An ecological stock-flow-fund modelling framework

Transcription

1 An ecologcal stock-flow-fund modellng framework Yanns Dafermos, Unversty of the West of England Gorgos Galans, New Economcs Foundaton Mara Nkolad, Unversty of Greenwch Abstract: Ths paper develops an ecologcal stock-flow-fund (ESFF) modellng framework that provdes an ntegrated platform for the analyss of the nteractons between the ecosystem, the fnancal system and the macroeconomy. The ESFF framework has three dstnct features. Frst, t formulates explctly the monetary stocks and flows and the physcal stocks and flows takng nto account the accountng prncples and the laws of thermodynamcs. Second, t pays partcular attenton to the dstncton between stock-flow resources and fund-servce resources and formulates the nteracton of funds wth monetary and physcal stocks and flows. Thrd, t allows an explct analyss of the varous stock-flow-fund channels through whch the stablty of the ecosystem, the fnancal system and the macroeconomy are nterconnected. The paper llustrates how the ESFF framework can form the bass for the combned examnaton of ecologcal, fnancal and macroeconomc ssues. In so dong, the suggested framework contrbutes to the development of an ecologcal macroeconomcs n whch fnance plays a nonneutral role and physcal and monetary varables are examned n an nterconnected and consstent way. Key words: Ecosystem, macroeconomy, fnance, accountng prncples, laws of thermodynamcs, ecologcal stock-flow-fund modellng. JEL codes: E1, E12, E44, Q57 Prelmnary draft: May 2015 Address for correspondence: Yanns Dafermos, Unversty of the West of England, Coldharbour Lane, Brstol, BS16 1QY, UK, e-mal: Yanns.Dafermos@uwe.ac.uk Acknowledgements: We are grateful to Sebastan Berger, Peter Bradley, Jo Mchell, Andrew Mearman, Ewa Karwowsk, Engelbert Stockhammer and Rafael Wldauer for valuable comments. An earler verson of ths paper was presented at the 19th SCEME Semnar n Economc Methodology, Brstol, May 2014 and the 18th Conference of the Research Network Macroeconomcs and Macroeconomc Polces, Berln, October-November We wsh to thank the partcpants for helpful comments. Ths research s part of a project conducted by the New Economcs Foundaton. The fnancal support from the Network for Socal Change s gratefully acknowledged. The usual dsclamers apply.

2 An ecologcal stock-flow-fund modellng framework 1. Introducton Ecologcal macroeconomcs s a new nterdscplnary feld that examnes the macroeconomy as part of the ecosystem, takng explctly nto account the bophyscal lmts of a fnte planet (Harrs, 2009; Jackson, 2011; Reza et al., 2013; Jackson et al., 2014). It largely draws on the synthess of ecologcal and post-keynesan macroeconomcs whch has been dentfed as a frutful avenue for the combned examnaton of economc and ecologcal ssues (e.g. Holt and Spash, 2009; Mearman, 2009; Kronenberg, 2010; Spash and Ryan, 2012; Fontana and Sawyer, 2013, 2015). The ratonale for ths synthess can be brefly descrbed as follows: Ecologcal economcs provdes a sold framework for the analyss of the economy-ecosystem nteractons whch s based on the conceptualsaton of the economy as an open subsystem of the closed ecosystem as well as on the detaled analyss of the mplcatons of the Frst and the Second Law of Thermodynamcs. Post-Keynesan economcs provdes a qute rch explanaton of the dynamcs of modern captalst economes by puttng at the centre of ts analyss the mportance of aggregate demand, the non-neutral role of money and fnance, the mpact of fundamental uncertanty on economc decsons and the lnks between ncome dstrbuton and economc actvty. Ecologcal economcs lacks the sold macroeconomc framework of post-keynesan economcs. Post-Keynesan economcs almost totally gnores the ecologcal constrants of macroeconomc actvty. Therefore, by synthessng these two felds, ecologcal macroeconomcs can analyse n an ntegrated way the nteractons between the ecosystem and the macroeconomy and can suggest new polces that are lkely to attan a combnaton of macroeconomc stablty and ecologcal sustanablty. Recent research has contrbuted to the development of the buldng blocks of ecologcal macroeconomcs. Vctor and Rosenbluth (2007), Vctor (2012) and Barker et al. (2012) have presented large-scale models wth Keynesan features that take nto account the energy sector and varous envronmental ssues. Jackson (2011), Fontana and Sawyer (2013), Reza et al. (2013) and Taylor and Foley (2014) have put forward certan frameworks that combne 1

3 ecologcal wth Keynesan (or post-keynesan) nsghts. Godn (2012), Jackson et al. (2014), Berg et al. (2015), Naqv (2015) and Fontana and Sawyer (2015) have examned envronmental problems wthn stock-flow consstent or monetary crcut models that nclude a fnancal sector. However, n the lterature there s stll a lack of an ntegrated framework that combnes physcal stocks, flows and funds and monetary stocks and flows n a consstent way. The development of such a consstent framework s mportant for the jont analyss of ecologcal ssues (such as the depleton of ecosystem servces and the degradaton of natural resources), fnancal ssues (such as fnancal fraglty and the fnancng of green nvestment) and macroeconomc ssues (such as growth and unemployment). Ths paper puts forward an ecologcal stock-flow consstent (ESFF) modellng framework that provdes such an ntegrated analytcal platform. Our modellng framework has three dstnct features. Frst, t formulates explctly the monetary stocks and flows and the physcal stocks and flows takng nto account the accountng prncples and the laws of thermodynamcs; the formulaton of monetary stocks and flows draws on the stock-flow consstent lterature (Godley and Lavoe, 2007); the formulaton of physcal stocks and flows draws on the tradton of Georgescu-Roegen (1971) and the lterature on physcal nput-output tables (see e.g. Gljum and Hubacek, 2009). Second, the ESFF framework pays partcular attenton to the dstncton between stock-flow resources and fund-servce resources and formulates the nteracton of funds wth monetary and physcal stocks and flows. The mportance of funds n the examnaton of envronmental ssues has been pnponted by Georgescu-Roegen (1971). Thrd, our framework allows an explct analyss of the varous stockflow-fund channels through whch the ecosystem, the fnancal system and the macroeconomy are nterconnected. The purpose of ths paper s to descrbe the man features of ths framework by presentng a benchmark ESFF model and by dscussng the envronmental, fnancal and macroeconomc ssues that can be analysed by usng ths framework. The paper s organsed as follows. Secton 2 descrbes the man features of the ESFF modellng framework. Secton 3 presents the matrces and the equatons of a benchmark ESFF model. Secton 4 outlnes the man stock-flow-fund nteractons between the ecosystem, the macroeconomy and the fnancal system. Secton 5 concludes. 2

