## Abstract

The stock-flow consistent (SFC) approach to macroeconomic dynamic modelling was developed in the 2000s by Godley and Lavoie (in Monetary Economics: An Integrated Approach to Credit, Money, Income, Production and Wealth. Palgrave, New York, 2007a; Cambridge Journal of Economics, 31(1), 1–23, 2007b), who paved the way for the flourishing of SFC models. These models are based on four accounting principles (flow consistency, stock consistency, stock-flow consistency and quadruple book-keeping), which allow inferring a set of accounting identities. The latter are then coupled with a set of equations defining the equilibrium conditions. Finally, difference (or differential) stochastic equations are added to define the behaviour of each macro-sector (or agent) of the economy. SFC models’ coefficients can be calibrated to obtain a theoretical baseline scenario and/or estimated through standard econometric techniques. Baseline results are then compared with a variety of ‘possible worlds’ or shocks. This theoretical and analytical flexibility is the reason SFC models are used by economists with different theoretical backgrounds. While SFC models are affected by some limitations, we believe that advantages outdo weaknesses.

## Access this chapter

Tax calculation will be finalised at checkout

Purchases are for personal use only

### Similar content being viewed by others

## Notes

- 1.
More specifically, there must be always an inflow in favour of a unit, call it A, that matches the outflow faced by another unit, call it B, along with a reduction in assets held by (or an increase in liabilities of) unit A that matches the increase in assets held by (or the reduction in liabilities of) unit B.

- 2.
However, the accumulation of (unsold) inventories is possible when actual demand falls short of expected demand and hence firms’ production plans turn up to be too optimistic. In addition, credit rationing is considered, and supply-side constraints may well arise from the ecosystem (e.g. climate change and the depletion of natural reserves of matter and energy). The central role played by aggregate demand is the reason some authors refer to these models as ‘post-Keynesian stock-flow consistent’ models (e.g. Caverzasi and Godin 2015).

- 3.
Algebraic or analytical solutions are sometimes provided for the simplest models but cannot be calculated for the most sophisticated models.

- 4.
Also the simpler, benchmark 3-equation model, also known as the New Consensus Model, is built upon an IS curve, a Phillips curve and some sort of a monetary rule. See for example Lavoie (2015).

- 5.
- 6.
The transversality condition rules out explosive paths or bubbles, when the current value of a certain variable, say the inflation rate, depends on its expected future value. It holds that the increase in expected inflation is not ‘too fast’. As a result, the path of inflation is convergent.

- 7.
As mentioned, some agent heterogeneity has been allowed for in the last decade. For instance, Ricardian households (who can borrow and lend to smooth their consumption over time) are now sometimes coupled with non-Ricardian households (who cannot rely on the credit market). However, this is just a different type of friction, which in no way affects the qualitative behaviour of the model in the long run.

- 8.
The IMF defines China’s regime of exchange rate as ‘stabilized arrangements’ (IMF 2017).

- 9.
The meaning of country names is clarified in Sect. 5.

- 10.
Consequently, one needs not to worry about the exchange rate when summing the elements of each row, except for the stock of gold reserves in the BS, the export (import) entries, and the change in gold reserves in the TFM.

- 11.
It is here defined as the quantity of Brownland currency in exchange for one unit of Ecoland currency.

- 12.
These are the key hypotheses underpinning the so-called Model OPEN, i.e. the simplest 2C-SFC model presented in sections 6.6–6.9 of Godley and Lavoie (2007a).

- 13.
This is just a useful modelling simplification. It is well known that gold bars are no longer traded, and reserves of central banks are mainly made up of foreign currencies (US dollars, Euros and other key currencies).

- 14.
See for example Goodwin (1967).

- 15.
For the sake of clarity, when simulating the model, we assume that CO

_{2}-intensity coefficients do not vary across areas. - 16.
Assumptions (e), (f), (i), (j) and (m) have been relaxed in a more advanced version of our model.

- 17.
Table 4 shows coefficients and initial values of stocks at http://models.sfc-models.net/. We are happy to provide the program file of our model upon request.

- 18.
See the fifth column of Table 4 for information about the source of data.

- 19.
In our model, this effect is considered by assuming that Brownland’s propensity to import is positively associated with changes in government green spending. Ecoland’s propensity to import, in contrast, is a decreasing function of government green spending, as most green products are made in Ecoland. See Eqs. (108) and (109) in Appendix ‘Depletion Ratios, Damages and Feedbacks’ and Table 4.

- 20.
In principle, above effects can be further strengthened by a lower CO

_{2}-intensity coefficient of Ecoland compared with Brownland. As mentioned, we assume away this additional effect in our simulations.

## References

Altissimo, F., Siviero, S., & Terlizzese, D. (2002, July–December). How Deep Are the Deep Parameters?

*Annales d’Economie et de Statistique*67/68: 207–226.Backus, D., Brainard, W. C., Smith, G., & Tobin, J. (1980). A Model of U.S. Financial and Nonfinancial Economic Behavior.

*Journal of Money, Credit and Banking, 12*(2), 259–293.Berg, M., Hartley, B., & Richters, O. (2015). A Stock-Flow Consistent Input–Output Model with Applications to Energy Price Shocks, Interest Rates, and Heat Emissions.

*New Journal of Physics,**17*(1), 1–21.Blanchard, O. (2018). On the Future of Macroeconomic Models.

*Oxford Review of Economic Policy,**34*(1–2), 43–54.Botta, A., Caverzasi, E., & Tori, D. (2015). Financial–Real-Side Interactions in an Extended Monetary Circuit with Shadow Banking: Loving or Dangerous Hugs?

