., 2020, 2021), the ABMIAM model of
Safarzynska & van den Bergh (2022), the model of Czupryna et al. (2020) (CFHS
hereafter), and the model of Gerdes et al. (2022) (GRSW hereafter). This
section introduces the models, their purposes and general macroeconomic
structure.

The DSK model is a climate-extension of the well-established Keynes+Schumpeter
model (Dosi et al., 2010, 2010). The purpose of the DSK presented in Lamperti
et al. (2018, 2020) is to provide an alternative to the specification of
climate damages due to increases in atmospheric $CO_{2}$ concentration. The
model consists of heterogeneous firms in the consumption and capital goods
sectors, both of which are powered by electricity from an energy sector.
Capital goods firms produce machines, with an innovation and imitation process
leading to newer capital vintages (more energy efficient, higher labor
productivity) based on R&D investments. Consumption good firms invest in
different machines to produce a generic consumption good purchased by the
households. These investments are financed by through imperfect capital
markets, where firms are subject to credit limitations. The energy sector
produces electricity using stylized green (renewable) and brown (fossil) power
plants, which differ in their cost structure and emissions. Again power plants
may invest in R&D and pursue an imitation-innovation strategy. Finally, a
climate module connects $CO_{2}$ emissions by all sectors to a carbon cycle,
and thus to an increase in the temperature anomaly over pre-industrial times.
This leads to a disaster generating distribution with increasing average
damage, and a higher probability of extreme damages to firms’ capital stock
and labor productivity as $CO_{2}$ concentration rises.

In Lamperti, Bosetti, et al. (2019); Lamperti et al. (2021), the DSK model is
extended with a detailed set of heterogeneous banks to study the effects of
changes in financial regulation on the transition to a low-carbon economy in
the presence of financial instability. Their study responds to a growing body
of literature suggesting that climate change feedbacks could be increased by
financial market instability, especially with a banking system exposed to
physical risks (Monasterolo, 2020). In doing so, they also simplify the
climate module, thus for the remainder of the paper I will distinguish between
the main branch of the DSK model and the extension to a financial system,
referred to as DSK-FIN.

The second model, the ABMIAM proposed by Safarzynska & van den Bergh (2022)
studies how heterogeneous agents and emerging inequalities in labor and
capital income can lead to larger estimates of the social cost of carbon than
the aggregate Dynamic Integrated Climate Economy (DICE) models based on
Nordhaus (1992) that have been subject to strong critique. Building on the
work of Safarzynska & van den Bergh (2017a, b), the ABMIAM considers a set of
consumption good firms with quality differentiated products, which households
purchase based on a combination of quality, price and peer-effects. Over time,
firms can improve their production technology by investing in R&D. To expand,
firms may request loans from a bank which is subject to credit regulation and
an interbank market. To produce goods, the firms apply labor, capital and
electricity. The energy sector is based on heterogeneous power plants fueled
by gas, coal or renewable energy with different cost structures, efficiencies
and emission intensities. The emissions of the energy sector lead to increases
in the atmospheric stock of carbon, and consequent damage feedbacks. These
were modeled like the cost-benefit DICE IAM to compare calculations of the
social cost of carbon, but unlike DICE the shocks are distributed amongst
agents based on their relative share of wealth similar to Dennig et al.
(2015).

Czupryna et al. (2020) propose a global ABIAM model including ten regions and
multiple different goods. In each region consumer and capital firms produce
their respective goods, and households purchase with preferences for price and
a minimum necessary consumption. To expand their capacities, firms receive
investments from households rather than a financial system, paying back a
share of profits as returns. As in the previous models, production requires
the use of electricity which is supplied by a two-layer energy sector. In the
first instance, fuel-extraction firms mine from finite regional stocks. The
collected fossil fuels are then sold to a heterogeneous set of power plants,
who provide electricity regionally. Over time, production technology improves
at an exogenously given rate, with renewable technology costs also dropping.
The combustion of fossil fuels increases the mean temperature anomaly over
pre-industrial times, which leads to region-specific agricultural shocks
(reduced productivity), labor productivity reductions, and natural disasters
(capital damage).

Finally, Gerdes et al. (2022) propose a fourth ABIAM model.444The authors
themselves do not consider it to be an IAM, however, they do link the economy
and environment both ways, so it falls under the definition of an IAM as
applied here The GRSW model considers two regions, one with a mining sector (a
stylized global south) and one with a capital goods sector (a stylized global
north). Both regions have local labor and consumption good markets, with a
lower wage in the south than the north. Households purchase a homogeneous
consumption good from their regional consumption firms, who produce using
capital and labor. The capital goods sector additionally requires resources
from the mining sector in the south. In the GRSW model, the mines cause
localized pollution that reduces workers health and thus labor productivity.
Simultaneously, the capital goods sector emits $CO_{2}$ when producing
machines, which causes natural disaster shocks to hit firms across both
regions. Using this model, the authors explore unequal exchange and a double
burden faced by the global south (economic dependence on the north, resulting
in lower wages, and heavy damage to the local environment).

In terms of the economic systems represented, these four models differ
primarily in their representations of the financial system, with more detail
in the DSK-FIN and ABMIAM, innovation (endogenous methods in DSK, ABMIAM and
GRSW), spatial scope, energy system (see Section 3), and policy institutions
(see Section 5). With respect to the climate modules, the structure in each is
similar and oriented to $CO_{2}$ emissions, they differ in the types of
damages andc their distribution (Section 4).

By construction, each of the four main models considered in this review
respond to the IAM critique of missing heterogeneity and interactions. Even
when initialized with perfectly similar agents, over time the interactions and
market protocols lead to emerging heterogeneity, such as through
differentiated innovation. Many of the models, such as the ABMIAM or CFHS
initially impose some form of heterogeneity in order to study its effects and
to calibrate the model more closely to empirically observed heterogeneity. The
results indicate that this heterogeneity is indeed important. For example,
Safarzynska & van den Bergh (2022) find that reducing inequalities in labor
income leads to a larger social cost of carbon, while inequalities in capital
income (rent) lead to a larger share of the population driven into poverty,
thus reducing GDP and emissions, and consequently the social cost of carbon.