4 2. Man features of the ESFF modellng framework Over the last decade or so, stock-flow consstent (SFC) modellng has become a very popular technque n post-keynesan macroeconomcs. Followng the contrbutons of Godley (1999), Lavoe and Godley (2001-2) and Godley and Lavoe (2007), varous post-keynesan macroeconomsts have used SFC models to analyse a plethora of macroeconomc ssues. 1 SFC models rely on the use of balance sheet and transactons matrces whch allow the explct consderaton of the dynamc nteractons between flows (e.g. nterest, profts, wages) and stocks (e.g. loans, deposts, equtes). The ntegraton of accountng nto dynamc macro modellng permts the detaled exploraton of the lnks between the real and the fnancal spheres of the macroeconomy and llumnates the non-neutral role of money and fnance. However, a promnent drawback of the SFC models s the absence of any analyss of the transformaton of matter and energy that takes place due to the economc processes. In SFC models t s assumed that the energy and matter that are necessary for producton and consumpton are avalable wthout lmt and the degradaton of ecosystem servces has no feedback effects on the macroeconomy. Therefore, provded that there are no captal or labour constrants, the output of the economy s demand-determned and, hence, f an adequate polcy mx s mplemented, economc growth s theoretcally feasble for an nfnte perod of tme. Ths feature comes n stark contrast wth the fundamental propostons of ecologcal economsts accordng to whch that the macroeconomy s an open subsystem of the closed ecosystem 2 and economc actvty unavodably respects the laws of thermodynamcs. 3 Ecologcal economsts pont out that, n lne wth the Frst Law of Thermodynamcs, the macroeconomy contnuously uses energy and matter nflows from the ecosystem and contnuously produces waste whch s an outflow to the ecosystem. Moreover, t s argued that by convertng low-entropy materals and energy (e.g. fossl fuels and mnerals) nto hgh-entropy materals and energy (e.g. materal waste and thermal energy), macroeconomc actvtes tend to ncrease the entropy n the 1 See, for example, Le Heron and Mouakl (2008), Zezza (2008), van Treeck (2009), Dafermos (2012) and Nkolad (2014). See also Caverzas and Godn (2014) for a recent revew of the post-keynesan stock-flow consstent modellng lterature. 2 In thermodynamcs, an open system s a system that exchanges both energy and matter wth ts surroundng envronment. A closed system exchanges only energy, not matter. An solated system exchanges nether energy nor matter. 3 For a presentaton of the laws of thermodynamcs and ther mplcatons for economcs see e.g. Amr (1994), Baumgärtner (2002) and Daly and Farley (2011). 3

5 ecosystem. Ths stems from the Second Law of Thermodynamcs and suggests that current economc actvty reduces the ablty of the macroeconomy to reproduce tself n the future. Physcal nput-output accountng provdes an adequate platform for the consderaton of these ecologcal lmts. Drawng on the flow-fund model of Georgescu-Roegen (1971, ch. 9; 1979; 1984) and the tradtonal Leontef monetary nput-output tables, physcal nput-output accountng s a framework that records n a consstent way the physcal flows assocated wth macroeconomc actvtes. 4 In ths framework the formulaton of physcal flows (uses of natural resources, emssons to nature etc.) reles explctly on the Frst and the Second Law of Thermodynamcs. Moreover, the energy-matter relatonshps between the varous processes s depcted usng nput-output technques that allow the researcher to analyse the use of resources and the amount of waste that correspond both to fnal and ntermedate output. Importantly, n physcal nput-output tables all flows are measured n physcal unts (e.g. tonnes or tonnes of ol equvalent), avodng thereby the problems that arse when market prces are assgned to natural resources. The ESFF framework put forward n ths paper s a synthess of the post-keynesan SFC models and the physcal nput-output framework. Ths synthess allows us to combne the aforementoned advantages of these two approaches and to formulate the fnancal system and the macroeconomy as part of the ecosystem. Although the ESFF framework ncorporates wthout modfcatons the transactons and the balance sheet matrces of the SFC framework, two mportant extensons are made n the physcal nput-output formulaton. Frst, based on the flow-fund model of Georgescu-Roegen a dstncton s made between the stock-flow resources and the fund-servce resources (see also Mayum, 2001 and Daly and Farley, 2011). The stock-flow resources (energy and matter) are materally transformed nto what they produce (ncludng by-products), can theoretcally be used at any rate desred and can be stockpled for future use. The fund-servce resources (labour, captal and Rcardan land) are not emboded n the output produced can be used only at specfc rates and cannot be stockpled for future use. The dstncton between these two types of resources s sgnfcant bascally for two reasons. Frst, t ponts out that producton needs both fund-servce and stock-flow resources, and there s no possblty to replace the one wth the other. In conventonal presentatons of the producton functon ths s not the case as captal, labour and natural 4 For a detaled analyss of the features of physcal nput-output tables see Strassert (2002), Hoekstra and van den Bergh (2006) and Gljum and Hubacek (2009). 4

