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Friday, August 23, 2013

What are Stock-Flow Consistent (SFC) Models?

This article is a short definition of what Stock-Flow Consistent (SFC) models are. I view this class of models as being the most promising among the existing types of macroeconomic models. This article is literary, I will write others which may actually have some equations (or at least pretty charts of the output). References are given below.

The stock-flow consistent modeling methodology is based on modeling the economic national accounts explicitly, with the impact of financial flows correctly accounted for by the change of stocks of financial assets and liabilities. The approach towards accounting identities is very rigourous, with checks made to see that all assets are accounted for properly (someone's financial asset is another's liability). And in particular, there is a notion of stock-flow norms taken into account when modeling the behaviour of entities (typically sectors) within the model. (A stock-flow norm is the assumption that entities will adjust flows based on their existing stock of liabilities and assets.)

For those who are unfamiliar with the terms stock and flow as used in economics, stock is not related to the usage of the common usage of the word as a financial asset. (Stocks are another name for equities in North America, whereas gilt-edged stocks refers to government bonds on the other side of the Atlantic.) A stock is the value (in the monetary unit of account) of an asset or liability on a balance at the end of the period. For example, if you have $1000 in your banking account at the end of the day, your stock of bank deposits is $1000 for that period. A flow is the amount of money that changes hands across a time period. For example, a salary of $100 paid daily is a flow variable, as it is an amount of money per unit of time. The most well-known flow variable in economics is Gross Domestic Product (GDP).

As a simplified example, one could have a household sector that follows the following rules:
  1. It spends 95% of income received during the period (which implies it saves 5%). The remaining income is used to purchase financial assets; and
  2. it sells 10% of financial assets owned at the beginning of the period, and the proceeds are also spent. (This relationship represents a stock-flow norm.)
(These flows will have to consistent with the behaviour of the other sectors of the economy. Therefore, other sector(s) will have to buy/sell financial assets to offset the household sector net purchases. I am ignoring the other sectors for simplicity, just giving an example rules followed by one sector.) If the household sector income is $100, and it has previous financial assets of $50, it will have a net savings of zero (and thus spend $100 during the period). This is because:
  1. it will save $5 out of income (5% of $100), and
  2. spend $5 of previous savings (10% of $50).
If the sector has less than $50 of assets, the net savings will be positive, raising future financial assets. Conversely, if it  has more than $50 of financial assets initially, the sector will spend more than 100% of income, and future financial assets will be lower (note that interest income is part of income in this example). If the time history of the model is calculated, if the household sector income is stable near $100, its financial asset holdings will converge towards $50.

I will not attempt to discuss the history of SFC models herein; this is covered in the references. But I will note that Modern Monetary Theory (MMT), which has a very large presence on the web, can be best viewed as an offshoot or evolution of SFC modelling.

One problem with the name for this class of models is that they imply that other classes of macroeconomic are not stock-flow consistent. Even if this is a true state of affairs, it probably generates needless controversy. Stock-flow inconsistency was a valid critique of older mainstream approaches to macro, but this is not a weakness of modern Dynamic Stochastic General Equilibrium (DSGE) models theoretically. The standard frameworks do the accounting correctly when the initial optimisation problems are set up. That said, these initial optimisation problems are generally not solved; instead a linearisation of the model is taken, and the linearised system is the actual system that is analysed. The step of linearisation will break the accounting identities among the model variables. Therefore, critics of DSGE models can point out that the resultant models are stock-flow inconsistent, whereas the defenders of DSGE can point to the initial problem statement, which is stock-flow consistent. This creates a circular argument that will never be resolved.

(c) Brian Romanchuk 2013

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