In terms of geographic and spatial heterogeneity, the considered ABIAMs lag
behind their process-based counterparts. Only the CFHS model represents
multiple consumption sectors and a larger number of regions, though both are
still small in comparison to some other more heterodox IAMs such as ACCLIMATE
(Otto et al., 2017) or E3ME (Mercure et al., 2018). Incorporating this might
lead to a more detailed description of the production process and the global
value chains that underlie it. Agent-based Models have already been applied
successfully to production networks, and could be integrated here as well
(e.g. see the models of Wolf et al., 2013; Gualdi & Mandel, 2019).

Across the DSK, ABIAM and GRSW, innovation and technology diffusion are also
endogenized. For instance, through the innovation-imitation process of
different firms that lead to new technologies but also to the imitation of
technology that are in use by industry leaders. However, technologies still
primarily affect the productivity coefficients of the firms’ production
function, and are thus not necessarily related to specific technology paths
such as those considered in process-based IAMs. It is thus unclear whether
these models are overly optimistic or pessimistic, as noted in the critiques
of Krey et al. (2019).

Finally, in terms of the financial system, both the DSK-FIN and the ABMIAM
incorporate a detailed representation of imperfect capital markets that may
lead to bank failures. In particular, the DSK-FIN extension is focused around
studying the financial fragility emanating from increasing climate damages.
The ABMIAM also offers a heterogeneous banking sector, which also includes
interbank loans, thus creating an impcit interbank network that may be subject
to cascading crises and the types of systemic risk that is not captured in
more common IAMs Monasterolo (2020).

##  3 Energy and Resource Modules

In this section, I address how the four considered models treat the energy-
resource-environment nexus. The representations range from very stylized (GRSW
and DSK) to more sophisticated (CFHS) in terms of the variety of energy
sources used in electricity production.

Beginning with the raw sources of materials and primary energy sources, the
DSK and ABMIAM models consider stylized primary energy types, involving an
extracted fossil fuel (gas and coal in ABMIAM) and a form of renewable energy
that functions without the requirement for fuel inputs. In both these models,
the extraction and provision of these fuels are outside of the model’s
boundary, and are thus infinitely available with exogenously given price
processes. While the GRSW model does not have an energy sector and primary
energy sources, it does have a mining sector that extracts material resources
in the southern region and sells them to the capital goods sector in the
northern, yet here too there are no dynamics of mine-depletion as the purpose
is primarily to study unequal exchange between north and south in the presence
of local and global pollution.

CFHS goes beyond this, by considering not only the conversion of primary
energy to electricity, but also the extraction of fossil fuels. In particular,
they consider seven distinct fuel types (coal, gas, oil, nuclear, hydro, wind
and solar), with a regional fuel-extraction sector. The presence of a fuel
extraction sector is important, as the dynamics of reserve depletion through
extraction and the shifts in regional extraction will impact the agents
decisions about which type of power plant to invest in, what degree of
emissions are possible, and how technological innovation interacts with
depletion (see debates in Höök & Tang, 2013; Capellán-Pérez et al., 2014). In
the CFHS model, each region has an empirically determined reserve of all
fossil fuels. The marginal cost of their extraction is increasing in the
cumulative amount of extraction (modelled by a Rogner curve as in Nordhaus &
Boyer (2003)), reflecting the principle that the easiest-to-extract reserves
are captured first. Likewise, there is thus a regional shift as local reserves
become depleted, favoring those regions with more abundant resources. This is
an important driver in evolving regional inequalities, in the sense of the
unequal exchange studied in the GRSW model (though they do not include
depletion dynamics), as investments and employment will increase in those
regions with the cheapest to extract resources.

Turning to the transformation of primary energy into energy carriers, the DSK,
ABMIAM and CFHS models all consider only electricity as a final energy
carrier. Notably, the CFHS model has a demand for fuel by households, but
considers this to be part of the primary energy sector (there is no
transformation to liquid fuels). All three of these models consider
heterogeneous power plants in terms of their fuel type, cost structure, energy
and emission intensity. For the DSK and ABMIAM the production is centrally
cleared in a given period: sectors present their electricity demand and power
plants are activated until this demand is met. The price is then determined as
a markup on the operating cost of the final power plant to be activated such
that supply meets demand. The CFHS model takes this one step further by
considering the variability in renewable electricity generation. They split
each simulation step into a series of substeps with alternating zero and peak
production of solar. Markets are then cleared in the same procedure as the DSK
and ABMIAM but on a subperiod base, which leads to an average price per
simulation step. Furthermore, fossil and nuclear plants are also considered
stochastic, activating with a beta distribution proportional to their capacity
factors in order to simulate the effects of maintenance which can lead to
price jumps.555Such as simultaneous refueling and maintenance of nuclear
plants in France in 2022 that increased the electricity price in the context
of the gas crisis

Across all models, investment in the replacement of power plants once they
become obsolete, and the decision about the type of power plant to construct
are similarly based on the net present value of each powerplant option, the
candidate plant with the highest expected value (lowest lifetime cost) is then
selected. Where the models differ is in how innovation in the energy-sector
occurs. The DSK applies an endogenous innovation framework, which allows for
reductions in the fixed costs of renewable power plants while for fossil-fuel
plants there is an improvement in emission intensities. By contrast, the CFHS
considers an exogenous noisy decrease in the investment cost for solar and
wind, to a specified minimum, as well as an increase in the substitutability
of electricity for fuels in consumer demands. While the technology process of
the DSK is endogenous, it is unclear whether the reviewed technological
innovations are overly optimistic or pessimistic, and thus whether they
adequately respond to similar critiques of process-based IAMs (Keppo et al.,
2021).

In summary, the energy sector remains rather stylized in three out of the four
models, thus limiting the description of energy source substitution and
technological advances in this respect, as well as the dynamics of fuel
extraction and the multi-scale nature of energy flows through the economy
(Giampietro et al., 2012). However, the CFHS model showed that a more detailed
representation of the energy sector is feasible within ABIAM, including an
implementation of resource extraction in a multi-regional context. Agent-based
approaches have already been applied to energy-sector specific elsewhere,
suggesting that more detailed energy-sector representations in ABIAM should be
feasible (see Castro et al., 2020, for more information).

##  4 Climate Modules

This section addresses how ABIAMs model the environment and crucially the
feedback mechanisms between socioeconomic system and environment. Table A
summarizes the climate and environmental modules of the four reviewed ABIAMs.
The climate modules of the four reviewed models use similar simplified models
of the carbon cycles as in the IAMs based on Nordhaus (2017). These climate
boxes have been critiqued as over-simplifying the carbon cycle, in particular
with relation to irreversible climate tipping points that lock-in certain
temperature changes Dietz et al. (2021).

