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Endogenous economic growth, climate change and societal values: A conceptual model

Michael W.M. Roos

Ruhr-Universität Bochum

Department of Management and Economics

Chair of Macroeconomics

44801 Bochum, Germany

Michael.Roos@rub.de

9 November 2015

Abstract

In this paper, I propose a model that is an alternative to conventional neoclassical models of growth

and the environment. The model is a novel conceptual framework that can be extended in many

dimensions and applied to a host of policy questions. Global economic growth, the evolution of the

human population, C02 emissions, and the state of the environment are endogenous. The main driver

of all economic variables are societal values which determine the different types of investment, the

level of aggregate consumption and employment. The model is applied to generate possible scenarios

for the 21st century. A baseline calibration generates an average global GDP growth rate of 3.4% p.a.

and a global population level of 9.2 billion people in 2100. Mean global temperate in 2100 will be 2.8°C

higher than in 1995. A policy analysis shows that green investment should neither favor environmental

restoration nor climate protection but weigh both uses equally.

Keywords: endogenous growth, societal values, climate change, environment, system dynamics,

evolutionary economics

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1 Introduction Although climate change and environmental destruction are serious challenges to global civilization,

they are only fringe topics in current mainstream macroeconomics. Fischer and Heutel (2013) argue

that that there should be more work on environmental policy in macroeconomics and review some

Real Business Cycle models and economic growth models that address environmental issues. Rezai et

al. (2013) also call for more macroeconomic research on climate change and identify a particular need

for more theoretical analysis and modeling. There is some literature that analyzes the relation between

economic growth and the environment in neoclassical growth models, as reviewed in Xepapadeas

(2005) and Brock and Taylor (2005). And of course, the integrated assessment models such as DICE

(Nordhaus and Sztorc 2013), FUND (Anthoff and Tol 2013) and PAGE (Hope 2011) can be seen as

macroeconomic models.

In this paper, I propose a model that is an alternative to conventional neoclassical models of growth

and the environment and that takes into account the complex interaction of economic growth,

temperature change, population change, and the evolution of societal values. My model is an example

of a novel conceptual framework that can be extended in many dimensions and applied to a host of

policy questions. In the model, global economic growth, the evolution of the human population, C02

emissions, and the state of the environment are endogenous. The main driver of all economic variables

are societal values which determine the different types of investment, the level of aggregate

consumption and employment. Societal values vary on a materialist/post-materialist spectrum and

respond to the degradation of the natural environment. When the state of the environment

deteriorates, society becomes more post-materialistic and invests more into carbon efficiency

improvements and the restoration of the environment. However, since the global average

temperature depends on the already emitted stock of carbon dioxide, society may respond too slowly

to the environmental damage caused by the industrial production of output.

Conventional integrated assessment models like FUND or PAGE are very detailed with respect to the

ecological part of the model, but economic growth is simply an exogenous process which is hardly

convincing from the perspective of economic theory (see Bonen et al. 2014). In line with the literature

on economic growth and the environment, the economic part of the DICE model is a conventional

neoclassical Ramsey growth model. These neoclassical growth models can be criticized for a variety of

reasons. Regarding their usefulness to analyze climate change, Rezai et al. (2013) observe that in these

models the adjustment of aggregate economic variables such as output or the capital stock to changing

environmental conditions typically occurs smoothly and optimally. The ecological system’s response

to climate change, however, is likely to be characterized by tipping points and systemic instabilities,

which might also imply sudden and drastic effects on the economy. Neoclassical models hence might

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provide misleading guidance how the economy will and should respond to climate change.

Furthermore, most economic models, apart from the more detailed integrated assessment models,

have a fairly simple structure and focus on very few variables. Such a reductionist approach that leaves

out many variables or assumes them to be exogenous is helpful to understand how certain

mechanisms work and might be appropriate for short-run analyses. Yet for realistic scenarios over

several decades that are intended to inform economic policy, these models are too stylized. Climate

change might induce major societal transformations, either preemptive ones seeking to mitigate its

effects or forced adjustments, if mitigation is not successful. Major transformations of society involve

complex interactions between many economic and non-economic variables which the mainstream

models cannot capture adequately.

At a more fundamental level, there are well-justified methodological critiques against the standard

microfoundations paradigm in macroeconomics with representative agents, rational expectations and

perfectly rational maximizing agents (Kirman 1992; Hartley 2002; Setterfield and Suresh 2012). In the

presence of interaction between heterogeneous agents and market failure due to externalities the

representative agent assumption is highly problematic. And as discussed in (Roos 2015), climate

change and the resulting transformation of the socio-economic system involve radical uncertainty so

that maximization and rational expectations are inadequate assumptions. As a consequence of these

problems, the model presented in this paper does not have explicit microfoundations. I argue that the

standard approach to microfounded macroeconomic models forces researchers to leave out many

aspects relevant to the analysis of climate-induced transformations of the economy and to make very

strong assumptions that compromise the external validity of these models. A purely aggregate

structural model makes the interactions and feedback effects between different parts of the economic

system and the environmental system more transparent.

The main methodological novelty of the paper is the introduction of societal values as a driving force

of all macroeconomic variables. This modelling approach allows me to endogenize the economic

processes without having to resort to dubious microfoundations. Societal values serve as a summary

variable for potentially quite complicated social dynamics of individual agents’ motives and individual

and collective decision processes. They are measurable and have been studied extensively by Ronald

Inglehart (e.g. Inglehart 1977, 1995). Introducing social values into a macroeconomic model brings

macroeconomics closer to sociology, social psychology, and political science. While in the recent years

microeconomics has been strongly influenced by behavioral economics that studies the behavior of

real humans, macroeconomics might benefit greatly from socio-economics (Etzioni 2003). Socio-

economics analyzes the relationships between society and the economy and uses insights from history,

political science, anthropology, sociology and other fields dealing with social processes.

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Conventional neoclassical models of economic growth and the environment explore questions such

as1: Is there a balanced growth path without accumulation of pollution? Are pollution and

environmental protection a drag on economic growth? How are the steady state levels and growth

rates of consumption, income, or pollution affected if the environment is taken into account? How

does the market outcome differ from the social optimal and how could policy interventions correct

market failure, e.g. by pollution-internalizing taxes? These questions are surely interesting and highly

relevant for our theoretical understanding of the economic growth process. However, focusing on

these questions alone is problematic from a policy perspective for several reasons. First, steady state

analysis that makes statements about the long run is of little help for political decisions and their

consequences in the next years of decades. Knowing that a balanced growth path with sustainable

levels of pollution exists in the long run is not helpful if we do not known when and how it will be

reached. Second, neoclassical models with microfoundations typically do welfare analyses and try to

assess the costs and benefits of climate change and the policies to mitigate it. Apart from the already

mentioned problems related to the use of perfectly rational representative agents in this kind of

inquiry, costs-benefit analyses of climate change involve serious challenges. Referring to the influential

Stern Review (Stern 2006) some authors (Ackerman 2010; Aldred 2009) discuss that cost-benefit

analysis crucially depends on the choice of the discount rate, the treatment of uncertainty about the

effects of climate change, and the techniques for monetizing non-monetary impacts such as loss of life

or loss of biodiversity. Scrieciu et al. (2013) also argue against the use of traditional cost-benefit

analysis and propose to analyze the interaction between economy, environment and society with

alternative methodologies such as those based on multi-criteria analysis, which endogenize

technological and institutional change. Finally and related to the previous point, the policy analyses in

many neoclassical models are not very helpful for practical policy. It is common practice to determine

an optimal policy with the tool of the fictitious social or Ramsey planner whose optimization problem

incorporates all market externalities. Comparing the optimality conditions of the representative

private agents and those of the social planner, one can derive optimal policy instruments such as taxes

or subsidies that would induce the private agents to internalize the external effects of their actions on

the environment. Even if such optimal policies could be found – which is hardly possible if the

uncertainty about the complex dynamics of the economy and the natural environment is properly

acknowledged -, this kind of research does not say anything about the crucial question how optimal

policies could be implemented in the political process. The use of a Ramsey planner always assumes

that all the complications of implementing optimal policies have been solved. But real politics is all

1 See Xepapadeas (2005)

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about distributional issues, power, social acceptance, and institutional constraints. Economics models

that are meant to inform actual policy-making must take these factors into account.

