Addition to my theoretical macroeconomic stock-flow consistent model in system dynamics.

Article was published on at Acta at 30th December,2025 DOI: 10.37355/acta-2025/2-05

First, following standard notations in SFC literature (see in Godley&Lavoie, 2007; and simply put, in Dos Santos,2004), let’s define the balance sheet, transaction flow matrix and the flow of funds.

Instrument	HH	F	B	CB	G	RoW	Σ
Household deposits, HH	+HH		−HH				0
Firm deposits HF		+HF	−HF				0
Gov. deposits at CB HG				−HG	+HG		0
Bank reserves R			+R	−R			0
Loans to firms LF		−LF	+LF				0
Loans to households LHH	−LHH		+LHH				0
Government bonds B			+B		−B		0
Nostro accounts HBROW			+HBROW			−HBROW	0
CB FX reserves FXCB				+FXCB		−FXCB	0
Σ	0	0	0	0	0	0	0

Source: Author.

One comment on balance sheet. I strongly believe that in order to follow correct balance sheet structure, general SFC models should introduce 7th sector in addition to typical six (Government, Banks, Central Bank, Firms, ROW and Households), and that is the foreign banks sector. Nostro-accounts are claims on the foreign banking system, and liabilities of foreign banks, while there is no counter-party of the nostro in non-financial corporations or households, so treating as either an asset or a liability of the consolidated ROW sector is not correct. Needless to say that many modern socioeconomic energy SFC models have huge variety of relevant sectors.

Now let’s define the transaction flow matrix, and the flow of funds.

Flow	HH	F	B	CB	G	RoW	Σ
Wages, W	+W	−W					0
Consumption, C	−C	+C					0
Gov. spending, G		+G			−G		0
Bank spending, CB		+CB	−CB				0
Exports, MF		+MF				−MF	0
Firm imports, MimpF		−MimpF				+MimpF	0
HH imports, MHH	−MHH					+MHH	0
HH taxes, TH	−TH				+TH		0
Firm taxes, TF		−TF			+TF		0
Interest on HH loans, ΦLHH	−ΦLHH		+ΦLHH				0
Interest on firm loans, ΦLF		−ΦLF	+ΦLF				0
Interest on bonds, ΦB			+ΦB		−ΦB		0
Firm dividends, DF		−DF				+DF	0
Bank dividends, DB			−DB			+DB	0
Saving, S	SHH	SF	SB	0	SG	SROW	0
HH deposits, ΔHH	−ΔHH		+ΔHH				0
Firm deposits, ΔHF		−ΔHF	+ΔHF				0
TGA, ΔHG				+ΔHG	−ΔHG		0
Reserves, ΔR			−ΔR	+ΔR			0
Firm loans, ΔLF		+ΔLF	−ΔLF				0
HH loans, ΔLHH	+ΔLHH		−ΔLHH				0
Gov. bonds, ΔB			−ΔB		+ΔB		0
Nostro, ΔHBROW			−ΔHBROW			+ΔHBROW	0
Σ	0	0	0	0	0	0	0

Source: Author.

Model was purely theoretical, with (almost) no normative engine. Unlike my upcoming models, which are defined in a mixed post-keynesian tradition, this one was purely to test the nominal behaviour of accounting identities under different fiscal and interest rate regimes.

Now let’s define the Forrester diagram.

Set all flows moving

Click a stock to see what fills and drains it. Click a flow to see where it leaves one stock and enters another.

Finally, let’s define the casual loop diagram, in a tradition of Forrester (1968,1969), and Sterman (2001).

All loops Reinforcing Balancing

Click a loop to follow it through the diagram. The switches turn loops on and off.

Now model is formally complete. I have not included equity revaluations in this version, but even such a simple model could be of some use in net financial positions and sectoral analysis.

I will shortly stress the model and run reasonable simulations with stocks at more or less realistic magnitudes, reflecting Czech empirical reality of later 2025. The goal is to check which sector nominally absorbs a) abruptly declining central gov net financial position.

Initial model was built in Ravel system dynamics software with RK45 by and retested in Python with RK45 and LSODE (results did not differ much).

Stay tuned!

References

• Dos Santos, C. H. (2004). Keynesian theorising during hard times: Stock-flow consistent models as an unexplored “frontier” of Keynesian macroeconomics (Working Paper No. 408). Levy Economics Institute of Bard College. https://www.levyinstitute.org/publications/keynesian-theorising-during-hard-times
• Forrester, J. W. (1968). Principles of systems. Wright-Allen Press.
• Forrester, J. W. (1969). Urban dynamics. MIT Press.
• Godley, W., & Lavoie, M. (2007). Monetary economics: An integrated approach to credit, money, income, production and wealth. Palgrave Macmillan.
• Sterman, J. D. (2001). System dynamics modeling: Tools for learning in a complex world. California Management Review, 43(4), 8–25. https://doi.org/10.2307/41166098