Where the ABIAMs differentiate themselves is in modeling the damage feedback
from increasing temperature anomalies, and in the case of the GRSW model also
the effects of localised pollution. As a reference point, consider the case of
Nordhaus (1992), where a deterministic (quadratic) function of temperature
gives a multiplier that is applied to the total production. For example, a
given temperature might map to a 5% reduction in total GDP compared to an
“absence-of-damages” world. This approach has been quite heavily critiqued as
underestimating damage impacts and their spatial heterogeneity, and ignoring
non-linear tipping points (Lenton et al., 2019; Steffen et al., 2018). In
contrast, each of the ABIAMs has a specific treatment of the size of the
damage as well as its distribution amongst the model agents. With the
exception of the ABMIAM model, there are also multiple types of damage,
generally including damage to capital stocks and labor reductions (the ABMIAM
considers only shocks to the consumers’ budgets) that are applied at the
agent-level. This approach alone already differs from the cost-benefit IAMs.

Turning to the calculation of damage magnitude and distribution, there is
significant heterogeneity between the models dependent on their intended
purpose. The DSK model directly aims to address the issue of the increasing
variability and risk of rare climate events omitted in deterministic damage
functions. In this spirit, the increase in temperature anomaly changes the
parameters of a beta distribution, leading to a higher mean damage and a
stronger skew. With each firm hit by a random draw affecting capital and labor
productivity, Lamperti, Mandel, et al. (2019) conclude that “under the same
’business-as-usual’ emission scenario, roughly adherent to the Representative
Concentration Pathway 8.5, the average climate shock from DSK and the damage
function in DICE2013r (Nordhaus, 2014) are vaguely similar: the 2100--level
shock averages 5.4% while the DICE damage function implies a GDP loss of
approximately 5.2%. However, aggregate impacts are radically different, with
end-of-century projected output being around 90% of the ’without-climate-
change’ scenario in DICE while amounting to 15% in DSK (with shocks assumed to
target labor productivity)”.

The choices made across models differ. The DSK-FIN uses the deterministic
damage function from Nordhaus (2017), applying the damage perturbed with noise
to all firms, in order to facilitate comparison to the cost-benefit IAM
research. Meanwhile, the ABMIAM and the CFHS model aim to understand how
heterogeneity in agents and shocks can lead to different results than when
using the representative agent and aggregate damages. In particular, the
ABMIAM looks at the social cost of carbon and its associated optimal tax rate
when shocks are distributed amongst individual agents in relation to their
wealth, finding significant impacts of wealth and rent-inequalities on the
social cost of carbon, such as increased poverty rates, leading to a
deterioration of the economy. CFHS aim to verify whether the aggregate damage
functions arise when considering different agents and empirically calibrated
deterministic micro-shocks. To do so they take literature estimates of
agricultural and labor shocks, and empirically estimate the damage of natural
disasters for each of their 10 sub-regions. Running the model, they then study
the shape of the aggregate damage function to compare it to cost-benefit type
deterministic functions. They find that depending on remaining fuel
availability and the speed of renewable energy growth, the aggregate damage
function can take different shapes, and have differing magnitudes. Finally,
the GRSW model proposes that damages are proportional to the total stock of
capital, while the frequency of shocks per period increases with the
temperature anomaly. Thus increasing the probability that one firm may be hit
multiple times per period in a non-linear way. This is in conjunction with
being the only model to consider localised pollution as well. In the mining
sector, workers’ health, proxied by their labor productivity, decreases with
the period of their employment in the mine, thus requiring ever more new
labor. They find that in an accelerated climate scenario, damages outstrip
efforts to repair and innovate, leading to a long-term collapse of the
economy.

In summary, ABIAMs have begun addressing the underestimation of climate
damages suggested by Stern (2016). The benefit of the modular structure of
ABMs is that many different forms and distributions of damage can be
considered, such as regional damages, as applied in CFHS, or agent-specific
damages as in the ABMIAM. Thus models can easily incorporate on-going research
on the micro-impacts of climate change (Carleton and Hsiang, 2016) and
contribute to the ongoing debate on climate damage modelling (Diaz & Moore,
2017).

##  5 Policy Implications

The considered models differ markedly in the scope of implemented and tested
policy options, depending on the respective authors’ stated purpose. With the
exception of CFHS, each model considers some form of policy aimed at
mitigating carbon emissions and hence the negative feedback effects from
increases in $CO_{2}$ concentration. Overarchingly, the benefit of the modular
ABIAMs is that policies that have been suggested in the literature but are not
typically possible in cost-benefit IAMs can be tested. To highlight this, I
consider the case of green financial regulation in the DSK-FIN model and the
implementation of a global markets institution in the GRSW model.

The literature on the climate-finance nexus suggests that an active role of
financial regulators can help shape climate related risk management
(Monasterolo, 2020) and a low-carbon transition (Campiglio et al., 2018). The
DSK-FIN model has a detailed set of heterogeneous banks that are subject to
credit regulation. In this context, the authors test three regulatory
policies: (i) green Basel requirements which excludes loans to green firms are
excluded from banks capital requirements, (ii) green credit guarantees where
the government guarantees the value of loans to green firms, and (iii) carbon-
adjusted credit ratings where greener companies receive an improved credit
rating. In the context of the model, the authors find that individually none
of the policies manage the trade-off between climate mitigation and stable
growth, with either a mitigation at the cost of more frequent banking crises,
or a stable economy until climate damages become extreme enough to lead to
collapse. In addition to the new financial regulations, the DSK model also
includes standard leaning-against-the wind policies such as unemployment
benefits and taxes on firm profits, as well as credit-multipliers to limit
total debt.

