Tag Archives: transactions flow matrix

Income ≠ Expenditure?

I like Steve Keen. He is terrific in debunking economics! In a recent debate with Paul Krugman, Keen put Krugman on the defensive and exposed his weaknesses. Krugman obviously didn’t want to accept defeat and tried to escape with the help of comments in the comments section of Nick Rowe’s blog (that DSGE is not neoclassical – whatever!).

There are however some issues with Keen’s own methodologies. In a recent talk (video here), he claims that income is not equal to expenditure due to debt creation. Keen also claims in the video that Schumpeter and Minsky claimed that is the case.

Keen is right about an individual sector but not an economy as a whole when it is closed.

In the following I assume a closed economy – as does Keen. At least he doesn’t make any distinction and thereby his claim is a claim for a closed economy as well. So here is Keen’s claim:

Further he attributes this difference to discontinuities due to debt injections.

In the above Keen forgets that expenditure creates income.

There is no need for a claim that income is not equal to expenditure. In fact it is convenient to have them equal.

Wynne Godley and Francis Cripps wrote a nice book in 1983 named Macroeconomics. Here is from just the second page of Chapter 1: National Accounts:

It is extremely useful to choose definitions such that total income and expenditure in any year, month, day or second are identically equal to one another; they will be – because we choose to define them so that they are – two different ways of looking at the same process. We are only going to admit into the category of flows called income things which have an exact counterpart in the category of flows called expenditure. [footnote]

(with a footnote on qualifications for the case of an open economy).

Further in pages 27-29:

Although the definitions so far imply that the income of all individuals and institutions taken together equals their total expenditure on goods and services in each and every period, this need not be true of any particular person or institution …

… It is easy to understand that any one individual who does not spend all his or her income in a period will have more money left over at the end of the period. But we have chosen a system of definitions which ensures that total income in each period when summed across the whole economy equals total expenditure in the same period. It must therefore be the case that if some people or institutions are accumulating money or other financial assets, others are incurring debts on an exactly equal scale. In the economy as a whole the total increase in financial assets must always be equal in each period to the total increase in debt (financial liabilities).

But since the possibility of borrowing is included as a source of funds for spending, our formal representation of the budget constraint for any individual or institution including the government, is

Equation 1.4 simply says that any excess of income over spending must equal the acquisition of financial assets less the acquisition of debts. As this is true for all individuals it must also be true for the economy as a whole.

But since total national income equals total national expenditure (i.e., Y ≡ E) it must follow for the economy as a whole the change in financial assets must be equal to the aggregate change in debt, i.e.,


Back to Keen. He has this slide in this talk:

In the above, households consume by getting wages and going into debt. Hence households have their expenditure higher than income. Similar story for firms.

However, Keen forgets that consumption is income for firms and his accounting has black holes. The whole thing can be done right by creating a Transactions Flow Matrix, so that one is sure that nothing is missed out.

The reason Keen gets into paradoxes can be seen by looking at the following slide where he changes the definition of expenditure.

The right definition of expenditure does not include purchases of financial assets. For Keen if  a household purchases financial assets, it will be counted as “expenditure”. From the above slide, it can be seen that Keen’s definition of expenditure itself is different to begin with from standard ones and obviously he gets the paradoxical claim that Income ≠ Expenditure!

If Keen wants to do an empirical study of the rise in gross assets and liabilities, there is a systematic way to do this: for example see this Bank of England paper Growing Fragilities – Balance Sheets In The Great Moderation.

I won’t pursue this further except saying a few things.

I think Keen’s intuition is that households and firms incurred liabilities at an increasing scale before the financial crisis for both expenditures and purchases of financial assets and this led to increases in asset prices and hence capital gains and hence a feedback loop leading to debt-fuelled growth. Etc etc etc. There is a way to do this but changing definitions is not the right way.

Keen’s model will look accounting consistent (highly important) and more realistic (with no need to define aggregate demand = gdp + change in debt) if he uses some sort of econometric modeling in which Private Expenditure PX is dependent on many things – for example PX-1 so that income need not be equal to expenditure for the economy as a whole (as the time periods for which they are recorded are different) and there is some sort of econometric relation with change in debt.

