Tag Archives: sectoral balances


FRED Graph: US 🇺🇸 Sectoral Balances

Tracking the sectoral balances of a nation’s economy is a great way to build a narrative about its economic dynamics. It’s true, that an accounting identity doesn’t say much about causation. But they hint it and if we have a behavioural model around it, then we learn a lot more. It was used by Wynne Godley to highlight the predicament on the horizon in the 2000s.

The Federal Reserve Bank of St. Louis has a nice website FRED where you can create charts and even observe them when new data gets updated. Below is the U.S. sectoral balances chart. This is a static image file. For the dynamic chart, track the link above (the header of this page).

The blue line is the private sector net lending—its income less expenditure— which was in deficit and led to the crisis. The red line is the government’s deficit and the green line is the current account balance of international payments.

The Economist And Brad Setser On Current Account Surpluses

There is no branch of economics in which there is a wider gap between orthodox doctrine and actual problems than in the theory of international trade.

– Joan Robinson, The Need For A Reconsideration Of The Theory Of International Trade, 1973

Orthodox trade theory tells us that the “market mechanism” should work to resolve imbalances in the current account of balance of international payments. Although, the economics profession has conceded that Keynesianism is correct, it is still far from thinking clearly about international trade.

So it is a bit surprising that The Economist would say something unorthodox about this. In a recent article it complains about Germany:

The Economist On German Fiscal Policy And Trade Surpluses


This is the Post-Keynesian idea that surplus economies put a burden on deficit economies.

A fiscal expansion by the German government has the effect of raising domestic demand and imports and reducing the German current account balance of payments. This allows the rest of the world to grow both because of German imports and also because they are less “balance-of-payments constraint”.

Second, Brad Setser has a blog post on the current account surplus of the Republic of Korea (South Korea).

It’s impressive to see Setser get the causality right:

Fiscal policy alone doesn’t determine the current account (even if tends to be the biggest factor in the IMF’s own model). A boom in domestic demand, for example, would improve the fiscal balance and lower the current account surplus, just as a fall in private demand improves the current account balance while raising the fiscal deficit.

The current account balance, government’s budget balance and the private sector financial balance are related by an identity and sum to zero. But the identity itself shouldn’t be confused with causation.

The correct causation between the balances is between domestic demand and output at home versus abroad. This causality has been highlighted by Wynne Godley in the past. See more on this blog post by me here.


Simon Wren-Lewis On Wynne Godley’s Models

Simon Wren-Lewis has an article on his blog on stock-flow consistent/coherent models by Wynne Godley. Unlike other articles, this has a more engaging tone and isn’t dismissive.

This is a  good thing but it has the tone “Oh, there’s hardly anything new” about stock-flow consistent modeling and the sectoral balances approach. 🤦. To me this is highly inaccurate, to say the least. None of the models outside SFC models —with one exception—come anywhere close to the important question about what money is and how money is created. Even in the Post-Keynesian literature, while there are various non-mathematical approaches, there’s hardly anything that comes close. That important exception is the work of James Tobin as is summarized in his Nobel Prize lecture Money and Finance in the Macroeconomic Process. Except that Wynne Godley’s model greatly improve upon the deficiencies of Tobin’s approach.

The sectoral balances approach is a mini-version of stock-flow coherent modeling. Wren-Lewis seems to say there’s hardly anything great and don’t tell much. First, almost nobody was making a cri de coeur as much as Wynne Godley. Second, the approach makes it clear why a huge recession was coming. This is because US private expenditure was rising faster than private income and the US private sector was in deficit for long and the private sector was accumulating debt on a huge scale relative to income. It’s difficult to say when this would have reversed pre-2007, but had to reverse. Once this is reversed, i.e., when private expenditure slows relative to private income, so that the private sector goes into a surplus, output will fall as a result of a slowdown of private expenditure.

Moreover, the US economy had a critical imbalance in its trade with its current account balance of payments touching almost 6.5% at the end of 2005, hemorrhaging the circular flow of national income at a massive scale.

Wynne Godley’s argument was that because of the external imbalance, the US fiscal policy will be unable to expand output to full employment easily, once the US enters a recession. Hence, he proposed import controls for the United States.