In contrast to the financial system regulation, Gerdes et al. (2022) use the
GRSW model to explore the implications of a “civilized market institution”
that has the power to fine capital-goods companies for emissions and mines for
local pollution, and redistribute the collected fines in the form or subsidies
for retrofitting firms’ capital to reduce their pollution and emission
intensities. Their results suggest that fines alone, which may include items
such as carbon taxes, are insufficient to counter natural disaster damage nor
unequal exchange, regardless of the severity of the fines. On the other hand,
when these fines are used to subsidize innovation activities in the form of
retrofitting capital, does the value chain become sustainable over the long
run. All cases are cost-neutral, as subsidies are funded by sanctions, thus
converging to zero as emissions are mitigated. They find that the most
promising results include a North-South transfer as capital firms in the north
still invest in carbon reductions at the same rate, but significantly boosts
mitigation in mines. In a similar vein to the DSK, the model contains
unemployment benefits and taxes on firm profits as well.

The ABMIAM of Safarzynska & van den Bergh (2022) considers the more common
policy of carbon taxation. Specifically, they use an adapted form of the
analytically derived optimal policy by Rezai & Van der Ploeg (2016), with
revenues being redistributed as equal lump-sum payments to citizens. They then
analyze to what degree these taxes may reduce inequalities versus the same
scenarios in their absence. Their findings suggest that income inequality can
be addressed by these policies, while consumption and wealth inequality are
not strongly affected.666Consumption inequality is addressed in an unjust
economy where damages are allocated to the lowest wealth households, as this
essentially functions as a non-damaged income such that households can
maintain their consumption where otherwise they would be in poverty

The policies highlighted in the DSK-FIN and GRSW model show the potential for
ABIAM in policy analysis because ABIAM are able to also incorporate regulatory
policies and a wide array of policy mixes. This would allow for consultation
with policymakers to study in more expansive terms policy interactions and
implications. It also allows to address some of the critiques that a focus on
carbon pricing omits the interaction with innovation and diffusion processes
(Rosenbloom et al., 2020), as well as the interactions and trade-offs with
other sustainable development goals such as equity (Geels et al., 2016). At
the same time, Keppo et al. (2021) note that policies alternative to the
commonplace carbon taxation or trading are also possible in process-based
IAMs, and suggest that the focus is driven by how models are meant to be used
and what policymakers have demanded.

##  6 The Path Ahead

While ABIAMs have made advances in understanding the micro-impacts of climate
shocks, the effects of inequality on policy, and the interlinkages between the
economy, the financial system and climate feedbacks, there is much yet to be
done to match the detail of process-based IAMs. In first place, the current
set of ABIAMs should continue developing to incorporate features common to
process-based IAMs, such as a fine-grained representation of the energy
system, as started in CFHS, a multi-sectoral structure beyond stylized
consumption and capital goods, and a connection with land-use and change
models. Several of these areas have already been addressed by agent-based
models, such as electricity markets (see Castro et al., 2020, for reference))
or multi-sectoral and multi-regional structures as in the LAGOM models (Wolf
et al., 2013), ACCLIMATE (Otto et al., 2017) or Caiani et al. (2018, 2019).
Beyond the addition of detail and combination of these models, there are
several areas worth highlighting.

Bardi and Pereira (2022) point out that “In recent years, global warming and
climate change have become the main focus of the environmental movement. That
may have led to the importance of resource depletion being neglected - more
evidence of the importance of an integrated approach.” A review by Pollitt et
al. (2010) confirms these suspicions by reviewing 60 energy-environment-
economics models and coming to the conclusion that “consumption of material
inputs is largely unexplored within a dynamic macroeconomic framework”. More
recent reviews by Pauliuk et al. (2017) find that IAMs have missing material-
energy-economy linkages in their descriptions of installed capital and
infrastructures. Indeed, also in the reviewed ABIAMs only GRSW consider the
extraction of a physical resource to construct capital, while also not
treating its end-of-lifecycle implications. Given the scale of resource
extraction and the different required resources, even a saturation of
installed capital levels would require large quantities of new virgin
materials in developing countries, and for the energy transition (Wiedenhofer
et al., 2019, 2021; Watari et al., 2019), which may make a full transition
infeasible (Michaux, 2021). Noting here that the extraction and processing of
raw materials is typically an emission-intensive process. Finally, also the
end-of-life waste and recycling may become an important factor in a circular
economy system with reduced virgin material extraction, this is also
underappreciated in current models (McCarthy et al., 2018). The detailed and
heterogeneous structure of ABMs should learn from and implement insights from
industrial ecology to assess not just the socioeconomic but also the material
dimensions of a climate transition. In particular, I suggest considering
modeling at the stock-flow-practices nexus (Haberl et al., 2021), where the
practices and demands of individual consumers become important in the
requirements for various materials. Modeling individual agents also allows for
interactions and social phenomena on the demand-side that may change the path
of the climate transition (e.g. see the review of Castro et al., 2020, for
some ABM-based approaches), where there are unexplored policy avenues (e.g.
see Fitzpatrick et al., 2022).

All of the ABIAMs reviewed in this model show that there are distributional
effects of climate change, especially when considering the differential
impacts of climate feedbacks both regionally in the CFHS and GRSW models, and
amongst individuals in ABMIAM and DSK. More broadly, ABM-type models may be
able to incorporate more indicators and analyses relating to the interaction
amongst different Sustainable Development Goals such that policymakers and
citizens may assess and decide on trade-offs. Such analyses may include
assessing the climatic impacts alternative forms of policy that address issues
of inequality and may restructure the socio-economic sphere such as proposals
for universal basic income (see Hoynes & Rothstein, 2019; Banerjee et al.,
2019, for recent reviews).

Finally, additions and enlargements of Agent-based Models can run into
computational issues. Thus one wishes to carefully choose where to model
heterogeneity to capture key aspects of the overall system behavior (Keppo et
al., 2021). To facilitate this, a process of agentization should be considered
(Guerrero & Axtell, 2011). This involves beginning the modeling exercise with
a system dynamics approach that aims to capture overall system behavior at an
aggregate level, and then slowly replacing sectors or aggregations with
individual agents. This would facilitate both the computational exercise,
validation, and communicability of the results of agent-based models.

##  7 Conclusion

In this paper, I have reviewed four distinct Agent-based Integrated Assessment
models as examples of an alternative framework with which to develop economy-
energy-environment models that address the global climate crisis. ABIAMs have
several advantages to aggregated equilibrium-based models, and are able to
respond to the critiques directed at IAMs. These advantages include: (1)
heterogeneity within and across different groups of agents, which enables the
study of distributional and equity issues. (2) The allocation of damages
across micro-agents in the model with differentiated magnitudes, and in the
case of DSK also increasing variability. (3) ABIAMs have an easier time
representing a financial system populated by multiple banks. This allows for
an explicit consideration of how financial regulation may impact the
transition to a low-carbon economy through different investment channels, and
the associated effects on financial system risk, which leads to (4) a wider
range of policy-mixes can be examined, including their distributional impacts.

