View
223
Download
2
Category
Tags:
Preview:
Citation preview
An ecological stock-flow-fund modelling
framework
Yannis Dafermos, University of the West of England Giorgos Galanis, New Economics Foundation
Maria Nikolaidi, University of Greenwich
Abstract: This paper develops an ecological stock-flow-fund (ESFF) modelling framework that integrates the flow-fund model of Georgescu-Roegen (1971, 1979) with the stock-flow consistent modelling approach of Godley and Lavoie (2007). The ESFF framework combines various fundamental features of post-Keynesian and ecological economics, most notably the consideration of macroeconomy as an open subsystem of the closed ecosystem, the impact of aggregate demand on economic growth and employment, the biophysical limits to economic activity, the effects of finance on growth and the importance of the laws of thermodynamics. It is argued that the ESFF framework provides a quite rich platform for the analysis of the complex interactions between the macroeconomy and the ecosystem. Key words: Ecosystem, macroeconomy, laws of thermodynamics, ecological stock-flow-fund modelling. JEL codes: E1, E44, Q57
Preliminary and incomplete
Paper prepared for the 18th Conference of the Research Network Macroeconomics and Macroeconomic Policies (FMM), Berlin, 30 October-1 November 2014.
Address for correspondence: Yannis Dafermos, University of the West of England, Coldharbour Lane, Bristol, BS16 1QY, UK, e-mail: Yannis.Dafermos@uwe.ac.uk Acknowledgements: We are grateful to Sebastian Berger for constructive discussions and for drawing our attention to the work of Nicholas Georgescu-Roegen. We are also grateful to Andrew Mearman for valuable comments. An earlier version of this paper was presented at the 19th SCEME Seminar in Economic Methodology, Bristol, UK, May 2014. We wish to thank the participants for helpful comments. This research is part of the ‘Great Transition Project’ of the New Economics Foundation. The financial support from the Network for Social Change is gratefully acknowledged. The usual disclaimers apply.
1
1. Introduction
Over the last years the synthesis of ecological and post-Keynesian economics has been identified
as an important inquiry that can open the avenue for a fruitful combined examination of
economic and ecological issues (e.g. Holt and Spash, 2009; Mearman, 2009; Kronenberg, 2010;
Spash and Ryan, 2012; Fontana and Sawyer, 2013). Ecological economics provides a solid
framework for the analysis of the economy-ecosystem interactions. This framework is based on
the conceptualisation of the economy as an open subsystem of the closed ecosystem and the
detailed analysis of the implications of the First and the Second Law of Thermodynamics. Post-
Keynesian economics provides a quite rich explanation of the dynamics of modern capitalist
economics by putting at the centre of its analysis the importance of aggregate demand, the non-
neutral role of money and finance, the impact of fundamental uncertainty on economic
decisions and the links between income distribution and economic activity. Ecological
economics lacks the solid macroeconomic framework of post-Keynesian economics. Post-
Keynesian economics almost totally ignores the ecological constraints of macroeconomic
activity. Therefore, the synthesis of these two branches of economics would be a significant step
forward.
Although the importance of this synthesis has been recognised by a plethora of scholars, only a
few attempts have been made in developing an integrated approach in this direction and, even
more, in developing a modelling framework that combines ecological and post-Keynesian
economics in a systematic way. The most important of these attempts can be found in Victor and
Rosenbluth (2007), Victor (2012) and Barker et al. (2012) who have presented large-scale
models with Keynesian features that take into account the energy sector and various
environmental issues. Moreover, Jackson (2011), Fontana and Sawyer (2013) and Rezai et al.
(2013) have put forward building blocks for modelling frameworks that could combine
ecological economics with Keynesian (or post-Keynesian) insights. Although these contributions
are very significant, they can only be considered as the first steps towards the integration of
ecological with post-Keynesian economics. For example, in the aforementioned contributions
the role of money and finance, which is fundamental in post-Keynesian economics, is not
explicitly incorporated. Moreover, the full implications of the fact that the macroeconomy is an
open subsystem of the closed ecosystem are not analysed in an integrated way.
This paper develops a new modelling framework that synthesises post-Keynesian and ecological
approaches. This framework integrates the post-Keynesian stock-flow consistent (SFC)
2
modelling approach, developed by Godley and Lavoie (2007), with the flow-fund model of
Georgescu-Roegen (1971, ch. 9; 1979). The stock-flow consistent approach makes a coherent
analysis of the stocks and flows in the macroeconomy and the financial system allowing thereby
a consistent formulation of the links between the real and the financial spheres of the economy.
The flow-fund model of Georgescu-Roegen is an analytical framework that describes in detail
the energy and matter flow interactions of the economy with the environment as well as the role
of funds in the economic processes. The formulation of these interactions takes explicitly into
account the First and the Second Law of Thermodynamics. By combining and extending these
approaches, our ecological stock-flow-fund (ESFF) modelling framework incorporates
fundamental features of both post-Keynesian and ecological economics, most notably the
consideration of macroeconomy as an open subsystem of the closed ecosystem, the impact of
aggregate demand on economic growth and employment, the biophysical limits to economic
activity, the effects of finance on growth and the importance of the laws of thermodynamics.
