Uehara, Takuro with Yoko Nagase and Wayne Wakeland, "Using System Dynamics to Contribute to Ecological Economics", 2012 July 22-2012 July 26

Using System Dynamics to Contribute to Ecological Economics

Takuro Uehara
Doctoral Student, Systems Science Graduate Program and Dept. of Economics, Portland State
University, SYSC, P.O. Box 751, Portland, OR 97207, USA
Tel: 503-725-3907
ueharatakuro@yahoo.co.jp

Yoko Nagase
Senior Lecturer, Department of Accounting, Finance and Economics, Oxford Brookes University,
Wheatley Campus, Wheatley, Oxford, OX33 1HX, U.K.
Tel: 44-01865-485-997
ynagase@brookes.ac.uk

Wayne Wakeland
Ph.D., Associate Professor, Systems Science Graduate Program
Portland State University, SYSC, P.O. Box 751, Portland, OR 97207, USA
Tel: 503-725-4975 Fax: 503-725-8489
wakeland@pdx.edu

Abstract

This paper demonstrates the usefulness of the system dynamics approach to the development of
ecological economics, the study of the interactions between economic systems and ecological systems.
We build and analyze an ecological economic model: an extension of a population-resource dynamics
model developed by Brander and Taylor and published in American Economic Review in 1998. The
focus of the present paper is on the model building and analysis to contribute to theory building rather
than eliciting policy implications from the model. Hence, this is an example of model-based theory
building using system dynamics. Our analysis sheds light on several problems with this type of
ecological economics model that can be attributed to three commonly taken approaches to model
building and analysis by traditional economics: simplification through the use of exogenous variables,
equilibrium thinking, and a focus on the so-called balanced growth path. To solve these problems
ecological economic models should adopt approaches that are not prevalent in traditional economics
such as taking an endogenous point of view and allowing for out-of-equilibrium (adaptation) which
are key principles of the system dynamics method.

Keywords: Ecological Economics; Model-Based Theory Building; Endogenous Point of View;
Adaptation (out-of-equilibrium); Population-resource dynamics

1. Introduction

Real problems in complex systems do not respect academic boundaries.
- Herman Daly and Joshua Farley (Ecological Economics, 2 ed. (2010), xvii)

This article demonstrates the usefulness of the system dynamics approach to ecological economics-the
study of the interactions between economic systems and ecological systems (Common and Stagl,

1
2005). We build and analyze an ecological economic model: an extension of a population—resource
dynamics developed by Brander and Taylor and published in American Economic Review in 1998
(henceforth the BT model). The model is characterized as a general equilibrium version of the Gordon-
Schaefer Model, using a variation of the Lotka-Volterra predator-prey model.

Ecological economics is an interdisciplinary approach to solve problems that stem from the
interactions between economic systems and ecological systems. Ecological considerations have often
been either neglected or not treated properly in economics. Given the essential dynamic complexity of
an ecological economic system, we need an approach that goes beyond the simplified, analytic
approaches by standard economics. System dynamics can provide such an alternative.

Although ecological economic systems are ‘undeniably’ complex (Limburg et al., 2002),
standard economics has generally taken a strategy of simplification to be able to employ analytic
approaches. However, simplification has many drawbacks. There are many examples of this. First,
simpler functions such as the Cobb-Douglas type function (e.g., Solow, 1974a; Anderies, 2003), while
easy-to-handle analytically, limit the analysis of substitutability between man-made capital and natural
resources that is essential for sustainable development under natural resource constraints. Second, the
system boundary is set narrowly for the sake of simplicity. In analyzing the role of substitutability in an
economy, the law of motion of resources is often ignored (e.g., Bretschger, 1998). However, feedbacks
between ecology and economy play an important role (Costanza et al., 1993). Whenever an element is
treated as exogenous, the feedback loops are dropped. Third, standard economic theories mostly focus
on equilibrium conditions. “Transition dynamics” has largely been neglected (Sargent, 1993), except
for the recent development of learning (expectation) theory in modern macroeconomics (e.g., Evans
and Honkapohja, 2009; Evans and Honkapohja, 2011; Bullard, 2006). States of disequilibrium and
equilibrium-seeking adaptive systems have not been investigated well in economics, but such
transition dynamics are important for studying ecological economic systems (Costanza et al., 1993).

This paper strives to bridge economics and system dynamics in order to provide deeper insights
into the dynamics of ecological economic systems. While system dynamics has often neglected
economic theories because of its unrealistic tendencies (in the views of system dynamicists),
economics seems to largely ignore system dynamics (except for the notable reaction against The Limits
to Growth) because of its inconsistencies with economic theories. On the one hand, it is true that
economic theories provide a solid foundation for modeling economic systems. On the other hand,
system dynamics provides tools and a way of thinking for studying complex systems. We particularly
focus on the role of system dynamics as model-based theory building (Schwaninger and Grosser,
2008). We propose to employ standard economic theories as a base for ecological economic models
and to employ the system dynamics approach to build and validate the models. Since the research
employs the system dynamics approach as a primary method, the analysis of model results will look
different from how they are typically presented in economic journals.

In addition to technical characteristics of system dynamics as a computer-aided approach to
solve a system of coupled, nonlinear, first-order differential equations, system dynamics provides
useful tools and approaches to analyze complex systems. What characterizes system dynamics is its
emphasis on 1) feedback thinking, 2) loop dominance and nonlinearity, and 3) taking an endogenous
point of view. The endogenous point of view is the sine qua non of systems approaches (Richardson,
2011). System dynamics also uses several unique techniques for mapping a model, including causal
loop diagrams, system boundary diagrams, and stock and flow diagrams, in order to visualize a
complex system.

The model developed by Brander and Taylor (1998) is adopted as a baseline ecological
economic model. The BT model explains a pattern of economic and population growth, resource
degradation, and subsequent economic decline. Since its initial appearance in the American Economic
Review, the BT model has generated many descendants (Anderies, 2003; Basener and Ross, 2005;
Basener et al., 2008; D'Alessandro, 2007; Dalton and Coats, 2000; Dalton et al., 2005; de la Croix and
Dottori, 2008; Erickson and Gowdy, 2000; Good and Reuveny, 2006; Maxwell and Reuveny, 2000;
Nagase and Mirza, 2006; Pezzey and Anderies, 2003; Prskawetz et al., 2003; Reuveny and Decker,
2000; Taylor, 2009; Nagase and Uehara, 2011). In addition to its high quality, the BT model is
attractive, because of its simplicity and potential extendability. Hence the BT model should serve as a
good starting point for investigating the role of such critical factors as substitutability, resource
management regimes, population growth, and adaptation in an economy under limited available natural
resources, to evaluate the sustainability and resilience of an ecological economic system.

This article will extend the BT model following the suggestions for further research by Nagase
and Uehara (2011): population growth, substitutability, innovation, capital accumulation, property
rights/institutional designs, and modeling approach. The model is also an extension of the model
developed by Uehara et al (2010) presented at the ISDC 2010 conference held in South Korea.
Although their model resulted in unexpected inflation, the cause of the problem was later identified (an
issue related to Euler’s Theorem) and the problem has now been fixed. The model developed here will
be most applicable to developing economies where their economies may depend on natural resources
and population dynamics in a significant way.

Contrasted with the substantial body of work on limits to growth (c.f,, Meadows, et al. 2004),
the underlying equations in the present model are much simplified and are tied more directly to
traditional economic theory.