While there are a multitude of benefits to the agent-based modeling approach
when applied to integrated assessments (Balint et al., 2017; Lamperti, Mandel,
et al., 2019, see also), there are many avenues along which these models must
yet progress. These include more detailed descriptions of energy systems and
the inclusion of land-use and production sectors to match current process-
based IAMs. Furthermore, ABIAMs should consider the inclusion of insights from
industrial ecology and the full material lifecycle of capital and
infrastructure, as well as the testing of alternative policies and new policy
mixes to address some of the open questions and critiques surrounding IAMs
more generally.

##  8 Acknowledgements

This research was conducted within the Econophysics & Complex Systems Research
Chair, the latter under the aegis of the Fondation du Risque, the Fondation de
l’Ecole polytechnique, the Ecole polytechnique and Capital Fund Management. I
also acknowledge the support from the New Approaches to Economic Challenges
Unit at the Organization for Economic Cooperation and Development (OECD).

##  Appendix A Intercomparison of ABIAMs

Overview of the General Structure of four Agent-based Integrated Assessment Models. Details on the energy and resource sector are in Table A, the climate module in Table A, and policy institutions in Table A |  |  |  |  |
---|---|---|---|---|---
|  DSK |  DSK-FIN |  ABMIAM |  CFHS |  GRSW
|  DSK |  DSK-FIN |  ABMIAM |  CFHS |  GRSW
Table continues on next page |  |  |  |  |
Key References |  Lamperti et al. (2018, 2020) |  Lamperti, Bosetti, et al. (2019); Lamperti et al. (2021) |  Safarzynska & van den Bergh (2022) |  Czupryna et al. (2020) |  Gerdes et al. (2022)
Macroeconomic Framework |  K+S Model |  Lamperti et al. (2018) |  Safarzynska & van den Bergh (2017a, b) |  No prior framework |  Influenced by Rengs & Scholz-Wackerle (2019)
General Properties
Stock-flow Consistent |  Yes |  Yes |  Unspecified |  Unspecified |  Unspecified
Timestep |  Quarter |  Quarter |  Year |  Year |  Monthly with annual-only events
Regions |  Single |  Single |  Single |  10 regions: Africa, Japan, China, India, Rest of Asia, Europe, North America, Central and South America, Commonwealth of Independent States, Middle East |  Two: Global North (with capital goods), Global South (with mines)
Consumption
Reference |  Lamperti et al. (2018) |  Lamperti et al. (2018) |  Safarzynska & van den Bergh (2017b) |  Czupryna et al. (2020) |  Gerdes et al. (2022)
Goods |  Single C-Good |  Single C-Good |  Multiple goods. Each firm offers good with differentiated quality depending on maximum attainable quality and duration of producing a given good |  Multiple goods: agriculture, textiles, chemicals, other manufacturing, transport, and other services |  Single C-Good
Production |  Constant returns to scale with labour and capital vintages |  Constant returns to scale with labour and capital vintages |  CES production function with labour, capital and energy |  CES with capital, labour and energy |  Leontief function with capital and labour
Factor Demand |  Proportional to target production |  Proportional to target production |  Cost minimization of CES given production target |  Cost minimization of CES given production target |  Proportional to target production
Supplied Quantity |  Expected demand with adjustment for inventory |  Expected demand with adjustment for inventory |  Weighted average of current sales and actual demand |  Tatonnement: increase if excess demand and price above market (Assenza et al., 2015) |  Target production depends on expected demand with adjustment for target inventory
Pricing |  Variable markup based on market share |  Variable markup based on market share |  Variable markup on cost based on past market power. Costs include variable cost and fixed cost of producing quality good |  Tatonnement: increase if below market and excess demand, decrease if reverse (Assenza et al., 2015) |  Tatonnement: Price is adjusted downward if strongly lower sales, and upward if strong excess demand. Bounded from below by production costs. Adoption of a new price is successful with a fixed probability
Investment |  Based on expected demand, with scrapping based on expected gains. |  Based on expected demand, with scrapping based on expected gains. |  Based on expected demand |  Based on excess of capital factor demand over existing capital |  Target based on expected demand.
Household Demand |  All income consumed |  All income consumed |  Consume based on target wealth-to-permanent-income ratio |  Part of income (fixed propensity) plus any savings |  Budget is wage income plus proportion of savings
Household Choice |  N/A |  N/A |  Intensity of choice function with utility per product. Product-utility is a Cobb-Douglas type aggregation of quality, price and number of other buyers |  Stone-Geary utility function over $n$ goods, with a required minimum consumption. Energy consumption is split into electricity and fuels based on CES, then fuels is split into coal, gas and oil based on CES |  Household has shortlist of preferred firms, with 25% change household might change firm to a lower price one. With 25% chance household replaces firm that didn’t satisfy demand with random alternative
Market Protocol |  Not explicit |  Not explicit |  Not explicit |  Regional clearing except transport and other services. Consumers visit producers (unspecified order) adjusting demands based on prices as clearing proceeds |  Two purchasing rounds: a fraction of desired demand bought in round one, the remainder in round two. If a firm cannot satisfy demand, a household tries another firm until satisfied or no supply left.
Capital |
Reference |  Lamperti et al. (2018) |  Lamperti et al. (2018) |  Safarzynska & van den Bergh (2017b) |  Czupryna et al. (2020) |  Gerdes et al. (2022)
Capital Goods |  Multiple vintages: labour-productivity, energy-efficiency, emission intensity |  Multiple vintages: labour-productivity, energy-efficiency, emission intensity |  N/A no explicit sector |  Single type of capital |  Single type of machine
Production Technology |  Constant returns to scale with labour and energy |  Constant returns to scale with labour and energy |  N/A |  CES with capital, labour and energy |  Leontief with capital, labour and resources
Technological Change |  Nelson & Winter (1982) imitation-innovation process based on R&D investment (See Dosi et al., 2010) |  Nelson & Winter (1982) imitation-innovation process based on R&D investment (See Dosi et al., 2010) |  Nelson & Winter (1982) two-step process for improving CES technical coefficients. Maximum product quality and technical coefficients increase exogenously over time |  Exogenous noisy growth in CES technical coefficients |  None. Fixed technical production coefficients
Prices |  fixed markup |  fixed markup |  N/A since not a sector |  Tatonnement: increase if below market average and excess demand (Assenza et al., 2015) |  Tatonnement: Price is adjusted downward if strongly lower sales, and upward if strong excess demand. Bounded from below by production costs. Adoption of a new price is successful with a fixed probability
Quantity |  Proportional to expected demand |  Proportional to expected demand |  N/A |  Based on expected demand, subtracting own requirements first |  Target depends on expected demand with an inventory adjustment
Market Protocol |  Choice by price, productivity, energy-efficiency. Can consume froma subset of producers. Delivery at end of period |  Choice by price, productivity, energy-efficiency. Can consume froma subset of producers. Delivery at end of period |  N/A since not a sector |  Assenza et al. (2015): each consumer connected to fixed number of producers, purchasing from lowest producers in order of lowest price first. Excess demand is partially satisfied. Once fixed network is completed, additional demand is fulfilled by excess supply or proportionally allocated. Adjustment for import/export: if a region has an export surplus, imports are preferred |  Consumption good firms have shortlist of capital firms, updated every 3 months with 25% change household might change firm to a lower price one. With 25% chance household replaces firm that didn’t satisfy demand with random alternative. Firm attempts to buy equal fraction of demand from all sellers, if unsatified continues until at least 95% satisfied or no more stock