The paper is organised as follows. Section 2 describes the main features of the ESFF modelling
framework. Section 3 presents the matrices and the equations of a simplified ESFF model.
Section 4 outlines some potential applications of our framework. Section 5 concludes.
2. Main features of the ESFF modelling framework
Over the last decade or so, stock-flow consistent (SFC) modelling has become a very popular
technique in post-Keynesian macroeconomics. Following the contributions of Godley (1999),
Lavoie and Godley (2001-2) and Godley and Lavoie (2007), various post-Keynesian
macroeconomists have used SFC models to analyse a plethora of macroeconomic issues.1 SFC
models rely on the use of balance sheet and transactions matrices which allow the explicit
consideration of the dynamic interactions between flows (e.g. interest, profits, wages) and stocks
(e.g. loans, deposits, equities). The integration of accounting into dynamic macro modelling
permits the detailed exploration of the links between the real and the financial spheres of the
macroeconomy and illuminates the non-neutral role of money and finance.
However, a prominent drawback of the SFC models is the absence of any analysis of the
transformation of matter and energy that takes place due to the economic processes. In SFC
models it is assumed that the energy and matter that are necessary for production and
1 See, for example, Le Heron and Mouakil (2008), Zezza (2008), van Treeck (2009), Dafermos (2012) and Nikolaidi (2014). See also Caverzasi and Godin (2014) for a recent review of the post-Keynesian stock-flow consistent modelling literature.
3
consumption are available without limit. Therefore, provided that there are no capital or labour
constraints, the output of the economy is demand-determined and, hence, if an adequate policy
mix is implemented, economic growth is theoretically feasible for an infinite period of time.
This feature comes in stark contrast with the fundamental propositions of ecological economists
that the macroeconomy is an open subsystem of the closed ecosystem2 and that economic
activity unavoidably respects the laws of thermodynamics.3 Ecological economists point out
that, in line with the First Law of Thermodynamics, the macroeconomy continuously uses
energy and matter inflows from the ecosystem and continuously produces waste which is an
outflow to the ecosystem. Moreover, it is argued that by converting low-entropy materials (e.g.
fossil fuels) into high-entropy materials (e.g. waste), macroeconomic activities tend to increase
the entropy in the ecosystem. This stems from the Second Law of Thermodynamics and suggests
that current economic activity reduces the ability of the macroeconomy to reproduce itself in the
future.
The flow-fund model of Georgescu-Roegen (1971, ch. 9; 1979) provides an adequate platform for
the consideration of these ecological limits. Using as a basis the First and the Second Law of
Thermodynamics, this model explicitly formulates the transformation of energy and matter that
takes places due to the economic processes. It also presents in detail the energy and matter links
between the various economic processes. Therefore, the biophysical limits to economic activity
are explicitly considered.
In the flow-fund model of Georgescu-Roegen the conceptualisation of production and
consumption relies on the distinction between the stock-flow resources and the fund-service
resources (see also Mayumi, 2001 and Daly and Farley, 2011). The stock-flow resources (such as
fossil fuels and minerals) are materially transformed into what they produce, can theoretically
be used at any rate desired and can be stockpiled for future use. The fund-service resources
(such as labour and capital) are not embodied in the output produced, can be used only at
specific rates and cannot be stockpiled for future use. The distinction between these two types of
resources is significant basically for two reasons. First, it points out that production needs both
fund-service and stock-flow resources, and there is no possibility to substitute the one with the
other. In conventional presentations of the production function this is not the case as capital,
2 In thermodynamics, an open system is a system that exchanges both energy and matter with its surrounding environment. A closed system exchanges only energy, not matter. An isolated system exchanges neither energy nor matter. 3 For a presentation of the laws of thermodynamics and their implications for economics see e.g. Amir (1994), Baumgärtner (2002) and Daly and Farley (2011).
4
labour and natural resources are described as ‘factors of production’ without a clarification of
their different role; it is also argued that perfect substitutability is possible. Second, the
distinction between stock-flow and fund-service resources is crucial for our understanding of
biophysical limits: it emphasises that while people cannot use the services of fund resources at
the rate that they wish, they can do so with the stock-flow resources. This implies that the stock-
flow resources can be exhausted in a short period of time if people decide to increase
substantially the associated flow rate.
The ESFF framework put forward in this paper is a synthesis of the post-Keynesian SFC models
and the flow-fund model of Georgescu-Roegen. This synthesis allows us to combine the
aforementioned advantages of these two approaches. The ESFF modelling framework relies on
four matrices: 1) the energy-matter flow-fund matrix; 2) the energy-matter stock matrix; 3) the
transactions flow matrix; 4) the balance sheet matrix. The first matrix is an extension of
Georgescu-Roegen’s (1979, p. 1042) flow-fund matrix and captures the energy and matter flows
in the ecosystem as well as the funds are necessary for the various economic and natural
processes. The second matrix represents the stock of matter and energy in the ecosystem. The
third and the fourth matrix describe the changes in the stocks and flows of the macroeconomic
and financial systems, following the traditional formulations in SFC literature.