6 resources are descrbed as factors of producton wthout a clarfcaton of ther dfferent role; t s also argued that perfect substtutablty s possble. Second, the dstncton between stock-flow and fund-servce resources s crucal for our understandng of bophyscal lmts: t emphasses that whle people cannot use the servces of fund resources at the rate that they wsh, they can do so wth the stock-flow resources. Ths mples that the stock-flow resources can be exhausted n a short perod of tme f people decde to ncrease substantally the assocated flow rate. Second, whle the physcal nput-output framework focuses only on the physcal flows, the ESFF analyss developed n ths paper analyses also the dynamcs of physcal stocks that are consdered to be the most mportant for economc actvtes. Ths s crucal because wthout the consderaton of physcal stocks t s not possble to explore ssues of ecologcal sustanablty. As explaned below, ths becomes possble by constructng a physcal stock matrx. Overall, the ESFF modellng framework reles on four matrces: 1) the physcal nput-outputfund matrx; 2) the physcal stock matrx; 3) the transactons flow matrx; 4) the balance sheet matrx. The frst matrx s an extenson of the physcal nput-output tables. The second matrx represents selected stocks of matter and energy. The thrd and the fourth matrx descrbe the changes n the stocks and flows of the macroeconomc and fnancal systems, followng the tradtonal formulatons n the SFC lterature. 3. Matrces and equatons The ESFF modellng framework wll be presented by postulatng a hghly smplfed structure of the economc processes. In partcular, we consder a closed macroeconomy n whch there s no government and no central bank. Frms make conventonal and green nvestment by usng retaned profts, loans and equtes. Households buy durable consumpton goods. They do not take out loans. Commercal banks dstrbute all ther profts to households. There s one type of materal good n the economy that can be used for both (durable) consumpton and nvestment purposes. Frms produce ths good by usng useful matter and useful (renewable and nonrenewable) energy from the ecosystem, whch have been prevously transformed nto a controlled form. Frms recycle a part of ther waste whch s then used as an addtonal nflow n the producton of goods. In lne wth the post-keynesan tradton, the producton of goods s equal to ther demand (consumpton plus nvestment). However, ths happens only when there are no supply constrants due to the unavalablty of useful matter, useful energy, labour and 5

7 captal. If these constrants arse, the producton s supply-constraned. We have explctly consdered ths by postulatng a Leontef-type producton functon. To avod complcatons related to nflaton, t s assumed that the prce of the consumpton and nvestment goods s equal to unty; ths means that real values are equal to nomnal values. However, the model consders fnancal nflaton snce the prce of equtes s allowed to fluctuate. We wll begn by analysng the physcal stocks, the physcal flows and the funds. Then, we wll turn to monetary stocks and flows. 3.1 Physcal stocks, flows and funds Table 1 depcts the physcal nput-output-fund matrx. Ths matrx shows the transformatons of matter and energy as a result of the economc processes. The matrx ndcates flows of energy and matter that are measured ether n mass unts (e.g. tonnes) or n energetc unts (e.g. tonnes of ol equvalent). The tems that represent both mass and energy are measured n both mass and energetc unts. Columns ndcate the nputs that are necessary n each process as well as the by-products of the processes; the by-products (recyclable matter and emssons to nature) are denoted by a mnus sgn. 5 The rows show how the outputs of the processes are used. The funds that are necessary for the economc processes (labour and captal) are presented at the bottom of the matrx. 6 The matrx captures the followng processes: (1) Producton of controlled matter: Ths s the process through whch the useful matter that s n the ground (ths could be, for example, slver, manganese or ron ore) s extracted and transformed n order to be used as an nflow n the producton of goods and recycled matter. Controlled energy s necessary for ths process to take place. The by-products of the process are the matter that can be recycled (ths s used as an nflow n the fourth process) and the emssons to nature that nclude harmful matter (e.g. carbon emssons, chemcal waste), nonharmful matter and dsspated energy (e.g. thermal energy). (2) Producton of controlled energy: Ths process creates energy that can be used as an nflow n all economc processes. The energy s suppled ether from renewable resources (e.g. solar, wnd) 5 In the related lterature there s a debate about the way that the emssons to nature should be reported n physcal nput-output tables (see Hubacek and Gljum, 2003; Suh, 2004; Gljum et al., 2004; Detzenbacher, 2005; Detzenbacher et al., 2009). Here we adopt the approach that has been ntroduced by Suh (2004). 6 In the flow-fund model of Georgescu-Roegen (1971, ch. 9; 1979; 1984) Rcardan land s ncluded n the funds. For smplcty, ths fund s not ncorporated n Table 1. 6

8 or non-renewable resources (e.g. ol, gas coal). Importantly, controlled energy s necessary as an nflow n ths process. The emssons to nature nclude harmful matter, non-harmful matter and dsspated energy. (3) Producton of goods: Ths process produces goods for consumpton and nvestment purposes usng controlled energy, controlled matter and recycled matter. A part of the byproducts s recycled. The rest s emtted to nature. (4) Recyclng: Ths process produces recycled matter usng recyclable matter, controlled energy and controlled matter. Agan, the by-products nclude harmful and non-harmful matter as well as dsspated energy. Table 1: Physcal nput-output-fund matrx Input Output Controlled matter Intermedate output Controlled energy Goods Recycled matter Fnal output Total output Controlled matter x 13 x 14 TO 1 Controlled energy x 21 x 22 x 23 x 24 TO 2 Materal goods x f TO 3 Recycled matter x 43 TO 4 Natural resources Useful matter m 1 Useful energy e 2 Renewable energy er 2 Non-renewable energy en 2 Use of resduals Recyclable matter r 4 Supply of resduals Recyclable matter -w 1 -w 3 Emssons to nature Dsspated matter -s 1 -s 2 -s 3 -s 4 Harmful matter -sh 1 -sh 2 -sh 3 -sh 4 Non-harmful matter -sn 1 -sn 2 -sn 3 -sn 4 Dsspated energy -d 1 -d 2 -d 3 -d 4 Total nput TI 1 TI 2 TI 3 TI 4 Funds: Labour L 1 L 2 L 3 L 4 Captal UK 1 UK 2 UK 3 UK 4 7

