Saturday, December 14, 2019

A Mechanical View of SFC Modeling for Beginners

[Disclaimer: I am writing this article as a method of personally improving my own SFC techniques. (Over the years, I find that new material is understood much quicker and with more comprehension if I first try to put-it-together myself. It's kind of a 'put-it-together first, then read the instructions' approach.)]

The Stock-Flow consistent (SFC) model technique is a method students and thinkers can use to build models by using consistent money flows and stocks. Accounting principals are followed by ensuring that all monetary trades are balanced with an exchange of product and monetary equivalent.

SFC models can be built to display the NIPA sectors and GDP, or they can be built to display other economic events. The focus here will be to build two progressively more detailed SFC models, thereby preparing the reader for the next step of understanding the yet more detailed models found in 'beginning' texts.

The Concepts Underlying SFC Models

The first concept we will identify is that a sector can both divest itself of money and buy a substitute product by interacting with another sector. Thus, we can have the Household sector buying food from the agriculture sector (here represented by "Firms"). The two simultaneous transactions are recorded in two sector columns on a single line. (See Figure 1a.) The line total (shown at far right) will be zero if the exchange was equal in both directions.

Figure 1.* Two SFC models demonstrating technique and the flexibility of the SFC method

Restated in a slightly different way, rows record the instantaneous exchange of product and money (usually of equal value) so that the value change from a macroeconomic perspective will be zero. The zero sum will be recorded in a separate value column at far right.

A plus value will always represent inventory of money. Negative values will carry dual representation. A negative sign indicates both that a monetary inventory has flowed away from this sector and that another counter-flow inventory of product/services, labor or some other exchangeable has been substituted. (As with all models, beware of exceptions to any of these 'rules'.)

In Figure 1, the actual products exchanged are identified using a 'a<>b' style of notation.

Vertical columns are intended to cover period of time so that additional rows detailing additional events can be recorded. The productive effort of labor (resulting in a sequenced replenishment of products for future sale) is a good example of an exchange taking time to develop but settled instantaneously. The time period is usually assumed to be one year.

Vertical columns, when used to represent sectors, need to sum to zero in an absolute monetary sense if we are to achieve accounting accuracy. Simply stated, when money flows away from a sector, it must be replaced. In Figure 1a, we replace money used to buy products with money earned from firms by selling labor. Column sums of zero (at the bottom) indicate that stability has been achieved.

Memo lines can be inserted to convey additional information. In Figure 1a, the total output of firms could would be indicated with the term "[Y]".

How to Model an Outrageous Event [an exercise]

Boy-oh-boy--are the SFC models flexible! Next we will consider an outrageous but possible event that can occur in any economy. We could have a counterfeiter at work. We will assume this guy prints green money good enough to fool at least some people (sales clerks). How would we enter his activity into our SFC model?

Here we will give the counterfeiter a line of his own. We could give him an entire column but here we will just call him a deviant consumer and consider how he might affect the stability of the otherwise stable system. In Figure 1b you see a SFC matrix displaying the author's description of how the event would go down:
"The culprit fooled the clerk with bad money, got a product and left the store. The money made it to the next level but not before the event was counted as an GDP output event. At the next money level, the fraud was discovered and reversed out of the Firms sector. The Household sector entry was also reversed but no decision was made on what might have been exchanged."
By now, the reader has gained an inkling of the flexibility of this modeling system. As is always true of models, the model builder decides what the model is to say. Models don't give us answers--they only help us convey ideas that are better connected mechanically.

Now Read the Book!

If you are still reading, you should have gained an appreciation of the flexibility and power of SFC modeling. If you want more information, try the Wikipedia article "Stock-Flow consistent Model".

For university level information, try Wynne Godley and Marc Lavoie's co-authored "Monetary Economics". The authors develop and explain extensive macroeconomic SFC  models ready for computer simulation.

Hopefully, with a little mechanical SFC background in mind, the reader has gained confidence to undertake further study using advanced texts. Perhaps the reader can also articulate and present his own views and visions more accurately. [Writing this post helped this author]

*The matrices found in Figure 1 originated in the Wikipedia article "Stock-Flow consistent Model".

