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Thursday, November 3, 2016

Primer: Understanding Hoarding Behaviour In A SFC Model

In this article, I tweak the simplest Stock-Flow Consistent (SFC) model ("model SIM") to demonstrate the effect of hoarding behaviour on an economy. This example is not meant to be entirely realistic (improvements are discussed), but I use it as an example of how the ability to tweak models provide a good platform for learning about economics. (The advantage of my Python modelling library is that it should allow users to easily make such tweaks, without having to do laborious algebra.) At the end of the article, I have a digression which explains how this fits in with the whole "whither economics?" debate that has shown up in recent internet discussion (on my site, and elsewhere).

The Difficulty with Economics Textbooks

The normal starting point for learning about a field is to pick up an undergraduate textbook. Within economics, this strategy generally does not work.

In order to be comprehensible to undergraduates, a textbook consists mainly of two types of material.
  1. Rote learning. In economics, this consists of topics such as the definition of GDP, what are price indices, why unemployment is defined the way it is, the definition of various monetary aggregate, etc. (The definitions of various econometric tools fits in here as well.)
  2. Simple models that undergraduates can reproduce on an exam, which are supposed to illustrate various principles.
If we look at mainstream undergraduates textbooks (and most of them are mainstream), the rote learning aspect is entirely reasonable, whereas the models are an unmitigated disaster. As a result, I believe that people interested in economics should pick up an undergraduate textbook, read the definitional parts, and not read any text that discusses economic behaviour.

Figure: Model SIM
Money Flows in Model SIM
There is at least one exception that I am aware of -- Godley and Lavoie's Monetary Economics. The focus on the book is on the models, but it is tied in with the background material (if you read the text, and not just jump to the mathematical bits). The difficulty with the methodology used therein is that the equations are derived by hand, and there are lots of equations. It is difficult to play around with the models, and see how they behave.

Model SIM with Profits

I discussed building model SIM (from Chapter 3 of Monetary Economics) using Python in a recent article.  (For those of you who do not have Monetary Economics, the linked article references other articles which describe the model, and alternative ways of finding the model solution.)

One of the peculiarities of SIM is that business profits are assumed to be zero, and that property helps eliminate business sector behaviour from the model. This has to be done to make the model the simplest possible, as otherwise business sector behaviour adds new dynamics. 

Observant readers of the code of my Python model will have noted the following lines:

# A literally non-profit business sector
bus = FixedMarginBusiness(can, 'Business Sector', 'BUS', profit_margin=0.0)

What happens if we set profit_margin to be something other than 0? (For those of you who wonder I why I specify 0.0 instead of 0, the answer is not false precision, rather that I want Python to interpret the number as floating point, and not an integer.)

I built a model with two countries, that I labelled "Canada" and the "United States." The hapless Canadian business sector matches the original model SIM with zero profits, and the red-blooded capitalists in the United States have a fixed profit margin of 10%. (Although it is a two-country model, there are no cross-border linkages added; I just put them into a single model so that I can compare the outputs easily. The number of equations explodes, of course.)

Chart: Model Output (GDP)

The results above show total output (GDP). What we see is that for this simple model, profits are bad for output.Both countries converge to a steady state value, but the steady state is lower in the "United States".

Hoarding Business Sector

Chart: Business Sector Financial Asset Holdings

The chart above explains the root of the problem. The business sector in the United States is assumed to always have positive profits, and it uses those profits to increasingly hoard financial assets.

Chart: Government Fiscal Balance
The financial assets being hoarded by the business sector have to come from somewhere; and that somewhere is the government. In "Canada", the government moves towards a balanced budget (fiscal balance of zero), whereas the "United States" has to run a persistent budget deficit to meet the demand for hoarding by the business sector. (The household sector financial assets -- not shown -- stabilise at a steady state value.)

The Lesson?

It would be quite easy to imagine the thinking of the hypothetical people living inside the model. One would imagine business leaders in the United States wringing their hands about persistent government budget deficits (and exploding debt-to-GDP ratio), but that is entirely the result of their hoarding behaviour. If we lump pension funds and mercantilist central banks within the "business sector," there is an analogy to what is happening in the real world.

However, these analogies are stretched. The problem is that this model has removed capitalists from capitalism. We need to see what happens when profits are recirculated via dividends. If we do, we get more sensible-looking steady state behaviour. My modelling framework supports that step, and it will probably be the subject of a follow up article (which will be delayed, as I have a backlog of rants to cover).

Digression: Whither Economics?

Some recent articles have underlined my view that some of the outside critics of economics do not understand what is really going on. (Since I have no training in economics, I am also an outsider, but I am familiar with the issues involved as a result of my old day jobs.)