None of anybody outside Wynne Godley’s circle came anywhere close to saying anything of this sort.

But these empirical analysis is a much more complicated discussion. At a simpler level, nobody has come closer to what stock-flow coherent models achieve. All we see is economists struggling with basic questions on how money is created, what role it plays and so on.

Wren-Lewis also criticises SFC models saying they have minimal behavioural hypothesis. Now, this is far from the truth. If you write stock-flow consistent models, which are more realistic, you’ll end up with having a lot of equations and parameters. Behaviour of each “sector” is articulated in these models. How money is created by the act of loan making by banks, to how households and firms accumulate assets and liabilities, to how firms making pricing decisions and how much they produce and how much households consume. In addition, the importance of fiscal policy is articulated: how governments make spending decisions, whether government expenditure can be thought of as exogenous and how in normal times—when politicians pay attention to how much the government’s deficit and debt it has—governement’s fiscal policy can be thought of as endogenous. And crucially, the supreme importance of the government’s finance in the financial assets/liabities creation process. While most economists stop at one time-step for the expenditure process, using stock-flow consistent models, you can see the full process. Moreover, the analysis highlights the correct direction of causalities. A good example is the direction of causation from prices to money.

I want to however highlight another important point. A lot about how the economy works can be understood without going too much into behaviour. Just national accounts, flow of funds and a minimal set of behavioural assumptions would be a great progress. The rest of the profession however struggles to even understand basic flow of funds. A lot can be understood because most of the times, economists are erring on basic accounting. Hence their story doesn’t add up and produces something completely unrelated to the real world. If only economists understood this, that’ll be a lot of progress. Stock-flow consistent models are rich in behavioral analysis but even without it, understanding flow of funds with a minimal set of assumptions is the right direction.

Stephen Roach, Accounting Identities And Behavioural Relationships

A well known economic identity states:

Snational = Inational + CAB

where Snational and Inational are national saving and national investment and CAB is the current account balance of international payments. In calculating national saving and investment, one adds saving and investment, respectively, of all resident sectors of the economy.

However, an accounting identity shouldn’t be confused with behavioural relationships.

Steven Roach is a good economist and it’s sad to see him confusing this. In a recent article for Project Syndicate titled America’s Trade Deficit Begins at Home, he uses this identity to conclude that if America wants to reduce her trade deficit, the solution is more saving.

Roach says:

What the candidates won’t tell the American people is that the trade deficit and the pressures it places on hard-pressed middle-class workers stem from problems made at home. In fact, the real reason the US has such a massive multilateral trade deficit is that Americans don’t save.

Total US saving – the sum total of the saving of families, businesses, and the government sector – amounted to just 2.6% of national income in the fourth quarter of 2015. That is a 0.6-percentage-point drop from a year earlier and less than half the 6.3% average that prevailed during the final three decades of the twentieth century.

Any basic economics course stresses the ironclad accounting identity that saving must equal investment at each and every point in time. Without saving, investing in the future is all but impossible.

A little thought on behavioural relationships tell a different story. The main causality connecting accounting identities is behaviour of demand and output at home and abroad. While it is true that by accounting identity, the U.S. current account balance will improve by more saving (such as households saving more, firms retaining higher earnings and government (both at the federal and state level) attempting to increase its saving tighten fiscal policy, it happens via a contraction of output.

Wynne Godley was one who stressed this before the crisis. In his paper The United States And Her Creditors: Can The Symbiosis Last? written with Dimitri Papadimitrou, Claudio Dos Santos and Gennaro Zezza, this is made clear:

A well-known accounting identity says that the current account balance is equal, by definition, to the gap between national saving and investment. (The current account balance is exports minus imports, plus net flows of certain types of cross-border income.) All too often, the conclusion is drawn that a current account deficit can be cured by raising national saving—and therefore that the government should cut its budget deficit. This conclusion is illegitimate, because any improvement in the current account balance would only come about if the fiscal restriction caused a recession. But in any case, the balance between saving and investment in the economy as a whole is not a satisfactory operational concept because it aggregates two sectors (government and private) that are separately motivated and behave in entirely different ways. We prefer to use the accounting identity (tautology) that divides the economy into three sectors rather than two—the current account balance, the general government’s budget deficit, and the private sector’s surplus of disposable income over expenditure (net saving)—as a tool to bring coherence to the discussion of strategic issues. It is hardly necessary to add that little or nothing can be learned from these financial balances measured ex post until we know a great deal more about what else has happened in the economy—in particular, how the level of output has changed