*International Journal of Political Economy,**44*(3), 196–227.Botta, A., Caverzasi, E., Russo, A., Gallegati, M., & Stiglitz, J. E. (2018).

*Inequality and Finance in a Rent Economy*(Greenwich Papers in Political Economy, No. 20377).Bovari, E., Giraud, G., & Mc Isaac, F. (2018, May). Coping with Collapse: A Stock-Flow Consistent Monetary Macrodynamics of Global Warming.

*Ecological Economics, 147,*383–398.Burgess, S., Burrows, O., Godin, A., Kinsella, S., & Millard, S. (2016).

*A Dynamic Model of Financial Balances for the United Kingdom*(Working Paper No. 614). Bank of England.Caiani, A., Godin, A., Caverzasi, E., Gallegati, M., Kinsella, S., & Stiglitz, J. E. (2016). Agent Based-Stock Flow Consistent Macroeconomics: Towards a Benchmark Model.

*Journal of Economic Dynamics and Control,**69,*375–408.Cardaci, A., & Saraceno, F. (2016).

*Inequality, Financialisation and Credit Booms: A Model of Two Crises*(SEP Working Papers, No. 2016/2). LUISS School of European Political Economy.Caverzasi, E., & Godin, A. (2015). Post-Keynesian Stock-Flow-Consistent Modelling: A Survey.

*Cambridge Journal of Economics,**39*(1), 157–187.Copeland, M. A. (1949).

*Social Accounting for Moneyflows*. The Accounting Review 24 (July), pp. 254–264. Reproduced in Dawson, J. C. (Ed.). (1996).*Flow-of-Funds Analysis: A Handbook for Practioners*. Armonk, New York, USA: M.E. Sharpe.Coutts, K. J., Godley, W., & Gudgin, G. D. (1985). Inflation Accounting of Whole Economic Systems.

*Studies in Banking and Finance, 9*(2), 93–114. Supplement to Journal of Banking and Finance, Amsterdam: North Holland.Dafermos, Y., Nikolaidi, M., & Galanis, G. (2017, January). A Stock-Flow-Fund Ecological Macroeconomic Model.

*Ecological Economics, 131*, 191–207.Dafermos, Y., Nikolaidi, M., & Galanis, G. (2018, October). Climate Change, Financial Stability and Monetary Policy.

*Ecological Economics, 152*, 219–234.Deleidi, M., Pariboni, R., & Veronese Passarella, M. (2018).

*Supermultiplier, Innovation and the Ecosystem: A Stock-Flow Dynamic Model*(Working Paper 2019-01). UCL Institute for Innovation and Public Purpose.Dos Santos, C. H. (2006). Keynesian Theorising During Hard Times: Stock-Flow Consistent Models as an Unexplored ‘Frontier’ of Keynesian Macroeconomics.

*Cambridge Journal of Economics,**30*(4), 541–565.Duwicquet, V., & Mazier, J. (2012). Financial Integration and Stabilization in a Monetary Union Without or with Bank Rationing. In D. B. Papadimitriou & G. Zezza (Eds.),

*Contributions in Stock-Flow Modeling*(pp. 197–234). London: Palgrave Macmillan.Escobar-Espinoza, A. (2016).

*Stock-Flow Consistent Models for Developing Countries: The Case of Colombia*(Unpublished Working Paper). Available at: https://www.gtap.agecon.purdue.edu/resources/download/8168.pdf.Georgescu-Roegen, N. (1971).

*The Entropy Law and the Economic Process*. Cambridge: Harvard University Press.Georgescu-Roegen, N. (1979). Energy Analysis and Economic Valuation.

*Southern Economic Journal,**45*(4), 1023–1058.Georgescu-Roegen, N. (1984). Feasible Recipes Versus Viable Technologies.

*Atlantic Economic Journal,**12*(1), 21–31.Godin, A., Tiou-Tagba Aliti, G., & Kinsella, S. (2012).

*Method to Simultaneously Determine Stock, Flow, and Parameter Values in Large Stock Flow Consistent Models*(Unpublished Working Paper). Available at: https://papers.ssrn.com/sol3/papers.cfm?abstract_id+2094996.Godley, W. (1996).

*Money, Finance and National Income Determination: An Integrated Approach*(Levy Institute Working Paper No. 167). Annandale-on-Hudson, New York, USA: Levy Economics Institute of Bard College.Godley, W. (1999).

*Seven Unsustainable Processes: Medium-Term Prospects and Policies for the United States and the World*. Annandale-on-Hudson, New York, USA: Levy Economics Institute of Bard College.Godley, W., & Cripps, F. (1983).

*Macroeconomics*. Oxford, UK: Oxford University Press.Godley, W., & Lavoie, M. (2007a).

*Monetary Economics: An Integrated Approach to Credit, Money, Income, Production and Wealth*. New York: Palgrave.Godley, W., & Lavoie, M. (2007b). A Simple Model of Three Economies with Two Currencies: The Eurozone and the USA.

*Cambridge Journal of Economics,**31*(1), 1–23.Godley, W., & Zezza, G. (1992). A Simple Stock Flow Model of the Danish Economy. In H. Brink (Ed.),

*Themes in Modern Macroeconomics*. London: Palgrave Macmillan.Godley, W., & Zezza, G. (2006).

