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Stock-Flow Consistent Dynamic Models: Features, Limitations and Developments

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Frontiers of Heterodox Macroeconomics

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.

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Notes

  1. 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. 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. 3.

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

  4. 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. 5.

    Allegedly, the most famous DSGE model is the so-called Smets–Wouters model, developed by the European central bank (Smets and Wouters 2003; see also, Lindé et al. 2016).

  6. 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. 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. 8.

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

  9. 9.

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

  10. 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. 11.

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

  12. 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. 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. 14.

    See for example Goodwin (1967).

  15. 15.

    For the sake of clarity, when simulating the model, we assume that CO2-intensity coefficients do not vary across areas.

  16. 16.

    Assumptions (e), (f), (i), (j) and (m) have been relaxed in a more advanced version of our model.

  17. 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. 18.

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

  19. 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. 20.

    In principle, above effects can be further strengthened by a lower CO2-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.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Blanchard, O. (2018). On the Future of Macroeconomic Models. Oxford Review of Economic Policy, 34(1–2), 43–54.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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).

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • Caverzasi, E., & Godin, A. (2015). Post-Keynesian Stock-Flow-Consistent Modelling: A Survey. Cambridge Journal of Economics, 39(1), 157–187.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • Dafermos, Y., Nikolaidi, M., & Galanis, G. (2017, January). A Stock-Flow-Fund Ecological Macroeconomic Model. Ecological Economics, 131, 191–207.

    Google Scholar 

  • Dafermos, Y., Nikolaidi, M., & Galanis, G. (2018, October). Climate Change, Financial Stability and Monetary Policy. Ecological Economics, 152, 219–234.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Chapter  Google Scholar 

  • 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.

    Book  Google Scholar 

  • Georgescu-Roegen, N. (1979). Energy Analysis and Economic Valuation. Southern Economic Journal, 45(4), 1023–1058.

    Article  Google Scholar 

  • Georgescu-Roegen, N. (1984). Feasible Recipes Versus Viable Technologies. Atlantic Economic Journal, 12(1), 21–31.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • Godley, W., & Cripps, F. (1983). Macroeconomics. Oxford, UK: Oxford University Press.

    Google Scholar 

  • Godley, W., & Lavoie, M. (2007a). Monetary Economics: An Integrated Approach to Credit, Money, Income, Production and Wealth. New York: Palgrave.

    Book  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • IMF. (2017). Annual Report on Exchange Arrangements and Exchange Restrictions. Washington, DC: International Monetary Fund.

    Google Scholar 

  • IPCC. (2018). Special Report: Global Warming of 1.5°C. Geneva, Switzerland: World Meteorological Organization.

    Google Scholar 

  • Ioannou, S. (2018). Sovereign Ratings, Macroeconomic Dynamics, and Fiscal Policy. Interactions Within a Stock Flow Consistent Framework. Metroeconomica, 69(1), 151–177.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • Kalecki, M. (1972). Selected Essays on the Dynamics of the Capitalist Economy. Cambridge, UK: Cambridge University Press.

    Google Scholar 

  • Keynes, J. M. (1936). The General Theory of Employment, Interest and Money (2017 edition). Ware, UK: Wordsworth Editions.

    Google Scholar 

  • 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).

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Krugman, P. (2018). Good Enough for Government Work? Macroeconomics Since the Crisis. Oxford Review of Economic Policy, 34(1–2), 156–168.

    Article  Google Scholar 

  • Kydland, F. E., & Prescott, E. C. (1982). Time to Build and Aggregate Fluctuations. Econometrica: Journal of the Econometric Society, 50(6), 1345–1370.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • Lavoie, M. (2014). Post-Keynesian Economics: New Foundations. Cheltenham: Edward Elgar.

    Book  Google Scholar 

  • Lavoie, M. (2015). Book Review: Macroeconomics: Institutions, Instability, and the Financial System. European Journal of Economics and Economic Policies: Intervention, 12(1), 135–142.

    Google Scholar 

  • Lavoie, M., & Daigle, G. (2011). A Behavioural Finance Model of Exchange Rate Expectations Within a Stock-Flow Consistent Framework. Metroeconomica, 62(3), 434–458.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • Long, J. B., Jr., & Plosser, C. I. (1983). Real Business Cycles. Journal of Political Economy, 91(1), 39–69.