[boldening: mine]

This was pre-crisis from a few who were avowed Keynesians all their life! It’s unfortunate to see Steve Roach make an error even after so many years into the global economic and financial crisis. One should study Keynes seriously. While I am sure Roach appreciates the paradox of thrift, he forgets applying it to the analysis of United States of America’s trade deficits.

Nick ROKE, Thrift, And Hoarding

The new issue of ROKE is out and celebrates 80 years of The General Theory. Nick Rowe has a new paper in the issue titled, Keynesian Parables Of Thrift And Hoarding. Requires access. Nick has a post on his blog where he welcomes comments.


I argue that Keynes missed seeing the importance of the distinction between saving in the form of money (‘hoarding’) and saving in all other forms (‘thrift’). It is excessive hoarding, not excessive thrift, that causes recessions and the failure of Say’s law. The same failure to distinguish hoarding from thrift continues from The General Theory into the IS–LM model and into New Keynesian macroeconomics. On this particular question, economists should follow Silvio Gesell rather than John Maynard Keynes. The rate of interest in New Keynesian models should be interpreted as a negative Gesellian tax (that is, a subsidy) on holding money issued by the central bank.

In my opinion, a part of it, the distinction between what’s called “hoarding” and “thrift” above is not something which Keynesians haven’t considered. In fact, in the sectoral balances approach, it is net lending and not saving whose behaviour is more highlighted.

A sector’s or an economic unit’s saving is defined as its disposable income less consumption expenditure.

S = YD − C

On the other hand, a sector’s net lending is defined as its disposable income less expenditure.

NL = YD − C − I

These things are not as straightforward as they look. Here’s an example. I can be both a saver and borrower. 

Let’s say, I start with no assets/liabilities, earn $1mn in a year, pay taxes of $200,000, have consumption expenditure of $100,000 and buy a house worth $5m by borrowing $4.3m from a bank.

My saving is $700,000 and my net lending is minus $4.3 million [ = ($1mn − $200,000) − $300,000 − $5m].

Of course, the fact that I am a net borrower doesn’t make me poor. My house is worth $5m and I have a liability of $4.3m which implies my net worth is $700,000.

However, my liquidity is low. If tomorrow the economy collapses and I lose my job, I will be in a bad situation. In short, negative net lending (or a negative financial balance) of an economic unit or a sector contributes to financial fragility.

There’s another important point: even though I am a saver, my saving rate is 7/8, I have contributed hugely to aggregate demand. This can happen at a sectoral level as well. So perhaps this is the reason why Nick Rowe makes this distinction.

So if we were to blindly believe in Keynes, we would have concluded wrongly by just looking at the saving rate. But it is a matter of emphasis: economists make ceteris paribus arguments and I do not think Keynes didn’t understand this. He was perhaps holding everything else constant and changing the propensity to consume to highlight an important fact. But in real life ceteris is never paribus. What Keynes was arguing was that saving is not necessarily a good thing at the macro level.

Back to sectoral balances. Since, a sector’s (such as the household sector’s) negative net lending (or negative financial balance) adds to its financial fragility, this process will reverse. Private expenditure relative to private disposable income will fall. But this has an effect of being a drain on aggregate demand. And this can cause a recession.

Nick Rowe would have argued that it is the demand for money which caused a recession. Till here, it’s the same as argued above, because private expenditure falling relative to income is due to economic units trying to increase their liquidity. (There’s a “paradox” here: all units trying to reduce their fragility causes more fragility!).

There is however a difference: a sector’s or economic units’ demand for “money” can also be independent to income/expenditure and is more related to asset allocation between various kinds of financial assets. But here it cannot be said to cause a fall in aggregate demand and output. So a higher demand for money per se cannot be said to cause a recession.