Else one gets hodgepodge and/or endless redefinitions.

I think his “model” mixes identities, behaviour and plausible econometric relationships.

Below are some “endnotes”

Change in Inventories

“Change in Inventories” create some issues for “Y ≡ E”.  The right way is to have Expenditure equal Final Purchases plus change in inventories. As per Godley & Cripps (p 33):

Y ≡ E = FE + ΔI

Open Economies

Funnily, it is in the case of an open economy that for an economy as a whole, Income ≠ Expenditure! The difference between expenditure and income is equal to the increase in net indebtedness to foreigners.

GDP by Expenditure

Expenditure (of a resident sectors) used here shouldn’t be confused with the expenditure in “gdp by expenditure”. In the former, we include expenditures of residents while in the latter, the export component refers to expenditure of the rest of the world sector of goods and services produced by resident sectors.

Updated 7 Oct 2012 4:15pm GMT. 

Kalecki’s Profit Equation

In my post The Transactions Flow Matrix, I went into how a full transactions flow matrix can be constructed using a simplified national income matrix. Let us reanalyze the latter. The following is the same matrix with some modifications – firms retain earnings and there are interest payments.

FU is the undistributed profits of firms. From the last line we immediately see that

SAVh + FU – If – DEF = 0

or that

FU = If + DEF – SAVh

This is Kalecki’s profit equation which says among other things that firms’ retained earnings is related to the government deficit! The equation appears in pages 82-83 of the following book by Michal Kalecki but Google Books may not allow the preview of the pages!

In their book Monetary Economics, Wynne Godley and Marc Lavoie say this in a footnote:

Note that neo-classical economists don’t even get close to this equation, for otherwise, through equation (2.4), they would have been able to rediscover Kalecki’s (1971: 82–3) famous equation which says that profits are the sum of capitalist investment, capitalist consumption expenditures and government deficit, minus workers’ saving. Rewriting equation (2.3), we obtain:

FU = I+ DEF − SAVh

which says that the retained earnings of firms are equal to the investment of firms plus the government deficit minus household saving. Thus, in contrast to neo-liberal thinking, the above equation implies that the larger the government deficit, the larger the retained earnings of firms; also the larger the saving of households, the smaller the retained earnings of firms, provided the left-out terms are kept constant. Of course the given equation also features the well-known relationship between investment and profits, whereby actual investment expenditures determine the realized level of retained earnings.

The above can of course also be written as:

I = SAVh + SAVf + SAVg = SAV

if one realized that the retained earning of firms is also their saving:


Business accountants know the connection between retained earnings and shareholders’ equity and in our language – which is that of national accountants/2008 SNA – it adds to their net worth just like household saving adds to their net worth.

Assuming away capital gains, we know from many posts that:

Change in Net Worth = Saving

Another View: Where Do Profits Come From

(h/t Magpie) I found this paper Where Do Profits Come From: Answering The Critical Question That Few Ever Ask – published by The Jerome Levy Forecasting Center – which has the following diagram among others:

(click to expand)

Where do we find the undistributed profits in the Federal Reserve’s Flow of Funds Statistic Z.1?

In Table F.102, there’s an item called “Total Internal Funds”:

(click to expand)

Income And Expenditure Flows And Financing Flows

In the previous two posts, I went into a description of the transactions flow matrix and the balance sheet matrix as tools for an analytic study of a dynamical study of an economy.

During an accounting period, sectors in an economy are making all kinds of transactions. These can be divided into two kinds:

  1. Income and Expenditure Flows
  2. Financing Flows

Let’s have the transactions flow matrix as ready reference for the discussion below.

(Click for a nicer view in a new tab)

The matrix can easily be split into two – on top we have rows such as consumption, government expenditure and so on and in the bottom, we have items which have a “Δ” such as “Δ Loans” or “change in loans”. We shall call the former income and expenditure flows and the latter financing flows.