*Debt and Lending: A Cri de Coeur*. Levy Institute Policy Note. Annandale-on-Hudson, New York, USA: Levy Economics Institute of Bard College. Available at: http://www.levy.org/pubs/pn_4_06.pdf.Godley, W., Papadimitriou, D. B., Hannsgen, G., & Zezza, G. (2007).

*The US Economy: Is There a Way Out of the Woods?*Levy Institute Strategic Analysis. Annandale-on-Hudson, New York, USA: Levy Economics Institute of Bard College. Available at: http://www.levyinstitute.org/pubs/sa_nov_07.pdf.Godley, W., Papadimitriou, D. B., Hannsgen, G., & Zezza, G. (2008).

*Prospects for the United States and the World: A Crisis that Conventional Remedies Cannot Resolve*. Levy Institute Strategic Analysis. Annandale-on-Hudson, New York, USA: Levy Economics Institute of Bard College. Available at: http://www.levyinstitute.org/pubs/sa_dec_08.pdf.Goodwin, R. M. (1967). A Growth Cycle. In C. H. Feinstein (Ed.),

*Socialism, Capitalism and Economic Growth*(pp. 54–58). London: Cambridge University Press.Hein, E., & Van Treeck, T. (2010). Financialisation and Rising Shareholder Power in Kaleckian/Post-Kaleckian Models of Distribution and Growth.

*Review of Political Economy,**22*(2), 205–233.IMF. (2017).

*Annual Report on Exchange Arrangements and Exchange Restrictions*. Washington, DC: International Monetary Fund.IPCC. (2018).

*Special Report: Global Warming of 1.5°C*. Geneva, Switzerland: World Meteorological Organization.Ioannou, S. (2018). Sovereign Ratings, Macroeconomic Dynamics, and Fiscal Policy. Interactions Within a Stock Flow Consistent Framework.

*Metroeconomica,**69*(1), 151–177.Jackson, T., & Victor, P. A. (2015, December). Does Credit Create a ‘Growth Imperative’? A Quasi-stationary Economy with Interest-Bearing Debt.

*Ecological Economics, 120,*32–48.Kalecki, M. (1972).

*Selected Essays on the Dynamics of the Capitalist Economy*. Cambridge, UK: Cambridge University Press.Keynes, J. M. (1936).

*The General Theory of Employment, Interest and Money*(2017 edition). Ware, UK: Wordsworth Editions.Keen, S. (2016).

*The Need for Pluralism in Economics*. Steve Keen’s Debtwatch. Available at: http://www.debtdeflation.com/blogs/2016/08/13/the-need-for-pluralism-in-economics/.Kinsella, S., & Tiou-Tagba Aliti, G. (2012a).

*Towards a Stock Flow Consistent Model for Ireland*(Unpublished Working Paper).Kinsella, S., & Tiou-Tagba Aliti, G. (2012b).

*Simulating the Impact of Austerity on the Irish Economy Using a Stock-Flow Consistent Model*(Unpublished Working Paper). Available at: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2157420.Kinsella, S., & Tiou-Tagba Aliti, G. (2013). Modeling Moments of Crisis: The Case of Ireland.

*Journal of Economic Issues,**47*(2), 561–566.Krugman, P. (2018). Good Enough for Government Work? Macroeconomics Since the Crisis.

*Oxford Review of Economic Policy,**34*(1–2), 156–168.Kydland, F. E., & Prescott, E. C. (1982). Time to Build and Aggregate Fluctuations.

*Econometrica: Journal of the Econometric Society,**50*(6), 1345–1370.Lavoie, M. (2008). Financialisation Issues in a Post-Keynesian Stock-Flow Consistent Model.

*Intervention: European Journal of Economics and Economic Policies,**5*(2), 335–361.Lavoie, M. (2014).

*Post-Keynesian Economics: New Foundations*. Cheltenham: Edward Elgar.Lavoie, M. (2015). Book Review: Macroeconomics: Institutions, Instability, and the Financial System.

*European Journal of Economics and Economic Policies: Intervention,**12*(1), 135–142.Lavoie, M., & Daigle, G. (2011). A Behavioural Finance Model of Exchange Rate Expectations Within a Stock-Flow Consistent Framework.

*Metroeconomica,**62*(3), 434–458.Lavoie, M., & Zhao, J. (2010). A Study of the Diversification of China’s Foreign Reserves within a Three-Country Stock-Flow Consistent Model.

*Metroeconomica,**61*(3), 558–592.Lequain, M. (2003, February). A Three-Country Study of the Euro Zone Versus the Rest of the World: The Implications of a Monetary Union in an Open Environment. In

*Annual Conference of the Eastern Economic Association.*New York.Lindé, J., Smets, F., & Wouters, R. (2016). Challenges for Central Banks’ Macro Models. In J. B. Taylor & H. Uhlig (Eds.),

*Handbook of Macroeconomics*(Vol. 2, pp. 2185–2262). Amsterdam: Elsevier.Long, J. B., Jr., & Plosser, C. I. (1983). Real Business Cycles.

*Journal of Political Economy,**91*(1), 39–69.Mankiw, N. G. (2006). The Macroeconomist as Scientist and Engineer.

*Journal of Economic Perspectives,**20*(4), 29–46.Mazier, J., & Tiou-Tagba Aliti, G. (2012). World Imbalances and Macroeconomic Adjustments: A Three-Country Stock-Flow Consistent Model with Fixed or Flexible Prices.

*Metroeconomica,**63*(2), 358–388.Mazier, J., & Valdecantos, S. (2015). A Multi-Speed Europe: Is It Viable? A Stock-Flow Consistent Approach.

