Stock-flow consistent macro models Part 1

This blog introduces what is called stock-flow consistent macroeconomic accounting structures. It is based on a paper I (Bill Mitchell) wrote in 2008 with James Juniper called There is no financial crisis so deep that cannot be dealt with by public spending.

It is at the pointy end of my blogs and won’t appeal to all. But if you really want to start understanding the quality of modern monetary theory then stock-flow accounting is a good place to start.

What this framework allows you to understand is why the prevailing orthodoxy in macroeconomics has failed. The framework shows you that the mainstream belief that markets self-equilibrate at levels that are remotely socially acceptable is erroneous. Markets do not self-regulate in ways that avoid major financial upheavals and these crises have profound impacts on the real economy.

In particular, the body of literature that is built upon the belief that fiscal policy should only be a passive support to an inflation targeting monetary policy is shown to be highly damaging to the long-term growth prospects of modern monetary economies.

The current crisis confirms that the only way that the non-government sector can save is for the government sector to run continual budget deficits. The stock-flow framework allows you to understand why this fiscal conduct is non-inflationary and, if managed properly, exerts downwards pressure on nominal interest rates and underpins full employment.

To understand how the modern monetary economy operates we need to take a step back into national accounting. First, a modern monetary system has three essential features. Hit the link for what we’ve covered before and then come on back.

Nominal (or real) wage cuts per se do not clear the labour market, unless they somehow eliminate the private sector desire to net save and increase spending. Thus, unemployment occurs when net government spending is too low to accommodate the need to pay taxes and the desire to net save. This is a fundamental mistake that neo-liberals (and Austrians make).

For example, if you read the classic Austrians, such as Murray Rothbard, you will get this sort of claim in his Power and Market (pages 204-205):

Unemployment is caused by unions or government keeping wage rates above the free-market level.

And this gem from America’s Great Depression (pages 43-44):

Generally, wage rates can only be kept above full-employment rates through coercion by governments, unions, or both. Occasionally, however, the wage rates are maintained by voluntary choice (although the choice is usually ignorant of the consequences) or by coercion supplemented by voluntary choice. It may happen, for example, that either business firms or the workers themselves may become persuaded that maintaining wage rates artificially high is their bounden duty. Such persuasion has actually been at the root of much of the unemployment of our time, and this was particularly true in the 1929 depression.

In a fiat monetary system where the government has currency sovereignty this analysis couldn’t possibly be true.

All of the modern monetary propositions can be understood within a flow of funds framework which renders the underlying accounting between flows and stocks consistent. Mainstream economic models do not have stock-flow consistency and therefore fail to understand how the spending relations tie in with the wealth and other stock relations.


To understand the difference between a stock and a flow think of a bath-tub. The water in the bath is a stock – it is measured at a point in time. The water that comes into the bath (via the taps) and/or out of the bath (via the sink) are flows and you measure them as a rate of water flow per unit of time. So many litres per minute.

If the inflows are stronger than the outflows the water level in the bath will rise and vice-versa. In other words, flows add to and subtract from stocks.

In economics, this distinction is very important and most students fail to really understand it. I think that is because mainstream macroeconomics then doesn’t go onto to use the distinction properly, especially in the area of fiscal relations.

So the level of bank reserves is a stock – measured at some point each day. Government spending and taxation, consumer spending, saving, investment, exports, imports, etc are all flows of dollars per unit of time. Government spending adds to bank reserves and taxation reduces (drains) the stock of reserves.

Clearly, a theory of the economy that doesn’t recognise the intrinsic relations between the flows and stocks is missing the boat. Given that modern monetary theory is ground out of the operational accounting of the monetary system, its stock-flow consistency is impeccable and unique (a major strength).

A Flow of funds view of modern monetary macroeconomics

A Flow-of-funds approach to the analysis of monetary transactions highlights both the importance of the distinction between and vertical and horizontal transactions and the fundamental accounting nature of the budget constraint identity.

It shows categorically that the Government Budget Constraint (GBC) is an ex post accounting identity rather than an ex ante financial constraint. You will recall that mainstream macroeconomics (and the Austrians) all believe the GBC somehow represents a financial constraint on government prior to it spending.

It doesn’t and cannot in a fiat monetary system unless the government adopts, voluntarily, a framework that replicates the operations of the ex ante GBC. In doing so it reduces its fiscal authority and bows to the pressure of those who oppose government intervention at a sufficient level to generate full employment.

A Flow-of-funds approach also shows that if the sovereign government runs cumulative surpluses which destroy net financial assets then the non-government must accumulate deficits in the form of increasing indebtedness which are unsustainable.