3. Matrices and equations
The ESFF modelling framework will be presented by postulating a highly simplified
macroeconomy and a highly simplified ecosystem. In particular, we consider a closed
macroeconomy in which there is no government and no central bank. Firms make conventional
and green investment by using their retained profits and by taking out loans from commercial
banks. Households do not take on debt. Commercial banks distribute all their profits to
households. There is one type of good in the economy that can be used for both consumption
and investment purposes. Firms produce this good by employing controlled energy and
controlled matter from the ecosystem. Controlled energy is produced by using energy in situ.
Controlled matter is produced by using matter in situ. Firms recycle a part of their waste which
is then used as an inflow in the production of the investment and consumption goods.
Depreciation of capital is assumed away. There are no durable goods and no houses. Households
consume all the goods within one period. The price level is set equal to unity; this implies that
real and nominal variables coincide.
5
Table 1 depicts the ecosystem flow-fund matrix. The matrix illustrates the changes in the matter
and energy of the ecosystem as a result of economic and natural processes. It also shows the
funds that are necessary for each process. The upper part of the matrix indicates flows of energy
and matter. These flows are expressed in kilograms (they could also be expressed in kilojoules).
Symbols with a plus sign illustrate inflows to the ecosystem. Symbols with a minus sign indicate
outflows from the ecosystem. The lower part of the matrix captures funds.
The matrix presents the following economic and natural processes:
(1) Production of controlled matter: It produces controlled matter using matter in situ and
controlled energy.
(2) Production of controlled energy: It produces controlled energy using energy in situ.
(3) Production of capital goods: It produces capital goods using controlled energy, controlled
matter and recycled matter.
(4) Production of consumption goods: It produces consumption goods using controlled energy,
controlled matter and recycled matter.
(5) Recycling: It produces recycled matter using recyclable matter, controlled energy and
controlled matter. This recycling is conducted by firms.
(6) Consumption by households.
(7) Natural recycling: It produces matter in situ using dissipated matter and controlled energy.
This recycling stems from nature’s waste absorption capacity.
(8) Energy exchange with the outer space: It captures the fact that the ecosystem exchanges
energy with the outer space.
The first 7 columns in the upper part of the flow-fund matrix sum to zero. This is due to the First
Law of Thermodynamics which suggests that energy and mass are conserved in these processes.
The last two columns in Table 1 show the changes in the total matter and total energy of the
ecosystem. Since the ecosystem is a closed thermodynamic system, the total matter does not
change (and, hence, the respective column sums to zero) but the total energy does change (and,
therefore, the respective column does not sum to zero). Importantly, the flow-fund matrix is
also in line with the Second Law of Thermodynamics: dissipated energy and matter are
produced in the economic process leading to an increase in the entropy of the ecosystem.
6
Table 1: Ecosystem flow-fund matrix
(1) Production
of controlled
matter
(2) Production of
controlled energy
(3) Production of
capital goods
(4) Production of
consumption goods
(5) Recycling (6) Consumption (7) Natural
recycling
(8) Energy
exchange with
the outer space
Total matter Total energy
Flows:
Energy in situ -E S2 -E S7 +E S8 +ΔSE S
Controlled energy -E C1 +E C2 -E C3 -E C4 -E C5 -E C6 0
Dissipated energy +ED1 +ED2 +ED3 +ED4 +ED5 +ED6 -ED8 +ΔSED
Matter in situ -M S1 +M S7 +ΔSM S
Controlled matter +MC1 -MC3 -MC4 -MC5 0
Capital goods +IM +IM
Consumption goods +CM -CM 0
Recyclable matter +MW1 +MW3 +MW4 -MW5 +MW6 0
Recycled matter -MR3 -MR4 +MR5 0
Dissipated matter +MD1 +MD3 +MD4 +MD5 +MD6 -MD7 +ΔSMD
Total 0 0 0 0 0 0 0 E S8 -ED8 0 E S8 -ED8
Funds:
People P 1 P 2 P 3 P 4 P 5 P 6
Capital UK 1 UK 2 UK 3 UK 4 UK 5
Ricardian land RL 1 RL 2 RL 3 RL 4 RL 5 RL 6
Natural resources R 7
7
The lower part of the matrix indicates that people, capital and Ricardian land (i.e. land as a
location and physical substrate) are the necessary funds for the first five processes. In our
simplified framework, capital is not used as a fund in the consumption process. Natural
resources are the only fund in natural recycling.