*European Journal of Economics and Economic Policies: Intervention,**12*(1), 93–112.Miess, M., & Schmelzer, S. (2016a, June 10). Stock-Flow Consistent Modelling of Real-Financial Cycles and Balance Sheet Dynamics. In

*Preliminary Version for 13th EUROFRAME Conference*, Utrecht (The Netherlands). Available at: http://www.euroframe.org/files/user_upload/euroframe/docs/2016/conference/Session%206/EUROF16_Miess_etal.pdf.Miess, M., & Schmelzer, S. (2016b).

*Extension of the Empirical Stock-Flow Consistent (SFC) Model for Austria: Implementation of Several Asset Classes, a Detailed Tax System and Exploratory Scenarios*. Final Report, Study Commissioned by the Austrian Chamber of Labour, Vienna (Austria). Available at: http://irihs.ihs.ac.at/4135/1/Report_MiessSchmelzer_SFCfinal.pdf.Michell, J., & Toporowski, J. (2012). The Stock-Flow Consistent Approach with Active Financial Markets. In D. B. Papadimitriou & G. Zezza (Eds.),

*Contributions in Stock-Flow Modeling*(pp. 173–196). London: Palgrave Macmillan.Monasterolo, I., & Raberto, M. (2018, February). The EIRIN Flow-of-Funds Behavioural Model of Green Fiscal Policies and Green Sovereign Bonds.

*Ecological Economics, 144,*228–243.Morris, N., & Juniper, J. (2012). Modern Money Theory (MM) and Minsky: Towards a Stock-Flow-Consistent (SFC) Synthesis.

*AHE Panel on Modern Monetary Theory*, pp. 5–7.Naqvi, S. A. A. (2015).

*Modeling Growth, Distribution, and the Environment in a Stock-Flow Consistent Framework*(Working Paper No. 2015/02). Institute of Ecological Economics.Nikiforos, M., & Zezza, G. (2017). Stock-Flow Consistent Macroeconomic Models: A Survey.

*Journal of Economic Surveys,**31*(5), 1204–1239.Papadimitriou, D. B. (2009). Global Imbalances: Strategic Prospects for the US and the World. Intervention.

*European Journal of Economics and Economic Policies, 6*(1), 55–62.Papadimitriou, D. B., Hannsgen, G., & Zezza, G. (2011).

*Jobless Recovery Is No Recovery: Prospects for the US Economy*. Levy Institute Strategic Analysis. Annandale-on-Hudson, New York, USA: Levy Economics Institute of Bard College. Available at: http://www.levyinstitute.org/pubs/sa_mar_11.pdf.Papadimitriou, D. B., Nikiforos, M., & Zezza, G. (2013a).

*A Levy Institute Model for Greece. Levy Institute Technical Report*. Annandale-on-Hudson, New York, USA: Levy Economics Institute of Bard College. Available at: http://www.levyinstitute.org/pubs/rpr_7_13.pdf.Papadimitriou, D. B., Nikiforos, M., & Zezza, G. (2013b).

*The Greek Economic Crisis and the Experience of Austerity*. Levy Institute Strategic Analysis. Annandale-on-Hudson, New York, USA: Levy Economics Institute of Bard College. Available at: http://www.levyinstitute.org/pubs/sa_gr_7_13.pdf.Papadimitriou, D. B., Nikiforos, M., & Zezza, G. (2015, May).

*Greece: Conditions and Strategies for Economic Recovery*. Levy Institute Strategic Analysis. Annandale-on-Hudson, New York, USA: Levy Economics Institute of Bard College. Available at: http://www.levyinstitute.org/pubs/sa_gr_5_15.pdf.Rankin, N. (2011).

*Calvo’s Continuous-Time Model of Staggered Pricing: A Basic Exposition*(Unpublished Working Paper).Reyes, L., & Mazier, J. (2014). Financialized Growth Regime: Lessons from Stock Flow Consistent Models.

*Revue de la régulation. Capitalisme, institutions, pouvoirs*, 16(2e semestre).Richters, O., & Siemoneit, A. (2017, June). Consistency and Stability Analysis of Models of a Monetary Growth Imperative.

*Ecological Economics, 136,*114–125.Romer, P. (2016).

*The Trouble with Macroeconomics*. Available at: https://paulromer.net/wp-content/uploads/2016/09/WP-Trouble.pdf.Sawyer, M., & Veronese Passarella, M. (2017). The Monetary Circuit in the Age of Financialisation: A Stock-Flow Consistent Model with a Twofold Banking Sector.

*Metroeconomica,**68*(2), 321–353.Smets, F., & Wouters, R. (2003). An Estimated Dynamic Stochastic General Equilibrium Model of the Euro Area.

*Journal of the European Economic Association,**1*(5), 1123–1175.Skott, P., & Ryoo, S. (2008). Macroeconomic Implications of Financialisation.

*Cambridge Journal of Economics,**32*(6), 827–862.Stiglitz, J. E. (2018). The Rebuilding Macroeconomic Theory Project: An Analytical Assessment.

*Oxford Review of Economic Policy,**34*(1–2), 70–106.Tobin, J. (1969). A General Equilibrium Approach to Monetary Theory.

*Journal of Money, Credit and Banking, 1*(1), 15–29.Tobin, J. (1982). Money and Finance in the Macroeconomic Process.

*Journal of Money, Credit and Banking, 14*(2), 171–204.Valdecantos, S., & Zezza, G. (2015). Reforming the International Monetary System: A Stock-Flow-Consistent Approach.

