15 min read

Stock-Flow Modelling: Boom or Bust?

Where does my money go? Where does it come from? Accounting at the macro level - the stock-flow consistent approach
Stock-Flow Modelling: Boom or Bust?

Recently (in march) I joined #EconTwitter and began following the debates about the U.S. stimulus in the form of the American Rescue Plan and now the infrastructure bill. What jumps out to me is the Bidenomics avoidance of engaging with the mainstream (neo-classical, yes its a loaded phrase) of academic economics. Academia, it turns out after studying some of the top journals, is still populated by the now patched-up versions of models that didn't predict the financial crisis of 2008-09. In any case, there was frequent mentioning of modern monetary theory  in the news recently (I read and review Kelton's Deficit Myth here). While I don't see myself as a full-blown #MMT proponent, I do find strong appeal in starting with the accounting of the economy as a whole. It was Krugman's references to flow of funds and Lerner's functional finance that got me on this track of reading.

Models based on economic accounting has been around for a long time in heterodox economics under the name of Stock-flow Consistent Modeling (the appropriateness of the name is debatable and somewhat misleading) and was successful in predicting the 2008-09 financial crisis, which garnered some renewed interest in these approaches. To quote Dimitri Papadimitriou on Wynne Godley (one of the major figures):

Not only did he forecast the scale and duration of Britain’s early 1990s recession and the corresponding recessions in 2001–02 and 2007–09 in the US quite accurately and at an early stage, but he also wrote about the future in a circumstantial way documenting, before they happen, the same reasons that were given by everyone to explain them after they had occurred. (Papadimitriou, 2012, Conntributions in stock-flow modeling : essays in honour of Wynne Godley)

Today, I want to present the basic blocks of this approach, and some of its recent works. Without further ado, let's dive into this methodology.

All About Stock-Flow Consistent Models

What is Stock-Flow Consistent Modelling?

In what follows I will simply refer to it as SFC for brevity. SFC presents a framework for treating the real and financial sides of the economy in an integrated way. We cannot understand the real side without understanding the financial side (e.g. household debt pre-financial crisis). This is also where the debate about the name comes from (Noah Smith, with response from Steve Keen): the models of economic orthodoxy are technically stock-flow consistent, but they neglect the financial side of the economy. Taking Steve's point, in future it should be called Monetary Stock-flow Consistent Modeling...

Why look at this particular approach? It seems to work as an underlying framework: the assumptions are clear and the predictive results are promising (see quote in intro). One starts with the national accounting of stocks and flows and then adds some behavioral rules. Before getting into those details, let me introduce the people who brought about this approach.

Where did all this come from? A history

The initial inspiration for stock-flow consistent models stems from the work of John Maynard Keynes and Michal Kalecki's writings on demand-led economics and where profits come from. It was Morris Copeland who then combined national accounting identities (we can think of decomposing GDP for instance) with the flow of funds in the economy.

John Maynard Keynes, Michal Kalecki and Morris Copeland set the wheels in motion for the Stock-Flow Modelling approach
John Maynard Keynes, Michal Kalecki and Morris Copeland set the wheels in motion for the Stock-Flow Modelling approach

The combination of Keynes & Kalecki's theories and Copeland's method was then done by James Tobin at Yale. In particular, Tobin is known for addressing the choice of how to allocate wealth and savings between the different available financial assets (more on that later). But that, by no means, is all (see Carnevalli et al). His focus too was on integrating real and financial sides of the economy. What differentiates the real and financial sides? So the real side is anything that doesn't require a monetary system to be represented. E.g. if we imagine a barter economy where I trade my blog posts for food directly (and starve eventually....) then we can express everything in units of goods. Beyond integrating monetary and real economy Tobin tracked the stocks of the economy dynamically over discrete time (i.e. t, t+1, t+2,...), and figuring out how people split their savings between cash, bonds, stocks, real estate, and all the other things.

James Tobin and Wynne Godley, the two most impactful people in Stock-Flow Modelling
James Tobin and Wynne Godley, the two most impactful people in Stock-Flow Modelling

As Tobin worked, so did Wynne Godley. After Kaldor convinced him to join the University of Cambridge as the Director of Applied Economics he began writing with Francis Cripps, developing early ideas. In 1994 he moved again to the Levy institute at Bard college, there he published Monetary Economics with Marc Lavoie. Coming from the U.S Treasury, Godley's aim was a to combine theory with policy, and build rigorous models that combine the real and financial sides of the economy (as did Tobin). In doing so, and developing the Levy Macroeconomic Model with which, in 1999 he foresaw the housing crisis that would engulf the world in 2008. To be honest, I am really intrigued by these models partially by my fascination of the accounting itself (I do identify as a numbers nerd...) as well as the fact that in 1999 Godley knew of 2001-02 and 2008-09. Meanwhile, the narrative of economic orthodoxy is that nobody knew!