Table 2 depicts the ecosystem stock matrix. This matrix shows the stock of matter and stock of
energy in the ecosystem, expressed in kilograms (these stocks could also be expressed in
kilojoules). The stock of matter and energy changes due to the inflows and outflows represented
in Table 1. Since the ecosystem is a closed thermodynamic system, the stock of total matter
remains unchanged, while the respective stock of total energy varies.
Table 2: Ecosystem stock matrix
Matter Energy
Matter in situ SM S
Capital stock KM
Dissipated matter SMD
Energy in situ SE S
Dissipated energy SED
Total SM SE
Table 3 and 4 represent the macroeconomic system. Table 3 is the transactions flow matrix. This
matrix shows the transactions that take place between the various sectors of the economy. For
each sector inflows are denoted by a plus sign and outflows are denoted by a minus sign. At the
aggregate level, monetary inflows should be equal to monetary outflows.
8
Table 3: Transactions flow matrix
Households Total
Current Capital Current Capital
Consumption -C +C 0
Conventional investment +IC -IC 0
Green investment +IG -IG 0
Wages +wL -1 -wL -1 0
Firms' profits +DP -TP +RP 0
Commercial banks' profits +BP -BP 0
Interest on deposits +r M M -1 -r M M -1 0
Interest on conventional loans -r LC LC -1 +r LC LC -1 0
Interest on green loans -r LG LG -1 +r LG LG -1 0
Δdeposits -ΔM +ΔM 0
Δconventional loans +ΔLC -ΔLC 0
Δgreen loans +ΔLG -ΔLG 0
Total 0 0 0 0 0 0
Firms Commercial banks
Table 4 shows the assets and the liabilities of the sectors. We use a plus sign for the assets and a
minus sign for the liabilities. Household and firms have non-zero net worth. Commercial banks
have a zero net worth due to our assumption that they distribute all their profits. At the
aggregate level, the net worth of the economy is equal to the capital stock of firms which is the
only real asset in the macroeconomic system.
Table 4: Balance sheet matrix
Households Firms Commercial
banks
Total
Capital +K +K
Deposits +M -M 0
Conventional loans -LC +LC 0
Green loans -LG +LG 0
Total (net worth) +M +V F 0 +K
We proceed to describe the equations of the model. In the presentation the equations that
capture identities derived from the matrices are denoted by using an ‘i’ next to the equation
number.
9
3.1 Firms: macroeconomic equations
Y C I (1)
1 1 1LC LGTP Y wL r LC r LG (2i)
TPsRP f (3)
DP TP RP (4i)
RPr
K (5)
vKY * (6)
*/ YYu (7)
1 2 3 4 5L P P P P P (8)
Lre
LF (9)
1 KgI CCD (10)
1 KgI GGD (11)
( ) ( )
0 1 1( , , )Cg f f r u
(12)
( ) ( )
0 1 1( , , )Gg q q r u
(13)
C CDI I (14)
G GDI I (15)
minminmin
4min
3
minminmin
2
minminmin
1
minmin
&,
&,
&,
&,1
SSSSS
S
S
S
SSSSS
S
SSSSS
S
SSSS
SMSMSESEifSE
SE
SM
SM
SMSMSESEifSE
SE
SMSMSESEifSM
SM
SMSMSESEif
(16)
C GI I I (17)
GI
I (18)
GLG I RP (19)
LC LG I RP (20i)
K I (21)
10
Equation (1) shows that the output of the economy ( Y ) is equal to the number of consumption
goods ( C ) plus the number of investment goods ( I ). The total profits of firms (TP ) are given by
equation (2i); w is the wage rate, L is the number of employed workers, LCr is the interest rate
on conventional loans, LGr is the interest rate on green loans, LC is the amount of conventional
loans and LG is the amount of green loans. Firms’ retained profits ( RP ) are a proportion ( fs ) of
their total profits (equation 3). The distributed profits of firms ( DP ) are determined as a
residual (equation 4i). Equation (5) gives the rate of retained profits ( r ); K is the total capital
stock of firms. The full-capacity output ( *Y ) is a function of the capital stock (equation 6); v is
the full-capacity output-to-capital ratio. The rate of capacity utilisation ( u ) is given in equation
(7). The total number of employed workers is equal to the sum of the people ( 54321 PPPPP )
that are used as a fund in the economic processes conducted by firms (equation 8). The rate of
employment ( re ) is given by equation (9); LF is the labour force.
Firms make two types of investment: (a) conventional investment ( CDI ) that does not affect
energy and matter efficiency (this efficiency is defined below); (b) green investment ( GDI ) that
increases energy and matter efficiency. In line with the conventional post-Keynesian
formulations of investment function, both investment rates rely on the rate of profit and the rate
of capacity utilisation (see equations 12 and 13). However, while the conventional investment
rate ( Cg ) is basically associated with the ‘animal spirits’ of entrepreneurs, reflected in 0f , the
green investment rate ( Gg ) is associated with some other factors, reflected in 0q . These factors
might pertain to environmental policy, the interest rate on green loans, the scarcity of matter
and energy in situ and the prices of natural resources.