The model and the analysis in this paper reflect these criticism of the conventional approach. Rather

than analyzing the properties of some long-run steady state or balanced growth path, I simulate the

potential evolution of the global socio-ecological system in the 21st century. The model generates

scenarios how the system might evolve under plausible initial conditions and parameter values and

shows how sensitive these scenarios are to the assumptions. Although the model is roughly calibrated

to empirical data, it is not meant to be predictive in the sense that it makes reliable forecasts about

the most likely future paths of the endogenous variables. It is anticipatory in the sense of showing

which outcomes are possible. In contrast to social planning approaches, my model implicitly treats

policy as endogenous by assuming that societal values are constraints to and drivers of both private

behavior and public policy. Although in principle the effects of climate change on population and the

environment could be monetized, I deliberately abstain from doing this in order to emphasize the real

effects in the model. Instead of suggesting optimal policies or trajectories, that might be highly

misleading given the involved uncertainties, the model is intended to raise awareness of how the

future of the global economy and the natural environment might look like in the coming decades and

how possible trajectories depend on the model assumptions.

The paper is structured as follows. In Section 2, I discuss the concept of societal values and their

relationship with the economy more in depth. Section 3 presents the model description and Section 4

contains the parameterization of the model. In Section 5, I analyze some properties of the model. Given

that the main contribution of this paper is to propose a concept of a modeling framework, the model

analysis is not exhaustive but rather exemplary. Section 6 discusses the model and its results and

presents some thought on potential extensions and applications and Section 7 concludes.

2 Societal values It is common in integrated assessment models to run different scenarios that predict how the socio-

ecological system might evolve in the future under different assumptions about the behavior of

economics agents and about climate policy. Typically, there is a business-as-usual scenario that

extrapolates the current behavior and policy into the future and some policy scenarios in which

different policy measures to fight climate change are implemented. The comparison of the policy

scenarios with the business-as-usual scenario allows the researchers to evaluate the effectiveness and

efficiency of the various policies. This approach is reasonable if the aim is to come to a hypothetical

assessment of different policies. However, it treats policy and the fundamentals of agents’ behavior as

if they were exogenous to the socio-ecological system, which is implausible in the long run.

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Exogenously imposing some policy action on the system does not take into account how likely it is that

such a policy actually will be implemented, such that this approach is normative rather than positive.

It is the central proposition of this paper that both the behavior of economic agents and economic

policy depend on societal values, attitudes, and preferences. The values endorsed by the members of

a society determine consumption and production choices both directly and indirectly through

regulation and policy measures such as taxes or subsidies. But this also implies that it is unlikely that

the government will implement regulations or policies that contradict important societal values. In this

section, I will review different strands of literature that support the notion that behavior both at the

individual and at the aggregate level is to a significant extent determined by social values and norms.

The two sister disciplines economics and sociology historically differed in the way they described

human behavior. Homo oeconomicus is self-interested and maximizes his material well-being by

rational choice. In contrast, the actor model of sociology, homo sociologicus (Dahrendorf 1958),

assumes that human behavior is mainly determined by social roles and norms that prescribe what the

adequate behavior of a person in a certain role is. Of course, both actor models are extremes and real

human behavior is determined both by rational choice aiming at maximizing private material well-

being and by compliance with norms and social roles. In the recent past, there has been some

convergence in the actor models of the two disciplines. Both economists (O'Boyle 1994; Akerlof 2007)

and sociologists (Weise 1989; Lindenberg 1990) argue that the more realistic and useful actor model

of homo socio-oeconomicus should acknowledge that humans are rational and self-interested, but

also motivated by social norms and values. There are also theories in social psychology that explain

how human behavior is influenced by egoistic motives and values and norms such as the theory of

planned behavior (Ajzen 1991) or the value-beliefs-norm theory (Stern et al. 1999).

From a macroeconomic perspective it is important to notice that different individuals can share certain

values which implies that values do not only determine behavior at the individual but also at the

aggregate level. In this sense, shared values and norms are part of a community’s culture which can be

an important determinant of economic outcomes. The more people share similar values, the more

relevant these values are at the macroeconomic level.

Several papers provide evidence that shared values actually determine behavior. Kahn (2007) shows

that in Californian communities with higher shares of Green party members, people make “greener’’

transportation choices than the average consumer. Greens are more likely to use public transit,

consume less gasoline and purchase hybrid vehicles. He also shows that green communities support

environmental protection ballots more and that the Congress representatives of green communities

are more likely to vote environmental positions. Ozaki and Sevastyanova (2011) analyze the motives

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of British consumers to purchase a Toyota Prius which is a well-known fuel-efficient hybrid vehicle.

They find that compliance with the norms of a social reference group is one important factor of the

purchase decision. Nayum and Klöckner (2014) develop a comprehensive socio-psychological model

of the determinants of buying a fuel-efficient car and show that purchase intentions are influenced by

normative processes involving personal norms and an ecological worldview. Gilg et al. (2005) present

a case study on sustainable lifestyles in Devon, UK. Their study documents that green consumers tend

to hold more pro-environmental and pro-social values. Consumers that are committed to

environmentally friendly behaviors are more likely to hold biospheric and ecocentric values. These

authors conclude from their empirical findings that “sustainable lifestyles may be formulated around

a distinctive pro-social ethic, which is open to change and values nature intrinsically” (p. 499).

The papers in the preceding paragraph relate pro-environmental values to environmentally-friendly

behavior, which is an unsurprising connection. We can also make more general statements about the

nexus between values and behavior. Marketing research identified types of consumers who share

values and convictions and have similar lifestyles that comprise predictable consumption patterns.

These values, lifestyles and behaviors are robust over time and measurable with survey methods. An

example for such category are the so-called LOHAS consumers2, where LOHAS stands for “lifestyles of

health and sustainability”. These consumers are characterized by a holistic, spiritual and

environmentalist worldview and have a strong interest in products that are eco-friendly, but also

conducive to their personal well-being of body and mind. Market research institutes such as SIGMA or

SINUS have used the “milieu approach” which describes the “life-worlds” of target groups of product

manufacturers, service providers, political parties, or publishers3. “Milieus describe people and their

specific attitudes and life orientations, and outline social groups, whose value orientations, goals in

life, lifestyles – and thus also their basic method of consumption – are sufficiently similar.”

(http://www.sigma-online.com/en/SIGMA_Milieus/). Knowing these milieus is useful for private

companies because it helps them predicting how consumers respond to new products and services

and hence how to optimize their marketing strategies.