Labour & Household Income
Reference |  Lamperti et al. (2018) |  Lamperti et al. (2018) |  Safarzynska & van den Bergh (2022) |  Czupryna et al. (2020) |  Gerdes et al. (2022)
Supply |  Fixed |  Fixed |  Fixed |  Fixed Regionally |  Fixed Regionally
Differentiation |  None |  None |  None |  None |  Global south adjusts labour productivity based on local pollution and duration of employment
Wages |  Single market wage based on productivity, price, unemployment |  Single market wage based on productivity, price, unemployment |  Wages are fixed, with a proportional increase when demand exceeds supply of labour |  Unspecified |  All firms adjust wage based on change in price of their good over prior 12 months, with a maximum adjustment rate. Downward rigid. Mining employee wages are adjusted for productivity
Other income |  None |  None |  A share of energy of energy and capital rents. Interest on deposits. |  Dividends from shareholdings in companies |  half of firm profits are distributed regionally in proportion to their existing savings. Excess R&D funds are distributed analogously
Market Protocol |  Not explicit |  Not explicit |  Randomly allocated workers |  Randomly allocated within regions |  Regional markets with random matching. Capital and consumption goods have a maximum amount of new hires, and maximum proportion of labour that can be fired. Mines
Credit & Financing
Reference |  Lamperti et al. (2018) |  Lamperti et al. (2021) based on Dosi et al. (2015) |  Safarzynska & van den Bergh (2017b) |  Czupryna et al. (2020) |  Gerdes et al. (2022)
Credit Demand |  Desired investment net of cash |  Desired investment net of cash |  Desired investment net of cash |  Desired investment |  Desired investment net of cash
External Finance |  Bank loans |  Bank loans, and government bonds for government purchased by banks |  Bank loans |  Household investment |  Bank loans
Firm Bankruptcy |  Negative liquid assets or zero market share. Replaced by firm’s representing industry averages |  Negative liquid assets or zero market share |  Inability to pay back loans, high market share firms can extend loan payback by some periods. Capital goes to the bank, which resells to new entrants with fixed probability |  Consumer & capital firms go bankrupt if there is a lack of demand or lack of production factors. Fuel extraction companies go bankrupt if all resources are exhaused. Ownership covers the losses |  No production for 12 months
Firm Entry |  Replace bankrupt firm by industry average firm |  Replace bankrupt firm by industry average |  new firm enters with fixed probability, offering random product quality with production technology greater than best current technology. Firm demands start-up loan for initial investments, successfully granted with a fixed probability. First period has a zero markup price |  Unspecified |  Unspecified
Credit Supply |  Pecking-order based on net-worth-to-sales. Upper bound to credit based on debt-to-sales |  Bounded by each banks’ equity, which is subject to a Basel-II capital rule. Pecking order based on firm’s credit worthiness |  Firm receives loan if below exogenous debt-to-equity ratio. |  Household decide on overall planned investment (income net of consumption) |  Unbounded
Interest rate |  Markup on central bank rate |  Risk premium based on client position in credit ranking (markup is based on quartile within the banks clientele) |  The same offer from all banks, with electricity having a lower interest rate |  No interest. Firms pay out profits |  Fixed rate
Regulation |  Maximum credit set by credit multiplier rule |  Time-varying capital adequacy ratio |  Minimum level of reserves held at central bank, with fixed minimum and higher reserves depending on deposits |  None |  None
Bank Bankruptcy |  None |  Equity (net worth) is negative |  Equity or reserves are negative. Lending banks write off the loans to defaulted banks |  None |  None
Bank Entry |  None |  Bankrupt bank is bailed out by the government. Bailout up to a (fraction of the equity of the smallest incumbent) |  None |  None |  None
Market Protocol |  Single bank, pecking-order credit |  Each bank has a pecking order process for its list of clients |  Loans granted based on debt-to-equity ratio. If a bank has insufficient funds to grant a loan, it asks other banks for loans (order of liquidity) until liquidity requirements are satisfied |  Households distribute planned investment among companies based on their current ownership shares and value of companies planned capital increase. If planned investment exceeds demand, money is distributed back to owners |  All credit granted if profit rate is larger than interest rate adjusted for credit-lenience
Overview of the Energy and Resource Module of four Agent-based Integrated Assessment Models |  |  |  |
---|---|---|---|---
|  DSK & DSK-FIN |  ABMIAM |  CFHS |  GRSW
|  DSK & DSK-FIN |  ABMIAM |  CFHS |  GRSW
Table continues on next page |  |  |  |
Reference |  Lamperti et al. (2018) |  Safarzynska & van den Bergh (2022) based on Safarzynska & van den Bergh (2011); Safarzynska (2012) |  Czupryna et al. (2020) |  Gerdes et al. (2022)
Energy Markets
Primary Energy Types |  representative fossil fuel, representative renewable flow |  three fuels: (1) increasing unit cost over time, (2) decreasing unit costs over time by Brownian motion, (3) constant price. Associated with gas, coal and renewable energy |  Coal, gas, oil, nuclear, hydro, wind and solar |  N/A
Producer Heterogeneity |  green (renewable) and brown (fossil) power plants with capital vintage dependent cost-structure, thermal efficiency, environmental impact. Production requires only capital, and fossil fuel for brown power plants (one unit per unit electricity) |  heterogeneous plants differentiated by: age, productivity, energy source, installed capacity, maximum lifespan, capacity factor |  Heterogeneous plants: fuel type, production capacity, storage capacity (solar and wind), lifetime, capacity factor, operation cost factor, electricity transmission loss factor, thermal efficiency factor |  N/A
Production Technology |  Production requires only capital, and fossil fuel for brown power plants (one unit per unit electricity) |  Cobb-Douglas function of capital, labour and fuel with plant-specific TFP inversely related to thermal efficiency increased by Gaussian every period and fixed exponents (substitution factors). |  Fixed capacities. Planned electricity fixed for nuclear, beta distribution for all other types (maintenance and weather) with a shape proportional to capacity factors. Solar has double capacity in daytime, and zero at night. Maximum supply augmented by storage and reserve rates for combustion plants |  N/A
Production Capacity |  Unitary per plant |  Plant-specific chosen at creation of plant |  Plant-specific |  N/A
Production Cost |  price of fossil fuels in relation to thermal efficiency for brown plants, zero for green plants |  cost of labour, fixed operating costs, fuel costs |  operation cost proportional to production, plus labour cost |  N/A
Pricing |  fixed markup on the marginal producers cost (supplier of last unit) |  Inverse demand function with markup |  Market clearing in each sub-period, with stress factors if demand > maximal provision |  N/A
Energy Storage |  No |  No |  Yes, for solar and wind plants |  N/A
Final Energy Types |  Electricity |  Electricity |  Electricity (Fuel considered a direct primary purchase) |  N/A
Market Structure |  Central authority activating plants until demand is met |  Cournot game: each plant produces to maximize profits given |  Time split into sub-steps (stochastic generation profiles) |  N/A
Depreciation |  All plants have a fixed lifetime |  Plants have a fixed lifetime |  Plants have a fixed lifetime, each period oldest part of capacity for a plant is depreciated. |  N/A