The purpose of our modeling and analysis is to find directions for the further development of
ecological economic models through conducting sensitivity analysis. Hence, this is an example of
model-based theory building using system dynamics. Through sensitivity analysis, we found two
problems with the BT model that are attributed to three commonly taken approaches to model building
and analysis by traditional economics: a simplification by the use of exogenous variables, equilibrium
thinking, and a focus on the so-called “balanced growth path.” The BT model relies on exogenous or
constant consumer preference, and maintains instantaneous equilibrium (i.e., no adaptive process).
These considerations are important in view of the desire to use the model for the sustainability of
dynamic and complex ecological economic systems, and indicate that ecological economic models
would benefit from the adoption of approaches that are not prevalent in traditional economics such as
taking an endogenous point of view and allowing for disequilibrium (adaptation) which are key
principles of the system dynamics method.

Section 2 presents the model and preliminary model testing, Section 3 provides the primary
results from conducting a variety model experiments focused on parameter sensitivity, and discussion
follows in Section 4. Model details are provided in an Appendix.

2. Model
2.1. Problem

We model a problem of sustainable development in developing economies which face a new economic
reality in which natural resource constraints are largely defining the future outlook (UNESCAP, 2010,
vii). While major economic growth models such as Solow growth model, neoclassical growth model,
Ramsey-Cass-Koopmans, and Overlapping Generations Model! do not embrace natural resource

1 For a good review of these standard economic growth models, see Romer (2011)

3
constraints as a primary component of their models, a report by UNESCAP (2010) argues that based
on real data, in Asia and the Pacific region, natural resource constraints such as food, water and energy
supplies, and climate change will play an increasingly important role in defining the sustainability of
economies in the region. Natural resource constraints are a real problem for sustainable development.

To develop a system dynamics model, we need graphs and other descriptive data showing the
behavior of the problem, which is called a reference mode. However, as the report by UNESCAP
addresses, this is a new phenomenon so that we do not have a good reference mode based on actual
data (either qualitative or quantitative). Therefore while the model developed here is to eventually be
used to elicit policy implications for developing economies, the model does not intend to seek fitness
to any particular historical data because developing economies may go through unprecedented
experiences since their situations could be quite different from the currently developed economies
(e.g., the availability of many technologies and the increased scarcity of natural resources).
Nevertheless, it will be worthwhile to discuss possible dynamic behaviors by considering possible
reference modes.

One possible reference pattern could be a collapse. As Diamond (2005) documented, there are
many historical cases of collapse. One of them is the boom and bust in Easter Island. As shown in
Figure | below, Easter Island faced a severe collapse after depleting natural resources.

wo. sk 10000
Population
wo] 20 oo
« |8 a 2 9
3 eo] & 40. {fh Soll Erosion 5 | cooo 7
= = wy & z
B ©} goo 4 Tao F
* z Ke
20. ea. 2000
0] 100. ° °
— T T 1 1
400 200 1200 1600 2000

Year (A.D.)

Figure 1. Easter Island dynamics from archaeological study by Bahn and Flenley (1992)

Another possibility could be dynamics in which population increases at the beginning and
become stabilized later without depleting natural resources, which we would prefer in terms of
sustainable development and can be found historically in Japan. Figure 2 shows the population and
cultivated land during Edo era (1603-1868). During Edo era, the Japanese economy was closed in that
imports, exports, immigration, and emigration were all negligible. Therefore, in terms of natural
resources, Japan’s growth during this period depended solely on its own natural resources in Japan.
Population growth was S-shaped and then stabilized until the Edo era ended and the new government
opened the country.* Compared with the peak cultivated land in 1948, there seemed to be enough
arable land uncultivated.

Given these reference modes, we choose 300 years as time horizon for our analysis. The choice

2 Leach et al. (2010) also argues that the current world is highly and dynamic in which environment,
science and technology, and social systems are changing rapidly.

8 After opening the country and till now, Japan is experiencing another similar dynamics where population
is being stabilized after a rapid increase. The structure which has caused the dynamics could be quite
different partly because Japan has depended on foreign economies.

4
35,000 0.5
30,000 VA

25;000 Tay Nw 3804
20,000 Wa + 0.3
15,000 A

ax + 0.2
10,000
+ 0.1
5,000
) r r r 0

1600 1650 1700 1750 1800 1850 1900

—— Population inJapan

=f Cultivated Land (Ratio to Cultivated Land at Peak in 1948)

Figure 2. Population and Cultivated Land in Japan during Edo Era (1603-1868). Source: Wikipedia and Kito (1996)

of time horizon influences the analysis of the dynamics of a system. Time horizon should be long
enough to reflect how problems emerge and how causes and effects impact the dynamics of the system.
Since dynamically complex systems involve many feedback loops, some of which might take a long
time to manifest, as pointed out by Sterman (2000). The Edo era was 265 years; Easter Island’s boom
and bust played out over 1600 years. Since as Leach et al. (2010) argue, we are currently facing
dynamic and faster changes in many respects including environmental, economical, and social aspects,
1600 years would be too long on the one hand. On the other hand, since Edo era would be simpler than
the situations mankind currently faces, it would be prudent to consider a somewhat longer time
horizon.

2.2. Background
2.2.1. Review of the Original BT Model

For completeness, we provide a thorough review of the original BT model. The BT model explains a
pattern of population growth, resource degradation, and subsequent economic decline. The model is
applied to the economy of Easter Island to depict its historical boom and bust. The authors characterize
the model as a Ricardo-Malthus model of renewable resources consisting of three central components.
The first component is Malthusian population dynamics in which increases in real income per capita
cause population growth, depressing the income level back to the subsistence level. The second
component is a common renewable resource regime and the absence of proper resource management,
such that the negative effect of population growth on the resource stock becomes exacerbated. The
third component is a Ricardian production structure at each point in time. Harvesting level of the
resource is determined endogenously by economic activities that follow economic theory. This model
setting allows us to study the effects of economic policies such as a price control and/or a labor cap.

In structural sense, the model is characterized as a general equilibrium version of the Gordon-
Schaefer Model, using a variation of the Lotka-Volterra predator-prey model. Resource (S) dynamics
and Population (Z) dynamics are given by (dropping the time argument for convenience)

dS Ss
B= (8) = 11-5) (1)
where G(S), r, K, and H are a logistic growth function of S, the intrinsic growth rate, the carrying
capacity, and the harvest of S, respectively, and

dL H
-i[o-a+g2) (2)

where b-d and ¢ are the base rate of population increase and a positive constant, respectively. The
population dynamics is Malthusian in the sense that the higher per capita consumption of the resource
good leads to higher population growth. There are two sectors, the harvested good (H) and
manufactured good (M).

At any point in time, the production functions for goods H and M are given by

H’= aSLy @)
M=Ly (4)

where a, L; and Ly are a productivity coefficient, labor allocated to producing H and labor allocated to
producing M, respectively.

Assuming common access without explicit rental cost for using S, the contribution of additional
labor in monetary value (i.e., the marginal revenue product of labor) must equal the price of labor,

w =pas (5)

where w is wage.
A representative consumer who is endowed with one unit of labor maximizes utility:

u=hhm'?
subject to the budget constraint:
Puht+pyum = w (6)

where h, m, £, pu, and py are individual consumption of H and M and preference for consumption of
H, price for H, and price for M respectively.

Solving the representative consumer’s maximizing problem and multiply that by the size of
population yields the market demand for H and M as

H?= wip (7)
M? = w(1-BL/pu (8)

Plugging (5) into (7) (i.e., quantity demanded = quantity supplied) yields an equilibrium resource
harvest, H.