The SIGMA milieus have a status dimension and a value dimension. The status dimension distinguishes

five classes between the lower class and the upper class and the value dimension ranges from

“traditional” over “modern” to “post-modern”. Modern values are “having, consuming, and enjoying”

while post-modern values are rooted in subjectivism and centered on “being”. One of the ten SIGMA

milieus in Germany is the “consumption materialistic milieu”, which comprises about 9.54 million

people or 13.6% of the German population older than 15 and is located in bottom-left corner (lower

2 See http://www.lohas.com/about; http://www.lohas.com/sites/default/files/consval_sm.pdf 3 http://www.sigma-online.com/en/Home/; http://www.sinus-institut.de/en/solutions/sinus-milieus.html

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class – traditional/modern values) of the status-value space. The SIGMA institute describes these

people as4 “economically and socially marginalized … with few chances of making it in the post-

industrial labour force … The `rich and beautiful´ people featured in `yellow press´ magazines serve as

role models and are opposed to their everyday life with limited financial means. Important: keeping

up with the mainstream in social and economic terms, money and consumption.” The “liberal

intellectual milieu” is located in the opposite corner of the status-value space. The SIGMA institute

characterizes this upper-class/post-modern milieu5 – that forms about 10.1% of the German 15+

population – as “liberal educational bourgeois and modern functional elite with post-materialistic

orientation. High importance of self-realisation at work and in leisure time. Rejection of outer values

(but appreciate exclusive, very selected items). A flat in a dignified old building in historical residential

areas (e.g. ‘Jugendstil’), a cultivated lifestyle, and a donation to Amnesty International at the end of

the year. Upper Liberals like it when things are cultivated and social at the same time. Important: Look

after themselves and the world, sense of social justice, ecological and political correctness.”

This very applied kind of research has foundations in the academic research of the political scientist

Ronald Inglehart (Inglehart 1977, 1997; Inglehart and Welzel 2010) who developed a new version of

“modernization theory that integrates socioeconomic development, cultural change, and

democratization under the overarching theme of human development” (Inglehart and Welzel 2010, p.

1). This Evolutionary Modernization Theory argues that economic development, welfare state

institutions and peace in most advanced countries after World War II have led to a deep change in

human motivations with implications not only for economic behavior, but also for the role of religion,

gender roles, democracy and aspects of life. In particular, many countries experienced a shift from

survival values to self-expression values, especially among late-born generations. Survival values are

materialistic and center on consumption and the accumulation of wealth. Self-expression values are

more people-centered and post-materialistic. Inglehart’s work resulted in the World Values Survey

project which has been conducting representative surveys in more than 100 countries since 1981 with

the aim of exploring people’s beliefs and values with respect to many dimensions of life.

Attitudes towards the natural environment are one of the dimensions in the World Values Survey and

a high valuation of the natural environment and support for environmental protection are typically

seen as post-materialistic values. However, recent empirical evidence suggests environmental concern

and willingness to pay for environmental protection are not only related to self-expression and

4 http://www.sigma-online.com/en/SIGMA_Milieus/SIGMA_Milieus_in_Germany/Konsum-materialistisches_Milieu/ 5 http://www.sigma-online.com/en/SIGMA_Milieus/SIGMA_Milieus_in_Germany/Liberal-Intellektuelles_Milieu_/

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affluence, but also the experience of environmental degradation in the local communities of people

(Knight and Messer 2012; Fairbrother 2013; Mostafa 2013).

3 Model The model describes a socio-ecological system, in which human decisions and environmental

processes interact. The level of analysis is highly aggregated with just one decision-maker (global

human civilization) and a very simplified model of the global ecosystem. This means that “decisions”

are not to be interpreted as conscious decisions of a single, rational decision-maker but rather as the

outcomes of rather complicated societal processes involving many different and interacting decision-

makers. In order to clearly work out the effects at the global level, I keep the analysis as simple as

possible and do not consider the level of individual decision-making of households, firms and other

agents of society, but rather focus on the dynamics of the aggregated system.

There is no presumption that the aggregate decisions are in any sense rational, optimal or welfare-

maximizing. Complex systems defy direct centralized control and even if individual decisions are in

some sense rational, it would be a fallacy of composition to assume the same for the aggregate

outcome of these individual decisions. Furthermore, the model implicitly features a number of

externalities (effect of production on CO2 generation, effect of CO2 on global temperature, effects of

environment and temperature on population, effects of economic and environmental variables on

societal values) so that the assumption of global rationality seems very implausible.

The economic submodel is very similar to the standard endogenous growth models from

macroeconomic theory, such as Romer (1990). However, in contrast to conventional neoclassical

theory, I do not focus on the steady state of the model or perform any kind of equilibrium analysis.

Equilibrium analysis is at odds with the idea of a system breakdown or collapse. Furthermore, since

aggregate economic behavior is adaptive and environmental conditions change, equilibrium analysis

is not possible most of the time. The model contains multiple feedback effects between global

temperature, production, efficiency, population, and societal values. Furthermore, there is a

considerable time lag between actions (CO2 emissions) and consequences (climate change and its

effects). The lagged response of temperate on CO2 emissions generates a stock-flow problem, which

can lead to societal responses which are too late and can result in a collapse of global civilization.

The model is a theoretical model which is not directly based on empirical data. Its main purpose is to

demonstrate theoretically possible scenarios rather than being a calibrated policy or prediction tool.

However, the model is roughly calibrated with data on global production, population, C02 emissions

etc.

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Figure 1: Model overview

Figure 1 provides an overview of the model. The model has three submodels: (1) The economic

submodel, which is represented by the blue boxes, determines output, the inputs, investment levels

and saving/consumption. (2) The climate and nature submodel in green determines the global average

temperature change and the state of the natural environment as a consequence of production’s

carbon emissions and the resulting carbon stock in the atmosphere. (3) The global population and its

values are the represented by the orange boxes and are the central variables of the model. The arrows

between the boxes show the direction of influence and the numbers stand for the equations which are

presented in the following subsections. As can be seen, I have assumed one-way causations only to

keep the model tractable. Furthermore, the model features three stochastic shocks (grey boxes) that

affect the level of employment, the level of population, and societal values. Note that apart from the

shocks, all variables are endogenous.

3.1 Economy The global economy is characterized by production Yt, employment Lt, investment into physical capital

Kt, productivity At, carbon efficiency Bt, and the restoration of the natural environment Et, aggregate

consumption Ct and aggregate saving St. All of these variables are endogenous and vary over time.

Output is produced with a conventional Cobb-Douglas production function:

(1) 𝑌𝑡 = 𝐴𝑡𝐿𝑡𝛼𝐾𝑡

1−𝛼

Employment Lt depends is a fraction of the total population Pt:

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(2) 𝐿𝑡 = 𝜆𝑡𝑃𝑡

The employment ratio 𝜆𝑡 fluctuates stochastically around a “natural” level �̅�𝑡:

(3) 𝜆𝑡 = (1 − 𝜙)�̅�𝑡 + 𝜙𝜆𝑡−1 + 휀𝑡𝜆 with 휀𝑡

𝜆~𝑁(0, 𝜎𝜆2)

These fluctuations capture business cycle movements and short-run adjustments. The natural level �̅�𝑡

depends on society’s values 𝑉𝑡 and can change over time if these values change. If society is strongly

materialistic (V=0), the natural employment ratio is maximal (�̅�𝑚𝑎𝑥). If society is strongly post-

materialistic (V=1), the employment ratio is minimal (�̅�𝑚𝑖𝑛). In a post-materialistic society people want

to enjoy more leisure and non-labor market activities than in a materialistic one, in which people work

both in order to afford consumption and to achieve social status. I assume that �̅�𝑡 is a linear function

of societal values:

(4) �̅�𝑡 = �̅�𝑚𝑖𝑛 + (�̅�𝑚𝑎𝑥 − �̅�𝑚𝑖𝑛)(1 − 𝑉𝑡)

New physical capital Kt is built by investment into capital goods in the previous period, 𝐼𝑡−1𝐾 , and the

depreciation rate 𝛿 is constant so that the capital stock evolves according to a standard accumulation

equation:

(5) 𝐾𝑡 = (1 − 𝛿)𝐾𝑡−1 + 𝐼𝑡−1𝐾

Total factor productivity 𝐴𝑡 is deterministic and cumulative. New knowledge is generated by

investment into productivity, 𝐼𝑡−1𝐴 . The productivity investment function is assumed to be concave to

capture the idea that there are decreasing marginal returns to productivity investment. R&D is a

function of the investment to output ratio:

(6) 𝐴𝑡 = 𝐴𝑡−1(1 + 𝑎1 (𝐼𝑡−1

𝐴

𝑌𝑡−1)

𝑎2

)

Consumption is modelled as a simple Keynesian aggregate consumption function (without an

intercept):

(7) 𝐶𝑡 = 𝑐𝑡𝑌𝑡

The marginal propensity to consume ct depends on the values of society and is maximal (minimal) if

society is most (post-)materialistic.

(8) 𝑐𝑡 = 𝑐𝑚𝑖𝑛 + (𝑐𝑚𝑎𝑥 − 𝑐𝑚𝑖𝑛)(1 − 𝑉𝑡)

This captures the idea that consumption in materialistic societies has a strong social function and

generates social status. Of course, even in a fully post-materialistic society, there must be a minimum

level of consumption. Aggregate saving is

(9) 𝑆𝑡 = 𝑌𝑡 − 𝐶𝑡

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The way in which consumption is modelled here implies that post-materialistic societies save more.

This can be justified by less time discounting (because future generations count more) or higher

willingness to invest, e.g. in environmental restoration or increases carbon efficiency.

At the global level, world investment must be financed by world savings. The relative allocation of

savings on investment types is determined by societal values. A materialistic society invests a lot into

physical capital and productivity in order to produce ever more consumption goods.

(10) 𝐼𝑡𝐾 = (1 − 𝑉𝑡)𝑘𝑆𝑡

(11) 𝐼𝑡𝐴 = (1 − 𝑉𝑡)(1 − 𝑘)𝑆𝑡

The parameter k governs the importance of investment into new physical capital relative to investment

into productivity improvements. If k is high, the economy is capital-biased, if k is low, it is productivity-

biased.

If the society is post-materialistic, it channels relatively more of its savings into investments that lower

the carbon emissions of output production (improve carbon efficiency Bt) and the restoration of

environmental quality. The parameter e describes the relative importance of environmental

restoration compared to carbon efficiency:

(12) 𝐼𝑡𝐵 = 𝑉𝑡(1 − 𝑒)𝑆𝑡

(13) 𝐼𝑡𝐸 = 𝑉𝑡𝑒𝑆𝑡

k and e are exogenous model parameters that can be used for experiments.

I assume that the production of output generates carbon dioxide emissions due to the use of fossil

fuels:

(14) 𝐶𝑂2𝑡 =𝛾

𝐵𝑡𝑌𝑡

The efficiency variable Bt improves by investment and evolves analogously to total factor productivity.

There are decreasing marginal returns to investment into carbon efficiency.

(15) 𝐵𝑡 = 𝐵𝑡−1(1 + 𝑏1 (𝐼𝑡−1

𝐵

𝑌𝑡−1)

𝑏2

)

3.2 Climate and environment The climate submodel is adopted from Janssen and de Vries (1998). The change of the average global

temperature is a function of carbon dioxide emissions. In this greatly simplified model, the change in

atmospheric CO2 concentration (pCO2 in ppmv) is modelled using the reduced-form carbon cycle model

developed by Maier-Reimer and Hasselmann (1987). Carbon emissions 𝐶𝑂2𝑡 are devided into 5 classes

(CS1 to CS5) with different atmospheric lifetimes:

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(16) 𝐶𝑆1𝑡 = 𝐶𝑆1𝑡−1 + 0.131 ∗ 0.471 ∗ 𝐶𝑂2𝑡

(17) 𝐶𝑆2𝑡 = 𝐶𝑆2𝑡−1 + 0.471 ∗ 𝐶𝑂2𝑡 ∗ 0.201 ∗ 𝑒𝑡−𝑡0362.9

(18) 𝐶𝑆3𝑡 = 𝐶𝑆3𝑡−1 + 0.471 ∗ 𝐶𝑂2𝑡 ∗ 0.321 ∗ 𝑒𝑡−𝑡073.6

(19) 𝐶𝑆4𝑡 = 𝐶𝑆4𝑡−1 + 0.471 ∗ 𝐶𝑂2𝑡 ∗ 0.249 ∗ 𝑒𝑡−𝑡017.3

(20) 𝐶𝑆5𝑡 = 𝐶𝑆5𝑡−1 + 0.471 ∗ 𝐶𝑂2𝑡 ∗ 0.098 ∗ 𝑒𝑡−𝑡0

1.9

The lifetimes of carbon dioxide in the latter four classes are 362.9, 78.6, 17.8, and 1.9 years. The

concentration is then given by

(21) 𝑝𝐶𝑂2𝑡 = 𝐶𝑆1𝑡 + 𝐶𝑆2𝑡 ∗ 𝑒−(𝑡−𝑡0)

362.9 + 𝐶𝑆3𝑡 ∗ 𝑒−(𝑡−𝑡0)

73.6 + 𝐶𝑆4𝑡 ∗ 𝑒−(𝑡−𝑡0)

17.3 + 𝐶𝑆5𝑡 ∗ 𝑒−(𝑡−𝑡0)

1.9

The actual temperature change 𝑑𝑇𝑡 is a function of the potential temperature change and the lagged

change in temperature, because oceans take a long time to warm up:

(22) 𝑑𝑇𝑡 = 𝑑𝑇𝑡−1 + 0.05(𝑑𝑇𝑡𝑝

− 𝑑𝑇𝑡−1)

The change in the potential global mean surface temperature 𝑑𝑇𝑡𝑝 depends on the radiative forcing of

CO2, 𝑑𝑄𝐶𝑂2𝑡:

(23) 𝑑𝑇𝑡𝑝 =

𝑑𝑇2×𝐶𝑂2

𝑑𝑄2×𝐶𝑂2∗ 𝑑𝑄𝐶𝑂2𝑡

Which, in turn, is a function of carbon concentration:

(24) 𝑑𝑄𝐶𝑂2𝑡 =𝑑𝑄2×𝐶𝑂2

ln(2)∗ ln (

𝑝𝐶𝑂2𝑡

296)

The state of the environment Et can be interpreted for instance as natural beauty or the services that

the environment offers to human well-being. Temperature increases have a negative impact on the

state of the environment, because of negative effects on vegetation and biodiversity or damages by

extreme whether events. The impact is assumed to be convex, i.e. it becomes stronger and stronger

with higher temperature increases. Similarly, population growth 𝑑𝑃𝑡 damages the state of the

environment, because of increased land use for agriculture, residential areas, transportation

infrastructure etc. This effect is also convex. I assume that the effect of population changes on the

state of the environment is asymmetric, because environmental damages due to population increases

are not reversed automatically if the population shrinks again. Even if the population level decreases,

the land uses do not change immediately without investments. Finally, the state of the environment

can be improved by environmental investments, 𝐼𝑡−1𝐸 . Examples for such investments could be

reforestations, renaturation of rivers and landscapes.