9 The Frst Law of Thermodynamcs suggests that energy and mass cannot be created or destroyed n the economc processes. Therefore, n each process the total nputs of mass should be equal to the total outputs of mass (mass balance) and the total nputs of energy should be equal to the total outputs of energy (energy balance). The Second Law of Thermodynamcs s captured by the fact that the economc processes transform a part of useful energy and matter nto dsspated energy and matter that are charactersed by hgh entropy. Table 2 depcts the physcal stock matrx. Ths matrx refers only to the physcal stocks that are consdered to be the most mportant for economc actvtes. 7 These nclude the non-renewable energy, the useful matter, the harmful matter and the materal goods. Note that the stock of renewable resources s not represented n ths matrx snce the ablty of nature to regenerate these resources mples that depleton ssues are not very lkely to emerge. Table 2: Physcal stock matrx Useful matter Non-renewable energy Harmful matter Materal goods Openng stock M U-1 E N-1 M H-1 M G-1 Addtons to stock Dscoveres of new stock +DISC M +DISC E Emssons to nature Producton of goods Reductons to stock Extracton -m 1 -e 2 Natural dsspaton Destructons due to natural dsasters +sh -ND +x f -DES Closng stock M U E N M H M G The frst row of the matrx shows the stocks of the prevous perod. The last row presents the stock at the end of the current perod after the addtons and the reductons to stocks have taken place. The matrx ndcates that the stock of non-renewable useful energy tends to reduce due to the extracton that s related to economc actvty and tends to ncrease as a result of dscoveres of new stocks. The same holds for the stock of useful matter. 8 The stock of harmful matter tends to ncrease due to the emssons of the economc processes and tends to reduce as a result of natural dsspaton. Lastly, the stock of materal goods ncreases due to the economc 7 For a smlar presentaton of the physcal stocks see Unted Natons (2014). 8 It s assumed that the rate of creaton of new natural resources by the nature s extremely low. Therefore, ths nflow s assumed away. 8

10 producton. However, we assume that there s a reducton n ths stock whenever natural dsasters take place. Three physcal ratos are of partcular mportance for the analyss of ths paper. The frst rato s the depleton rato of useful matter ( dep useful matter ( m 1 ) to ts closng stock ( M U ): M ), whch s defned as the rato of the extracton flow of dep M m1 (1) M U The second rato s the depleton rato of non-renewable energy ( dep the extracton flow ( e 2 ) to ts closng stock ( E N ): E ), whch s also defned as dep E e2 (2) E N These two ratos capture the scarcty of useful matter and energy. The hgher the extracted amount of matter and energy relatve to the remanng stock, the hgher the scarcty of these resources. The thrd rato s the degradaton rato ( deg ) that captures the degradaton of ecosystem servces that s caused due to the emsson of harmful matter (greenhouse gas emssons and other types of waste); We assume that there s a threshold about the stock of the harmful matter ( M ). Beyond ths threshold the ecosystem destablses causng extreme envronmental events. The degradaton rato s wrtten as: T M H deg (3) M T where M H s the closng stock of harmful matter. As the degradaton rato ncreases, the ecosystem s absorpton capacty deterorates (see, e.g., Daly and Farley, 2011, ch. 6) and the clmate change becomes more severe. 9

11 We proceed to descrbe the equatons assocated wth the physcal stocks, the physcal flows and the funds. Note that the equatons that capture denttes derved from the matrces are denoted by usng an next to the equaton number Input-output relatonshps Intermedate nputs are the nputs that one process demands from other processes. For example, x 13 s the nput that the goods producton process demands from the controlled matter process. The nputs are determned as a proporton of the total output of each process. Algebracally: ^ X TO (4) where 0 0 x13 x14 TO x21 x22 x23 x 24 X, TO2 TO, and TO x43 0 TO FO. x f 0 We have that x j s the ntermedate nput that process j demands from process, TO s the total output of process, j 0 are techncal coeffcents and x f denotes the materal goods that are produced for consumpton and nvestment purposes (, j 1,2,3, 4 ). Note that n matrx algebra notaton, a hat over a vector denotes a dagonal matrx wth the elements of the vector along the man dagonal. The total outputs are gven by TO I FO 1, where I s the Leontef nverse matrx and I s the 4x4 dentty matrx (one n the man dagonal and zeros elsewhere). 9 The natural resources that the prmary nputs n the producton processes are the useful matter ( m 1 ) and the useful energy ( e 2 ). As n the case of ntermedate nputs, these quanttes are determned as a proporton of total output. In partcular: 9 For more detals on the related matrx algebra see Mller and Blar (2009). 10

12 m e 1 1TO1 (5) 2 2TO2 (6) where 0 ( 1, 2 ) are techncal coeffcents. Useful energy s dstngushed between renewable energy ( er 2 ) and non-renewable energy ( en 2 ). Renewable energy s a proporton ( ) of total useful energy: er (7) 2 e 2 Note that s a techncal coeffcent. Non-renewable energy s determned by Eq. (8): en 2 e2 er2 (8) As mentoned above, each process produces certan by-products (recyclable matter and emssons to nature). These by-products are determned as a proporton of total output. Algebracally: TO (9) where r 4 s, d w s1 d1 1 0 w3 0 s d 2 2 s d 3 3 s 4 d and We have that r 4 s the total recyclable matter, s s the total dsspated matter, d s the total dsspated energy, w s the recyclable matter produced by process, s s the dsspated matter produced by process, d s the dsspated energy produced by process and j 0 are techncal coeffcents, j 1,2,3,4. In Eq. (9) we use to denote a column vector of 1 s (of dmenson 4). 11

13 Dsspated matter s dstngushed between harmful dsspated matter ( sh ) and non-harmful dsspated matter ( sn ). Harmful dsspated matter s a proporton ( ) of total dsspated matter: sh d (10) Note that s a techncal coeffcent 1,2,3,4. Non-harmful dsspated matter s determned as a resdual: sn s sh (11) In Table 1 all types of matter are measured n mass unts. Renewable energy and dsspated energy are consdered to be weghtless and, therefore, they are measured only n energetc unts. Non-renewable energy s measured n both mass and energetc unts. Controlled energy s assumed to consst of a weghtless and a non-weghtless component. Therefore a proporton of controlled energy s measured only n energetc unts, whle the rest s also measured n mass unts by usng converson factors from mass to energy. For smplcty, ths proporton s consdered to be equal to (the proporton of renewable energy n total useful energy). The mass and energy balances reflect the fact that n all economc process total outputs (TO) are equal to total nputs (TI) n energetc and mass unts (namely TO TI for 1,2,3, 4 ). The balances are depcted followng the methodology descrbed n Lang et al. (2010). Usng the dsspated matter as a resdual, the mass balances are wrtten as follows: s x x2 x j m en r w TO (12) In Eq. (12) and 2 are the converson factors from energy to mass for useful energy and controlled energy respectvely. The energy balances for processes (1), (3) and (4) are shown n Eq. (13): d x2 j (13) 12