H= apls (9)

Substituting (9) into (1) and (2), we obtain

dS S

— =rS| 1-— |-aBLs 10

ria [ 2) of (10)
& = Lb-d + dap) (11)

Three characteristics of the model are worth highlighting. First, the harvest level H is
determined endogenously as a result of an economic activity explained by a general equilibrium
model, in contrast to some other similar studies on the dynamics of population and natural resource
(e.g., Shukla et al., 2011). Second, in contrast to standard approach in natural resource economics (e.g.,
Conrad, 2010), agents in this model face a period-by-period optimization problem, without taking into
account any consequences of the future resource availability and population size. It is a reasonable
approach for the situation where the resource stock is held in common and agents are atomistic (Taylor,
2009). Third, at the each moment of time, the economy reaches a temporary general equilibrium
instantaneously (i.e., quantity demanded equals quantity supplied for both sectors) given a fixed
amount of the natural resource stock and population at that point in time. Since the natural resource
stock and population will change over time, so do the equilibrium prices and quantities. The economy
is always in equilibrium, whereas the population and the natural resource stocks change over time.

Applying the above model to Easter Island, Brander and Taylor (1998) demonstrate the
dynamics of population and natural resource shown in Figure 3.

14000 12000

12000

10000

8000

6000

4000

2000

400 600 800 1000 1200 1400 1600 1800

—— Natural Resource S ----PopulationL

Figure 3. The Dynamics of Population and Natural Resource in the Original BT model

2.2.2. Six Directions for Further Study

Nagase and Uehara (2011) discussed six key attributes of population-resource dynamic models based
the BT model and its descendants; they are (1) population growth, (2) substitutability, (3) innovation,
(4) capital accumulation, (5) property rights/institutional designs, and (6) modeling approach. Here we
discuss these six attributes in terms of economics in general and the BT model and its descendants. The
discussion regarding the BT model and its descendants owes a great deal to Nagase and Uehara (2011).

(1) Population growth
Since population dynamics interacts with natural resources and economic growth in developing
economies, it should be incorporated endogenously into an ecological-economic model. However, as
Sir Partha Dasgupta, an economist at University of Cambridge, addressed, “The study of possible
feedback loops between poverty, population growth, and the character and performance of both human
institutions and natural capital is not yet on the research agenda of modern growth economists”
(Dasgupta, 2008, p. 2). There is a field of economic growth which incorporates population dynamics
endogenously into economic growth models. It is called the unified growth theory which focuses on
the transition to a steadily growing economy (e.g., Strulik, 1997; Galor and Weil, 2000; Hansen and
Prescott, 2002; Galor, 2005; Voigtlander and Voth, 2006; Strulik, and Weisdorf, 2008; Madsen et al.
2010).4 While there are many methodological variations to address the transition (e.g., using a one-
sector vs. a two-sector model), most studies attempt to explain a transition from one equilibrium to
another, e.g., from a low income per capita (Malthusian) steady-state to a high income per capita
(Modern Growth) steady-state (Galor, 2005), applying endogenously determined technological
progress and fertility rates.° However, these studies share a common feature with regard to stocks and
flows of natural resources: natural resources are fixed or ignored in their models.

Regarding the BT model and its descendants, they incorporate both the population and the
resources endogenously but in simpler way. Nagase and Uehara (2011) proposed two directions for
extending the original BT model to enhance its theoretical basis and empirical relevance in application.
First, incorporation of manufactured goods into population dynamics will capture demographic
transition more accurately because birth rates and death rates do not solely depend on the availability
of food but also the availability of medical technology, for example. Second, population growth will be
a function of the natural resource to allow people to respond to its scarcity.

(2) Substitutability (3) Innovation and (4) Capital Accumulation, Taken Together

The degree of substitutability between man-made capital and natural resources plays an important role
in determining the sustainability of ecological economic systems in which the economy faces natural
resource constraints. Under resource constraints, we want to replace the natural resources as
production inputs with man-made capital, which does not have the same constraints. Studies on
substitutability have been almost exclusively conducted using either constant elasticity of substitution
(CES) or Cobb-Douglas (C-D) production functions (with C-D being one type of CES).”* The CES
function is expressed as:

4 The unified growth theory is not the only realm from which studies of the transition have emanated.
Economic historians have also studied this phenomenon (e.g., Crafts, 1995).

5 Hansen and Prescott (2002), Voigtlander and Voth (2006), and Strulik and Weisdorf (2008) employ a two-
sector model, while Strulik (1997), Galor and Weil (2000), Galor (2005), and Madsen et al. (2010) employ a
one-sector model.

6 The unified growth theory is basically a variant of the endogenous growth theory in that the source of
growth is determined endogenously. However, Hansen and Prescott (2002) provide an exception. They
assume that changes in total factor productivity are given exogenously.

7 Here we focus on substitutability in production. Other studies argue with respect to substitutability in
consumption (e.g., Gerlagh, Reyer, and B.C.C. van der Zwaan, 2002).

8 Stern (1994) proposes the translog production function because it can effectively model minimum input
requirements, any elasticity of substitution, and uneconomic regions, for any number of inputs and
outputs.
F(K,R,L)=| aK * +pR* aa |
(12)

a, B>0, a+ B<1,0>0, 0% 0.

where K, R, and L are respectively man-made capital, a natural resource, and labor; @, £, and o are
fixed parameters; o is called the elasticity of substitution. In other words, o indicates the trade-off
between factors of inputs. With o> 1, inputs are substitutable so that the natural resource (R) is not
essential for production. We can produce the good without the natural resource by substituting other
inputs. With o< 1, inputs are complements so that the natural resource (R) is essential for production.
We cannot produce the good without the natural resource.”

In relation to sustainability, the key discussion of the substitutability is the trade-off between
natural resources and the accumulation of man-made capital. Whereas mainstream economics has
supported o = 1, which is the special case and the production function reduces to the C-D function,
ecological economists assert o < 1 for various reasons (e.g., Cleveland et al., 1984; Cleveland and
Ruth, 1997; Daly, 1991; Daly and Farley, 2010). However, according to Nuemayer (2002), the
empirical evidence is inconclusive.

The original BT model and its descendants do not include man-made capital. In addition to
recommending the inclusion of man-made capital in a production function, Nagase and Uehara (2011)
suggested two more points to consider. First, to allow o to evolve over time endogenously has both
theoretical and empirical basis through endogenous innovation. Second, other functional forms should
be investigated (e.g., a production function proposed by Prskawetz et al., 2003).

Thus, substitutability, innovation, and capital accumulation are intimately intertwined.

(5) Property rights/ institutional designs

The original BT model assumes a common property resource (CPR). Some controls over CPRs tend to
be beneficial in view of sustainability. Although there are many studies of CPRs, three points remain
underexplored, particularly in theoretical studies. The first point is the impact of population growth on
cooperation. While it is well known from empirical studies that a smaller group size of people who
have the right to use resources is preferable for cooperation, dynamic treatment of population size is
rare at best. Sethi and Somanathan (1996) point out the importance of population growth for
sustainable resource use and provide some “guess” of the impact of population growth on the resource
use, but without any formal analysis. One model, by Caputo and Lueck (2003), in which the population
size n affects an individual’s optimal decision, highlights this point. The second point is the interaction
between human beings and the environment (Agrawal, 2003; Janssen and Anderies, 2011). Most
studies do not capture “the relevant complexity of the ecological and social dynamics communities
face” (Janssen and Anderies, 2011, pp.1569). Through the incorporation of the institutional design into
the model, it will be possible to investigate the impact of the institutional design on the sustainability
of the economy in the context where population, economy and natural resources are dynamically
interrelated. Third, most models use partial equilibrium and assume players are price takers. However,
it will be important to use a general equilibrium model to reflect the endogenous changes in prices that
affect, for example, relative attractiveness of cheating (Copeland and Taylor, 2009).