(25) 𝐸𝑡 = 𝐸𝑡−1(1 − 𝜖1𝑑𝑇𝑡𝜖2 − max (0, 𝜓1 (

𝑑𝑃𝑡

𝑃𝑡−1)

𝜓2

) +𝐼𝑡−1

𝐸

𝑌𝑡−1)

14

3.3 Population and societal values The level of population Pt has two determinants. The long-run yearly growth rate is given by 𝑝𝑡 which

depends negatively on the level of per-capita income. This is consistent with the empirical evidence

from the last 60 years in many countries (see Weil 2012).

(26) 𝑃𝑡 = 𝑃𝑡−1((1 − 휀𝑡𝑃) + 𝑝𝑡)

(27) 𝑝𝑡 = 𝑝0 − 𝑝1𝑙𝑛𝑌𝑡

𝑃𝑡−1

In addition to the long-run trend, the population change is subject to random influences which are

driven by the change in the global temperature. I assume that these population shocks are beta-

distributed such that the mean and the variance of the distribution increase with the change in

temperature. Increases in temperature cause casualties due to floods, severe storms, draughts, heat

waves etc. The more the temperature rises, the more likely large population losses become.

(28) 휀𝑡𝑝~𝑏𝑒𝑡𝑎(𝑝2, 𝑝3) with 𝑝2 = {

1 𝑖𝑓 𝑑𝑇𝑡 ≤ 01 + 𝑑𝑇𝑡 𝑖𝑓 𝑑𝑇𝑡 > 0

The values Vt that society holds are the ultimate drivers of the model’s dynamics. Society makes

decisions on consumption and investment in line with its predominant value orientation. Values are

measured on the continuum from 0 (most materialistic) to 1 (most post-materialistic). One might

assume that every member of society can either be materialistic or post-materalistic. Vt can then be

interpreted as the fraction of society which has a post-materialistic orientation.

Values develop according to an inhomogeneous non-linear difference equation. I assume that the

recurrence relation is a sigmoid function Σ with the two stable fixpoints 0 and 1 and the unstable

fixpoint 0.5. The sigmoid function describes social pressure for conformity which means that there is

a tendency towards the two extreme value orientations. If there are no external influences, the

majority orientation will dominate the rest of society so that ultimately the whole society is either

materialistic or post-materialistic.

(29) 𝑉𝑡 = Σ(𝑉𝑡−1) − 𝑣1 (𝑑𝐸𝑡

𝐸𝑡−1)

𝑣2

+ 휀𝑡𝑉 with 휀𝑡

𝑉~𝑁(0, 𝜎𝑉2)

(30) Σ(𝑉𝑡−1) = 𝑉𝑡−1 − 𝑣0sin (2𝜋𝑉𝑡−1)

However, society’s value orientation is also affected by the socio-ecological system, more precisely the

change of the environmental quality. If the quality of the environment deteriorates, values shift away

from materialism. This effect is assumed to be convex, as the harm from environmental change

becomes more obvious if the losses are large. Finally, societal values are also driven by normally

distributed random shocks which are intended to capture all other non-modelled factors that drive a

society’s value orientation.

15

3.4 Process overview and scheduling It is not the purpose of this paper to analyze whether there is a long-run balanced growth path and

how this might look like. Instead I am interested in potential paths of the endogenous variables during

the 21st century. Therefore the model is simulated for discrete time steps of one year from year 1995

to 2100.

The sequence of the computation in each time step is as follows:

1) The human civilization first determines the state variables K, A, and B, which depend on the

investment decisions of the previous year. L is also determined. Then production,

consumption and saving are calculated

2) Production generates CO2.

3) The ecosystem determines the global stock of CO2 as a function of CO2 emissions and its

capacity to absorb atmospheric CO2. The CO2 stock, in turn, determines the temperature

change.

4) The new population level is determined.

5) The temperature change and the population change determine the state of the environment.

6) Investment is determined.

7) Societal values V are adjusted.

8) Model output is generated and recorded.

4 Parameterization Since the purpose of this paper is to make a theoretical contribution, I abstain from elaborate model

validation. A rough calibration of the models parameters and the variables’ initial values, which

generates values of the endogenous variables of realistic orders of magnitude, is sufficient to show

how the model works and which kinds of outcomes it can produce.

The calibration aims at making the model comparable to Janssen and de Vries (1998) and to reproduce

the values of the endogenous variables in their starting year, which is 1995. Where possible, I take the

same parameter values and starting values as in Janssen and de Vries (1998). Table 1 contains the

initial values of the endogenous variables in 1995.

The macroeconomic variables Y, K, L, and P for the global economy are taken from the Penn World

Table version 8.0 (see Feenstra et al. 2013). This data set can also be used to compute the employment

ratio λ in 1995.

16

Table 1: Initial values of endogenous variables

Variable Meaning Value Source Comment

P Population level 5,528 PWT8 Mio, in 1995

Y Economic output 41,128,516 PWT8 Mio US$, in 1995

K Capital stock 127,000,000 PWT8 Mio US$, in 1995

L Employment 2,376 PWT8 Mio, in 1995

A TFP 222 Own calculation

With α = 0.6

B Carbon efficiency 1,869,478 Own calculation

λ Employment ratio 0.43 PWT 8

V Value index 0.3 WVS

CO2 CO2 emissions 22.167 EIA Gt, in 1995

c Marginal propensity to consume

0.77 IMF 2015

E Environment 74,031,329 Costanza et al. 1997

Mio US$ 1.8 * GDP in 1994

Assuming a standard value of 0.6 for the labor share in output, α, it is straightforward to compute the

total factor productivity A, once output Y, capital K and employment L are given. The marginal

propensity to consume, c, is set to 0.77, which is in line with data from the IMF’s World Economic

Outlook Database6. The U.S. Energy Information Administration (EIA) provide the value of total carbon

dioxide emissions from the consumption of energy7. With an arbitrarily chosen value of 1 for γ, the

carbon efficiency variable B directly follows from equation (14). Costanza et al. (1997) estimate the

value of the world’s ecosystem services to be 1.8 times global GDP in 1994. Using this factor, I can

calculate the value of the environment E for 1995. The World Values Survey database

(http://www.worldvaluessurvey.org/WVSOnline.jsp) contains the materialist/post-materialist index.

This variable corresponds very closely to my concept of the societal values V. In wave 3 of the survey

(1995 – 1999), the share of respondents that is more post-materialist that materialist (responses 3 – 5

on a scale from 0 – “materialist” to 5 “post-materialist”) is roughly 30%.

Some of the parameters are taken from the data or the literature, other are calibrated to obtain

plausible values of the endogenous variables, and some are just chosen more or less arbitrarily. As

stated before, the paper’s objective is mainly a theoretical one. For empirical applications or policy

6 In 1995, global gross national saving was about 23% of GDP, see http://www.google.com/publicdata/explore?ds=k3s92bru78li6_&ctype=l&met_y=ngsd_ngdp&hl=en_US&dl=en_US 7 See http://www.eia.gov/cfapps/ipdbproject/iedindex3.cfm?tid=90&pid=44&aid=8&cid=ww,&syid=1995&eyid=2012&unit=MMTCD

17

analyses the calibration of the model can definitely be improved. This is left for future work. Table 2

lists all model parameters, their calibrated values and the data source (if there was any).