*Journal of Post Keynesian Economics,**38*(2), 167–191.Van Treeck, T. (2008). A Synthetic, Stock-Flow Consistent Macroeconomic Model of ‘Financialisation’.

*Cambridge Journal of Economics,**33*(3), 467–493.Veronese Passarella, M. (2012). A Simplified Stock-Flow Consistent Dynamic Model of the Systemic Financial Fragility in the ‘New Capitalism’.

*Journal of Economic Behavior & Organization,**83*(3), 570–582.Veronese Passarella, M. (2019). From Abstract to Concrete: Some Tips to Develop an Empirical SFC Model.

*European Journal of Economics and Economic Policies: Intervention*. First published online: February 2019. https://doi.org/10.4337/ejeep.2019.0044.

### Disclaimer

Responsibility for the information and views expressed in the paper lies entirely with the author.

## Author information

### Authors and Affiliations

### Corresponding author

## Editor information

### Editors and Affiliations

## Appendix: Eco-2C-SFC Model Equations

### Appendix: Eco-2C-SFC Model Equations

The model is made up of 109 equations. Exogenous variables and parameters are 66. The model is split in four blocks of equations: basic equations of the open economy model; equations for government budgets and balances of payment of the two areas; and equations for the ecosystem (including matter reserves, energy reserves, CO_{2} emissions and climate change, ecological efficiency, depletion ratios and damages). The latter are based on Dafermos et al. (2017, 2018). The redundant equation of the system is the amount of gold bars (or USD reserves) exchanged by the central banks. All coefficient values and initial values of stocks are shown by Table 4 at http://models.sfc-models.net/.

### 1.1 Basic Equations of the Open Economy Model

\(Y_{c} = C_{c} + G_{c} + X_{c} - IM_{c}\) | (1) National income of Carbonland |

\(Y_{g} = C_{g} + G_{g} + X_{g} - IM_{g}\) | (2) National income of Ecoland |

\(IM_{c} = m_{c} \cdot Y_{c} \cdot \left( {1 - \delta_{T, - 1}^{c} } \right)\) | (3) Import of Carbonland |

\(IM_{g} = m_{g} \cdot Y_{g} \cdot \left( {1 - \delta_{T, - 1}^{g} } \right)\) | (4) Import of Ecoland |

\(X_{c} = IM_{g} /E\) | (5) Export of Carbonland |

\(X_{g} = IM_{c} \cdot E\) | (6) Export of Ecoland |

\(YD_{c} = Y_{c} - T_{c} + r_{c, - 1} \cdot B_{hc, - 1}\) | (7) Disposable income in Carbonland |

\(YD_{g} = Y_{g} - T_{g} + r_{g, - 1} \cdot B_{hg, - 1}\) | (8) Disposable income in Ecoland |

\(T_{c} = \theta_{c} \cdot (Y_{c} + r_{c, - 1} \cdot B_{hc, - 1} )\) | (9) Tax payments in Carbonland |

\(T_{g} = \theta_{g} \cdot (Y_{g} + r_{g, - 1} \cdot B_{hg, - 1} )\) | (10) Tax payments in Ecoland |

\(V_{c} = V_{c, - 1} + YD_{c} - C_{c}\) | (11) Wealth accumulation in Carbonland |

\(V_{g} = V_{g, - 1} + YD_{g} - C_{g}\) | (12) Wealth accumulation in Ecoland |

\(C_{c} = (\alpha_{c1} \cdot YD_{c} + \alpha_{c2} \cdot V_{c, - 1} ) \cdot \left( {1 - \delta_{T, - 1}^{c} } \right)\) | (13) Domestic consumption in Carbonland |

\(C_{g} = (\alpha_{g1} \cdot YD_{g} + \alpha_{g2} \cdot V_{g, - 1} ) \cdot \left( {1 - \delta_{T, - 1}^{g} } \right)\) | (14) Domestic consumption in Ecoland |

\(H_{hc} = V_{c} - B_{hc}\) | (15) Cash money held in Carbonland |

\(H_{hg} = V_{g} - B_{hg}\) | (16) Cash money held in Ecoland |

\(B_{hc} = V_{c} \cdot \lambda_{c0} + V_{c} \cdot \lambda_{c1} \cdot r_{c} - \lambda_{c2} \cdot YD_{c}\) | (17) Demand for government bills in Carbonland |

\(B_{hg} = V_{g} \cdot \lambda_{g0} + V_{g} \cdot \lambda_{g1} \cdot r_{g} - \lambda_{g2} \cdot YD_{g}\) | (18) Demand for government bills in Ecoland |

\(B_{sc} = B_{gc, - 1} + \left( {G_{c} + r_{c, - 1} \cdot B_{gc, - 1} } \right) - (T_{c} + r_{c, - 1} \cdot B_{c, - 1}^{cb} )\) | (19) Supply of government bills in Carbonland |

\(B_{sg} = B_{gg, - 1} + \left( {G_{g} + r_{g, - 1} \cdot B_{gg, - 1} } \right) - (T_{g} + r_{g, - 1} \cdot B_{g, - 1}^{cb} )\) | (20) Supply of government bills in Ecoland |

\(B_{c}^{cb} = B_{gc} - B_{hc}\) | (21) Bills held by central bank in Carbonland |

\(B_{g}^{cb} = B_{gg} - B_{hg}\) | (22) Bills held by central bank in Ecoland |

\(OR_{c} = OR_{c, - 1} + \left( {H_{gc} - H_{gc, - 1} - \left( {B_{c}^{cb} - B_{c, - 1}^{cb} } \right)} \right)/p_{or,c}\) | (23) Gold held by central bank in Carbonland |