° For a comprehensive discussion about the relationship between substitutability and sustainability, see
Hamilton (1995).
(6) Modeling approach

By employing the system dynamics approach, this article models a complex ecological economic
system without making undue simplifications. Standard economics has generally taken a strategy of
simplification to be able to employ analytic approaches. However, simulation exercises are unlikely
avoidable for models of complex systems that are used primarily to increase understanding (Dasgupta,
2000). In addition, while economics generally puts emphasis on the existence of a steady state and its
comparative statics, and growth theory employs growth accounting, the system dynamics approach
puts its focus on the transition path; that is, how the dynamics of a system change over time.

2.3. Methods

2.3.1. Main Extensions

The present model implements four of the six suggestions by Nagase and Uehara (2011) to extend the
original BT model: population dynamics, substitutability, capital accumulation, and modeling
approach. These extensions are summarized here, with details provided in the Appendix.

(1) Population dynamics

While the original BT model incorporates endogenous population dynamics in a simple manner in that
a change in the rate of the population growth is linearly proportional to the food per capita (H/Z) in
order to reflect Malthusian population dynamics, we will incorporate Anderies’ (2003) formulation
which incorporates the impact of the manufactured good per capita (//L) as well in order to reflect the
demographic transition hypothesis, which consists of four basic stages between population dynamics
and the structure of the economy:

I. Population has both high birth and death rates that are nearly equal leading to slow population
growth;
II. Death rate falls, birth rate remains high leading to rapid population growth;
Il. Birth rate falls;
IV. Birth and death rates are both low and nearly equal and the population stabilizes at a higher
level than at stage I.

More specifically, Anderies (2003) models two essential aspects of demographic mechanism: income
and fertility are negatively correlated as observed in developing economies, and mortality is negatively
correlated with improved nutrition and infrastructure. The fertility rate is defined as

1 1
b,| 1-——

1 , 2 Hie * was
The term a(i-zr represents increases in birth rates, up to a maximum of by as q,(nutrition)
e" h

increases. The term

hi represents downward pressure on birth rates as gm (manufactured goods)

10
increases. The death rate is defined as

1
0 adie) (14)

Improved nutrition reduces death rates via the term g;d;, while improved infrastructure reduces death
rates via the term g;d2gm.

(2) Capital Accumulation

The original BT model and most of its descendants do not include capital accumulation. However, it is
essential to incorporate capital accumulation into the model in order to investigate the role of
substitutability between man-made capital and natural resources for sustainability. While there is one
important difference in its treatment, capital accumulation is also an essential component in growth
literature.

To model capital accumulation, standard economic approach is adopted as a base structure.
That is:

vR, = H,-oK
dt (15)

where Hy, 6, and K are respectively harvested good for capital formation, capital depreciation rate, and
current stock of man-made capital. There are two things worth mentioning about Hy. First, this
equation indicates that the source of capital formation, Hi, is produced using the same technology as
producing H good for consumers, as standard economics assumes. Second, in contrast to capital
formation in standard economics, capital formulation depends on natural resources for H = aSLy.
Therefore, in our model, natural resources are a so-called “growth-essential” (Groth, 2007).

(3) Substitutability

To investigate the substitutability between man-made capital and natural resources, a CES function is
used for manufacturing sector instead of a function of labor alone (M’ = Ly) used in the original BT
model.

The manufacturing sector maximizes its profit by solving the following maximization problem.

x
1-
max my = pyvlyy (Hf, + K?)? — py ly —wy ly — eR
Ly Hu Ku (16)
v: Efficiency parameter
1
p: Substitution parameter (p<0) = elasticity of substitution = o = 1-¢

# Positive parameter (0<y<1)

(4) Modeling Approach

1
Modeling takes two steps. For the first step, a general equilibrium model drawing from economic
theory is built. For the second step, the first step model is expanded so as to incorporate adaptation
(out-of-equilibrium) using the system dynamics approach.

To be more specific, the second step employs an approach suggested by Sterman (1980, 2000).
For example, the manufacturing sector seeks to find the optimal amounts of inputs, labor (Ly),
harvested good (Hx), and man-made capital (K) to satisfy the following first order conditions:

x
On, = ”
M = (1 y)pyvlQ7? (HY, + KP)? = wy

OL (17)
é fy

7, Ie =i

IM = ypyvl\ HE (HE +KP)P = pip
OH y (18)
é -

TC, ly fee
EM = yyy vIN OKP (HE + KP)P =

OK a9)

In a standard equilibrium model used in economics, agents are assumed to be able to find such optimal
values instantaneously.

In addition, price for H(py), price for M (py), and the return to man-made capital (zz) will be
adjusted to clear the market (that is, quantity demanded = quantity supplied). The full description of
the model can be found in appendix.

2.3.2. Summary Model Diagrams

To help grasp the whole picture of our model, two model descriptions are provided: a causal loop
diagram (CLD) and a description of the model boundary.

Figure 4 shows CLDs for the original BT model and our extended model, with the differences
highlighted. The original BT model has population, natural resource, harvesting, manufacturing, and
labor sector. Although the harvesting sector and manufacturing both sectors have demand and supply,
they are kept equal by the instantaneous adjustment of prices to clear the market. The extended model
allows for disequilibrium and has a man-made capital sector. Thick arrows indicate important newly
added connections. Manufacturing and man-made capital are connected to each other. Manufacturing
also depends on harvested goods (natural resources). Population dynamics depend not only on
harvested goods but also on manufactured goods (e.g., medical technology).

Figure 5 documents the boundary of our model and clarifies what is exogenously given and
what is excluded, in order to avoid misinterpretation of our model results and to underscore the
limitations of our model. Exogenous variables for population dynamics follow Anderies (2003) to
capture the basic demographic transition. The carrying capacity and the regeneration rate of natural
resources are exogenous (constants) as in the original BT model. However, they could be endogenous.
Particularly, the regeneration rate may be modified via innovation. The other exogenous variables
except for adjustment times are standard economics treatment. Adjustment times are often exogenously
given in system dynamics models, but these could be endogenous as well.'°

10 For example, Kostyshyna (forthcoming) suggests an adaptive step-size algorithm to allow a time-varying
learning speed (or a time-varying gain parameter) that change endogenously in response to changes in
environment.

12
The choice to highlight specific excluded variables is somewhat subjective. They are chosen for
their importance in view of ecological economic systems for developing economies. The inclusion of
money, for example would likely lead to different results. Nonrenewable resources are also important,
as most studies on the economics of sustainability focus on nonrenewable resources (e.g., Hartwick,
1977). As is often discussed in environmental economics textbooks, societies tend to use less
expensive nonrenewable resources first, such as oil, and then switch to more expensive renewable

13
Populati

Fons

Poulton © Ph

Food per”

4B) capita

vesting

[Natural Resource

te

Regen” /
Sratrg @p Natl —]

Resource
Ey

Original BT model

Populati ing
Ys we ~Derand
Population “BPS
+

®
(Se
4B) _ capita

[Natural Resource

rad

erating

@& Natural _|
ese

A)

wY

Man-made-Capital

“|

aon @ aris
Sod ~

a
&

ac |

Our Extended Model

Figure 4. Causal Loop Diagrams for the original BT Model and our Extended Model. Red text and thick arrows indicate newly added items.