Table 2: Parameters

Variable Meaning Value Source

�̅�𝑚𝑖𝑛 min employment rate 0.127 PWT 8

�̅�𝑚𝑎𝑥 max employment rate 0.56 PWT 8

𝜙 persistence of employment rate 0.9 none

𝜎𝜆 standard deviation of employment shocks

0.002 PWT 8

δ depreciation rate 0.1 common in the literature

𝑎1 productivity parameter investment sensitivity of TFP

0.15 calibration to get about 2% TFP growth

𝑎2 productivity parameter 0.5 calibration to get about 2% TFP growth

α labor share in Cobb-Douglas production function

0.6 common in the literature

𝑐𝑚𝑖𝑛 min marginal propensity to consume 0.47 none

𝑐𝑚𝑎𝑥 max marginal propensity to consume 0.9 none

𝑘 degree of capital bias 0.85 calibration to get IA = 2% of GDP

𝑒 degree of environmental bias 0.5 none

𝑏1 efficiency parameter 1.8 calibrated to match time series

𝑏2 efficiency parameter 1 calibrated to match time series

𝛾 coefficient in CO2 function 1 none

𝜖1 temperature on environment temperature sensitivity of E

0.01 none

𝜖2 temperature on environment 1.3 none

𝜓1 population on environment 1 none

𝜓2 population on environment 1 none

𝜎𝑉 variance of value shocks 0.05 none

𝑣0 non-linearity of values 0.1 none

𝑣1 environment on values 1 none

𝑣2 environment on values 1 none

𝑑𝑄2×𝐶𝑂2 radiative forcing associated with a doubled CO2 concentration

4.3 Janssen and de Vries (1998)

𝑑𝑇2×𝐶𝑂2 global mean surface temperature change in the event of a doubled CO2 concentration

2.5 Janssen and de Vries (1998)

𝑝0 max growth of population 0.027 own estimation

𝑝1 income on population growth 0.0008 own estimation

𝑝3 coefficient of population shocks 199 none

Apart from the persistence parameter 𝜙, all employment parameters are calculated from the Penn

World Tables. The depreciation rate δ is set to 0.1 and the labor share in the production function α is

0.6 which are common values in the macroeconomic literature. The minimum and the maximum of

the marginal propensity to consume are arbitrarily set to 0.47 and 0.9 respectively. The parameters in

18

the productivity function (6) are calibrated to obtain a growth rate of TFP of 2% in 1995 which is a

plausible long-run value. The degree of capital bias of investment k is calibrated to get investment into

productivity equal to 2% of GDP, which roughly corresponds to global R&D spending8 if V = 0.3.

The World Bank’s world development indicator database shows that there was an almost linear

decrease in the CO2 emissions intensity from 1990 to 2010. In 1990, the global economy produced 0.78

kg of CO2 emissions per PPP$ of GDP, and in 2010, 0.38 kg of carbon dioxide were generated per $ of

GDP. Fitting a simple linear time trend by OLS yields an R2 of 0.98. This fit can be reproduced almost

perfectly with γ = 𝑏2 = 1 and 𝑏1 = 1.8 assuming that IB = 2% of GDP each year.

The environmental function (25) and the value function (29) are harder to calibrate with empirical

data. I hence choose arbitrary values that generate plausible time paths. The calibrated environmental

function generates a yearly loss of environmental quality of 8% if the temperature change is 5°C, which

is consistent with the projection in the Stern review (Stern 2006). The parameters for the climate

model are completely taken from the calibration in Janssen and de Vries (1998).

The parameters 𝑝0 and 𝑝1 in the population growth function (27) are estimated by OLS using data from

the Penn World Tables 8 for time between 1970 and 2011. 𝑝3 is chosen such that the mean of

population shocks is 0.5% if the temperature does not change.

5 Results I first present some simulation outcomes9 for the baseline calibration in Table 2. Due to the stochastic

influences and the path dependency the model must be simulated several times.

In the next step, I present two examples of sensitivity analyses that show how the simulation outcomes

depend on certain parameters. Since a full sensitivity analysis with respect to all parameters cannot be

presented here due to space limitations, I focus on the investment sensitivity of TFP, 𝑎1, and the

temperature sensitivity of the environment, 𝜖1. These parameters are of particular interest due to their

a priori ambiguous effects. If total factor productivity responds more strongly to R&D investment,

output with grow stronger for the same values of society. Ceteris paribus, this will generate more

carbon emissions, but also a higher level of savings and hence resources for further investment that

could be used for efficiency improvements or the restoration of the environment. Similarly, if the

environment is harmed more by higher temperature, this is a direct negative effect. Yet the stronger

environmental degradation will cause values to change more with all the implied consequences. The

8 see World Bank data: http://data.worldbank.org/indicator/GB.XPD.RSDV.GD.ZS/countries?display=graph 9 The model was implemented and run in NetLogo (Wilensky 1999). The program code is available from the author upon request.

19

temperature sensitivity of the environment captures a large number of very complicated mechanisms

and is hence highly uncertain. Therefore, analyzing how the choice of this parameter affects the

evolution of the system is of particular importance.

Finally, I conduct a policy-related analysis by varying the degree of environmental bias of investment,

e. This parameter determines, how the amount of “green” investment is allocated on improvements

in carbon efficiency and on the restoration of the environment. In a sense, this parameter captures the

degree of future-orientation of the global society. Improving carbon efficiency of production is a

mitigation measure that helps limiting global warming. Improving environmental quality by

investment, in contrast, is a repair approach that deals with the consequences but not the causes of

climate change.

5.1 Baseline calibration Figure 2 shows the paths of output, population, environmental quality, temperature, carbon

emissions, and societal values in 100 model runs.

Figure 2: Outcomes of 100 runs in baseline calibration

Output grows exponentially in all runs and is 23 to 50 times higher in 2100 than in 1995 which

corresponds to an average yearly growth rate between 3.0% and 3.8%. The mean and the median

population level in 2100 are about 9.2 billion people which is lower than the 2015 U.N. median

20

projection of 11.2 bn. However, this level is well included in the simulation here, which generates a

maximum level of population in 2100 of 12.1 billion and a minimum of 6.4 billion people.

The quality of the environment on average deteriorates from a value of US$ 74 trillion in 1995 to 55

trillion in 2100. In the case of the environment, the range of outcomes in enormous: in the best case,

the environmental quality doubles to US$ 147 trillion, but in the worst case only US$ 14 trillion will be

left in 2100. The main cause for the evolution of population and environmental quality is the change

in temperature, which is measured relative to the base year 1995. The smallest temperature increase

is 1.97°C and the largest 3.89°C, which means that the critical 2-degrees threshold is always passed as

this refers to the preindustrial level. The median of the temperature increase is 2.77°C. By 2100 the

level of yearly CO2 falls below the level of 22 Gt in 1995 and ranges from 1.5 Gt to 14.9 Gt with a median

of 3.9 Gt. While this is a significant reduction of carbon emission, the graph in Figure 1 shows that this

is only part of the story. In some runs, there is a dramatic increase of emissions until the middle of the

century, before they ultimately go down.

Regarding societal values the most remarkable result is that the never become strongly post-

materialistic in none of the 100 runs. The mean and median over all runs and years are 0.25, which is

lower than the starting value of 0.3. The 99%-percentile is 0.52 and the maximum is 0.66. Especially in

the first half of the century, society becomes totally materialistic in many cases.