\(OR_{g} = OR_{b, - 1} + \left( {H_{gg} - H_{gg, - 1} - \left( {B_{g}^{cb} - B_{g, - 1}^{cb} } \right)} \right)/p_{or,g}\) | (24) Gold held by central bank in Ecoland |

\(H_{gc} = H_{hc}\) | (25) Supply of cash money in Carbonland |

\(H_{gg} = H_{hg}\) | (26) Supply of cash money in Ecoland |

\(p_{or,c} = \bar{p}_{or}\) | (27) Unit price of gold in Carbonland |

\(p_{or,g} = p_{or,b} \cdot E\) | (28) Unit price of gold in Ecoland |

\(E = \bar{E}\) | (29) Exchange rate (fixed) |

\(r_{c} = \bar{r}_{c}\) | (30) Interest rate in Carbonland |

\(r_{g} = \bar{r}_{g}\) | (31) Interest rate in Ecoland |

Notes: \(m_{c}\) and \(m_{g}\) are the propensities to import of Carbonland and Ecoland, respectively; \(E\) is the nominal exchange rate; \(\theta_{c}\) and \(\theta_{g}\) are the average tax rates; \(\alpha_{c1}\) and \(\alpha_{g1}\) are the propensities to consume out of income; \(\alpha_{c2}\) and \(\alpha_{g2}\) are the propensities to consume out of wealth; \(\lambda_{c0}\), \(\lambda_{c1}\), \(\lambda_{c2}\), \(\lambda_{g0}\), \(\lambda_{g1}\) and \(\lambda_{g2}\) are parameters of household portfolio equations.

### 1.2 Additional Equations for Government Budgets and Balances of Payment

\(B_{s} = B_{sc} + B_{sg}\) | (32) Worldwide supply of government bills |

\(DEF_{c} = G_{c} + r_{c, - 1} \cdot B_{sc, - 1} - T_{c} - r_{c, - 1} \cdot B_{c, - 1}^{cb}\) | (33) Government deficit of Carbonland |

\(DEF_{g} = G_{g} + r_{g, - 1} \cdot B_{sg, - 1} - T_{g} - r_{g, - 1} \cdot B_{g, - 1}^{cb}\) | (34) Government deficit of Ecoland |

\(NAFA_{c} = DEF_{c} + CAB_{c}\) | (35) Net accumulation of financial assets in Carbonland |

\(NAFA_{g} = DEF_{g} + CAB_{g}\) | (36) Net accumulation of financial assets in Ecoland |

\(CAB_{c} = TB_{c}\) | (37) Current account balance in Carbonland |

\(CAB_{g} = TB_{g}\) | (38) Current account balance in Ecoland |

\(KABP_{c} = d\left( {OR_{c} } \right) \cdot p_{orc}\) | (39) Financial account balance in Carbonland |

\(KABP_{g} = d\left( {OR_{g} } \right) \cdot p_{org}\) | (40) Financial account balance in Ecoland |

\(TB_{c} = X_{c} - IM_{c}\) | (41) Trade balance of Carbonland |

\(TB_{g} = X_{g} - IM_{g}\) | (42) Trade balance of Ecoland |

\(BP_{c} = CAB_{c}\) | (43) Balance of payments of Carbonland |

\(BP_{g} = CAB_{g}\) | (44) Balance of payments of Ecoland |

### 1.3 Equations for the Ecosystem

#### 1.3.1 Material Resources and Reserves

\(y_{matc} = \mu_{c} \cdot Y_{c}\) | (45) Production of material goods in Carbonland |

\(y_{matg} = \mu_{g} \cdot Y_{g}\) | (46) Production of material goods in Ecoland |

\(mat_{c} = y_{matc} - rec_{c}\) | (47) Extraction of matter in Carbonland |

\(mat_{g} = y_{matg} - rec_{g}\) | (48) Extraction of matter in Ecoland |

\(rec_{c} = \rho_{c} \cdot dis_{c}\) | (49) Recycled socio-economic stock in Carbonland |

\(rec_{g} = \rho_{g} \cdot dis_{g}\) | (50) Recycled socio-economic stock in Ecoland |

\(dis_{c} = \mu_{c} \cdot (C_{c} - TB_{c} )\) | (51) Discarded socio-economic stock in Carbonland |

\(dis_{g} = \mu_{g} \cdot (C_{g} - TB_{g} )\) | (52) Discarded socio-economic stock in Ecoland |

\(k_{sec} = k_{sec, - 1} + y_{matc} - \mu_{c} \cdot TB_{c} - dis_{c}\) | (53) Socio-economic stock in Carbonland |

\(k_{seg} = k_{seg, - 1} + y_{matg} - \mu_{g} \cdot TB_{g} - dis_{g}\) | (54) Socio-economic stock in Ecoland |

\(wa_{c} = mat_{c} - d(k_{sec} )\) | (55) Waste generated in Carbonland |

\(wa_{g} = mat_{g} - d(k_{seg} )\) | (56) Waste generated in Ecoland |

\(k_{mc} = k_{mc, - 1} + conv_{mc} - mat_{c}\) | (57) Stock of material reserves in Carbonland |

\(k_{mg} = k_{mg, - 1} + conv_{mg} - mat_{g}\) | (58) Stock of material reserves in Ecoland |