14 where 1,3, 4. For process (2) the energy balance s as follows: d 2 en er x21 x23 x24 (14) Techncal coeffcents and effcency Techncal coeffcents determne the effcency of the underlyng processes. 10 We make a dstncton between three types of effcency: (a) resource effcency, (b) recyclng effcency and (c) polluton effcency. Resource effcency s captured by the techncal coeffcents j and, whch measure the rato of nputs to useful output. The lower these ratos the hgher the effcency. Of partcular nterest s the coeffcent 22 whch measures the rato of the energy nput that s necessary to produce energy to the total energy produced n process (2). Ths coeffcent captures the energy return on nvestment (EROI). Snce EROI ( TO2 x22) x22, we have that EROI It s assumed that resource effcency ncreases when green captal becomes hgher as a result of green nvestment (green nvestment wll be dscussed n secton 3.2). Moreover, n lne wth the related emprcal lterature (see e.g. Hall et al., 2014), EROI s assumed to declne as the non-renewable energy resources reduce. The growth rate of j and s shown n Eqs. (15)-(17). ( ) f ( g ) (15) j j j G1 ( ) ( ) f ( g, dep ) (16) j ( ) G1 E1 f ( g ) (17) G1 In Eq. (15), j 1,3, 4 and n Eq. (17) 1, 2 ; g G s the growth rate of green captal. 10 For defntons of effcency see, for example, Baumgärtner (2002) and Ayres and van den Bergh (2005). 13

15 Recyclng effcency s captured by the techncal coeffcents 1 j, whch are defned as the ratos of recyclable matter to total output n process (1) and process (3). Green nvestment mproves recyclng effcency. Thus: ( ) f ( g ) (18) 1 j 1 j 1 j G1 where j 1, 3. Polluton effcency s captured by the proportons of harmful matter n total dsspated matter. The hgher these proportons the lower the polluton effcency. Polluton effcency mproves when green nvestment takes place as well as when the rato of renewable energy n total useful energy becomes hgher (the latter s also affected by green nvestment). Therefore: ( ) ( ) f ( g, ) (19) G1 ( ) f ( g ) (20) G1 where 1,2,3, Funds Of partcular mportance are the productvtes of the funds n the economc processes (labour and captal). Labour productvty ( ) can be wrtten as follows: (21) where Total output, Energy and matter nputs Energy and matter nputs and Hours per worker Hours per worker for Number of workers 1,2,3,4. The rato s determned by the techncal coeffcents 14 j and, the rato denotes the energy and matter nputs that the workers use per hour and the rato s determned by the

16 workng hours arrangements. Note that s the total output per labour hour. Ths expresses the servce rate of labour. Eq. (22) postulates that the growth rate of s affected by the growth rate of conventonal captal stock ( g C ). It also expresses the dea that labour productvty s negatvely affected by the degradaton rato whch places upward pressures on the temperature of the earth and can adversely affect the health of the ecosystem, both of whch tend to reduce productvty (see, for example, Dell et al., 2014). ( ) ( ) f deg, gc1 (22) Eq. (23) shows the number of workers per economc process: L TO (23) Captal productvty can be expressed as: (24) where Total output, Energy and matter nputs Energy and matter nputs and Hours per captal unt Hours per captal unt for Captal unts 1,2,3,4. The rato expresses the servce rate of captal. The utlsed captal process s determned accordng to Eq. (25). UK n each producton UK TO (25) Fnal output and the Leontef-type producton functon The fnal output, n mass unts, whch s demanded for consumpton and nvestment purposes ( x D f ) s gven by: 15

17 x D f Y (26) where denotes the mass unts per unt of output (Y ). However, the actual output mght be constraned due to the unavalablty of energy, matter, labour and captal n at least one of the economc processes. Therefore, the actual fnal output n mass unts s gven by the mnmum between the demanded fnal output ( x total one ( x * f ): D f ) and the potental D * x mn( x, x ) (27) f f f We have that: * * * * * x mn( x, x, x, x ) (28) f f 1 f 2 f 3 f 4 where * * x f s the potental fnal output that can be produced based on the potental total output TO ( 1,2,3,4, ). For the four economc processes we have that: * * TO x f (29) 21 * TO * 2 1 x f (30) * * x f 3 TO3 (31) * * TO x f (32) The total output n each economc process can be restrcted by the remanng stock of useful matter ( M U 1 ), the remanng stock of non-renewable energy ( E N 1 ), and the labour force and captal stock that are avalable n each process. For smplcty, t s postulated that the labour force n each process s a proporton of the total labour force (LFO): 16

18 LFO LFO (33) 1 4 where 1. Smlarly, the total avalable stock n each process s gven by: 1 1 K K (34) 2 4 where We have that: TO TO TO EN , LFO1 1 K M U 1 mn, (35) 1 2 * 1, EN1,, LFO22 K M U 1 21 mn (36) * 2, EN1 1 22, LFO33 K M U 1 mn, (37) * 3, 43EN11 22, LFO44 K * 43MU 1 TO4 mn,, (38) Stock changes n energy and matter Eqs. (39)-(42) show the denttes that stem from Table 2. These denttes show the changes n the stock of matter and energy that are of partcular nterest for the sustanablty of economc processes. M DISC (39) U M e 2 m 1 E DISC (40) N E sh ND (41) M H M x DES (42) G f 17

19 We have that DISC M s the stock of useful matter that s dscovered every perod, DISC E s the respectve stock of non-renewable energy, sh denotes the total harmful materal emssons to nature ( sh sh1 sh2 sh3 sh4 ), ND s the natural dsspaton of harmful matter due to ecosystem s waste absorpton capacty and DES s the destructon of materal goods due to natural dsasters and M G s the stock of materal goods. It s postulated that the dscoveres of new stocks are a proporton ( 0 ) of the remanng stocks. Thus: 1, 2 DISC M M DISC E E 1 U 1 2 N1 (43) (44) Every perod nature absorbs a specfc fracton ( 3 0 ) of the stock of harmful matter: ND M 3 H1 (45) However, as mentoned above, the absorpton capacty of the ecosystem reduces as the degradaton rato ncreases. Ths s reflected n Eq. (46): () 3 f deg (46) Fnally, a proporton ( 4 0 ) of the stock of materal goods s destructed due to dsasters related to clmate change. It s assumed that ths destructon refers only to captal stock. 11 DES MK 4 1 (47) where MK s the captal stock expressed n mass unts (note that MK K, where K s the number of captal goods). 11 See also Taylor and Foley (2014) and Naqv (2015). 18