Figure 3 illustrates one of the possible worst-case scenarios. I have chosen the run with largest increase

in temperature here, because this scenario is likely to cause the most severe long-term consequences

due to the melting of artic ice shields, sea level rise and other temperature-related effects. Of course,

one could also see the largest decimation of the population or the strongest degradation of the

environment as worst cases. Interestingly, this scenario is one in which to total increase in output until

2100 is lowest. The population reaches a maximum in the 2040s, stagnates for about 25 years and then

declines by about 1 billion people in the last 25 years of the century. The quality of the environment

gets steadily worse and drops below a value of US$ 20 trillion in the 2080s.

The reason for these bad outcomes is that society become strongly materialistic in the first half of the

century. In this run, V drops sharply to 0 by 2004 and remains very low well into the 2020s. In 2029, V

jumps up, but the initial level of 0.3 is only reached again in 2045. Only at the very end of the century,

V passes the 0.5 threshold. The consequence of this materialistic turn is a strong increase in carbon

emissions in the first 50 years. The peak year is 2045 and afterwards yearly emissions fall steadily due

to improved carbon efficiency, but this reduction comes far too late to slow down the temperature

increase. This case demonstrates the effect of negative shocks on societal values. Negative shocks

make societal values more materialistic. They are unrelated to the state of the environment and

21

capture the impact of political propaganda and campaigns of the fossil fuel industry against climate

change or of media reports that question global warming due to weather events such as El Niño and

La Niña.

Figure 3: Worst case scenario with largest temperature increase

5.2 Sensitivity analysis I first look at how the system responds to a change in the investment sensitivity of total factor

productivity. In the baseline calibration, 𝑎1 is set to 0.15, which – together with 𝑎2 = 0.5 – generates

a yearly growth rate of TFP of 2.12% if investment into A is equal to 2% of output. For the sensitivity

analysis, I compare the baseline case with a low value of 𝑎1 of 0.075 (low calibration) and a high one

of 0.225 (high calibration), which correspond to an average annual TFP growth rate of 1.06% and 3.18%

respectively. Figure 4 summarizes the results. Each of the graphs is the mean path of the respective

variable over 100 runs.

Varying the investment sensitivity of TFP has quite strong effects on the endogenous variables. The

differences in the level of production are most pronounced. In the baseline calibration, the mean level

of output in 2100 is US$ 1430 trillion which is about 36 times higher than the initial level in 1995. In

the high calibration, average output in 2100 is US$ 6760 trillion, while it is only US$ 300 in the low

22

calibration. Hence tripling 𝑎1 results in output that is 22 times higher in the high calibration than in the

low calibration.

Figure 4: Effects of the investment sensitivity of TFP

The differences in output growth lead to obvious differences in the average emission paths. In the high

calibration and the baseline calibration, the average emission paths are hump-shaped with a peak in

the middle of the century. In contrast, average emissions decline monotonously in the low calibration.

Consequently, the average temperature increase until the year 2100 is 1.82 times higher (3.76°C vs.

2.05°C) with 𝑎1 = 0.225 than with 𝑎1 = 0.075.

In the high calibration, the average population path is also inverted-U-shaped and reaches a level of

6.8 billion people10 in 2100. Population levels decline so strongly because high per income leads to low

fertility and because of many temperature-related fatalities. When 𝑎1 is low the population grows

almost linearly throughout the century to an average level of 11.5 billion.

Somewhat surprisingly, the evolution of environmental quality is very similar in the high calibration

and the baseline calibration. This is the result of countervailing forces. In the high calibration,

temperature-related damages are higher, but there is less consumption of the environment caused by

10 The lowest population in one of the 100 runs in that calibration is 4.3 billion people, which is considerably lower than the initial value in 1995.

23

population growth. Furthermore, the investment level into environmental repairs can be higher

because more output is available. In the low calibration, the smaller effect of temperature seems to

dominate the larger population effect so that environmental damages are relatively modest with the

result that the mean environmental quality in 2100 is virtually the same as the starting value in 1995.

The evolution of values is very similar in all three calibrations in the first half of the century. In the

second half, society becomes more post-materialistic with higher 𝑎1, which is a direct consequence of

the parameter’s effect on the environment.

The second example of a sensitivity analysis concerns the temperature sensitivity of the environment

𝜖1. As in the previous analysis, I compare the baseline value (0.01) with a value that is 50% lower (low

calibration, 0.005) and a high calibration in which it is 50% higher (0.015). The results are shown in

Figure 5.

Figure 5: Effects of the temperature sensitivity of the environment

This parameter hardly affects output, but has a considerable effect on carbon emissions. In all three

calibrations, emissions drop in the first 15 years, but then they rise again in the low calibration. The

reason for this it obvious: In the low case the quality of the environment improves strongly in the first

decade and then remains high well into the 2050s, although the average temperature rises

continuously. The good condition of the natural environment prevents that values become post-

24

materialistic. On average, V is below 0.2 from 2010 until 2070 and never reaches the initial level of 0.3

again. This implies that there is very little green investment throughout most of the century which

leads to a rather high average temperature increase of 3.5°C. The temperature increase, in turn, causes

many climate-induced deaths such that the average population level declines starting in the 2060s.

If the environment responds relatively strongly to temperature changes (high calibration), the

outcomes look quite different. The quality of the environment reaches its maximum in the first decade

of the century and then decreases almost linearly until the end. The evolution of values is the mirror

image of the evolution of the environment: After reaching their minimum level, the increase until the

middle of the century and remain high until the end. Notice, however, that even in the high calibration,

values from the 2050s on are only slightly higher than in 1995 and remain well in the mostly

materialistic domain. The increase in V, however, is strong enough to reduce emissions through carbon

efficiency improvements. By this it is possible to stabilize the temperature increase at 2.3°C on average,

which is reached in the 2060s. The early halt of global warming at a moderate temperature leads to a

modest increase of the population level to 9.8 billion until 2100.

5.3 Policy scenarios The model has two kinds of “green” investment: Improvements in the carbon efficiency of production

and direct improvements of the environmental quality. The overall level of both depends on the degree

of post-materialism in society, while the relative allocation of savings on the two types of investment

is exogenous here. Therefore, I can use this exogenous parameter e as a policy parameter that captures

whether the global society is able to look ahead and to avoid future damages by reducing carbon

emissions and temperature change or whether society is more short-sighted and primarily deals with

the already observed damages in the environment.

In the baseline calibration, green investment has no bias and is allocated equally on carbon efficiency

and environmental restoration (e=0.5). If there is an environmental bias, e is larger than 0.5 and the

larger part of green investment is used to repair environmental damages. For the policy analysis with

an environmental bias, I set e=0.75. In the opposite case with e < 0.5 green investment has an efficiency

bias and most of it is channeled into efficiency improvements. I analyze this constellation with e=0.25.

The effects of the different policy orientations are shown in Figure 6, which contains the average

outcomes of 100 runs for each calibration.

Not surprisingly an environmental bias (green lines, e=0.75) initially causes significant improvements

in environmental quality. This, however, turns out to be counterproductive as the value indicator

drops, leading to much less green investment. As a consequence, carbon emissions and temperature

rise strongly with strong adverse effects on population and the environment. In this scenario, the

temperature in 2100 on average is 5°C higher than in 1995. This very large increase causes large

25

numbers of climate deaths such that the average population number (5.8 billion) is almost the same

as in 1995. In this scenario, we observe an effect on output, although the manipulated parameter has

no direct influence on output. With an environmental bias, output in 2100 is only 61% of the output

produced in the neutral baseline case (US$ 929 trillion vs. US$ 1510 trillion). The reason for the slower

output growth is the drop in population and hence employment. On average, the population level in

2100 is 38% lower than in the baseline case.