To get a better grip on the concept, let us describe household behaviour in an economy. Households receive wages (+WB) and dividends from production firms (called “firms” in the table) and banks (+FD_{f} and +FD_{b}) respectively) on their holdings of stock market equities. They also receive interest income from their bank deposits and government bills. These are sources of households’ income. While receiving income, they are paying taxes and consuming a part of their income (and wealth). They may also make other expenditure such as buying a house or a car. We call these income and expenditure flows.

Due to these decisions, they are either left with a surplus of funds or a deficit. Since we have clubbed all households into one sector, it is possible that some households are left with a surplus of funds and others are in deficit. Those who are in surplus, will allocate their funds into deposits, government bills and equities of production firms and banks. Those who are in deficit, will need funds and finance this by borrowing from the banking system. In addition, they may finance it by selling their existing holding of deposits, bills and equities. The rows with a “Δ” in the bottom part of transactions flow matrix capture these transactions. These flows will be called financing flows.

How do banks provide credit to households? Remember “loans make deposits”. See this thread Horizontalism for more on this.

This can be seen easily with the help of the transactions flow matrix!

The two tables are some modified version of tables from the book Monetary Economics by Wynne Godley and Marc Lavoie.

It is useful to define the flows NAFA, NIL and NL – Net Accumulation of Financial Assets, Net Incurrence of Liabilities and Net Lending, respectively.

If households’ income is higher than expenditure, they are net lenders to the rest of the world. The difference between income and expenditure is called Net Lending. If it is the other way around, they are net borrowers. We can use net borrowing or simply say that net lending is negative. Now, it’s possible and typically the case that if households are acquiring financial assets and incurring liabilities. So if their net lending is $10, it is possible they acquire financial assets worth $15 and borrow $5.

So the the identity relating the three flows is:


I have an example on this toward the end of this post.

I have kept the phrase “net” loosely defined, because it can be used in two senses. Also, some authors use NAFA when they actually mean NL – because previous system of accounts used this terminology as clarified by Claudio Dos Santos. I prefer old NAFA over NL, because it is suggestive of a dynamic, though the example at the end uses the 2008 SNA terminology.

While households acquire financial assets and incur liabilities, their balance sheets are changing. At the same time, they also see holding gains or losses in their portfolio of assets. What was still missing was a full integration matrix but that will be a topic for a post later. Since, it is important however, let me write a brief mnemonic:

Closing Stocks = Opening Stocks + Flows + Revaluations

where revaluations denotes holding gains or losses.

This is needed for all assets and liabilities and for all sectors and hence we need a full matrix.

We will discuss more on the behaviour of banks (and the financial system) and production firms some other time but let us briefly look at the government’s finances.

As we saw in the post Sources And Uses Of Funds, government’s expenditure is use of funds and the sources for funds is taxes, the central bank’s profits, and issue of bills (and bonds). Unlike households, however, the government is in a supreme position in the process of “money creation”. Except with notable exceptions such as in the Euro Area, the government has the power to make a draft at the central bank under extreme emergency, though ordinarily it is restricted. Wynne Godley and Francis Cripps described it as follows in their 1983 book Macroeconomics:

Our closed economy has a ‘central bank’ with two principle functions – to manage the government’s debt and to administer monetary policy. [Footnote: The central bank has to fund the government’s operations but this in itself presents no problems. Government cheques are universally accepted. When deposited with commercial banks the cheque become ‘reserve assets’ in the first instance; banks may immediately get rid of excess reserve assets by buying bonds.]. The only instrument of monetary policy available to the central bank in our simple system is the buying and selling of government bonds in the bond market. These operations are called open market operations. We assume that the central bank does not have the right to directly intervene directly in the affairs of commercial banks (e.g., to prescribe interest rates or quantitative lending limits) or to change the 10% minimum reserve requirement. But the central bank is in a very strong position in the bond market since it can sell or buy back bonds virtually without limit. This gives it the power, if it chooses, to fix bond prices and yields unilaterally at any level [Footnote: But speculation based on expectations of future yields may oblige the central bank to deal on a very large scale to achieve this objective.] and thereby (as we shall soon see) determine the general level of interest rates in the commercial banking system.

Given such powers, we can assume in many descriptions that the government’s expenditure and the tax rate is exogenous. However, many times, there are many constraints such as price and wage rises, high capacity utilization and low production capacity and also constraints brought about from the external sector due to which fiscal policy has to give in and become endogenous.