20 Snce clmate change becomes more severe as the degradaton rato ncreases, we assume that: () 4 f deg (48) 3.2 Monetary stocks and flows We turn now to descrbe the monetary stocks and flows n the macroeconomy and the fnancal system. Table 3 s the transactons flow matrx of our economy. Ths matrx shows the transactons that take place between the varous sectors of the economy (each row represents a transacton). For each sector nflows are denoted by a plus sgn and outflows are denoted by a mnus sgn. The upper part of the matrx shows transactons that are related wth the revenues and expendtures of the varous sectors. The bottom part of the matrx ndcates changes n fnancal assets and labltes that arse from transactons. The columns represent the budget constrants of the sectors. For frms and commercal banks a dstncton s made between current and captal accounts. The current accounts regster payments made or receved. The current accounts show the changes n assets and labltes as well as the funds that are used to fnance nvestment (n the case of frms). At the aggregate level, monetary nflows are equal to monetary outflows. The economc actvtes of the sectors of the macroeconomy are summarsed as follows: (1) Frms: They conduct the 4 economc processes, descrbed n secton 3.1, whch are necessary for the producton of materal goods. They nvest both n conventonal and green captal. They acqure external fnance from equtes and bank loans. The frm sector has not been dsaggregated, whch means that the monetary transactons between the 4 economc processes are netted out n our model. 12 (2) Households: They provde ther labour servces to frms and receve labour ncome. They also receve the dstrbuted profts of frms, the profts of banks and the nterest on deposts. Ther ncome not consumed s saved n the form of deposts and equtes. For smplcty, there s no household heterogenety However, future extensons of the model could ncorporate such a dsaggregaton whch s partcularly mportant because t allows the explct formulaton of the role of the prces of raw materals and energy. For stock-flow consstent models wth ecologcal aspects that make such a dsaggregaton see Berg et al. (2015) and Naqv (2015). 13 However, future extensons of the model could ntroduce dfferent types of household n order to formulate the dstrbuton of ncome. For a stock-flow consstent model wth household heterogenety see Dafermos and Papatheodorou (2015). 19

21 (3) Banks: They provde green and conventonal loans to frms. Snce they mpose credt ratonng, they provde only a proporton of the loans that are demanded. Deposts are ther only lablty. Table 3: Transactons flow matrx Households Frms Commercal banks Total Current Captal Current Captal Consumpton -C +C 0 Conventonal nvestment +I C -I C 0 Green nvestment +I G -I G 0 Wages +wl -1 -wl -1 0 Frms' profts +DP -TP +RP 0 Commercal banks' profts +BP -BP 0 Interest on deposts + D D -1 - D D -1 0 Desctructon of conventonal captal -DES C +DES C 0 Desctructon of green captal -DES G +DES G 0 Interest on conventonal loans - C LC -1 + C LC -1 0 Interest on green loans - G LG -1 + G LG -1 0 Δdeposts -ΔD +ΔD 0 Δequtes -p e Δe +p e Δe 0 Δconventonal loans +ΔLC -ΔLC 0 Δgreen loans +ΔLG -ΔLG 0 Total Table 4 shows the assets and the labltes of the sectors. We use a plus sgn for the assets and a mnus sgn for the labltes. Household and frms have non-zero net worth. Commercal banks have a zero net worth due to our assumpton that they dstrbute all ther profts. At the aggregate level, the net worth of the economy s equal to the captal stock of frms and the durable consumpton goods of households whch are the only real assets. 20

22 Table 4: Balance sheet matrx Households Frms Commercal banks Captal +K +K Total Durable consumpton goods +DC +DC Deposts +D -D 0 Equtes +p e e -p e e 0 Conventonal loans -LC +LC 0 Green loans -LG +LG 0 Total (net worth) +V H +V F 0 +K+DC The equatons that are related to frms, households and banks are presented below. Note that, as n secton 3.1, the equatons that capture denttes derved from the matrces are denoted by usng an next to the equaton number Frms Y C I (49) TP Y wl 1 C LC1 G LG1 DES C DES G (50) RP s TP (51) f DP TP RP (52) K K C K G (53) DES K C 4 C1 DES K G 4 G1 LF LC LG r RP K (54) (55) (56) (57) eq E K (58) lev LF * Y vk K (59) (60) * u Y /Y L L 1 L2 L3 L4 re L / LFO (61) (62) (63) 21

23 I DES C ( ) ( ) ( ) ( ) ( ) f f 0, r1, u1, lev 1 eq 1, C KC 1 DES C (64) I DES G K K g g C G C G ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) q q0, r1, u1, lev 1, eq 1, G, dep M 1, dep E1, deg 1 KG 1 DES G (65) I I C G K K C G DES DES K K C1 G1 C G (66) (67) (68) (69) e e 1 I 1 p e (70) I G (71) I C I G NLC NLG DES DES I I DES C DES G 1 RP 1 pee replc 1 DES C (72) RP p e replg DES (73) e 1 G I I I I D C D G e C G D G RP p e LC LG DES DES I (74) RP p e LG DES (75) D C I C e G (76) D G I G (77) * D 1, f x f x f * x f * D, f x f x D f x f (78) I I C I G (79) Eq. (49) shows that the output of the economy s equal to the number of consumpton goods ( C ) plus the number of nvestment goods ( I ). The total profts of frms (TP) are gven by equaton (50); w s the wage rate, L s the number of employed workers, C s the nterest rate on conventonal loans, G s the nterest rate on green loans, LC s the amount of conventonal loans, LG s the amount of green loans, DES C s the destructon of conventonal captal and RP are a proporton s of DES G s the destructon of green captal. Frms retaned profts ther total profts (Eq. 51). The dstrbuted profts of frms DP are determned as a resdual (Eq. 52). Eq. (53) shows that total captal ( K ) s equal to conventonal captal ( K ) plus green C f 22