In any case, there are several other notable authors that have had an influence on the development of SFC that I will simply listt: Paul Davidson, Alfred Eichner, Lance Taylor (CGE models), Peter Skott, Duncan Foley (formalized capital circuit of Marx)

Principles of Stock-Flow Consistency

SFC models rest on two pillars that are common to other models, but often not made as explicit. Firstly, there is accounting consistency. Yes, this is precisely what we think it is — every balance, and every change in balance must be recorded with a party and counter-party involved. This ensures that there are no leaks in the model (e.g. in some models firms go bankrupt and simply get re-instated but without accounting for who pays for it). This also makes explicit the interlinkages between the financial and real sides of the economy. The second step that follows is behavioral closure, which is the entry-point for different views on economic behavior. The majority of the work labelled as SFC model behavior in the post-Keynesian tradition, i.e. demand matters in the short- and long-run, and full employment is not the general state of the economy. More on this later when we look at the different tranches of behavior.  For now, I would just like to point out that, in my opinion, this way of starting models of the economy leads to a very structured and clear approach that avoids, as much as possible, the black-box nature of some models (and the 15-page model expose so common in top-5 journals).

IMPORTANT: if you are not interested in the details or any mathematics, skip to the section Applications of Stock-Flow Modeling

Accounting Consistency

Accounting, didn't you hate that class in university? Personally, I find accounting satisfying as the identities usually sum to zero, so there are effective checks on whether its correct or not. And really, building a deep understanding of processes in accounting leading to large matrices is somehow fascinating (sorry Paul Krugman, and your proposition of simple models for intuition). This is accounting on the macroeconomic scale. I digress. Accounting consistency is thought of through two guiding principles:

Stocks and the Balance Sheet

So I spoke of accounting, lets start with what everyone owns. The essence of stock-consistency is that my assets are someone else's liability. This is simple enough when we think of a mortgage, I have the loan to pay back (a debt, a liability) while the bank records me as an asset (I have to pay them back). This principle extends further. The 20 Euro or Dollar note in your wallet is an asset to you, but a liability to the government (after all, the government spent it into existence...). All of these stocks are represented by a large matrix (or table if you will), for instance this one that I unashamedly copied from Nikiforos and Zezza (great review...):

Balance Sheet Matrix example from Nikiforos and Zezza (2017)
Balance Sheet Matrix example from Nikiforos and Zezza (2017)

Here we note that there are 7 different assets (A-G) which result in a net worth (H), and total to 0 (I). There are some interesting things to note here, without even having to make any behavioral modelling assumptions:

  • The only tangible asset here is fixed capital, in other words the firm's machines. The sum of all agents' net worth must be equal to what physically exists, the fixed capital. An economy's worth are its real assets. Though here we do not ignore the monetary / financial side.
  • For a monetary sovereign, thinking of government debt as a liability that future generations must pay is somewhat misguided. We may have to pay for them, yes, but we also get all of the benefits, since these are assets for us, so really its not much of an issue in those terms. BUT what my own and future generations really will pay for is in real terms: climate change and inequality.
  • Finally, the number of assets and agents in the model is up to the modeler, as long as the accounting works. In later sections, we have a look at some work with SFC models.  In principle they are all expansions on the number and type of assets and agents in different agents. The beauty: we can study different aspects of an economy while keeping the accounting correct, thus should we want to, we can put it all together for a mega-model to study things as a whole.

Flows and the Transaction Matrix

The simple adage is that all flows come from somewhere and must go somewhere. In other words, there are always two parties to a transaction. It is represented by a large matrix (again, I know) with two properties: (a) horizontal consistency, the sum of all the flows between all agents is zero (every transaction has a start and end), and (b) vertical consistency, all flows involve a form of debit and credit (you credit, i.e. remove, some of your bank account balance in exchange for groceries). This is known as quadruple-entry bookkeeping. So here is an example of what that looks like on a macroeconomic scale:

Transaction flow matrix example from Nikiforos and Zezza (2017)
Transaction flow matrix example from Nikiforos and Zezza (2017)

Some quick notation, for the really keen, sources of founds = +, uses of funds = -. Current = inter-sector, Capital = intra-sector.