Physical Investment |  Cost of new brown plant is zero, while new green plant has vintage-dependent fixed cost. Expansion is done when demand exceeds maximum production. Green plants are preferred as long as their fixed cost is less than present value of the cost of the most efficient brown plant |  Once a fixed lifetime is reached, a plant exists and the owner invests in a new plant. The type of fuel is chosen based on expected profits from that fuel. A new plant receives a loan to construct, this has to be paid back at the end of its lifetime |  Each period a share of old capacity is replaced by investment if maximum expected demand cannot be met post-depreciation. Maximal capacity increases are bounded from above. Solar and wind also invest in storage if electricity prices are volatile. |  N/A
Technological Innovation |  Fraction of toal past sales invested in R&D, allocated in proportion to revenue generated. Nelson & Winter (1982) two-step process: (1) draw for successful innovation, (2) beta-distribution draw or proportional improvement |  None - fixed Cobb-Douglas exponents |  Overnight investment costs for solar and wind decrease to a specified floor. Substitution of electricity for fuels inreases to match intra-fuel substitutability |  N/A
Final Demand |  C-Good and K-good sectors |  C-good market |  All sectors except electricity producers |  N/A
Market Protocol |  Plants activated in order of cost (green first) until demand is met |  Plants choose production to maximize profit based on Cournot game with linear inverse demand function (coefficient adapte to guarantee i). Factor demands are based on marginal productivity |  In each region, time is in sub-steps with half as night (no solar, low demand) and half as day (higher demand) and cleared each time to develop an average price for the period. |  N/A
Resource Markets
Types of Resources |  Representative fossil fuel |  Three stylized fuels |  Coal, Crude Oil, Natural Gas |  Representative extracted resource
Stock and Extraction |  Infinite stock |  Infinite stock |  Finite, regional stocks. Marginal costs of extraction follow Rogner curve. Planned production is adjusted for regional depletion rates (easy to extract first). |  Infinite stock
Production Technology |  N/A |  N/A |  Capital gives capacity, fixed total labour. Capital adjusted based on expected vs. realized demand. No innovation. |  Leontief dependent on labour and capital
Price |  Exogenous variable |  Geometric Brownian Motions |  Intersection of supply and vertical demand (short-term inelasticity) |  Tatonnement: Price is adjusted downward if strongly lower sales, and upward if strong excess demand. Bounded from below by production costs. Adoption of a new price is successful with a fixed probability
Market Protocol |  N/A |  N/A |  Centrally cleared per fuel (coal, crude, gas). Supplied at the marginal extraction cost, consumers bid quantities and acecpt market price. If demand>planned supply, the highest price is taken and excess demand distributed over suppliers (assuming below maximum extraction). If demand>max.extraction, proportional rationing. |  Capital good firms have shortlist of capital firms, updated every 3 months with 25% change household might change firm to a lower price one. With 25% chance household replaces firm that didn’t satisfy demand with random alternative. Firm attempts to buy equal fraction of demand from all sellers, if unsatified continues until at least 95% satisfied or no more stock
Overview of the Implementation of Climate Modules in four Agent-based Integrated Assessment Models |  |  |  |  |
---|---|---|---|---|---
|  DSK |  DSK-FIN |  ABMIAM |  CFHS |  GRSW
|  DSK |  DSK-FIN |  ABMIAM |  CFHS |  GRSW
Table continues on next page |  |  |  |  |
Reference Paper |  Lamperti et al. (2020) |  Lamperti, Bosetti, et al. (2019) |  Safarzynska & van den Bergh (2022) |  Czupryna et al. (2020) |  Gerdes et al. (2022)
Climate System
Reference Framework |  C-ROADS model of Sterman et al. (2012, 2013). Similar to Nordhaus (1992) |  Single-equation framework similar to Matthews et al. (2009, 2012) |  Nordhaus (2017) |  Petschel-Held et al. (1999) |  Single equation framework
Timescale |  Annual |  Quarterly (like model) |  Annual |  Annual |  Monthly
Pollution Sources |  Consumption Goods Sector, Capital Goods Sector, and Energy Sector emit CO2 |  Consumption Goods Sector, Capital Goods Sector, and Energy Sector emit CO2 |  Energy sector (fuel-specific) emits CO2 |  Energy sector (fuel-specific). Unclear Emits CO2 |  Capital firms in the global North emit CO2. Mines in the global South cause local Pollution
Description |  Two-layer model with two loops: (1) increased “natural” primary CO2 production with CO2 levels, (2) oceans’ capacity to uptake carbon falls with CO2 concentration increases. Radiative forcing determines mean temperature increase. |  Fixed ratio for change in temperature following change in cumulative emissions |  Changes in atmospheric carbon depend on existing stock and past emissions with a permanent and transient part. Stock of carbon affects global mean temperature anomaly
$T=\omega\frac{\ln\frac{E_{t}}{E_{pre}}}{\ln 2}$ |  Three-equation carbon cycle. Cumulative emissions increase by economy, leading to increase in carbon concentration (cumulative + annual emission - difference to prehistoric values). Temperature change is proportional to carbon intensity vs. prehistoric and temperature vs. prehistoric. Regional temperatures differ, but increase by the same as global mean temperature |  Emission increases monthly, and decreases as a fixed proportion of initial concentration. Local pollution of the global south depends on mine production rate and their pollution coefficients
Damage Feedback
Types of Damage |  Capital stocks, labour productivity, inventories, energy-efficiency |  Labor productivity, capital stocks |  Consumer budgets |  Agricultural, Labour, Natural Disasters |  Capital stocks, Labor productivity of workers in mines due to local pollution
Damage Distribution |  Beta distribution of damage proportion (uni-modal right-skewed), with a mean increasing in temperature, and the right tail increasing with temperature variability (higher risk of extreme events) |  Damage follows Nordhaus (2017) deterministic damage function: a quadratic function of temperature levels with two response parameters |  Total damage proportional to increase in temperature
$\left(1+{}_{1}T_{t}^{{}_{2}}\right)^{-1}$ |  Deterministic functions. Agriculture: literature estimates for Europe/Africa/Rest-of-World. Labour: quadratic function of temperature difference to $13^{\circ}C$. Natural disasters: regional regression estimates of USD bn. loss per degree increase in temperature |  Damage magnitude is a proportion of total capital level, monthly number of disasters (hits) is a nonlinear function of current emissions compared to the baseline, parameterized by an acceleration rate.
Damage Allocation |  Each firm is hit with a random draw affecting capital or labour productivity |  All firms are hit by the aggregate shock modified by a small Gaussian noise parameter |  Based on modification of Dennig et al. (2015): consumption post damage is reduced by consumer-specific share of total damage, dependent on the share of wealth (through wealth-elasticity of damage) |  Agricultural damages are reductions in all CES coefficients for Agriculture sector. Labour damages are reductions to labour efficiency of capital/consumer good companies. Natural disasters: reduce all firms’ capital, reduce output of consumer and capital good firms |  Each hit hits a random firm (capital, consumption or mine) allowing for multiple hits per month. Firms lose capital equivalent to the damage value. Local pollution per mine decreases the mine’s employees productivity (from 1 down to a minimum of 1/3). Workers are replaced every 30 years (same employer and savings)
Tipping Points |  Implicit due to higher probability of extreme events |  None |  None |  Non-linearity in data, but no tipping points |  None