Equations (14)-(16) show that the demand for investment goods, which is shown in equations
(10) and (11), is satisfied only when the stock of matter in situ ( SSM ) and the stock of energy in
situ ( SSE ) are above (or equal to) some certain thresholds ( minSSM and minSSE ). When
minSS SMSM and/or minSS SESE , only a proportion of the demanded investment goods is
produced ( 4,3,2,1,1 ii ). This happens because the available energy and matter in the
11
ecosystem is not enough to support the production of the investment goods and, thus, firms
cannot (or avoid to) satisfy all the demand.4
Equation (17) gives total investment. Equation (18) defines the ratio ( ) of green investment to
total investment. For simplicity, it is assumed that this ratio determines the proportion of
retained profits used for financing green investment. The rest finance is provided through green
loans that firms take out from banks (see equation 19). Equation (20i) shows the change in
conventional loans.5 The change in capital stock is given in equation (21).
3.2 Production of controlled matter
5431 CCCC MMMM (22i)
1111 CS MM (23)
1121 CC ME (24)
1131 CW MM (25)
1141 CD MM (26)
111111 DWCSCD MMMMEE (27i)
221111
11
1
SC
C
ME
Me (28)
)()(
11
GIwe (29)
)()(
114
GIy (30)
Equation (22i) shows that the controlled matter that firms need to produce ( 1CM ) is equal to the
controlled matter that is essential for the production of capital goods, consumption goods and
recycled matter ( 3CM , 4CM and 5CM , respectively). Equations (23)-(26) express the technology
that is used in the production of controlled matter; )4,3,2,1(,01 ii are technical coefficients.6
1SM is the matter in situ and 1CE is the controlled energy, both of which should be used as
inflows in order to produce 1CM . 1WM and 1DM are the recyclable waste matter and the
4 Equations (14)-(16) is a formulation of the general idea that economic growth can be restricted in the long run by
the biophysical limits. 5 By combining equations (17), (19) and (20i), we get: (1 )CLC I RP . 6 Equations (23)-(26) show relationships between masses but they implicitly reflect relationships between moles.
See Baumgärtner (2002) for some examples.
12
dissipated matter which are by-products of the process. The dissipated energy ( 1DE ), which is an
additional by-product of the process, is determined as a residual so as to ensure that the First
Law of Thermodynamics is satisfied (equation 27i).
The matter and energy efficiency of the process ( 1e ) is captured by equation (28). This
efficiency is defined as the ratio of controlled matter to the inflow of energy and matter (see
Ayres and van den Bergh, 2005 for similar definitions). Equation (27i) implies 11 e . It is
postulated that the change in efficiency relies positively on green investment (equation 29).
Moreover, green investment reduces the dissipated matter produced per kilogram of controlled
matter (equation 30).
3.3 Production of controlled energy
654312 CCCCCC EEEEEE (31i)
2212 CS EE (32)
222 CSD EEE (33i)
212
22
1
S
C
E
Ee (34)
)()(
22
GIwe (35)
Equation (31i) gives the controlled energy ( 2CE ) that is necessary to be produced by firms. This
is determined by the inflow of controlled energy which is essential for the other five economic
processes. Equation (32) shows that the energy in situ ( 2SE ) is determined according to the
technical coefficient 021 . Dissipated energy ( 2DE ) is determined as a residual (see equation
33i). The energy efficiency in the production of controlled energy ( 12 e ) is defined in equation
(34). Equation (35) illustrates that green investment improves energy efficiency.
3.4 Production of capital goods
IIM (36)
53 RR MM (37)
IMEC 313 (38)
13
3323 RC MIMM (39)
IMMW 333 (40)
IMM D 343 (41)
333333 DRWCCD MMMIMMEE (42i)
32313333
1
RCC MME
IMe (43)
)()(
33
GIwe (44)
)()(
334
GIy (45)
Equation (36) shows the mass of investment goods in kilograms ( IM ); denotes the kilograms
per good. Equation (37) illustrates that a proportion ( ) of the total recycled matter ( 5RM ) is
used as an inflow ( 3RM ) in the production of capital goods. Equations (38)-(41) capture the
technology that is used in the production of investment goods; )4,3,2,1(,03 ii are technical
coefficients. 3CE and 3CM are the controlled energy and the controlled matter that should be
used as inflows in order to produce IM . 3WM and 3DM are the recyclable waste matter and the
dissipated matter which are by-products of the process. The dissipated energy ( 3DE ), which is
an additional by-product of the process, is determined as a residual (equation 42i). Equation
(43) defines the energy and matter efficiency in the production of capital goods ( 13 e ). The
change in this efficiency is a positive function of green investment (equation 44). Moreover,
green investment reduces the dissipated matter produced per kilogram of investment good
(equation 45).