As I was finishing writing this, JKH put up a comment at Nick’s blog saying Keynes understood it. I reproduce the comment below.


There’s no question that Keynes appreciated the distinction between thrift and hoarding:

GT Chapter 9

“The rise in the rate of interest might induce us to save more, if our incomes were unchanged. But if the higher rate of interest retards investment, our incomes will not, and cannot, be unchanged. They must necessarily fall, until the declining capacity to save has sufficiently offset the stimulus to save given by the higher rate of interest. The more virtuous we are, the more determinedly thrifty, the more obstinately orthodox in our national and personal finance, the more our incomes will have to fall when interest rises relatively to the marginal efficiency of capital. Obstinacy can bring only a penalty and no reward. For the result is inevitable.”

GT Chapter 13

“The concept of hoarding may be regarded as a first approximation to the concept of liquidity-preference. Indeed if we were to substitute ‘propensity to hoard’ for ‘hoarding’, it would come to substantially the same thing. But if we mean by ‘hoarding’ an actual increase in cash-holding, it is an incomplete idea — and seriously misleading if it causes us to think of ‘hoarding’ and ‘not-hoarding’ as simple alternatives. For the decision to hoard is not taken absolutely or without regard to the advantages offered for parting with liquidity; — it results from a balancing of advantages, and we have, therefore, to know what lies in the other scale. Moreover it is impossible for the actual amount of hoarding to change as a result of decisions on the part of the public, so long as we mean by ‘hoarding’ the actual holding of cash. For the amount of hoarding must be equal to the quantity of money (or — on some definitions — to the quantity of money minus what is required to satisfy the transactions-motive); and the quantity of money is not determined by the public. All that the propensity of the public towards hoarding can achieve is to determine the rate of interest at which the aggregate desire to hoard becomes equal to the available cash. The habit of overlooking the relation of the rate of interest to hoarding may be a part of the explanation why interest has been usually regarded as the reward of not-spending, whereas in fact it is the reward of not-hoarding.”

Being the supreme macro-accountant (the first one really), he would be totally in tune with the general stock/flow consistency theme of the post-Keynesians.

Hoarding is a stock/asset allocation of liquidity, interconnected with the determination of the interest rate, as he notes above. He correctly rejected the idea of the interest rate as being determined by an “equilibrium” of saving and investment. He maintained correctly that those two measures are continuously equivalent.

Recession dynamics are a flow phenomenon as he describes it, using reconciliation of income accounting at two different points in time.

The behavior of liquidity, hoarding, and the interest rate is stock behavior (including hoarding) within that saving flow dynamic (including thrift).

The Devil Is In The Detail

There are two ways in which the terminology “net lending” is used.

In national accounts, it is the difference between saving and investment for any economic unit or a sector. “− I”. It is the financial surplus.

Bankers and central bankers use “net lending” a bit differently. Here there is “netting” when redemptions are netted.  For example, suppose a bank lends 100 units in one period and for simplicity assume all 100 are redeemed. Also assume that it makes 110 units of loans in the next period. In this case, net lending is 10 units.

But these two shouldn’t be confused.

Steve Keen should perhaps understand that the devil is in the detail and if he is interested in making accounting models of the economy, he should improve his accounting.

In a recent Forbes piece, he says:

So if the private sector is to finance the government sector’s surplus, and if the economy is growing at the same time, then there has to be a net flow of new money created by the banking sector—part of which expands the non-banking public’s money stock, and part of which finances the government sector’s surplus. Therefore the banking sector has to “run a deficit”: new loans have to exceed loan repayments (plus interest payments on outstanding debt).

Call this net flow of new money NetLend.

[emphasis: mine]

In the scenario assumed, banks have a surplus because presumably their operations are profitable. In the absence of fixed capital formation by banks, their undistributed profits are their financial surplus. Banks are net lenders in the national accounting sense (and hence have a financial surplus not a deficit). They net lenders in bankers’ language because gross new loans exceed redemptions.

While it is not wrong redefine terminologies, Keen is doing a sectoral balance analysis where deficit/surplus has a different meaning.