The point of showing this rather large matrix with lots of notation is to make the following points: (1) the upper level of the matrix shows where all the flows go in any one period. In effect these are all the decisions made by the agents. The result is some change in the net wealth (net lending). (2) The lower part of the matrix maps this into the individual accounts in the balance sheet. This is kind of like having a bank account: you may have sub-accounts for the current, savings and portfolio. Every month you go about regular life and spend some money and (hopefully) make some money. Thus you have your own stock-flow consistency. You live this model....

Voila, we arrive at Stock-Flow consistency: the balance sheet shows us where things are at any period, and the flow matrix tells us how things change during the period. There is one additional matrix that comes into play, which we will not discuss here: the capital gains matrix. Namely beyond flows, the stock of existing assets might change in value over the period (e.g. your shares in Tesla might increase or decrease depending on Elon's most recent Tweet).

What can matrices tell us?

So this is also rather mechanical, we are just sorting things and tracking things but not really telling you why we observe the changes and dynamics we are noting (SFC is made fun of for being a non-causal hydraulic set of pumps). There is one very important relationship that does arise without behavioral assumptions:

The sum of net lending across all agents in the economy is zero

Why is this important? It goes to say that if the government runs a deficit, someone else must run a surplus (e.g. the household or the firms or the banks, or as we shall see, the foreign sector). Austerity, or government surpluses, imply some of us necessarily must be running a deficit ourselves. Its an accounting identity. A discussion in context of modern monetary theory here.

Really most macro models should just pop these matrices into the main text, or at least the appendix. Its like reading an abstract but for the model itself. It gives you an indication of what's being treated and where it becomes complicated. Also would be a good indication of where to look for behavioral assumption. Finally - easy to compare the models then.

The final ingredient: behavior

So the SFC literature was developed within the Keynesian theory, which means that demand sets the tone for the economy both in the short and the long run. E.g. our demand for cars, housing, groceries, or other goods is the key ingredient to the economy. This means it has been left on the fringes of economic publications. I am no expert but have a favorable opinion. I leave you to make your own behavioral choices. In any case, what I really like is that there is a clear set and delineation of behavioral choices that need to be made. In essence, it makes explicit the "closure", in other words, the direction of causality of the different economic theories. This really helps thinking systematically about the economy in the following series of steps:

  1. Expenditure: how does each agent spend wealth and income (e.g. how many groceries and goods to buy). This also includes how much firms invest, and how much governments spends. Typically this is modelled as proportional to your previous level of wealth and your income
  2. Financing: how to pay for your expenditure? Do you take on debt or reduce your cash holdings? A simple choice would be to take a linear function, for instance, a company may finance a fixed proportion of investment by issuing new shares
  3. Wealth: this is Tobin's very cool contribution. So we have spent, and we have financed the spending, but where do we put the remaining money? Bonds? Stocks? Cash? I'll skip the mathematics and give a verbal expose of my interpretation: you have some fixed idea of your allocation (e.g. I might want some rainy day cash reserves) and you essentially add to this some modulating factors. First, what are the expected returns of each asset (how much can I make) and how much does this depend on my purchasing (if I buy more, the prices will likely go down or at least not go up as much). In essence, I want to buy things with a higher return but want to ideally avoid risk. Secondly, you factor in your current disposable income. In this way, we smooth our allocations a bit over time, we save some more in good times and spend some more in bad times.
  4. Productivity, Wages, Inflation: these are some closing equations that are quite simple. Productivity (technology if you will) might remain constant, and prices are set based as some markup over cost (e.g. we want 10% profit). There is a literature on endogenous technological growth, and it is somewhat predictable (see here). But often we can just leave it constant. Wages, in most SFC models, are set based on conflict: earners have some aspirations based on their productivity (e.g. your CV) and the current state of the labour market (look at all those well paid data scientists...). The nominal wage then reacts to the gap between the desired wage and the actual wage.
  5. The Financial System: this is essentially modelling the behavior of the banking agents: how many loans do they take out? how much risk will they take? For instance, there might be some limits to the leverage (debt to equity) that banks may take on. Its a large field of study, so I wont go into that here.

Equilibrium and Analysis

So - economists love equilibrium. Its really a neat concept (though an unlikely state of the world) in which nothing changes that helps us think about the system as a whole. In SFC models this means that there is some stable ratio between the stock and the flow. For instance, the amount of cash inflow and your bank account holdings. Much of the literature is about finding the correct ratios to look at and how to interpret them. If all of these ratios are constant, then we have reached a state of long-run equilibrium.