3.5 Production of consumption goods
CCM (46)
354 RRR MMM (47i)
CMEC 414 (48)
4424 RC MCMM (49)
CMMW 434 (50)
CMM D 444 (51)
444444 DRWCCD MMMCMMEE (52i)
14
42414444
1
RCC MME
CMe (53)
)()(
44
GIwe (54)
)()(
444
GIy (55)
Equation (46) gives the mass of consumption goods in kilograms ( CM ). Equation (47i) shows
the recycled matter that is used as an inflow in the production of consumption goods ( 4RM ).
Controlled energy ( 4CE ), controlled matter ( 4CM ), recyclable waste matter ( 4WM ) and
dissipated matter ( 4DM ) are given by equations (48)-(51). Note that )4,3,2,1(,04 ii are
technical coefficients. The dissipated energy ( 4DE ) is the residual (equation 52i). Equation (53)
defines the energy and matter efficiency in the production of consumption goods ( 14 e ). The
favourable effects of green investment on efficiency and the production of dissipated matter are
shown in equations (54) and (55).
3.6 Recycling
64315 WWWWW MMMMM (56i)
5515 WR MM (57)
5525 RC ME (58)
5535 RC MM (59)
5545 WD MM (60)
555555 DRWCCD MMMMEE (61i)
153515251
51
555
55
WCC
R
MME
Me (62)
)()(
55
GIwe (63)
)()(
555
GIy (64)
Equation (56i) gives the total recyclable waste matter per period ( 5WM ). Equation (57) shows
how many kilograms of recycled matter are produced per kilogram of recyclable waste matter.
Controlled energy ( 5CE ), controlled matter ( 5CM ) and dissipated matter ( 5DM ) are given by
15
equations (58)-(60). Note that )4,3,2,1(,05 ii are technical coefficients. Identity (61i) shows
the dissipated energy ( 5DE ). The energy and matter efficiency ( 15 e ) is captured by equation
(62). Equations (63) and (64) show that 5e and 55 are affected by green investment.
3.7 People and capital fund-services in the production processes
iiii ple (65)
i
ii
QP
(66)
iiii khe (67)
i
ii
QUK
(68)
For equations (65)-(68) we have that 5,4,3,2,1i . Moreover: 11 CMQ , 22 CEQ , IMQ 3 ,
CMQ 4 and 55 RMQ . Labour productivity ( i ) is given by equation (65); il denotes the
energy and matter inflows used per person hour and ip denotes the hours per person employed.
Note that ii le is the useful output per person hour. This expresses the service rate of people (as a
fund in the production process). The number of people ( iP ) who work in each production
process is determined according to equation (66).
Capital productivity ( i ) is given by equation (67); ih denotes the energy and matter inflows
used per capital hour and ik denotes the hours per utilised capital. Note that ii he is the useful
output per capital hour. This expresses the service rate of capital (as a fund in the production
process). The utilised capital ( iUK ) in each production process is determined according to
equation (68).
3.7 Households: macroeconomic equations
1 1H MY wL DP BP r M (69)
1 1 2 1D HC c Y c M (70)
DC C (71)
16
minminmin
4min
3
minminmin
2
minminmin
1
minmin
&,
&,
&,
&,1
SSSSS
S
S
S
SSSSS
S
SSSSS
S
SSSS
SMSMSESEifSE
SE
SM
SM
SMSMSESEifSE
SE
SMSMSESEifSM
SM
SMSMSESEif
(72)
HM Y C (73i)
Equation (69) gives the disposable income of households ( HY ); BP denotes the profits of banks,
Mr is the interest rate on deposits and M is the amount of deposits. The number of goods that
households wish to consume are given by equation (70). Consumption depends on lagged
income (which is a proxy for the expected one) and lagged wealth; 1c is the propensity to
consume out of income and 2c is the propensity to consume out of wealth. Equations (71)-(72)
has the same rationale with equations (14)-(16): when minSS SMSM and/or minSS SESE , only a
proportion of the demanded consumption goods is produced ( 4,3,2,1,1 ii ). Equation (73i)
shows the change in deposits.
3.8 Consumption
CM C (74)
CMEC 616 (75)
CMMW 626 (76)
CMM D 636 (77)
6666 DWCD MMCMEE (78i)
Equation (74) expresses consumption goods in kilograms ( CM ). The controlled energy that is
necessary for consumption ( 6CE ) is given by equation (75). The recyclable waste matter ( 6WM )
and the dissipated matter ( 6DM ) that are produced due to consumption are shown in equations
(76) and (77). Note that )3,2,1(,06 ii . Equation (78i) gives the dissipated energy ( 6DE ).
17
3.10 Banks: macroeconomic equations
1 1 1LC LG MBP r LC r LG r M (79i)
1LC Mr spr r (80)
2LG Mr spr r (81)
LGLCM (82-redmac)
The profits of banks are equal to the interest on both conventional and green loans minus the
interest on deposits (equation 79i). The interest rate on loans is equal to the interest rate on
deposits plus a spread (see equations 80 and 81); 1spr and 2spr denote the spreads for
conventional and green loans, respectively. Equation (82-redmac) is the redundant equation of
the macroeconomic system described in Table 3: it is logically implied by all the other equations
of this system.