In short, in a growing economy, if the government is in surplus, it is more likely that non-financial corporations and households together have a deficit or a negative financial balance. Gross new loans by banks exceeding gross redemptions does not imply banks have a deficit (i.e., a negative financial balance). It is of course not impossible for banks to have a deficit in such scenarios: consider for example, banks purchasing a lot of buildings for their offices. In that case, banks’ “− I”  may be negative.

A Clueless Sveriges Riksbank Prize Winner

The subject of money, credit and moneyflows is a highly technical one, but it is also one that has a wide popular appeal. For centuries it has attracted quacks as well as serious students, and there has too often been difficulty in distinguishing a widely held popular belief from a completely formulated and tested scientific hypothesis.

I have said that the subject of money and moneyflows lends itself to a social accounting approach. Let me go one step farther. I am convinced that only with such an approach will economists be able to rid this subject of the quackery and misconceptions that have hitherto been prevalent in it.

– Morris Copeland, inventor of the Flow Of Funds Accounts of the United States, in Social Accounting For Moneyflows, in Flow-of-Funds Analysis: A Handbook for Practitioners (1996) [article originally published in 1949]

So the news is that Eugene Fama shares this year’s Economics Nobel with Robert Shiller and Lars Hansen.

Instead of going into Fama’s main work, I thought I will point out Fama’s quackery on national accounts and flow of funds – which economists are supposed to know but is rarely the case.

In an article from 2009, Bailouts and Stimulus Plans, Fama again puts down fiscal policy in a rather comical way. Fama starts with the sectoral balances identity:

There is an identity in macroeconomics. It says that in any given year private investment must equal the sum of private savings, corporate savings (retained earnings), and government savings (the government surplus, which is more likely negative, that is, a deficit),

PI = PS + CS + GS   (1)

In a global economy the quantities in the equation are global. This means the equation need not hold in a particular country, but it must hold in the world as a whole.

There is so much muddle to start the analysis. The above is incorrect to start with because “private savings” automatically includes corporate savings. Perhaps this error is a typo but going through his analysis doesn’t support the hypothesis that he even knows the equation right. Incidentally government saving is not government surplus in standard terminology. He seems to think these are equal.

Another error in the above equation is that the left hand side should include government investment as well.

Anyway …

Fama continues:

Government bailouts and stimulus plans seem attractive when there are idle resources – unemployment. Unfortunately, bailouts and stimulus plans are not a cure. The problem is simple: bailouts and stimulus plans are funded by issuing more government debt. (The money must come from somewhere!) The added debt absorbs savings that would otherwise go to private investment.

There are so many incorrect things with this. First, there is a reverse causality in the saving/investment identity. Investment creates saving. Second, Fama seems to think that government deficit reduces private saving but the identity itself is suggestive of another interpretation. If I write it as (in the context of a closed economy):

S = I + G – T

where S is the private saving, I is private investment and G and T are government expenditure and tax receipts, respectively. It then becomes clear that government deficit – instead of reducing private saving, creates private saving.

Even more worrisome is his statement “the money must be somewhere” – as if the stock of money is an exogenously fixed quantity. A fiscal expansion (meaning higher governmen expenditure and/or decrease of tax rate) can increase the stock of money in two ways. First is direct – if there is a government deficit with the fiscal expansion and banks purchase a fraction of government debt, the stock of money increases. The second is via a rise in domestic demand which will lead to higher borrowing by the private sector from banks thereby increasing the money stock. Of course there are other effects too via the non-bank private sector asset allocation decisions etc.

Not going in much details for now as I write a lot about it and in any case there is Post-Keynesian monetary economics on this. My aim was to show how an economics Nobel Prize winner is clueless about basic economics! The prize is to be awarded to people who have made great contributions to society but we have an example of someone – Fama – who pushes fiscal contraction with clueless analysis of national accounts.

Erroneous Use Of The Sectoral Balances Identity

Andrew Lilico of The Telegraph takes issue with the arguments presented using the sectoral balances identity. The website describes him as:

Andrew Lilico is an Economist with Europe Economics, and a member of the Shadow Monetary Policy Committee. He was formerly the Chief Economist of Policy Exchange.