\(k_{m} = k_{mc} + k_{mg}\) | (59) Worldwide stock of material reserves |

\(conv_{mc} = \sigma_{mc} \cdot res_{mc}\) | (60) Material resources converted to reserves in Carbonland |

\(conv_{mg} = \sigma_{mg} \cdot res_{mg}\) | (61) Material resources converted to reserves in Ecoland |

\(res_{mc} = res_{mc, - 1} - conv_{mc}\) | (62) Stock of material resources in Carbonland |

\(res_{mg} = res_{mg, - 1} - conv_{mg}\) | (63) Stock of material resources in Ecoland |

\(res_{m} = res_{mc} + res_{mg}\) | (64) Worldwide stock of material resources |

\(cen_{c} = emis_{c} /car\) | (65) Carbon mass of non-renewable energy in Carbonland |

\(cen_{g} = emis_{g} /car\) | (66) Carbon mass of non-renewable energy in Ecoland |

\(o2_{c} = emis_{c} - cen_{c}\) | (67) Mass of oxygen issued by Carbonland |

\(o2_{g} = emis_{g} - cen_{g}\) | (68) Mass of oxygen issued by Ecoland |

Notes: \(\mu_{c}\) and \(\mu_{g}\) are the matter-intensity coefficients in Carbonland and Ecoland, respectively; \(\rho_{c}\) and \(\rho_{g}\) are recycling rates; \(\sigma_{mc}\) and \(\sigma_{mg}\) are rates of conversion of material resources into reserves; \(car\) is the coefficient converting *Gt* of carbon into *Gt* of CO_{2}.

#### 1.3.2 Energy Resources and Reserves

\(e_{c} = \epsilon_{c} \cdot Y_{c}\) | (69) Energy required for production in Carbonland |

\(e_{g} = \epsilon_{g} \cdot Y_{g}\) | (70) Energy required for production in Ecoland |

\(er_{c} = \eta_{c} \cdot e_{c}\) | (71) Renewable energy in Carbonland |

\(er_{g} = \eta_{g} \cdot e_{g}\) | (72) Renewable energy in Ecoland |

\(en_{c} = e_{c} - er_{c}\) | (73) Non-renewable energy in Carbonland |

\(en_{g} = e_{g} - er_{g}\) | (74) Non-renewable energy in Ecoland |

\(ed_{c} = er_{c} + en_{c}\) | (75) Dissipated energy in Carbonland (end of period) |

\(ed_{g} = er_{g} + en_{g}\) | (76) Dissipated energy in Ecoland (end of period) |

\(k_{ec} = k_{ec, - 1} + conv_{ec} - en_{c}\) | (77) Stock of energy reserves in Carbonland |

\(k_{eg} = k_{eg, - 1} + conv_{eg} - en_{g}\) | (78) Stock of energy reserves in Ecoland |

\(k_{e} = k_{ec} + k_{eg}\) | (79) Worldwide stock of energy reserves |

\(conv_{ec} = \sigma_{ec} \cdot res_{ec}\) | (80) Energy resources converted to reserves in Carbonland |

\(conv_{eg} = \sigma_{eg} \cdot res_{eg}\) | (81) Energy resources converted to reserves in Ecoland |

\(res_{ec} = res_{ec, - 1} - conv_{ec}\) | (82) Stock of non-renewable energy resources in Carbonland |

\(res_{eg} = res_{eg, - 1} - conv_{eg}\) | (83) Stock of non-renewable energy resources in Ecoland |

\(res_{e} = res_{ec} + res_{eg}\) | (84) Worldwide stock of energy resources |

Notes: *ϵ*_{c} and *ϵ*_{g} are the energy-intensity coefficients in Carbonland and Ecoland, respectively; \(\eta_{c}\) and \(\eta_{g}\) are the shares of renewable energy to total energy; \(\sigma_{ec}\) and \(\sigma_{eg}\) are the rates of conversion of non-renewable energy resources into reserves.

#### 1.3.3 Emissions and Climate Change

\(emis_{c} = \beta_{c} \cdot en_{c}\) | (85) Industrial emissions of CO |

\(emis_{g} = \beta_{g} \cdot en_{g}\) | (86) Industrial emissions of CO |

\(emis_{l} = emis_{l, - 1} \cdot (1 - g_{l} )\) | (87) Land emissions of CO |

\(emis = emis_{c} + emis_{g} + emis_{l}\) | (88) Total emissions of CO |

\(co2_{AT} = emis + \phi_{11} \cdot co2_{AT, - 1} + \phi_{21} \cdot co2_{UP, - 1}\) | (89) Atmospheric CO |

\(co2_{UP} = \phi_{12} \cdot co2_{AT, - 1} + \phi_{22} \cdot co2_{UP, - 1} + \phi_{32} \cdot co2_{LO, - 1}\) | (90) Upper ocean/biosphere CO |

\(co2_{LO} = \phi_{23} \cdot co2_{UP, - 1} + \phi_{33} \cdot co2_{LO, - 1}\) | (91) Lower ocean CO |

\(F = F_{2} \cdot \log_{2} \left( {\frac{{co2_{AT} }}{{co2_{AT}^{PRE} }}} \right) + F_{EX}\) | (92) Radiative forcing over pre-industrial levels (W/m |

\(F_{EX} = F_{EX, - 1} + fex\) | (93) Radiative forcing due to non-CO |

\(T_{AT} = T_{AT, - 1} + \tau_{1} \cdot \left[ {F - \frac{{F_{2} }}{s} \cdot T_{AT, - 1} - \tau_{2} \cdot (T_{AT, - 1} - T_{LO, - 1} )} \right]\) | (94) (Change in) atmospheric temperature |