While I haven’t introduced open economy macroeconomics in this blog in a stock-flow coherent framework, we can make some general observations:

For a closed economy as a whole, income = expenditure. While it is true for the whole economy (worth stressing again: closed), it is not true for individual sectors. The household sector, for example, typically has its income higher than expenditure. In the last 15-20 years, even this has not been the case. If one sector has it’s income higher than expenditure, some sectors in the rest of the world will have its income lower than its expenditure. Many times, the government has its income lower than expenditure and we see misleading public debates on why the government should aim to achieve a balanced budget. When a sector has its income lesser than expenditure, it’s net lending is negative and hence is a net borrower from the rest of the world. It can finance this by borrowing or sale of assets. A region or a whole nation can have its expenditure higher than income and this is financed by borrowing from the rest of the world. A negative flow of net lending implies a net incurrence of liabilities – thus adding to the stock of net indebtedness which can run into an unsustainable territory. Stock-flow coherent Keynesian models have the power to go beyond short-run Keynesian analysis and study sustainable and unsustainable processes.

In an article Peering Over The Edge Of The Short Period – The Keynesian Roots Of Stock-Flow Consistent Macroeconomic Models, the authors Antonio C. Macedo e Silva and Claudio H. Dos Santos say:

… it is important to have in mind that it is possible to get three kinds of trajectories with SFC models:

  • trajectories toward a sustainable steady state;
  • trajectories toward a steady state over certain limits;
  • explosive trajectories.

The analysis of SFC models’ dynamic trajectories and steady states is useful, first because it makes clear to the analyst whether the regime described in the model is sustainable or whether it leads to some kind of rupture—either because the trajectory is explosive or because it leads to politically unacceptable configurations. In these cases, as Keynes would say in the Tract, the analyst can conclude that something will have to change and even get clues about (i) what will probably change (since the sensitivity of the system dynamics to changes in different behavioural parameters is not the same); and (ii) when this change will occur (since the system may converge or diverge more or less rapidly).


Note that Net Lending is different from “saving”. Say, a household earns $100 in a year (including interest payments and dividends), pays taxes of $20 and consumes $75 and takes a loan of to finance a house purchase near the end of the year whose price is $500. Assume that the Loan-To-Value (LTV) of the loan is 90% – which means he gets a loan of $450 and has to pay the remaining $50 from his pocket to buy the house. (i.e., he is financing the house mainly by borrowing and partly by sale of assets). How does the bank lending – simply by expanding it’s balance sheet (“loans make deposits”). Ignoring, interest and principal payments (which we assume to fall in the next accounting period),

His saving is +$100 – $20 – $75 = +$5.

His Investment is +$500.

His Net Incurrence of Liabilities is +$450.

His Net Accumulation of Financial Assets is +$5 – $50 = – $45.

His Net Lending is = -$45 – (+$450) = -$495 which is Saving net of Investment ($5 minus $500).

This means even though the person has “saved” $5, he has incurred an additional liability of $450 and due to sale of assets worth $45, he is a net borrower of $495 from other sectors (i.e., his net lending is -$495).

Assume he started with a net worth of $200.

Opening Stocks: 2010




Nonfinancial Assets


Liabilities and Net Worth


Net Worth



Now as per our description above, the person has a saving of $5 and he purchases a house worth $500 by taking a loan of $450 and selling assets worth $50. We saw that the person’s Net Accumulation of financial assets is minus $45. How does he allocate this? (Or unallocate $45)? We assume a withdrawal of $10 of deposits and equities worth $35. At the same time, during the period, assume he had a holding gain of $20 in his equities due to a rise in stock markets.

Hence his deposits reduce by $10 from $30 to $20. His holding of equities decreases by $15 (-$35 + $20 = -$15)

How does his end of period balance sheet look like? (We assume as mentioned before that the purchase of the house occurred near the end of the accounting period, so that principal and interest payments complications appear in the next quarter.)