14

Endogenous Exogenous Excluded
Population Popultion Money

- Population
- Birth Rate
- Death Rate

Natural Resource

- Renewable resource

- Natural Growth Rate of S
- Harvesting Rate of S
Harvesting

- Inventory of H

- Supply and demand of H
- Price for good H
Manufacturing

- Inventory of M

- Supply and demand of M
- Price for good M

Labor

- Labor to H industry

- Labor to M industry

- Wage for H industry

- Wage for M industry
Man-Made Capital

- Man-made capital

- Return to man-made capital

Household

- Total earning
- Earning

- Spending

- Impact of H on population

- Impact of M on population

- Maximum fertility rate

- Maximum mortality rate

Natural Resource

- Regeneration rate of natural
resource

- Carrying capacity

Harvesting

- Efficiency parameter

- Adjustment time for py

Manufacturing
- Adjustment time for py

- Efficiency parameter

- Substitution parameter
- Output elasticity
Labor

Man-Made Capital

- Capital depreciation rate

- Adjustment time for the
return to man-made capital

Household

- Consumer preference for
goods

-__ Savings rate

Non-renewable resources
Negative externalities of
production (pollution,...)
International relationships
(exports, imports,
immigration, emigration)

resources such as wind and solar when the marginal cost of the nonrenewable resource begins to
exceed that of the renewable resources (e.g., Tietenberg, 2011). Negative externalities such as pollution
may not be negligible. For example, a study by Asian Development Bank showed that the costs
associated with climate change could be equivalent to a loss of 6.7% of their combined gross domestic
product (GDP) by 2100 (ADB, 2009). International relationships may be most important factors
excluded from our model. When international relationships exist, as is the case for most developing

Figure 5. Model Boundary

economies, they can use resources and new technologies from abroad and perhaps avoid collapse.

2.4. Model Testing

Various model tests are used in the system dynamics method (Sterman, 2000). What is particularly
different in this paper compared to other system dynamics models is that structural assessment was

15

made based on economic theory. In other words, we assume that our model passes the structure
assessment tests because the basic structure of the model follows standard economic theory.

Of course we tested to verify that the integration step-size was adequate, and we made sure to
initialize the model in steady state by forcing population to be constant and setting the initial
conditions to the equilibrium values derived from economic theory. These initial values resulted in a
near equilibrium result, so minor changes were made to achieve a computational equilibrium.

In many cases, a full suite of model tests, including sensitivity tests, extreme condition tests and
many others would be performed prior to actually applying the model to find answers to the questions
posed at the outset of a modeling project. For the present research, however, which aims to show how
the use of the system dynamics method can contribute to economics research, the sensitivity analysis in
particular will be presented in Section 3 as a primary result. To complete this lengthy Section 2 which
presents the model, we describe a baseline run and compare this to the baseline run from the original
BT model.

The baseline model run is shown in Figure 6. Population grows rapidly, then declines and
reaches a steady state value well above the initial value. The Natural Resource declines to near half the
carrying capacity (the value at which the natural regeneration rate becomes zero). Not shown, but
inventories of H good and M good both increase significantly, and the prices for H and M both decline
significantly, due in part to the decline in Natural Resource and the fact that increasing population is
placing increased pressure on production. Labor shifts towards the harvesting sector initially, then
partially reverses as the Natural Resource is reduced. Capital increases rapidly, then declines and levels
off as population stabilizes. Wealth, as shown in Figure 6 declines somewhat initially, then increases,

14,000
300
50

0 30 60 90 120 150 180 210 240 270 300
Time (Year)

Natural Resource S : baselinedplotcomparedtoBT
Population L : baselinedplotcomparedtoBT
Total Wealth : baselinedplotcomparedtoBT

Figure 6: Extended Model Population and Resources
and settles at a value somewhat higher than the starting point.

The shape of the Natural Resource and Population curves are similar to the baseline BT model
results shown in Figure 3, and the extended model could be calibrated to match the BT model, but
much of its logic would need to be neutralized. Because the extended model has man-made capital
formation, the population decline is buffered somewhat.

3. Results of Sensitivity Analyses

For this paper we consider the sensitivity analyses to be a primary result in addition to serving as an
important model validation tool. Sensitivity analysis can be used to investigate possible transitional

16
paths for ecological economic systems. Given the complexity of such systems, it is almost impossible
to find an optimal solution by taking into account all the necessary information including possible
future states.!' Therefore what policy makers need to obtain from modeling and analysis is not an
optimal solution that would allow them to control an ecological economic system, but rather they need
to know what kinds of transition paths to expect so that society can prepare for these possible changes
(Leach et al, 2010). Given past experiences, Folke et al. (2002) suggested “structured scenarios” as a
tool to envision multiple alternative futures and the pathways for making policies.

Through the sensitivity analysis we found two critical issues that ecological economics should
consider in when developing models of ecological economic systems: 1) endogenous consumer
preference, and 2) adaptation (out-of-equilibrium). While they are critical issues in terms of policy
implications for a sustained economy, they have been rarely considered in economics. There are at
least three reasons inherent in standard economics. First, economics prefers to simplify a model, for
example by using exogenous variables, so that it can be solved analytically. However, resulting
implicit model boundary may give misleading policy implications. Second, an equilibrium-oriented
paradigm continues to prevail, in which there is a belief that society can find an optimal solution to
attain a sustained economy. Because ecological economic systems are complex and highly dynamic,
optimal management is very difficult (if not impossible) to implement (Folke et al, 2002).' Third, a
focus is put on the balanced-growth path (BGP) which strived to achieve a long-run steady state
characterized by constant growth rates. In the growth literature, the discussion of sustainability is about
finding conditions for the BGP (e.g., sufficient growth rate of technology which sustains the growth)
(e.g., Groth, 2007). Therefore, it is rare at best in the growth literature that sensitivity analysis is done
to study how changes in factors affect the transitional paths. In other words, the robustness of a model
is not its main focus. However, the steady state (BGP) could occur usually only in the very long run,
which may not be what policy makers want to know. What is important for policy makers given our
imperfect knowledge of dynamic and complex ecological economic systems may be to understand how
factors affect the transitional paths of an economy. Because of the absence of sensitivity analysis in
most economic studies, these needs have not received sufficient attention.

3.1. Sensitivity to Consumer Preference

In our model, following standard economics, a preference for good H (f) is exogenously given as a
constant. Solving the consumer’s utility maximization problem, we obtain an individual consumer’s
quantity demanded for H as a function of price for H and income as:

= wBlpu

Hence the quantity of good H depends on the preference for good H (f), wage (w), and price
for good H (py). Since wage depends on py, h° basically responds only to changes in py.

Although any preference seems to be acceptable as long as 0 < #< 1, a low # shows
unreasonable behavior, as shown in Figure 7, when f is 0.15 (i.e., a lower preference for H good),
population becomes extinct at time 100. This does not make sense because the natural resource S —

11 However, Leach et al. (2010) points out that dynamics and complexity have been ignored in conventional
policy approaches for development and sustainability. They relate this tendency to prevailing equilibrium
thinking as we mention later.

12 Folke et al. (2002) asserts that we should use adaptive management instead given imperfect knowledge
about the ecological economics systems.

17
300 14000
250 L£™ 12000 Wea===
200 rd N 10000
if NX 8000
150
Vi 6000
100 y 4000
50 Ko 2000
O eerste 0 heer
0 50 100 150 200 250 300 0 50 100 150 200 250 300
—— Population L (b = 0.4) Natural Resource S (b = 0.4)
=== Population L (b = 0.15) = =-—-=Natural Resource S (b = 0.15)

Figure 7. Dynamics of Population and Natural Resources with Different Values for Fixed Consumer Preference, 8

which is the source of food — remains abundant. This occurs because the preference for H (i.e., ) is
constant (i.e., exogenously given) regardless of the value for food per capita. However, a constant
preference for goods is a standard approach for economics. This problem has been rarely investigated
in standard economics. David Stern (1997) points out that neoclassical economists are very reticent to
discuss the origin of preferences and that preferences are normally assumed to be unchanging over
time.