3.11 Natural processes
DD SMM 7 (83)
SM
SM D10 (84)
7717 DS ME (85)
777 SDS EMM (86i)
8SE (87)
DD SEE 8 (88)
Equation (83)-(86i) capture the recycling that stems from nature’s waste absorption capacity.
Equation (83) shows that in each period the natural resources have the capacity to absorb (and
transform into matter in situ) only a (small) proportion ( 10 ) of the stock of dissipated
matter; 7DM is the dissipated matter that is recycled by nature. According to equation (84), the
capacity of the nature to recycle dissipated matter reduces as the stock of dissipated matter
increases relative to the total stock of matter. The energy in situ that is necessary for recycling
( 7SE ) is given by equation (85). Equation (86i) shows the matter in situ that is created from
natural recycling ( 7SM ).
18
Equation (87) shows that every period a specific flow of energy ( ) reaches the global
ecosystem in the form of energy in situ ( 8SE ). Moreover, the global ecosystem has an outflow of
dissipated energy to the outer space ( 8DE ). Equation (88) expresses this outflow as a proportion
( 0 ) of the stock of dissipated energy ( DSE ).
3.12 Total matter and energy in the ecosystem
17 SSS MMSM (89i)
IMKM (90i)
765431 DDDDDDD MMMMMMSM (91i)
728 SSSS EEESE (92i)
8654321 DDDDDDDD EEEEEEESE (93i)
0 DS SMKMSM (94-redeco)
Equation (89i) illustrates that the change in the stock of matter in situ is equal to the matter in
situ that is created due to nature’s waste absorption capacity minus the matter in situ that is
used due to the economic processes. The higher the matter in situ that is used by people relative
to the matter in situ that is created by nature the more adverse the effects of economic activity
on ecological sustainability. This is because less periods, ceteris paribus, will be needed till SSM
becomes lower than minSSM . Equation (90i) shows that, since capital depreciation has been
assumed away, the change in the matter that is in the form of capital ( KM ) is equal to the mass
of total investment. Equation (91i) shows the change in the stock of dissipated matter ( DSM ).
The stock of energy in situ increases due to the inflow of energy from the outer space but
reduces as a result of the economic process and the use of the nature (see equation 92i).
Equation (93i) describes the change in the stock of dissipated energy ( DSE ). Equation (94-
redeco) is the redundant equation of the ecosystem described in Table 1: it is derived from the
other equations of the system. This equation reflects the fact that the total matter in the
ecosystem remains unchanged given that the earth is a closed thermodynamic system.
4. Potential applications of the ESFF modelling framework
The ESFF model presented in the previous section (or other similar more complicated models)
can be solved numerically in future works, providing a simulation analysis of the interactions
19
between the ecosystem and the macroeconomy. Moreover, smaller models with various
simplifications could be solved analytically in the context of a detailed dynamic analysis. Future
work can also focus on the empirical applications of such models.
The ESFF framework provides a clear platform for the analysis of ecological sustainability
issues. For specific initial values of the stock of matter in situ and the stock of energy in situ, a
simulation analysis of the model presented in the previous section could illustrate how many
periods these stocks can remain above certain thresholds (beyond which the ecosystem cannot
support the desired macroeconomic activity). Such an analysis could also illustrate how green
investment and lower (or zero) economic growth could potentially increase the period over
which minSS SMSM and minSS SESE , improving thereby ecological sustainability. Importantly,
the model could indicate how such an improvement in ecological sustainability would affect (i)
unemployment under different working hours (i.e. under different ip ), (ii) financial stability
and (iii) inequality, if an extended version of the model with household heterogeneity would be
considered.
It is also crucial that the ESFF framework can analyse in detail how a fall in the stock of matter
in situ and the stock of energy in situ below the identified thresholds would affect the
macroeconomy. An ESFF model can show the implications of such a scenario for employment,
economic growth, inequality and financial stability and could potentially indicate the
irreversibility of such a situation.
Furthermore, the ESFF framework is flexible enough to allow more sophisticated threshold
analyses than the one presented in the model of the previous section. For example, instead of
adopting single threshold for the stock of matter and energy, a more realistic approach would be
to consider multiple thresholds which would imply more gradual effects of the reduction of SSM
and SSE on macroeconomic activities. With suitable extensions, this would illustrate the gradual
negative effects of the increase in entropy on the macroeconomy.
5. Conclusion
This paper put forward an ESFF modelling framework that integrates the post-Keynesian SFC
modelling approach with the flow-fund model of Georgescu-Roegen. The modelling framework
combines various fundamental features of post-Keynesian and ecological economics. Moreover,
20
it pays particular attention to the consistent formulation of the stocks and flows in the
macroeconomic system as well as to the integrated formulation of the stock-flow and fund-
service resources. In so doing, it allows a detailed analysis of the complex interactions between
the macroeconomy and the ecosystem. As outlined in section 4, the ESFF framework can be
used for various types of analyses that are related with the investigation of ecological
sustainability, macroeconomic viability and financial stability.