24 captal ( K G ). Eqs. (54) and (55) gve the destructon of conventonal and green captal due to natural dsasters. The total loans of frms (LF) are equal to conventonal loans plus green loans (Eq. 56). Eq. (57) gves the rate of retaned profts ( r ), Eq. (58) defnes the value of equty (E) as a rato of the captal stock (eq) and Eq. (59) gves the leverage rato of frms (lev). The full- * capacty output ( Y ) s a functon of the captal stock (Eq. 60); v s the full-capacty output-tocaptal rato. The rate of capacty utlsaton u s gven n Eq. (61). The total number of employed workers L s equal to the sum of workers L that are used as a fund n 1 L2 L3 L4 the economc processes conducted by frms (Eq. 62). The rate of employment ( re ) s gven by equaton (63); LFO s the labour force. Eqs. (64) and (65) show that frms make two types of nvestment: (a) gross conventonal nvestment ( I C DES nvestment ( I D DES ) that does not affect resource, recyclng or polluton effcency; (b) gross green ) that ncreases effcency, as descrbed n equatons (15)-(20). The two types of nvestment have some common determnants: the rate of proft, the rate of capacty utlsaton, the equty-to-captal rato and the leverage rato. 14 Conventonal nvestment s also affected by the term f 0 (whch reflects the anmal sprts of the entrepreneurs) and the nterest rate on conventonal loans. Green nvestment s also affected by q 0 (whch reflects envronmental polces or envronmental ethcs), the nterest rate on green loans and the depleton and the degradaton ratos. The ratonale behnd the ncluson of the depleton and the degradaton ratos s that, as the natural resources reduce or degrade, frms are nduced to nnovate n order to ncrease effcency. Note that although we have not ncluded the prce of energy n the smplfed model presented here, the postve mpact of the energy depleton rato on green nvestment s an mplct way to capture the postve lnk between the prce of non-renewable resource and green nvestment. 15 It s mportant to pont out that our model ncorporates explctly the macroeconomc rebound effect (see, e.g. Barker et al, 2009 and Stern, 2011): whenever effcency ncreases as a result of green nvestment, the resultng rse n total output produced partally offsets the ntal benefcal effects on the ecosystem. The change and the growth rate of the conventonal and the green captal stock are gven by Eqs. (66)-(69). A proporton ( ) of frms nvestment expendtures are fnanced by ssung equtes 14 For nvestment functons that nclude smlar determnants see, for example, Ryoo and Skott (2008) and van Treeck (2009). 15 Eyraud et al. (2013) provde emprcal evdence whch shows that green nvestment ncreases as the prce of fossl fuels becomes hgher as well as when the nterest rates reduce. 23

25 (Eq. 70); e s the number of frms equtes and p e s ther prce. Eq. (71) defnes the rato ( ) of green nvestment to total nvestment. For smplcty, t s assumed that ths rato determnes the proporton of retaned profts and equtes used for fnancng green nvestment. Due to the exstence of credt ratonng, only a proporton of new loans that are demanded by frms are DES provded by banks. Eq. (72) gves the desred new conventonal loans ( NLC ) and Eq. (73) gves the desred new green loans ( NLG DES ). The nvestment goods that are demanded, after credt ratonng has been mposed are shown n Eqs. (74) and (75). D I C s the demanded conventonal nvestment and D I G s the demanded green nvestment. However, due to supplysde constrants descrbed n secton 3.1.5, t s lkely that not all demanded nvestment goods wll be produced. In partcular, ths happens when total produced nvestment goods are gven by Eq. (79). x * D f x f. Eqs. (76)-(78) reflect ths fact. The Households Y H wl1 DP BP DD1 (80) C c Y c FV (81) D 1 H 1 2 H 1 C C D (82) * D 1, f x f x f * x (83) f * D, f x f x D f x f FVH YH C e1 p e FV D FV p e H re1 12D 13 H 1 FVH 1 e (84) Y (85) Y (86n) H re1 22D 23 H 1 FVH 1 D FV H ep e RP e1p e re (87) p e DC C e1 1 (86) (88) 24

26 Eq. (80) gves the dsposable ncome of households Y H ; BP denotes the profts of banks, D s the nterest rate on deposts and D s the amount of deposts. The number of goods that households wsh to consume are gven by Eq. (81). Consumpton depends on lagged ncome (whch s a proxy for the expected one) and lagged fnancal wealth ( FV H ); c 1 s the propensty to consume out of ncome and c 2 s the propensty to consume out of fnancal wealth. It s mportant to pont out that a rse n the prce of equtes can boost consumpton expendtures and, hence, the output of the economy, wth adverse effects on the ecosystem. Eqs. (82) and (83) follow the same ratonale wth Eqs. (76)-(78): when consumpton goods s produced. x * D f x f, only a proporton of the demanded Households allocate ther expected fnancal wealth between deposts and frms equtes. In the portfolo choce of households, Godley s (1999) mperfect asset substtutablty framework s adopted (Eqs ). 16 Note that Eq. (86n) s necessary to be replaced wth Eq. (86), wth deposts actng as a buffer. Eq. (87) shows the rate of return on frms equty ( r e ). Eq. (88) ndcates the ncrease n durable consumpton goods Banks CR C ( ) f c0, lev 1, eq ( ) 1 (89) CR G ( ) f g 0, lev 1, eq ( ) 1 (90) DES NLC 1 CR C NLC DES NLG 1 CR G NLG (91) (92) LC NLC replc LG NLG replg BP 1 1 (93) (94) C LC1 GLG1 DD1 (95) C spr1 D G spr2 D D LC LG (96) (97) (98-red) 16 The parameters n the portfolo choce equatons satsfy the horzontal, vertcal and symmetry addng-up constrants. 25