The obvious weaknesses of mainstream models creates a tendency for outsiders to completely discount the contents of undergraduate economics textbooks. That is, throwing the baby out with the bath water. We then end up with people attempting to completely reinvent economics, using insights from whatever field they come from. (Physicists are a clear leader in this category, but us engineers are in second place.) 

These outsiders with visions of reinventing macro ignore one point: there is not a whole lot of debate about the "rote learning" parts of textbooks. Yes, there are debates about how classify transactions within the national accounts (and how they should be constructed), but no serious economist debates how the national accounts are currently constructed.

The disputes within economics revolve around:
  1. How do economic entities behave?
  2. How should economies be organised ("normative" debates)?
I seriously doubt that a physicist is going to settle the latter question (normative debates) any time soon. As for the question of economic behaviour ("positive questions"), all I can say is: good luck. Take the current situation in Canada. The housing market is over-extended in a fashion very similar to that in the United States in 2007. Any economic forecast has to be conditional upon the outlook for housing. However, the odds of creating a mathematical model that can correctly forecast inflation, unemployment, and the housing market simultaneously are slim.

The best we can hope for is to have a framework to position our thinking about the economy, in particular the effect of policy changes. Stock-Flow Consistent models provide such a framework. My hope is that my Python module will make it easier for people to work through the basics of how the economic sectors fit together, and understand how the behavioural debates affect observed economic behaviour. Actually playing with the models is superior to reading stories about them, as the story telling needs to be validated.

Appendix: Python Code

(c) Brian Romanchuk 2016


  1. "but no serious economist debates how the national accounts are currently constructed."

    I'd question whether they should be national. There's a bit of an issue with them being in a reporting currency - which means there is implied conversion of denominations hidden in there.

    And it promotes the 'this economy and the rest of the world' viewpoint - rather than a roughly peer level network interaction of currency zones.

    1. That's under the "how they should be constructed" case...

      The good reason why they are national is the reality of getting the underlying data. National statistical agencies are well, national. The U.S. Bureau of Economic Analysis is not going to be particularly happy with working with data provided by developing countries that are dollarised. One could imagine theoretical models of such a form, but they cannot be compared to observed data.

  2. A while ago I studied the balance sheet expansion of the aggregate bank sector. I let profits = revenue - expenses (simplest model) and assume the aggregate bank makes profits over time.

    Bank Assets:

    Bank Liabilities & Equity:
    Paid-in Equity
    Adjusted Equity

    When any bank makes a profit it should initially accumulate reserves. This means reserves would grow for the aggregate bank if nothing else occurs. However, the central bank provides reserves to the aggregate bank, and reserves generally do not grow unless a financial crisis forces the central bank to provide more reserves. This means the banking sector would be "investing" profits in the purchase of securities and expansion of loans rather than accumulating reserves. The record of accumulated "profits" would be in the adjusted equity.

    During a financial crisis the write-off of bad loans destroys adjusted equity and paid-in equity, spooks away depositors and makes it harder for banks to get borrowings, and this forces the central bank to provide reserves in the liquidity cushion.

    In a non-financial growth firm the "profits" would convert to an increase of non-financial assets. If the valuation of non-financial assets is driven up faster than liabilities of the firm then the shareholders recognize past profits as asset valuations, less debt, less paid-in equity.

    The equity claims of ownership to banks and firms relate back to households and not-for-profit organizations. So net lending/borrowing in financial accounts should be resolved in the household sector.

    1. A couple points.

      Reserves are only created by central bank activity. Bank profits will result in either lower liabilities to the non-bank sector, or holding greater assets. (Depends upon how the profits are earned.) In either case, equity rises, and reserves are unchanged. (The exception would be if the profit is from interest on reserves...)

      In the nonfinancial sector, profits would generally show up as increased financial asset holdings. Nonfinancial assets only increase as a result of investment.

    2. I agree with your points about bank profits and bank balance sheets. Note bank equity and other bank liabilities are held by non-bank share owners, depositors, and lenders.
      Here is a basic balance sheet model of growth firm:

      Growth Firm Assets:
      Accounts Receivable
      Plant, Property, Equipment
      Patents, Trademarks, Copyright

      Growth Firm Liabilities & Equity:
      Paid-in Equity
      Adjusted Equity

      If the firm has a sales and profit growth opportunity it should convert retained earnings (adjusted equity) to an investment in assets other than cash deposits to grow its sales and future profits. The only financial asset that expands in a firm pursuing rapid sales growth is accounts receivable. This assumes, of course, the firm must use nonfinancial assets funded via retained profit, equity, and debt to operate its line of business.


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