However, as our sensitivity analysis shows, exogenous consumer preference is not a robust and
realistic formulation.'? The importance of endogenous preferences for sustainability issues has been
argued by several heterodox economics such as ecological economics (Common and Stagl, 2005;
Georgescu-Roegen, 1950; Stern, 1997), evolutionary economics (Gowdy, 2007), and institutional
economics (Hahnel and Albert, 1990; Hahnel, 2001). Gowdy (2007) argues that neoclassical
economics assumes that consumers not only respond to price signals as we modeled but also to other
incentives such as the individual’s personal history, their interaction with others, and the social context
of the individual choice. He called the former the se/f-regarding preference and the latter the other-
regarding preference. If these factors change over time, then preferences should reflect these changes.
Gowdy asserts further that modeling the other-regarding behavior would be more realistic for
sustainability research. Common and Stagl (2005) argue that to change preference is a normative
requirement from a sustainability perspective, including the idea that there could be an ethical basis for

13 It is not impossible to solve this problem using an exogenous preference. For example, a Stone-Geary
type utility function (Anderies, 2003) incorporates the minimum amount of the quantity demanded for H
into the utility function as U(h, m) = (a -h y m'‘* Then we can derive the demand function

=(I- vB
b= (1 BY hag +

Hence, the first part does not depend on the price. It means that people put their effort to harvest at least
the minimum level, Amin, irrespective of the price.

18
changing preferences. While there have been several discussions on endogenous preference, there is no
standard way of modeling endogenous preference in economics literature. '*

3.2. Sensi

ity to Adaptation (out-of-equilibrium responses)

The amplitude of oscillations increase with longer adjustment times, and the oscillations dampen out
more slowly if at all. The period of the oscillations does not change very much. Figure 8 shows the
dynamics of population with different adjustment times for the prices for H and M, the factor demand
of H (use of H to produce M), and for adjustments to the return to man-made capital. All of these time
constants were varied together from | year, to 5 years, to 10 years.

Although adaptation and oscillation caused by adaptive process are nothing new to system
dynamics, the concept of adaptation (out-of-equilibrium) and its importance have been recognized in
ecological economics only relatively recently (e.g., Common and Stagl, 2005; de Vries, 2010; Folke,
2002; Hanley, 1998; Holling, 1999; Leach et al., 2010; Levin et al, 1998; Stag], 2007).

Leach et al. (2010) argue that conventional policy approaches for development and for
sustainability have ignored the dynamics and complexity of ecological economic systems in order to be
able to use standard equilibrium thinking and its associated policy implications. Essentially, the hope is
that ecological economic systems are both predictable and controllable. However, as Leach et al. point
out, both ecological systems and economic systems are changing so rapidly that it is difficult if not
impossible to find an optimal solution in order to “control” these systems. Given the dynamic and
complex nature of ecological economic systems, we face risks, uncertainty, ambiguity, and ignorance
(Leach et al., 2010); that is, we have imperfect knowledge. The use of adaptation is more than a
philosophical or preference issue. Folke et al. (2002) argues, based on actual examples, that we should
adopt a dynamic view that emphasizes far-from-equilibrium conditions. Incorporating adaptation into
an ecological economic model enables us “to understand how humans have constructed environmental
problems (and opportunities) in particular ways. They depend on the particular contexts of governance
structures and cultures and over time shape and are shaped by biophysical environments, technologies
and human behavior.” (Stagl, 2007, p.59).°

In terms of modeling adaptation in ecological economic models, it has not been thriving.
Some studies were done by Hommes and Rosser (2001) and Forini et al. (2003). They applied

16, 17

14 One example of modeling endogenous preference is proposed by Stern (1997). Using the symmetric
characteristics of production and consumption, he proposes the factor augmentation model using an
analogy to endogenously augmenting technology in production.

15 Robert Solow, a Nobel Memorial Prize in Economic Sciences, pointed out the importance of
disequilibrium in early 1970s. He published two articles about natural resources and economic growth in
1974 (Solow 1974a and 1974b). Whereas one with an orthodox formal growth model employs equilibrium
model, the other paper without a formal model discussed importance of disequilibrium for its impact on
resource allocation.

16 There seems to be two types of adaptation. One is adaptive management in which natural resource
management and policy making in general are adaptive against changing situations. The other is
adaptation system where adaptation is incorporated to explain system’s behavior such as market
dynamics. We are talking the latter.

17 Learning is not absent at all in economics. Learning plays a key role in modern macroeconomics.
Learning in macroeconomics refers to models of expectation formation in which agents revise their forecast
rules over time, for example in response to new data (Evans and Honkapohja, 2008). Evans and
Honkapohja (2008) pick three roles of learning in macroeconomics: 1) assessing the plausibility
(learnability) of an equilibrium, 2) providing a selection criterion when there are multiple equilibria, and 3)
addressing macroeconomic fluctuations.

19
0 50 100 150 200 250 300

=== Population L (ATs = 1) Population L (ATs = 5)

seeeees Population L (ATs = 10)

Figure 8. Population Dynamics with Different Adjustment Times

adaptation to fishermen’s price expectation formation in their fishery market models in order to study
the “learnability” of equilibria.

3.3. Additional Sensitivity Tests

Additional sensitivity tests performed to more fully exercise the model are summarized in Table 1.
The implications of these experiments are discussed in Section 4.

4. Discussion

The extended ecological economics model developed and tested in this paper draws heavily on
economic theory and prior research by many economists, especially those focused on ecological
economics. Our aim was to demonstrate the benefits of employing the system dynamics method to
complement the methods used in the economics field. These benefits include: a) a greater reliance on
simulation rather than analytical solutions, which allows the use of more complex formulations; b) the
use of various diagrams to improve the transparency and accessibility of the model logic and
assumptions; c) a focus on the analysis of the feedback structures and the time dynamics as well as
equilibrium conditions; and d) an emphasis on running a wide variety of experiments to fully exercise
the models and increase understanding.

In addition to striving to remain faithful to economic theory, we have also begun to subject the
model to a variety of sensitivity tests. These have led to new insights and have revealed weaknesses in
the model logic. In some cases these weaknesses can be remedied by employing recent advances in
ecological economics, but in other cases, it may be necessary to develop new logic at the frontier of the

20
Table 1: Sensitivity Test Results

Parameter Base Exper Result Graph or Comments
(s) Value | iment
Tests related to Savings Rate
savings rate, | .2 to .1 Population increases more bic dad
s rapidly, overshoots and
settles at a somewhat higher SLL =
SS; Resources decline
further, but not drastically A
see #1 2 to .05 | mu, returns to capital is mu
much higher and more :
volatile; K is much less, as - BF
expected, M inventory is é E
less, but Price of M is not ir —-
affected; Wealth is more if —~—
volatile and lower ee
see #1 2 to .02 | Resource a bit lower
see #1 2 to.01__| Wealth much lower
Tests related to Natural Resource Carrying Capacity and Regen. Rate
Smax, 12000 | 6000 Population collapsed, even Likely related the problem with the
Resource though Nat, Resource stabil- | fixed value of Beta
Carry Cap. ized at the new (lower)
value.
r 04 2 Population up sharply then
Resource stable; Resources held
Regen.rate steady, kept from increasing
by Smax. Wealth is stable.
Tests related to the Sensitivity of Population to Natural Resources and Mfg. Good
Sens. of 1 to2 Pop grows faster, overshoots Porslaienl.
births to Nat. more and stabilizes a bit
Res. higher; Resource drops a
faster and further and ends 0
Sens. of up lower; Wealth up sig. bi
births to mfg. | 1 to .5
good ——