    Article  Google Scholar 

  • Mankiw, N. G. (2006). The Macroeconomist as Scientist and Engineer. Journal of Economic Perspectives, 20(4), 29–46.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Chapter  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • Nikiforos, M., & Zezza, G. (2017). Stock-Flow Consistent Macroeconomic Models: A Survey. Journal of Economic Surveys, 31(5), 1204–1239.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • 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).

    Google Scholar 

  • Reyes, L., & Mazier, J. (2014). Financialized Growth Regime: Lessons from Stock Flow Consistent Models. Revue de la régulation. Capitalisme, institutions, pouvoirs, 16(2e semestre).

    Google Scholar 

  • Richters, O., & Siemoneit, A. (2017, June). Consistency and Stability Analysis of Models of a Monetary Growth Imperative. Ecological Economics, 136, 114–125.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Skott, P., & Ryoo, S. (2008). Macroeconomic Implications of Financialisation. Cambridge Journal of Economics, 32(6), 827–862.

    Article  Google Scholar 

  • Stiglitz, J. E. (2018). The Rebuilding Macroeconomic Theory Project: An Analytical Assessment. Oxford Review of Economic Policy, 34(1–2), 70–106.

    Google Scholar 

  • Tobin, J. (1969). A General Equilibrium Approach to Monetary Theory. Journal of Money, Credit and Banking, 1(1), 15–29.

    Article  Google Scholar 

  • Tobin, J. (1982). Money and Finance in the Macroeconomic Process. Journal of Money, Credit and Banking, 14(2), 171–204.

    Article  Google Scholar 

  • Valdecantos, S., & Zezza, G. (2015). Reforming the International Monetary System: A Stock-Flow-Consistent Approach. Journal of Post Keynesian Economics, 38(2), 167–191.

    Article  Google Scholar 

  • Van Treeck, T. (2008). A Synthetic, Stock-Flow Consistent Macroeconomic Model of ‘Financialisation’. Cambridge Journal of Economics, 33(3), 467–493.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Google Scholar 

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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, CO2 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 CO2.

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: ϵc and ϵg 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 CO2 in Carbonland

\(emis_{g} = \beta_{g} \cdot en_{g}\)

(86) Industrial emissions of CO2 in Ecoland

\(emis_{l} = emis_{l, - 1} \cdot (1 - g_{l} )\)

(87) Land emissions of CO2

\(emis = emis_{c} + emis_{g} + emis_{l}\)

(88) Total emissions of CO2 worldwide

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

(89) Atmospheric CO2 concentration

\(co2_{UP} = \phi_{12} \cdot co2_{AT, - 1} + \phi_{22} \cdot co2_{UP, - 1} + \phi_{32} \cdot co2_{LO, - 1}\)

(90) Upper ocean/biosphere CO2 concentration

\(co2_{LO} = \phi_{23} \cdot co2_{UP, - 1} + \phi_{33} \cdot co2_{LO, - 1}\)

(91) Lower ocean CO2 concentration

\(F = F_{2} \cdot \log_{2} \left( {\frac{{co2_{AT} }}{{co2_{AT}^{PRE} }}} \right) + F_{EX}\)

(92) Radiative forcing over pre-industrial levels (W/m2)

\(F_{EX} = F_{EX, - 1} + fex\)

(93) Radiative forcing due to non-CO2 greenhouse gases (W/m2)

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

(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 CO2-intensity coefficients of production processes in Carbonland and Ecoland, respectively; \(g_{l}\) is the rate of decline of land-use CO2 emissions; \(\phi_{ij}\) are CO2 transfer coefficients; \(F_{2}\) is the increase in radiative forcing (due to doubling of CO2 concentration) since pre-industrial levels; \(co2_{AT}^{PRE}\) is the pre-industrial CO2 concentration; \(fex\) is the annual increase in radiative forcing due to non-CO2 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) CO2-intensity coefficient in Carbonland

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

(101) CO2-intensity coefficient in Ecoland

Notes: \(g_{ic}\) and \(g_{ig}\) (with i = μ, ϵ, β) define the rates of reduction over time of matter-, energy- and CO2-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

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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

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