Stock-flow consistent macro models Part 2


Government surpluses must equal non-government deficits

The bottom row of the Current Transactions Matrix indicates that government savings (surplus) or tax revenue net of government spending and payment of interest on bonds ((T – G – ibt-1Bt-1 – 1) are equal to the non-government sector’s dis-savings (deficit = pDK – Fu – Sh).

This is a crucial accounting identity because it implies that, in periods when governments run continual budget surpluses, although economic growth could well be sustained over the short run, this will only happen if the non-government sector runs an on-going deficit, thus accumulating ever-increasing levels of debt.

Moreover, as surpluses destroy net financial assets, this increase in private sector debt will be matched by a continuous decline in net financial assets or wealth.

To show this, we must interpret the flow-of-funds accounts more closely for each of the sectors in terms of how they interact together. However, before this is attempted it is desirable to incorporating transactions with the rest-of-the-world.

Extending the framework to the Rest of the world accounts

The next table is a simplified transactions table which while simplifying the components of GDP, now includes a column for the rest-of-the-world (ROW) account.

Here, Gross Domestic Product, Y, is equal to Private expenditure, PX, plus government expenditure, G, plus exports, X, minus imports, M. The ROW account reveals that imports minus exports and transfers paid by the external sector, TF, equals the balance of payments deficit.

Every item in the Production (GDP) account is matched by a corresponding negative entry in some other column. Taxes net of transfers are received by the government.

Net property income, taxes and transfers, TF and TP, are paid by the external and private sectors, respectively.

The final row totals reveal that public sector net borrowing, PSNB, equals the private net acquisition of financial assets, NAFA (private savings less investment) minus the balance of payments surplus (or plus the deficit), BP.


From the perspective of a stock-flow consistent approach to macroeconomic modelling outlined above, the fundamental accounting identity states that government savings (surplus) or tax revenue net of government spending and payment of interest on bonds is equal to the non-government sector;s dis-saving.

That is, public sector net borrowing equals the private net acquisition of financial assets (private savings less investment) minus the balance of payments surplus (or plus the deficit). As governments have moved away from deficit spending at levels typical of the post-war period of full-employment, private sector debt levels have escalated.

The reason why this has happened is that causality flows from fiscal policy to the private sector simply because economic influences over the rest-of-the-world account change quite slowly, with income effects dominating over the price effects that are championed by neoclassical theorists.

In contrast, fiscal policy responds immediately to government decisions about spending and taxing. The transmission mechanism behind these changes is complex, as it operates within a portfolio setting, by changing relative rates-of-return between real investment, the equity-premium, and the term structure of bonds.

Sectoral balances

So the framework translates straightforwardly into the familiar sectoral balances accounting relations. They allow us to understand the influence of fiscal policy over private sector indebtedness.

You have seen this accounting identity for the three sectoral balances before:

(S – I) = (G – T) + (X – M)

So total private savings (S) is equal to private investment (I) plus the public deficit (spending, G minus taxes, T) plus net exports (exports (X) minus imports (M)), where net exports represent the net savings of non-residents. That has to hold as a matter of accounting. It is not my opinion.

Thus, when an external deficit (X – M < 0) and public surplus (G – T < 0) coincide, there must be a private deficit. While private spending can persist for a time under these conditions using the net savings of the external sector, the private sector becomes increasingly indebted in the process.

For Australia, while the current account deficit has fluctuated with the commodity price cycle, it has continued to deteriorate slightly over the longer term. Accordingly, the dramatic shift from budget deficits to surpluses from the mid-1990s onwards was mirrored by a corresponding deterioration in private sector indebtedness.

The only way the Australian economy could keep growing in the period after 1996 was for the private sector to finance increased spending via increased leverage. This is an unsustainable growth strategy. Ultimately the private deficits will become so unstable that bankruptcies and defaults will force a major downturn in aggregate demand. Then the fiscal drag compounds the problem.

The solution is simple. The government balance has to be in deficit for the private balance to be in surplus for a stable external balance.

In terms of the slightly worsening current account deficit, we can interpret that as signifying an increased desire by foreigners to place their savings in financial assets denominated in Australian dollars. This desire means that that the foreign sector will allow us to enjoy more real goods and services from them relative to the real goods and services we have to export.

We note that exports are always a “cost” while imports are “benefits”. As long as there is a foreign desire for our financial assets, the real terms of trade will provide net benefits to Australian residents which manifests as the current account deficit. An external deficit presents no intrinsic problem despite views by the orthodoxy to the contrary.

In Japan, by way of contrast, the sectoral balances reveals that the private sector surplus increased on a par with the long-term increase in budget deficits. In other words, the persistent and substantial fiscal deficits financed the saving desires of the private sector and helped to maintain positive levels of real activity in the economy.


This stock-flow accounting structure conditions the way modern monetary theorists think. It is ground in the operational reality of the flow of funds within the economy.

So you cannot possibly say, for example, that the government can run indefinite surpluses while the current account is in deficit, and expect the domestic private sector to be able to save. It has to be that the only way the economy can grow in these circumstances is for the private domestic sector to be increasingly going into debt.

You may think that is fine and we can argue about that as a growth strategy and a reasonable way to manage the need for public goods. That is the debate part. But you cannot deny the former.

The problem is that the Austrians and mainstream economists do deny the accounting statements and demean the rest of their arguments as a consequence. Most of their solutions cannot “add up” in terms of the stock-flow relations.

Enough for now.

Bill Mitchell


7 responses to “Stock-flow consistent macro models Part 2

  1. Hi guys!

    I haven’t finished reading the article yet.

    But I believe there’s a little typo in the expression between brackets for “tax revenue net of government spending and payment of interest on bonds”: there’s a -1 at the end that might be wrong!

    When I finish the article, I’ll make some more comments.


    • Magpie, I can confirm it is supposed to be there. t-1 is right ~ interest is paid on bonds outstanding in private hands, not on the new increment of bonds in private hands. That is part of what links one period to the next in a stock-flow consistent module. v Bruce McFarling

  2. I found the discussion focused on Australia quite interesting and suggestive.

    For one, it explains the high levels of local private sector indebtedness and the (up to recently) tendency to negatively save (if that’s the expression).

    I wonder if this could not explain the overheated housing market, as well. For one, housing acquisition is counted in the system of national accounts as investment.

    But there is a subject that leaves me a bit uncertain: what about the terms of trade? I mean, with the coal and iron ore prices booms and industrial imports relatively cheap. How would this affect Australia (beyond the general notion that imports are benefits and exports are costs, that is)?

  3. Nathan Tankus

    Taking the more american protectionist route, i would argue that the loss of raw materials for the purpose of exporting represents a loss of resources that the private companies do not pay for and thus has costs external to the exporting (i say american protectionist because this was there argument against southern monocultures that ruined the soil in ways they didn’t have to pay for. they pushed this point so hard that they forced the creation of the department of agriculture to investigate it and quantify the damage done)

  4. Barry Thompson


    When there is net exports, are new deposits (and reserves) added to the balance sheets (and reserve accounts) of banks? In other words, does an export surplus add to the money stock?

  5. Barry Thompson

    To clarify my question further, it seems to follow from your accounting identity
    (S – I) = (G – T) + (X – M) that net exports must add deposits (and reserves) to the banking system.

    So how do central banks do this? Does each foreign country have a reserve account at the central bank like the home country’s treasury account? Does China have an account full of dollars at the US Fed?

  6. Barry, from my understanding, you are correct on all counts.

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