21

8 | Sens. of 1 to .5 Population rose slowly and
births to Nat. stabilized; Resource 4g
Resources declined modestly and
stabilized; wealth is flat; M
Sens. of 1 to2 production increases and
births to stabilizes; returns to capital =
mfg’d good decline steadily (but less
than baseline) and stabilize
9 | Sens. of § to 10 Similar to #7 except the
deaths to peak in Population (and
resources drop in Resource) occur
later, at the same time as in
Sens. of 1 to .5 the baseline run; Wealth up
deaths to significantly
mfg’d good
10 5 to 2.5 | Population flat lines, along
see #9 with everything else
1 to2
11 | Sens. of 5 to 10 | Population flat lines
deaths to
resources
12 | Sens. of 1 to .5 Negligible effect; looks just
deaths to like baseline
mfg’d good
13 | Sens. of 1 to .5 Population is a little higher i ee
births to than #8 (graph to the right “
resources shows pop for baseline, #8 al
and #13); Resource is a bit 200 + pa
lower than #8; Wealth is a “8 ee
little higher TT
=a) a 300
Tests related to Adjustment Times (AT) for Prices, Returns, and Demand
14 | AT for Price | 2 1to6 | No significant effect
of H good
15 | AT for Price | 2 1to6 | Minimal effect until near 6: | Wealth goes to zero; Man made capital
of M good Population is sig. higher begins to collapse
with wide swings; Natural
Resource is lower
16 | AT for 2. 1to6 | Smaller values lowers Nothing else seems to be impacted!
Return to Wealth; higher values
manmade increase Wealth
capital, mu considerably
17 | AT for Factor | 2 1-6 Little effect Factor demand is the demand for

Demand, Hm

Natural Resources by Manufacturing

22

field, a frontier that will be extended by bringing together the powerful traditions and disciplines from
economics and new ways of thinking about and addressing complexity from the system dynamics
discipline.

Some of the specific questions raised by the results of the present research include: 1) the
common practice of assuming fixed consumer preferences rather than endogenously determining the
relative preferences for different goods depending on current conditions, 2) the assumption that all
important results can be found by finding equilibrium solutions rather than taking into account how
complex systems learn and adapt based on disruptions and other changes that drive them out of
equilibrium perhaps for long periods of time, 3) the model’s response to very small savings rates
indicates a higher degree of volatility and vulnerability, 4) exploration of resource carrying capacity
and regeneration rates exhibit both favorable and adverse outcomes and constraints, 5) experiments
with the sensitivity parameters in the population model indicate the potential for both population
collapse and for trajectories that are more steady and do not lead to collapse, 6) testing the impact of
different speeds of adjustment to out-of-equilibrium conditions reveals major differences in system
response which reinforces the case for not relying on equilibrium methods.

These findings must not yet be taken very seriously, however, since the model on which they
are based is subject to many limitations, especially the restrictive model boundary documented in
Figure 5, and the need for much more testing, including the application/calibration of the model to
represent actual developing economies in a realistic fashion.

In conclusion, we have demonstrated that the system dynamics methods appears to have
considerable potential to complement economic research, especially ecological economics which
strives to address the complex interactions between the economy, ecological systems, and human
behavior.

23
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26
Appendix: Detailed Model Description

The model is developed in two steps: the first step is to build a model for an instantaneous equilibrium
without adaptation; the second step is to build a system dynamics model using the model developed in
the first step by incorporating adaptive process. The first step models employ economic theory so that
their mathematical descriptions follow economic approach. The second step models employ system
dynamics so that the model is represented using a flow-stock diagram.

The first step model

A Representative Consumer

max u=h'm'?
s.t. Puh+pym = (1-s)y
h: Individual consumption of the harvested good H. (= hL)
mz: Individual consumption of the manufactured good M. (= mL)
#: Preference for consumption of h, 0 < #< 1
s: Savings rate
pi: Price for good i, i= H, M
y: income; y= w+ uk/L > aggregate income Y = yL = wl + wk
w: wage; In disequilibrium, wages are different for two sectors: w, # Wy

“: Return to man-made capital

Solving the above, we get

je = Us) 98 = ne = ti = “DB ax)
Pu Pu
m* = (s)70+4) > mc* = Lm* = C=O") ur sr)
Pu Pu

Harvesting Sector
Harvesting sector has the same production function as the original BT model.

mas Ty = Py ASLy — Wy Ly
H

F.O.C. PyaS = Wy (1)

Manufacturing Sector
x
max ty = pyVvly? (HE, + KP)? — py —wyly — eK y
Ly Hy Ku

v: Efficiency parameter

27
p: Substitution parameter (p <0) = elasticity of substitution = o = Fa
y Positive parameter (<y<1)

F.0.Cs.
x

On, = Bi
M = (1 y)py vl (HY, + KP)? = wy

aLy

(2)
vy

On; 1-y - —
M = ypyvl HE HE +KPYP = py

OHy

(3)
ry

On, 1- 1 Dp.
EM = yyy viNe KE (HE + KP)P =

OK (4)
Equilibrium Conditions
H market:
aSLy, = (9)8 (wt tuk) +Hy (5)
Pu
M market:
ally” (Hf +KP yp = emer aa (6)

Pu M

This equation indicates that investment syL is used to purchase good M to form capital, as per Anderies
(2003). We assume that H goods as a factor of production and consumer goods employs the same
production technology.

Labor market
L=Ly+ Lu 2)
Capital market

K=Ky (8)

Dynamic Equations

1. Law of motion for S: $B -a4)-n=1s(1- 2 }-w
t

‘max

28
2. Law of motion for L
The formulation by Anderies (2003) is used to capture the hypothetical demographic transition.

dL 1 1 1
4 -(i(1-z} deat

1 . wa. . a:
The term ty(1- ie spresen increases in birth rates, up to a maximum of by as /A(nutrition)
e

P 1 3
increases. The term ——represents downward pressure on birth rates as m (manufactured goods)
ée

bam

increases. The death rate is defined as
1

0 elditdam)
Improved nutrition reduces death rates via the term g;h, while improved infrastructure reduces death
rates via the term hd2m.

3. Law of motion for K: Aa Hy ~ 6K =k 6K
it

Pu

29
Carrying Capacity
‘Smax

Rate

Sensitivity of birth
rate to resource. Maximum birth
good intake bl rate bO Regeneration
Rate r
——™ Indicated Factor

Demand Hm

Senstty of \ J
ath a

a ) “a
Consumption“*~ Current Factor
marie Current Facto

eb
Fractional Birth

cari es
au Vo SERLEN (Coes

\ oa porn Hn] soe henna gt

— im ___—— for Production of M

>| Popubtion L change in Lh va cast of H
(Change in Birth ; (Change in Death _foputaton Demnd StH ae
ee pase
\ t conse Maat
Sante > en

Change in Ph|
ae eal

lath ate dO
Ras go = |
Pa if Wage H
Q
y) fi pee

Sensitivity of

Maximum =———® Fractional Death {
Indicated Ph eetionbrhow i
nae ee
oe
VY

sie Sensitivity of death
resource 200 rate to manufictured shifting from Wage Ratio
intake dl god intake d2 Lh Lm

— 5 =
cs M invertor
Spencing =<] a a
—___Produetion Se

| sitet
gale
Poet aie M
Se as ST
\ Le Z
[= <7 apply ofM Preference
Commies a riba
al Factor Pa Demand Me
ern sy fang on Foohutn Demand Mk
Death Changin
Aphputtion Mipha Me
Triad Pm
Sg | Retin Change in Pmt
os Es S
lege 4
— es
“aa

Parameter nu

Positv

Figure 9. Flow diagram for the Extended Model
30
Using System Dynamics to Contribute
to Ecological Economics

Takuro Uehara'!, Yoko Nagase’, and Wayne Wakeland?