The distinction between vertical and horizontal transactions can be clearly demonstrated by examining the current transactions matrix for a simplified economy.

The last row of the current transactions matrix affords a crucial insight into the nature of (vertical) transactions between the government and non-government sectors.

These transactions must be clearly distinguished from their (horizontal) counterparts: those between banks, households, and firms. The basis for this distinction is that only vertical transactions give rise to net financial assets or increases in real wealth, whereas horizontal transactions net out to zero.

While transaction accounts (or T-accounts) are helpful for distinguishing between such things as high powered money and other forms of money, and for explaining why it makes theoretical sense to consolidate the central banking and treasury functions of government, they are not very helpful when it comes to establishing the difference between vertical and horizontal transactions.

However, this difference can easily be justified by examining a current transactions matrix for the economy, which depicts flows of goods and services and flows of monetary payments between institutions (households, banks, firms, and the government sector).

The following figure is what we call a current transactions matrix and is a highly simplified stock-flow consistent macroeconomic model. I recommend you print the figure by clicking on it and then using the print out it to follow the discussion. Note the -1 or t-1 just means last period’s value.

Here, consumption spending by households, C, comprises wages after tax, W-Tw, plus a fixed share a, of (lagged) household wealth, Vh.

Household wealth increases both through savings out of income, the latter including (lagged) interest receipts on deposits, ib, and dividends received from banks, Fb, and firms, Fd, inclusive of the capital gain on equities (a component subject to minor degree of simplification).

Firm investment is pDK (the D is the greek delta meaning change in), il is the loan rate of interest, and Tl is the tax rate on firm income. It is further assumed that the government chooses the bill rate of interest, ib, tax parameters and government spending as proportion of total capital.

Likewise, it is assumed that firms distribute a fixed share of after tax profits Fd as dividends, while banks distribute their total profits Fb to households. For simplicity, households are assumed to lend all their savings to firms without borrowing themselves.


The sources and uses of funds can be determined by reading the entries in each of the cells in any given column of the matrix.

For the household sector, the sources of funds include wages, interest on deposits, and distributed dividends from banks and firms. Uses of funds include consumption and payment of taxes on household income.

For firms, sources of funds include revenue from the sale of goods and services to households and government, as well as that component derived from the sale capital goods to other firms. These funds are used for investment, the payment of corporate taxes, the payment of interest on borrowings, and the distribution of dividends.

Banks receive interest on loans and issued bank bills, and use their funds for payment of interest on deposits and the distribution of profits.

By summing across the rows for the flow-of-funds accounts of banks, households and firms, it is apparent that all transactions cancel out with the exception of the interest paid on bank bills by government, the payment of taxes by firms and households, and the receipt of revenue by firms for the sale of goods and services to the government.

However, and very significantly, these components are all vertical transactions between the government and non-government sectors. That is they do not net to zero but create/destroy net financial assets in the non-government sector.

Bill Mitchell

Continued next week in Part II


7 responses to “Stock-flow consistent macro models Part 1

  1. That was a clear explanation and I was looking forward to it.

    Now, how do you move from this matrix and into the differential equations one sees in papers?

    What’s the difference between matrices like this, and the ones used by circuitists?

    In Leontieff’s I/O analysis there are closed form solutions; I don’t imagine anything similar is valid for these matrices. Am I right?

  2. Magpie The matrix works in terms of discrete time steps: period 1, 2, 3,… (which may represent years, or months or something) and the deltas represent changes from one time point to the next. To get to a differential equation, essentially all that is going on is that you shrink the timesteps, making them smaller and smaller.

    As for the circuitists, as I understand it (and I could be wrong here), there approach is basically the same, but they often impose some variant of the government budget constraint so, in Bill Mitchell’s terms, many of them are stuck in gold-standard thinking and tend to buy into things like the money multiplier.

    I don’t know enough about the Leontiff I/O work to comment on that.

  3. Thanks Sean!

    I’m just trying to imagine how a government budget constraint would look like in the matrix above.

    How would one include a GBC in that matrix?

    Would it simply be to stating that the sum of the Govt column to be nil?

  4. CBs do not loan out existing savings, they always create new money when they lend & invest. Thus, savings are impounded within the banking system, have a velocity of zero, & are a leakage in the Keynesian national income concept of savings. I.e., the bankers pay for what they already own. So your MMT is fatally flawed.

  5. Brad, nowhere do we make the claim that CBs loan out existing savings.

  6. You completely miss the point. Your equations don’t balance as a result. MMT’s thesis is contradictory.

    • Please read the relevant piece again. The working is shown in the stock flow matrix provided and it all balances. Please check your own working. MMT is factual and logical.

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