27 We defne ndcators of the degree of credt ratonng for both conventonal and green loans ( CR C and CR G ). These ndcators le between zero and one. The hgher they are the hgher the degree of credt ratonng. 17 As shown n Eqs. (89) and (90), these ndcators are postvely affected by the leverage rato and negatvely affected by the equty-to-captal rato. In the case of green loans, g 0 reflects the envronmental practces of banks. The actual new loans and the actual change n loans (after credt ratonng has been mposed) are gven by Eqs. (91)-(94). The profts of banks are equal to the nterest on both conventonal and green loans mnus the nterest on deposts (Eq. 95). The nterest rate on loans s equal to the nterest rate on deposts plus a spread (Eqs. 96 and 97); spr 1 and spr 2 denote the spreads for conventonal and green loans, respectvely. Equaton (98-red) s the redundant equaton of the macroeconomc system descrbed n Table 3 and Table 4: t s logcally mpled by all the other equatons of ths system. 4. Stock-flow-fund nteractons between the ecosystem, the macroeconomy and the fnancal system The ESFF framework presented n the prevous sectons provdes a platform for the analyss of the complex nteractons between the fnancal system, the macroeconomy and the ecosystem. Fgure 1 llustrates the most mportant channels through whch these nteractons take place. Fgure 1: Stock-flow-fund nteractons between the ecosystem, the macroeconomy and the fnancal system 17 For smlar formulatons see Dafermos (2012). 26

28 The four channels through whch the ecosystem nteracts wth the macroeconomy are the followng: Depleton channel: Macroeconomc actvty leads to the extracton of non-renewable resources placng upward pressures on the energy and matter depleton ratos. Ths s captured by Eqs. (1), (2), (4), (5) and (6). Ths channel becomes less strong when resource and recyclng effcency ncreases as a result of green nvestment (see Eqs ). Degradaton channel: The harmful matter that s emtted due to macroeconomc actvty (e.g. greenhouse gas emssons) tends to ncrease the degradaton of the ecosystem servces leadng to clmate change and natural dsasters. In our model, ths s captured by the upward pressures that macroeconomc actvty places on the degradaton rato (see Eqs. 3 and 9). Ths channel s attenuated when polluton effcency mproves due to green nvestment (see Eqs ). Natural resources constrant channel: As explaned n detal above, the ecosystem provdes the nflows of useful energy and matter that are necessary for the economc processes. These resources tend to reduce due to the depleton channel and they tend to ncrease as a result of dscoveres of new stocks (see Eqs ). When useful energy and matter are not suffcent, the demand for nvestment and consumpton goods mght be satsfed only partally. Ths s captured by Eqs. (76)-(78) and Eqs. (82)-(83). It s also mportant to pont out that, accordng to Eq. (65), a rse n the depleton ratos tends to ncrease green nvestment, weakenng thereby the depleton channel. Damage channel: The degradaton of the ecosystem can affect the servces of funds n the economc processes (labour and captal). Degradaton can reduce labour productvty (see Eq. 22). Ths mples that at some pont n tme the labour force mght not be suffcent to produce the fnal output demanded by households and frms. Moreover, degradaton can result n natural dsasters that destruct captal stock (see Eqs. 47 and 48). Ths mght mpose an addtonal supply-sde constrant and t mght reduce the proftablty of frms (see Eq. 50), wth adverse effects on economc actvty. Crucally, Eq. (45) shows that the hgher the depleton the lower the absorpton capacty of the ecosystem. Ths s a source of a destablsng dynamc n the degradaton rato. 27

29 The three channels through whch the fnancal system nteracts wth the macroeconomy are the followng: Fnancng of effcency channel: The fnancal system fnances green nvestment va loans and equtes (see Eqs. 74 and 75). In so dong, t contrbutes to the mprovement of the effcency ndcators n the economc processes, wth ndrect favourable effects on the depleton and the degradaton channel. In our model, the role of bank decsons s of partcular mportance: by reducng credt ratonng (see Eqs ) and the nterest rate on green loans they can contrbute to ecologcal sustanablty. Growth channel: The fnancal system has both postve and negatve effects on economc actvty. The postve effects nclude the provson of fnance that ncreases nvestment and the role that stock prce ncreases can play n boostng nvestment and wealth-related consumpton (see Eqs and Eq. 81). However, an ncrease n the leverage of frms and a reducton n stock prces can reduce the desred nvestment of frms and can ncrease credt ratonng, reducng economc growth. Fnancal stablty channel: The stablty of the fnancal system s affected by macroeconomc actvty. However, the lnks are not clear-cut. Hgh economc growth and low unemployment rates are conducve to the expanson of the fnancal system, whch mght be assocated wth hgher fnancal fraglty (reflected, for example, n hgher leverage ratos). Low economc actvty and hgh unemployment create debt repayment dffcultes that effect the stablty of the fnancal system. The model presented n secton 3 does not nclude default and, therefore, does not capture explctly the fnancal problems that may emerge from the real economy. However, smple extensons can ncorporate such problems. The channels descrbed n Fgure 1 can gve rse to varous complex and nterestng dynamcs. The ESFF modellng framework provdes the adequate platform for the analyss of these dynamcs, llumnatng thereby the condtons under whch fnancal stablty, macroeconomc stablty and ecologcal sustanablty mght be possble. Remarkably, the ESFF framework can be the bass for both small-scale and large-scale models. Small-scale models can focus on the examnaton of certan stock-flow-fund nteractons, adoptng smplfyng assumptons for the ssues that fall outsde the purposes of the analyss. Large-scale models can extend the model 28

30 presented n secton 3 by ncludng, for nstance, a central bank and a government, wth the am to assess the role of varous envronmental polces. 5. Concludng remarks We put forward an ESFF modellng framework that ntegrates the post-keynesan SFC modellng approach and the physcal nput-output accountng framework. The ESFF framework provdes a coherent analyss of the monetary and physcal stocks and flows usng the accountng prncples and the laws of thermodynamcs. Moreover, t pays partcular attenton to the dstncton between stock-flow resources and fund-servce resources, t combnes the post- Keynesan emphass on the role of aggregate demand wth ecosystem supply-sde contrants and ncorporates the non-neutral role of fnance n the analyss of macroeconomc and ecologcal ssues. We used a benchmark model n order to llustrate how an ESFF model can be constructed. We then presented how the ESFF framework can be used n order to analyse the varous stock-flowfund channels through whch the ecosystem, the macroeconomy and the fnancal system are nterconnected. We argued that the hgh flexblty of the ESFF framework allows t to be used for varous types of academc and polcy analyses n the feld of ecologcal macroeconomcs. 29