1. Systems Science Graduate Program and Department of Economics, Portland State University, USA
2. Department of Accounting, Finance and Economics, Oxford Brookes University, UK
3. Systems Science Graduate Program, Portland State University, USA

OXFORD

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| Purpose

™ Investigate possible contributions of SD to
ecological economics

4 Ecological economics is the study of interactions between
ecological systems and economic systems

" The main focus is on the usefulness of sensitivity
analysis

4 Economics has focused on comparative statics (i.e.,
analyzing the behavior of a system around a steady state).

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Approach: Use a Two-step Modeling
Process

" Build a base model using economic
theory

" Incorporate adaptation using system
dynamics

= Hill-climbing approach that solves first order
conditions numerically

" Allows for out-of-equilibrium states

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Portland State BROOKES

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| Context

" Extend a model of population-resource dynamics
by Brander & Taylor (1998)

4 Published in the American Economic Review

" Reflect some of the suggestions from Nagase &
Uehara (2011)

4 Population growth fn. (Demographic Transition)

4 Input substitutability (CES function)

4 Capital accumulation (Man-made capital)

4 Modeling approach (Economics & System Dynamics)

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Mathematical Spec. of the BT Model

General equilibrium version of the Gordon-Schaefer Model,
using a variation of the Lotka-Volterra predator-prey model

Static optimization (for given resource stock size S and

population L)
Consumers: Max u=hém!*? — s.t. ph+m=w
{h, m}
Producers: H = aSLy; a: tech parameter
M=L,,
Let Ly =

Equations of Motion (Predator-prey framework)
EGS = Soll a + ili

ATA ar

= H* where K: Carrying Capacit
Portland State BROOKES. ms %5

UNIVERSITY UNIVERSITY
% Forest Pollen

Reference Mode: pattern of behavior

of the system to be

modeled

Cultivated Land

Boom and Bust --OR--
0 3k 10000 Stabilization
.¢+, Forest Resource !
a. “ 8000 35,000 0.5
g tA | aK 9 30,000 + 7;
© 40. +! Soil Erosion 5 s 2 [
s AY i 3 ano J = 25,000 SL Wi% mw 3900-4
8 60 i 4 [Shercoal 3 4000 3 = 20.000 ZL 0.3
. ; Vy i we ‘| 4 15,000 TA
80. ana an ad 2000 Qt: a1 - 0.2
5 ee a ie co a & 16:00
100. 7 e 0 0 5,000 r 0.1
r T T T 1 °
400 800 1200 1600 2000 0 ; , , 0
wee nes 1600 1650 1700 1750 1800 1850 1900
Easter Island dynamics from —Population in Japan
archaeological study by Bahn and —@— Cultivated Land (Ratio to Cultivated Land at Peak in 1948)
Flenley (1992)
Population and Cultivated Land in Japan
during Edo Era (1603-1868). Source:
Wikipedia and Kito (1996)
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Model Description: Causal Loop Diagram
" Main feedback eee

loops wins ro
™ Red texts and /| “we )) A | (kN

thick arrows 48) ante F supa
indicate newly [Natural Resource Labor \
B
* Labor for H
added items. reser @
erating @ Natural Total Labor Relative

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| Model Description: Boundary

Endogenous Exogenous
Population Population
-Population (L) -Initial population (L,)
Birth Rate (b) -Impact of H and M on
‘Death Rate (d) population (b,, b, d,, d,)

Natural Resource
-Resource stock (S)
-Growth of S (G)
-Harvesting of S (H,)

Harvesting
‘Inventory of H

-Maximum mortality rate
(d,)

Natural Resource

-Regeneration rate of
natural resource (77)
-Carrying capacity (S,,)

-Maximum fertility rate (b,)

-Initial natural Resource (S,) _

Excluded
Non-renewable
resources
Negative externalities
of production
(pollution)
International
relationships (exports,
imports, immigration,
emigration)
Unemployment

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| Results: Baseline

= Calibrated to be consistent with chosen reference mode

Natural Resource S and Population L: Baseline

0 30 60 90 120 150 180 210 240 270 300
Time (Year)
Population L : Baseline 5 ee a a a a a
Natural Resource S : Baseline a a a a a

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| Results: Consumer Preference b

™ Exogenous consumer preference leads to implausible results

" Either exogenous preference with careful choice or
endogenous preference may solve the problem

Baseline
50%  —- 75% {05% | 100%
Population L.

800

Baseline

50% 75% | 95% J 100%
Natural Resource S
20,000

600

400
15,000

| 10,000%y

300 5,000

200

= Time (Year)
9 0 Res 150 225 300
Sensitivity of L to various / Tine. (Year)
Sensitivity of S to various 6
OXFORD
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| Results: Adaptation Processes

" Adaptation time constants significantly affect the numerical
results, but not the qualitative results (shape of curve)

350

300

250

Oooo

0 50 100 150 200 250 300

===-=PopulationL (ATs = 1) -—==—=PopulationL (ATs = 5)
seeeeee Population L (ATs = 10)

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11
| Results: S

(resource regeneration rate)
= While the impacts of S,,., and 77 on G(S) are both positive (dG/dS,,,>0
and dG/d7>0), their impacts on the system are quite different

(carrying capacity) and 7

max

Natural Resource S Population L

19,000 Seayceacresne “
Impacts of CCC aaa

Ei 5,000 2-24
Changes in 7 PRBS
0 0
oO 30 60 90 120150 180) 210.240 270-300
0 30 60 90 1220 150 180 «210 «240 «270 ©6300 Time (Year)
Tame (Year) Population L : Exos Tech Chat
eptoaL eepenie Teh Changes nen pea
Sul nanmes eles goes Population I: Baseline
Natural Resource $ Population L
20,000 800
Impacts of mn “
7 10,000 ann:
Changes in S
max >
5,000 ns = F|
; 0

pula
uurceS : Exogenous Tech Change in Sux: 333333 Population L: Baseline

vl Resource Baelne 12

Discussion: Consumer Preferences

™" Neoclassical economists are “very reticent” to talk
the origin of preferences and assume that they are
unchanging over time (Stern, 1997)

" Heterodox economists (e.g., ecological economists)
argue for the importance of changing preference for
sustainability issues.

" There is no well established approach in economics.

" SD could offer an approach to endogenize consumer
preferences

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Discussion: Adaptation

" Adaptation has been paid attention to in ecological
economics only recently (e.g., Common and Stagl,
2005)

" And, while its importance has been raised, no well
established modeling approach for adaptation is
available in economics

4 Learning in macroeconomic theory (e.g., Evans and
Honkapohja, 2011 ) could be one possibility

4 SD could offer an approach to incorporate adaptation in an
appropriate manner

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Discussion: S_. and 7

" System Dynamics view: A system oscillates if
4 Snax is not constant and the system involves delays to keep
seeking a new Steady state (cf., Sterman, 2000).
" Economics view; from Brander and Taylor (1998):
4 The system converges to a steady state with oscillations if
Nd = BW(Smmax P&P) + 4 ((d = b) — SraxboB ) < 0
4 The system converges monotonically to a steady state if
(d — bBY(SinaxP@P) + 4 ((d = b) = SraxboB ) > 0
 dy/dt > 0 may change the left-hand side from negative to
positive but dS,,,,,/dt > 0 reinforces the negativity

15
| Conclusion

" Making consumer preferences endogenous and
incorporating adaptation are quite important for an
ecological economic model, but these ideas are
relatively new to economics and not yet well
addressed

= SD has a rich experience and theory in making
variables endogenous and modeling adaptation
processes

OXFORD

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