References
Amir, S., 1994. The role of thermodynamics in the study of economic and ecological systems.
Ecological Economics, 10, 125-142.
Ayres, R.U., van den Bergh, J.C.J.M., 2005. A theory of economic growth with material/energy
resources and dematerialization: interaction of three growth mechanisms. Ecological
Economics, 55, 96-118.
Barker, T., Anger, A., Chewpreecha, U., Pollitt, H., 2012. A new economics approach to
modelling policies to achieve global 2020 targets for climate stabilisation. International
Review of Applied Economics, 26 (2), 205-221.
Baumgärtner, S., 2002. Thermodynamics of waste generation, in Bisson, K., Proops, J. (eds),
Waste in Ecological Economics. Edward Elgar, Cheltenham, UK and Northampton, MA, USA.
Caverzasi, E., Godin, A., 2014. Post-Keynesian stock-flow consistent modelling: a survey.
Cambridge Journal of Economics, forthcoming.
Dafermos, Y., 2012. Liquidity preference, uncertainty, and recession in a stock-flow consistent
model. Journal of Post Keynesian Economics, 34 (4), 749-776.
Daly, H. E., Farley, J., 2011. Ecological Economics: Principles and applications. Island Press,
2nd edition.
Fontana, G., Sawyer, M., 2013. Post-Keynesian and Kaleckian thoughts on ecological
macroeconomics. Intervention: European Journal of Economics and Economic Policies, 10
(2), 256 - 267.
Georgescu-Roegen, N., 1971. The Entropy Law and the Economic Process. Harvard University
Press, Cambridge, UK.
Georgescu-Roegen, N., 1979. Energy analysis and economic valuation. Southern Economic
Journal, 45 (4), 1023-1058.
Godley, W., 1999. Money and credit in a Keynesian model of income determination. Cambridge
Journal of Economics, 23 (2), 393-411.
21
Godley, W., Lavoie, M., 2007. Monetary Economics: An Integrated Approach to Credit, Money,
Production and Wealth. Palgrave Macmillan, Basingstoke, UK.
Holt, R. P. F., Spash, C. L., 2009. Post Keynesian and ecological economics: alternative
perspectives on sustainability and environmental economics, in Holt, R.P.F., Pressman, S.,
Spash, C.L. (eds), Post Keynesian and Ecological Economics: Confronting Environmental
Issues. Edward Elgar, Cheltenham, UK and Northampton, MA, USA.
Jackson, T., 2011. Prosperity without growth: Economics for a finite planet. Routledge, UK and
USA.
Kronenberg, T., 2010. Finding common ground between ecological economics and post-
Keynesian economics, Ecological Economics, 69, 1488–1494.
Lavoie M., Godley, W., 2001-2. Kaleckian models of growth in a coherent stock-flow monetary
framework: a Kaldorian view. Journal of Post Keynesian Economics, 24 (2), 277-311.
Le Heron, E., Mouakil, T., 2008. A Post-Keynesian stock-flow consistent model for dynamic
analysis of monetary policy shock on banking behaviour. Metroeconomica 59 (3), 405-440.
Mayumi, K., 2001. The Origins of Ecological Economics: The bioeconomics of Georgescu-
Roegen. Routledge, London, UK.
Mearman, A., 2009. Recent developments in Post Keynesian methodology and their relevance
for understanding environmental issues, in Holt, R.P.F., Pressman, S., Spash, C.L. (eds), Post
Keynesian and Ecological Economics: Confronting Environmental Issue, Edward Elgar,
Cheltenham, UK and Northampton, MA, USA. .
Nikolaidi, M., 2014. Margins of safety and instability in a macrodynamic model with Minskyan
insights. Structural Change and Economic Dynamics, forthcoming.
Rezai, A., Taylor, L., Mechler, R., 2013. Ecological macroeconomics: an application to climate
change. Ecological Economics, 85, 69-76.
Spash, C. L., Ryan, A. 2012. Economic schools of thought on the environment: investigating
unity and division. Cambridge Journal of Economics, 36 (5), 1091–1121.
van Treeck, T., 2009. A synthetic, stock-flow consistent macroeconomic model of
‘financialisation’’. Cambridge Journal of Economics, 33 (3), 467–493.
Victor, P.A., 2012. Gorwth, degrowth and climate change: a scenario analysis. Ecological
Economics, 84, 206-212.
Victor, P.A., Rosenbluth, G., 2007. Managing without growth, Ecological Economics. 61, 492-
504.
Zezza, G., 2008. U.S. growth, the housing market, and the distribution of income. Journal of
Post Keynesian Economics, 30 (3), 375-401.
Recommended