(c) Roger Sparks 2019


  1. Roger: Question 1: What is the 'a<>b' style of notation? What is it saying in English?

    Question 2: What is it you're seeing in an SFC model that isn't already in a conventional Earnings Statement/Balance Sheet model? To me they seem like the same thing, just different format. I'm trying to understand what differences you're seeing.

  2. This comment has been removed by the author.

  3. Ed: Thanks for taking a look.

    "Question 1: What is the 'a<>b' style of notation? What is it saying in English?"

    Here I am thinking of money as being a product owned by the holder. A line would record money being exchanged for a product(s) and the notation is something I thought would help the matrix builder (and viewer) use to keep track of things.

    "Question 2: What is it you're seeing in an SFC model that isn't already in a conventional Earnings Statement/Balance Sheet model?"

    Look at the titles of the two columns. They both use labor (a renewable resource) in a different way. They also 'consume' resources in different ways. Firms could be considered as 'converting' (not 'consuming') resources. Money is used as the medium of measurement and exchange. Strangely, labor is both consumed and renewably supplied.

    That whole collage of economic descriptors has been merged into a single internally- balanced matrix. While earnings statements and balance sheets do similar things, they are (I think) less focused on the extensive interactions that exist within a functioning economy.

  4. Roger: All financial statements are of the following form:
    BALANCE (total of all below, which equals zero)
    Assets (currency measure of what's owned)
    Liabilities (currency measure of what's owed)
    Equity (assets minus liabilities, ie, stock)
    Net (revenues minus expenses, ie, flow)
    Revenues (currency received during current period)
    Expenses (currency spent during current period)

    Each particular entity divides its Asset, Liability, Revenue, & Expense accounts into subsidiary accounts reflective of what's important to management of the particular entity. (Management has certain amount & ratio expectations for the Revenue & Expense accounts (by design or experience) & when they deviate from those expectations, they drill down into the subsidiary accounts to find the source of the deviation & assess their options for correcting it.)

    The national economy is such an entity. Its Revenue & Expense accounts are shown in Account 1 on page 9 of the NIPA Primer at (It's shown in T-account format, Revenues on the left, Expenses on the right. Subsidiary accounts are shown as separate tables (Accounts 2-7), but that's just formatting (because they believe it makes their meaning clearer) but they could as well be displayed inline (as above) or (from what I can see) in SFC format.

    Note that the NIPA is an agreed measure of the PRODUCTIVE economy (used by most nations) & its Net (ie, Revenues minus expenses) equals zero (showing that the economy has no Net profit (& therefore, builds no Assets or Liabilities) from its productive economy. Now there's a whole non-productive economy (banks, stock brokers, money advisors, insurance industry, federal income taxes, etc,) that IMO can't be measured (despite the Fed's FOFA program trying to do that) & I see as irrelevant ie, abolishing any or all would not negatively impact society.

    So I see SFC as simply a reformatted display of the same variables. It may show some relationships more clearly for some purposes, but I see no difference in information content. I'm still wondering if you're seeing something I'm not.

  5. Yes, I think I am seeing something different; but I am struggling to clearly explain what it is.

    First--nice job on briefly explaining balance sheets and what you are seeing in them.

    OK, let me try this. SFC formatting presents parallel balance sheets for (in my examples) Households and Firms. The interplay between the two balance sheets is shown. If every conceivable interplay is quantified, the two balance sheets should tally to zero (which reflects that one balance sheet is the reverse image of the other).

    So I see the SFC format as emphasizing the interplay between sectors, while a balance sheet details the flows of a selected sector. (The NIPA numbers (as you say) measure the productive sector.) The SFC format will include the financial sector as it is required to bring the sectors into balance.

    Now that I pointed out the differences (using my judgement), would you agree that this a a valid difference between the two formats?

    1. Roger: If you're saying that the SFC format makes certain relationships clearer (ie, easier to see & understand), we have no disagreement there. Depending on what you're looking for you might consider other formatting options, eg google "Flow of Funds Accounts" & look at the Investopedia & Wikipedia pages. The Wikipedia page describes (& links to) the Fed's attempt to do what it appears you're trying to do, ie, depict the whole economy, including the financial sector. I explained earlier why I don't think that possible (due to impossibility of measuring so much of what we call "wealth"), but you're in good company with the Fed, so I'm distinctly the outlier.


Comments are welcomed but are moderated. It may take awhile before they appear to be viewed by all.