After interpreting the accounting identities in his own way, Lilico goes on to say:

Here’s where the argument goes wrong.  When we talk about “private sector deleveraging” what do we mean?  We mean things like households paying off loans to the bank, or corporates paying off bonds or other loans.  The vast, vast majority of such loans are loans private sector agents make to each other.  So for every pound reduction in borrowing made by one household or company, there is one pound fall in savings by other households and companies.  The net change in the indebtedness of the private sector as a whole, relative to other sectors (i.e. relative to the government or to foreigners) is zero.  Within the private sector, households could pay off all of their debts to each other, and that would (in an accounting sense) make no difference whatever to the net lending of the private sector as a whole to the government.

Unfortunately for him, his argument is erroneous at the most elementary level.

What did the financial crisis lead to? Before the crisis, in many advanced economies, private expenditure was rising relative to income and the difference was increasing. A sudden U-turn in this behaviour led to a fall in output and simultaneously increased the public sector deficit because of lower taxes caused by the fall in output.

Lilico’s argument seems to think of the budget deficit as exogenous – i.e., under the control of the government but a careful study reveals that this ain’t so. His argument is another example where accounting identities are misinterpreted as behaviour.

There are various other errors: Lilico confuses the terms borrowing and saving – as if they are exact opposites. Various intuitions go wrong when one applies it without a proper understanding of national accounts and I showed this in my post from last year for this particular case: Saving And Borrowing.

The most fundamental error of Lilico of course is that he holds output constant in his entire argument. When discussing a scenario with sectoral balances, it is also important to keep in mind the behaviour of output. Most economists who come across the sectoral balances approach err on this. Part of the reason why he errs on this – knowingly or unknowingly – is the chimerical neoclassical production function view of the world where output is determined by supply side factors.


Seems Lilico has been arguing with people in Twitter. Here is a Tweet from him:

This is confusing the two usages of the phrase investment in macroeconomics – investment as fixed capital formation and investment as allocation in financial assets! If you give your mother £1000, she can consume or have investment expenditures or allocate the remaining in financial assets.

Claims Economists Make

Economists struggle with simple things. Two examples.

National Saving, Trade Deficits etc.

In a blog article Has Anyone Heard of the Trade Deficit?, Dean Baker uses the sectoral balances identity to make a claim which is presented like a no-go theorem.

Baker says:

Fans of arithmetic (a tiny minority among DC policy types) like to point out that a large trade deficit implies negative national savings. In other words, if we have a trade deficit then by definition the United States as a whole has a negative saving rate.

This means that we either must have budget deficits (negative public savings) or negative private savings, or both. There is no way around this fact.

Baker confuses saving with saving net of investment – just like the Neochartalists. (Confuses S with S minus I)

Without proof, the sum of saving of a whole economy is given by

S = I + BP

where (here) S is the sum of the savings of all resident sectors of the economy – the “national saving”, I is the total investment expenditure of the resident sectors of the economy (i.e., both private and public) and BP is the current account balance of international payments.

So it is possible for an economy to have a trade deficit and hence a negative BP (although it’s not always the case that the trade deficit translates into a current account deficit) and still have I + BP positive if investment is sufficiently high. So an economy can have positive national saving with a trade deficit.

Of course it must be said that the persons he is attacking are wrong. The claim (of the persons he is criticizing) is that the United States should save more (by a reduction in budget deficits brought about by a tightening of fiscal policy and/or higher propensity to save of the private sector achieved in some way). This is illegitimate as such a policy will induce a recession in the United States. Via the paradox of thrift, an increase in the private sector propensity to save can lead to lower saving of the private sector. Investment will fall because of lower sales expectations and the recession in the United States caused by the fiscal tightening will most likely lead to a recession in the rest of the world reducing its exports so that the only thing achieved is higher world unemployment.

Debt/GDP Ratio

In a series of posts aimed at showing something, Randall Wray claims the following:

… To simplify, if the interest rate is higher than the economy’s growth rate, then the debt ratio rises continuously…

Of course he also claims that if g>r, the debt ratio stabilizes.