Overview of the Policy Experiments of four Agent-based Integrated Assessment Models |  |  |  |  |
---|---|---|---|---|---
|  DSK |  DSK-FIN |  ABMIAM |  CFHS |  GRSW
|  DSK |  DSK-FIN |  ABMIAM |  CFHS |  GRSW
Table continues on next page |  |  |  |  |
Reference |  Lamperti et al. (2018, 2020) |  Lamperti, Bosetti, et al. (2019); Lamperti et al. (2021) |  Safarzynska & van den Bergh (2022) |  Czupryna et al. (2020) |  Gerdes et al. (2022)
Government
Fiscal Policy (Outflow) |  Unemployment benefits as a fixed fraction of current market wage |  Unemployment benefits as a fixed fraction of market wage. Bank bailout costs |  None |  None |  Unemployment benefits as 80% of mean regional wage
Budget Deficits |  Taxes on firm profits |  Taxes on firm incomes and worker incomes. Government pays interest on its bonds to banks and the central bank, which are issued if deficits are positive. |  None |  None |  Taxes on firm profits
Central Bank
Interest rate |  fixed baseline rate |  Taylor type rule with target inflation and unemployment rate |  Fixed rates |  None |  Fixed baseline rate
Credit regulation |  sets credit multiplier (on deposits) to limit total debt |  Bank specific credit multiplier depending on risk weighted assets and bank equity |  Minimum reserves and fraction of deposits. Critical Debt-to-equity value for loan-granting |  None |  None
Policy Experiments
Fiscal |  No Experiments |  No experiments |  Carbon Tax determined from the social cost of carbon in DICE models, the formula proposed by Rezai & Van der Ploeg (2016). Revenues are distributed as equal lump-sum to citizens |  No Experiments |  Global civilized market institution: sets base fine for emissions (capital firms) and local pollution (mines). Subsidises via: (a) no subsidy, (b) fines collected are redistributed in region of collection based on firms’ fraction of total capacity, (c) Same as b, but a share of global north funds is reallocated to the south, (d) same as b but funds are multiplied by a government grant scheme
Monetary |  No Experiments |  No Experiments |  No Experiments |  No Experiments |  No Experiments
Regulation |  No Experiments |  (1) Carbon-risk adjustment: firms rank in banks’ pecking order becomes the average of their credit rank and their emissions rank. (2) Green public guarantees: government backs loans to green firms completely. (3) Green Basel-II: exclude loans to green firms from the credit mutiplier regulation, thus increasing total credit supply |  No Experiments |  No Experiments |  No Experiments
Other |  Exogenous increases to fossil fuel prices mimicking a carbon tax / green investment subsidy, and decreases mimicking current fossil subsidies (Done in Lamperti et al., 2020) |  No experiments |  Test carbon tax when probability of a electricity plant being renewable is 50% exogenously (e.g. regulation driven) |  No Experiments |  No Experiments

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