\(T_{LO} = T_{LO, - 1} + \tau_{3} \cdot (T_{AT, - 1} - T_{LO, - 1} )\) | (95) (Change in) lower ocean temperature |

Notes: \(\beta_{c}\) and \(\beta_{g}\) are the CO_{2}-intensity coefficients of production processes in Carbonland and Ecoland, respectively; \(g_{l}\) is the rate of decline of land-use CO_{2} emissions; \(\phi_{ij}\) are CO_{2} transfer coefficients; \(F_{2}\) is the increase in radiative forcing (due to doubling of CO_{2} concentration) since pre-industrial levels; \(co2_{AT}^{PRE}\) is the pre-industrial CO_{2} concentration; \(fex\) is the annual increase in radiative forcing due to non-CO_{2} greenhouse gas emissions; \(\tau_{1}\) is the speed of adjustment of atmospheric temperature; \(\tau_{2}\) and \(\tau_{3}\) are coefficients of heat loss; and \(s\) is the equilibrium climate sensitivity

#### 1.3.4 Ecological Efficiency

\(\mu_{c} = \mu_{c0} \cdot \left( {1 + g_{\mu c} } \right)^{ - t}\) | (96) Matter-intensity coefficient in Carbonland |

\(\mu_{g} = \mu_{g0} \cdot \left( {1 + g_{\mu g} } \right)^{ - t}\) | (97) Matter-intensity coefficient in Ecoland |

\(\epsilon_{c} = \epsilon_{c0} \cdot \left( {1 + g_{\epsilon c} } \right)^{ - t}\) | (98) Energy-intensity coefficient in Carbonland |

\(\epsilon_{g} = \epsilon_{g0} \cdot \left( {1 + g_{\epsilon g} } \right)^{ - t}\) | (99) Energy-intensity coefficient in Ecoland |

\(\beta_{c} = \beta_{c0} \cdot \left( {1 + g_{\beta c} } \right)^{ - t}\) | (100) CO |

\(\beta_{g} = \beta_{g0} \cdot \left( {1 + g_{\beta g} } \right)^{ - t}\) | (101) CO |

Notes: \(g_{ic}\) and \(g_{ig}\) (with *i* = *μ, ϵ, β*) define the rates of reduction over time of matter-, energy- and CO_{2}-intensity coefficients of Carbonland and Ecoland, respectively; subscript ‘0’ refers to initial values of variables.

#### 1.3.5 Depletion Ratios, Damages and Feedbacks

\(\delta_{mc} = mat_{c} /k_{mc}\) | (102) Matter depletion ratio in Carbonland |

\(\delta_{mg} = mat_{g} /k_{mg}\) | (103) Matter depletion ratio in Ecoland |

\(\delta_{ec} = en_{c} /k_{ec}\) | (104) Energy depletion ratio in Carbonland |

\(\delta_{eg} = en_{g} /k_{eg}\) | (105) Energy depletion ratio in Ecoland |

\(\delta_{T}^{c} = 1 - \left( {1 + d_{1}^{c} \cdot T_{AT} + d_{2}^{c} \cdot T_{AT}^{2} + d_{3}^{c} \cdot T_{AT}^{{x_{c} }} } \right)^{ - 1}\) | (106) Proportion of gross damage in Carbonland due to changes in temperature |

\(\delta_{T}^{g} = 1 - \left( {1 + d_{1}^{g} \cdot T_{AT} + d_{2}^{g} \cdot T_{AT}^{2} + d_{3}^{g} \cdot T_{AT}^{{x_{g} }} } \right)^{ - 1}\) | (107) Proportion of gross damage in Ecoland due to changes in temperature |

\(m_{c} = m_{c, - 1} + m_{0}^{c} + m_{1}^{c} \cdot (G_{c} - G_{c, - 1} )\) | (108) Carbonland propensity to import |

\(m_{g} = m_{g, - 1} + m_{0}^{g} - m_{1}^{g} \cdot (G_{g} - G_{g, - 1} )\) | (109) Ecoland propensity to import |

Notes: \(d_{i}^{j}\) and \(x_{j}\) (with \(i = 1,2,3\) and \(j = c,g\)) are positive coefficients such that: \(0 < \delta_{T}^{j} < 1\) and \(T_{AT} = 6 \to \frac{{\delta_{T}^{c} + \delta_{T}^{g} }}{2} = 0.5\); \(m_{i}^{j}\) (with \(i = 0,1\) and \(j = c,g\)) are positive coefficients.

### 1.4 Redundant Equations

\(\Delta OR_{c} = -\Delta OR_{g}\) Zero reserve gains (losses) across areas

## Rights and permissions

## Copyright information

© 2019 The Author(s)

## About this chapter

### Cite this chapter

Carnevali, E., Deleidi, M., Pariboni, R., Passarella, M.V. (2019). Stock-Flow Consistent Dynamic Models: Features, Limitations and Developments. In: Arestis, P., Sawyer, M. (eds) Frontiers of Heterodox Macroeconomics. International Papers in Political Economy. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-030-23929-9_6

### Download citation

DOI: https://doi.org/10.1007/978-3-030-23929-9_6

Published:

Publisher Name: Palgrave Macmillan, Cham

Print ISBN: 978-3-030-23928-2

Online ISBN: 978-3-030-23929-9

eBook Packages: Economics and FinanceEconomics and Finance (R0)