Now, the debt sustainability conditions relating the interest rate and the growth rate of output are misleading. I showed this two posts back, where I showed that the claim that the condition that g>r ensures stabilization of the public debt/gdp ratio is incorrect. The above quote claims the opposite and is equally erroneous and misleading.

An economy can have the growth rate lower than the interest rate and still not have an exploding debt ratio.

A standard error in such analysis is to treat the budget deficit as exogenous. 

Consider an economy without a strong balance of payments constraint and with inflation less of a trouble. A fiscal expansion brings about an increase in output and this has the effect of stabilizing the debt ratio in two ways: the higher output itself and an increase in tax revenues of the government due to higher output. The budget balance may go into primary surplus automatically even though the government may not be targeting this.

In other words, if r>g, the sequence dgiven by the relation

dt – dt-1 = λdt-1 – pbt

(where λ is equal to (r-g)/(1+g) and  dt is the debt/gdp ratio at the end of time period t and pbt is the primary budget balance of the government in the period) would seem to explode because of the first time on the right hand side. But higher output will automatically lead to a dynamics for pbensuring sustainability.

How this works was shown by Wynne Godley in an article The Dynamics Of Public Sector Deficits And Debts written in 1994 written by his co-author Bob Rowthorn in J. Michie and J. Grieve Smith (eds), Unemployment in Europe (London: Academic Press), 1994 pp. 199-206 and which was originally a paper to the UK Treasury around ’92-’93.

For a demand constrained economy:

… Note that the primary budget balance adjusts automatically so as the stabilise the debt to GDP ratio. This spontaneous adjustment occurs through induced variations in GDP. The government cannot directly determine the primary balance. It can only control r, θ and G, and once the time path of these is fixed as above, the variable Y will evolve so as to stabilise the ratio B/Y. If this ratio is too large, Y will grow rapidly and generate sufficient tax revenue to bring this ratio down.

There is a standard proposition that the government cannot permanently maintain a primary deficit if the interest rate is greater than the growth rate (r>g) … even if true, the statement can be misleading. In a demand-constrained economy, the level of Y relative to G will automatically adjust so as to produce a primary balance (deficit or surplus) to stabilise the ratio B/Y …

[Emphasis mine]

(θ is the tax rate in the model in above paper). Also see this post Wynne Godley And The Dynamics Of Deficits And Debts

It is counterproductive to go around making statements about the conditions on interest rate and the growth rate without qualifications and care and considering a situation/history and future scenarios.

There is one place where this condition is useful. Consider a balance of payments constrained economy. In studying the sustainability of the external debt of a country, one can conclude that if r>g (where r is the effective interest rate paid on foreign liabilities), then the debt dynamics will lead to an exploding debt even if the trade balance is held constant. Of course that doesn’t mean if r<g alone ensures sustainability.

Wynne Godley And The Dynamics Of Deficits And Debts

In a five-part series in his blog, Functional Finance and the Debt Ratio Scott Fullwiler claims that if the interest rate is held below the growth rate of output, sustainability of the public debt/gdp ratio is guaranteed in the sense that the ratio converges and does not keep increasing forever. This is erroneous and his conclusions are misleading.

Wolfgang Schäuble understands the connection between public finances and international competitiveness, although his solutions are all wrong. Heteredox economists should understand this connection as well!

Rather than write a detailed essay, I thought I should directly get to the point and pinpoint his errors. Of course, several Post Keynesians even before Fullwiler wrote his 2006 paper Interest Rates And Fiscal Sustainability (referred in his posts) have made this claim and this criticism applies to them as well.

While there are future scenarios, where growth improves the public debt/gdp ratio, it does not mean that all scenarios lead to a convergence. Fullwiler has examples in his posts where he shows how the convergence happens. But it doesn’t prove much.