Figure 6: Effects of environmental bias

If there is a marked efficiency bias in green investment, the picture looks very different. With e=0.25

(blue lines) yearly emission fall steadily which stabilizes the temperature increase well below the 2°C

threshold. The average temperature increase peaks in 2070 (1.53°C) and then the temperature falls

again reaching a level in 2100 that is on average 1.48°C higher than in 1995. Output and population

grow considerably stronger than in the baseline or environmental bias case. Interestingly, the average

environmental quality in 2100 is the same in the two cases of biased green investment and lower than

in the neutral baseline. With an environmental bias there is a lot of investment into environmental

quality, but the high temperature and the relatively low output counteract this effect. In contrast, the

efficiency bias leads to a reduction in carbon emissions and halts the temperature increase, but there

is relatively low investment in the environment and the growing population generates additional

26

damage. From a pure environmental view, the neutral case seems preferable to either case of biased

green investment.

6 Discussion and potential extensions The model produces a rich set of outcomes, most of which appear quite plausible in the baseline

calibration. One might argue that an average global growth rate of output of 3.4% p.a. during the whole

century is too large and an average growth rate of the global population of 0.5% p.a. is too low.

However, as the sensitivity analysis has shown, this is easy to fix by reducing the investment sensitivity

of TFP (𝑎1) slightly. The median temperature increase of 2.77°C in the baseline calibration is well in line

with the most recent IPCC projections. In its 2014 report, the IPCC projects an average increase of the

global mean surface temperature between 1.0°C in the lowest scenario and 3.7°C in the highest

scenario by 2100 (IPCC 2014, p. 60).

The calibration in this paper is admittedly rough and can surely be improved. One way to do this is to

calibrate the model such that it reproduces the time series until the present as closely as possible.

It is also desirable to perform a more complete sensitivity analysis. In addition to an individual analysis

of single parameters it might be revealing to look at combinations of parameters that reinforce or

dampen the effects of changes in some variables. Furthermore, it is important to analyze in detail the

effects of parameters that are difficult to observe. One might also actively search for parameter

combinations that are still plausible and replicate the past, but lead to dramatic outcomes in the future.

Finding worst-case scenarios that appear plausible given the model design and available information

about the parameters is one of the most interesting and relevant applications of the model and might

be an important input to considerations about mitigation and adaptation policies.

There are numerous ways how modify the model. It is possible to incorporate new effects such a direct

impact of temperature on the stock of capital or on output. This modification appears quite plausible,

because natural disasters caused be climate change are likely to destroy physical capital and output

and also require resources to repair the damages. One could also include environmental services as an

input into the production function. Especially food production depends heavily on environmental

services such as pollination. The value function, which is a main driver of the model dynamics, should

be varied, too, for instance by including other or additional determinants. An obvious candidate that

might be included as a driver of societal values is the level of per capita income. Since most of the

functional forms are fairly arbitrary, experimenting with alternative functional forms would show how

robust the results are.

At least three extensions of the model suggest themselves. The first is to incorporate one or several

policy agents. In the present version, policy is implicit and works thought the value function. One could

27

include a government that has some discretion over variables such as output, consumption or

investment and that could also influence values. At the same time, the government cannot act

completely independent of societal values. Including a policy agent would allow more specific policy

analyses. The second obvious extension is to transform the global model into a multi-country or multi-

region model. Technology, values and environmental conditions are very different across the regions

of the world. In a multi-region model one could generate more specific scenarios about the effects of

climate change. Another relevant fact is that the countries or regions that are the main originators of

climate change are not the countries that are most severely affected by its direct consequences. The

regional separation of the causes and consequences of climate change is a major reason for

international coordination problems and a prime source of political, economic, and even military

conflict. A multi-regional version of the model could hence be informative about international

interactions and their relation to climate change. Finally, the model could be changed to include food

production, the use of non-renewable resources, and pollution. These issues are also important for

economic well-being and closely linked to production, the evolution of population and societal values.

All these proposed extensions cannot be done in a single step and are left for future research. Although

the present version of the model is quite simple, the results are already quite rich. It hence necessary

to study and understand the properties of the baseline version first, before the model is extended.

7 Conclusion In this paper I presented a model of economic growth and climate change. In this model output growth,

productivity growth, population growth and the evolution of carbon emissions are all endogenous.

Together, these variables endogenously determine the global average temperature and the condition

of the natural environment. The central novelty of this paper is that aggregate economic decisions are

determined by the value system of the global society, which in turn responds to climate change

through its effect on the natural environment. The assumption of societal values as main determinants

of aggregate investment and consumption is well founded in research on lifestyles, social milieus, and

Evolutionary Modernization Theory. Relating the evolution of aggregate variables such as aggregate

investment or consumption to another aggregate entity such societal values instead of preferences of

individuals simplifies the model design significantly and avoids the highly problematic assumption of

representative agents which is the usual way to relate macro variable to factors at the micro level. At

the same time this approach makes it possible to endogenize a large number of variables in a

consistent way and it is amenable to empirical testing, because data on societal values are available

for many countries and years.

28

The main results of the baseline model for the 21st century are as follows11. The average yearly growth

rate of GDP is 3.4%. In 2100, the global population reaches a level of 9.2 billion people, the global

temperature is 2.8°C higher and the quality of the environment is 25% lower than in 1995. Global

values are almost unchanged by the end of the century.

It is important to emphasize that these number should not be interpreted as reliable predictions. With

any model, predictions of the state of a complex system such as the economy and its interaction with

nature over long time horizons are extremely uncertain. Even with a much more thorough calibration,

the calculated numbers would hardly be more reliable. Already in the baseline calibration, the range

of possible outcomes for each variable are quite large. An as the sensitivity analyses have shown, some

parameters can have strong effects on the simulation results. The scenarios about the different policy

orientations showed that an environmental or an efficiency bias of green investment can have large

effect on temperature. It is exactly this kind of result that makes the model interesting. If institutional

conditions and the policy orientation favor environmental restoration over investments in improved

carbon efficiency at any level of green investment, global temperature will rise strongly which offsets

all efforts to restore the environment.

The main purpose of this paper is to propose a conceptual model that might open a discussion and

that can be the basis for future work. So far economic reasoning about economic growth and climate

change is limited by methodological conventions. In equilibrium models with well-informed optimizing

agents it is very difficult to analyze a large number of endogenous interacting variables. These models

quickly become intractable and hence must focus on a few variables and mechanisms. However, the

issue of sustainable production and growth is a very complicated one with many dimensions of equal

importance that should be studied together in a unified framework. Otherwise, the potentially

important feedback effects that might reinforce or dampen individual effects cannot be captured. My

model is a suggestion how such a unified framework might look like. It is an attractive feature of the

model that it is relatively simple and transparent – it is completely described by 30 equations with 11

endogenous variables and 28 parameters -, but can nevertheless produce rich results.

In future work the model can be modified and extended in many ways. It is not the purpose of this

paper to present a policy or even a prediction model. My main objective is to propose an alternative

modeling approach built upon a theory of societal values that could also be used for other

macroeconomic questions. The chosen model is meant to be an example and to trigger a scientific

discussion about sustainable growth and its multiple facets among economists.

11 As numbers refer to the median of 100 simulation runs.

29

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