Applications of Stock-Flow Consist Modeling

I have given an expose about SFC, its history, and hinted at the fact that Wynne Godley predicted 2008-09. So let's take a dive into some of the applications and works of SFC. As a disclaimer, I based my starting review here on Nikiforos and Zezza (2017) and Carnevalli et al. (2018) and will just highlight the models that stood out to me.


To consider the financialisation of the economy, (e.g. to study the effects of the prioritization of shareholder value as the firm's goal and the rise of the financial system), one can do this by expanding the banking agents and the possible different types of investment that can be made. For example, Botta et al. (2015) disaggregate into workers and rentiers, special purpose vehicles, mutual funds, investment funds, and broker-dealers. They also add real estate, loans, mortgages, deposits, obligations of firms, money shares, longer shares, asset-backed securities, and repos. Its a big data expose. In modeling this we can make explicit Minsky's financial instability hypothesis and other theories of the business cycle (e.g. see Dafernos 2015).

Income Inequality

To address inequality, one can diversify the set of different household agents. For instance including employed and unemployed households, entrepreneurs, high and low skilled to name a few distinctions. What caught my eye: Nikiforos (2016) suggest that the decrease in saving rate (indebtedness) of the bottom 90% of the income distribution was a pre-requisite for the maintenance of full employment in the three decades before 08-09 (a Kaldorian notion). In particular, the asset bubbles of the period (e.g. 2001 tech bubble) were necessary for sustaining this.

Globalisation and Trade

So I've talked a lot about the macroeconomy, but assumed that there is only one nation (one balance sheet). Making this into multiple nations essentially means adding an additional balance sheet for a foreign country (or the rest of the world). The one caveat is needing one place to be the currency issuer.  We can then update the equation to be the three balances that Godley considers key:

Net Lending Private + Net Lending Government + Net Lending Foreign = 0

The source to look up is Godley's Seven Unsustainable Processes (1999). In the 1990s there was an increase in the current account deficit and government budget consolidation. So the only way for the economy to sustain its trajectory was large increase in private spending relative to income, in other words, driving the private sector into debt. The debt-to-income ratio rose, which eventually led to 08-09, and the rest is well-known (I guess). The Greek austerity situation can also be analyzed through this lens (e.g. Semieniuk et al. 2011)

Sustainability and Eco-SFC

Let's talk climate change. Somehow economists have struggled with this topic. Nordhaus won the Nobel prize for his work on climate and economics. I find his work extremely questionable if not dangerous. An SFC critique of macroeconomic closures for ecological economics was written by Cahen-Fourot and Lavoie (2016). One could think of climate change also as a series of stocks and flows. For instance, the stock of CO2 pollution. The stock would then be considered to have negative impacts on quality of life and the economy. Conceiving of it as stocks and flows means we should be able to cleanly integrate this into our SFC models. This is what some people already did: Dafernos et al. (2017) build a model of monetary and physical stocks based on SFC accounting and the laws of thermodynamics. Carnevali et al. (2018) also present an integrated model.

Agent-based Models

Agent-based modelling for macroeconomics is a methodology that has been around a while, but has recently come into the spotlight due to a wash of new developments. Yours truly is working with ABMs, and I will write a, hopefully concise and simple introduction soon - in the meantime, have a look at Haldane & Turrell. In principle, it implies populating each sector with a large number of individual agents (e.g. n households or m firms) and a network for these agents, and specifying their individual rules. The SFC approach is a great first condition for Agent-based Models: it ensures the accounting is absolutely rigorous and it gives a concise overview of the model's workings. Some examples include Caiani et al. (I recently reviewed here), Kinsella (2011), Seppecher (2012+), Riccetti (2015), and many others.


As is probably obvious from my interjections throughout the article, I am tentatively a fan of this approach. The methodology itself is very neat and clean. Yes, technically the economic orthodoxy of Equilibrium models is also stock-flow consistent by design, but it is neither explicit nor do I agree with their behavioral foundations... A topic for another post. In any case, I think Godley and Lavoie's book on Monetary Economics is very much worthy of a read, and perhaps a replication of the models. Who wouldn't like to know where and when the next economic crisis will happen?

Admittedly, this post is somewhat more of a literature review than a model or contemporary analysis of the goings on in the world. However, these are the steps by which I believe one gets an impression and of what may or may not work, and which models could be a great starting point for further development.

** Coverphoto by Tyler Casey on Unsplash

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