Fullwiler’s error is a simple mathematical one. He sums the series for debt-sustainability equation and shows the the public debt/gdp ratio converges to

– pb/(g – r)

where pb is the primary balance/gdp ratio, g is the growth rate of output and r the interest rate. [notations are changed somewhat without any effect on conclusions]

This is a wrong result because it assumes that the primary balance is constant as a percentage of gdp. The series he sums need not converge if the primary balance in each period is different. One such scenario is when the deficit in each period is bigger than the deficit of the previous period. Fullwiler claims:

… in terms of convergence or unbounded growth of the debt ratio, as Jamie Galbraith put it, “it’s the interest rate, stupid!” since any level of primary deficit can converge if the interest rate is below the growth rate.

[italics and link in original]

This is repeated:

… More importantly, given an interest rate lower than GDP growth, any primary budget deficit will eventually converge …

Now this doesn’t make sense. The claim that “any” level of primary deficit can converge if the interest rate is below the growth rate is incorrect. For example, if we have primary balances pb0, pb1, pb2 and so on and each of them is growing sufficiently faster, the debt/gdp ratio is explosive even if interest rate is less than the growth rate of output. His result is valid if each of the balances pb0, pb1, pb2 … are equal to each other and not in general.

In other words, if g>r, the sequence dn given by the relation

dt – dt-1 = λdt-1 – pbt

where λ is equal to (r-g)/(1+g) need not converge for general values of pband only converges in special circumstances (if suppose the pbn are all equal or more realistic if there is a mechanism to bring the primary deficit into a surplus which may or may not be a discretionary attempt by the government.)


Nothing of the above is purely academic. So in what situation can the public debt explode?

Let us assume an open economy. Let us assume that a country’s exports is X0 and not growing because of its inability to increase its market share or because of limited demand in world markets due to deflationary policies adopted by the rest of the world. Or both.

If one imagines a scenario in which there is growth in output and hence income, imports rise as well in a world of free trade.  This implies the current account deficit explodes. While growth may work to improve the debt/gdp ratio, the current account deficits work to worsen the debt ratio. The net effect is that “growth” instead of improving the debt/ratio worsens it.

This can be seen if one remembers that the sectoral balances identity connects the public sector deficit and the current balance of payments. We have


where NAFA is the private sector net accumulation of financial assets, PSBR is the public sector borrowing requirement (the deficit) and BP is the current account balance of international payments.

Since the private sector typically wishes to have a positive NAFA (else there is another unsustainable process!), an exploding BP leads to an exploding PSBR if output grows much faster than exports. This implies the public debt/gdp grows forever and growth is not sustainable.

Now Fullwiler can potentially claim that the government can “simply credit bank accounts” and public debt/gdp and external debt/gdp rising forever is no cause for trouble but then why write a post claiming convergence of the ratios!

There is a diagram in the post which I modified below with a red line for a path for the sectoral balances. Is the claim that this line extrapolated leads to a stabilizing debt ratio?

[image updated]sf-p4-fig9-modified-corrected

Wynne Godley And Debt Dynamics

The above was pointed out by Wynne Godley in the 1970s. The following brings it out clearly. It is from an appendix to an article written by his co-author Bob Rowthorn in J. Michie and J. Grieve Smith (eds), Unemployment in Europe (London: Academic Press), 1994 pp. 199-206 and was originally a paper to the UK Treasury around ’92-’93

The main conclusions are as follows. Consider an economy in which neither inflation nor the balance of payments is a constraint on output, so that any permanent increase in demand leads to an equal and permanent rise in output. In such an economy, tax cuts or additional government expenditure are eventually self-financing. They lead to some increase in government debt, but not to an explosion, since this debt will ultimately stabilise. The factor stabilising the debt is the behaviour of output. Following a fiscal stimulus, output will rise and tax revenue will automatically increase. Moreover, the expansion will continue to the point where additional tax revenue is sufficient to halt government borrowing and stabilise the debt. In an inflation-constrained economy, the expansionary process will lead to an unsustainable inflation and the government will be compelled to half the expansion before tax revenue has increased sufficiently to stabilise the government debt. In a balance of payments constrained economy, the government debt will grow without limit because the output multiplier will be too small to generate the tax revenue required to stabilise government debt. The counterpart to expanding government debt will be an expanding national debt to foreigners.


Now this may sound as a pessimistic view for any individual nation or the world as a whole. The real problem is free trade – the most sacred tenet of the economics profession.