Closing Stocks: 2010




Nonfinancial Assets


Liabilities and Net Worth


Net Worth



Just to check: Saving and capital gains added $5 and $20 to his net worth and hence his net worth increased to $225 from $200.

Of course, from the analysis which was mainly to establish the connections between stocks and flows seems insufficient to address what can go wrong if anything can go wrong. In the above example, the household’s net worth gained even though he was incurring a huge liability. What role does fiscal policy have? The above is not sufficient to answer this. Hence a more behavioural analysis for the whole economy is needed which is what stock-flow consistent modeling is about.

One immediate answer that may satisfy the reader now is that the households’ financial assets versus liabilities has somewhat deteriorated and hence increased his financial fragility. By running a deficit of $495 i.e., 495% of his income, the person and his lender has contributed to risk. Of course, this is just one time for the person – he may be highly creditworthy and his deficit spending is an injection of demand which is good for the whole economy. After all, economies run on credit. While this person is a huge deficit spender, there are other households who are in surplus and this can cancel out. In the last 15 years or so, however (before the financial crisis hit), households (as a sector) in many advanced economies ran deficits of the order of a few percentage of GDP. If the whole household sector continues to be a net borrower for many periods, then this process can turn unsustainable as the financial crisis in the US proved.

Now to the title of the post. Flows such as consumption, taxes, investment are income/expenditure flows. Flows such as “Δ Loans”, “Δ Deposits”, “Δ Equities” are financing flows. Income/expenditure flows affect financing flows which then affect balance sheets, as we see in the example.

Sources And Uses Of Funds

In a recent post, I went into what is called the Transactions Flow Matrix. This is used heavily in Stock-Flow Consistent Modeling of the whole economy. The underlying theme is “everything comes from somewhere and goes somewhere, and there are no black holes”.

I also mentioned about a Balance Sheet Matrix. What is it?

Sectors in an economy have assets and liabilities. Assets can be both financial as well as nonfinancial. Since nonfinancial assets are nobody’s liability, liabilities are financial. Very quickly, a balance sheet matrix is created by assigning a + sign to assets and a (-) sign to liabilities.

As per the System of National Accounts, all assets and liabilities are to be evaluated at market prices. According to 2008 SNA,

So a corporation or the government may have issued bonds at $100 but since the value fluctuates everyday and even during the day, it is possible that the bond price may reach $103. If it is the last day of the period for which the balance sheet is compiled, then the liability should be entered as $103, not $100.

We will have more to see in another post but let us just have a cursory look at an item called net worth. Since balance sheets should balance, we include this item in liabilities or rather call the right hand side of a balance sheet “Liabilities and Net Worth”. The term Net Worth has an intuitive appeal. If I have assets worth $100 and owe someone (say a bank) $10 and nothing more or less, my net worth is $90.

So let us quickly jump into the balance sheet matrix of a model economy.

In the previous post on the Transactions Flow Matrix, I had amalgamated the sectors Government and Central Bank into one, but now I have separated them so that there is higher clarity.

The reason I am writing this post is to stress the importance of signs. So in the above you will notice that households have a liability of L_{h} and hence appears with a negative sign. We shall see below however, that since loans are a source of funds, it will appear as a positive sign in the transactions flow matrix!

So households hold currency notes, deposits, bills and equities and these have counterpart in some other sector. And this should be the case because every financial asset is someone else’s liability. Also, from the matrix, the sum of net worths of all sectors (for a closed economy, at any rate) is equal to the value of the nonfinancial assets. This result isn’t surprising since financial assets cancel out with their counterpart liabilities.

We now jump to the transactions flow matrix – which I remade and added a lot of complications as compared to the previously related post The Transactions Flow Matrix

(Click to enlarge in a new tab)

These matrices are almost exactly similar to what appears in Wynne Godley and Marc Lavoie’s book Monetary Economics. 

The difference between the two matrices is that the balance sheet matrix records assets and liabilities at the beginning or the end of a period, whereas the transactions flow matrix records transactions during an accounting period.

In the previous post I had briefly stressed the importance of signs but now we have the balance sheet matrix as well ready, let me stress this again using a few lines from G&L’s book on the transaction flow matrix (page 40):

The best way to take it in is by first running down each column to ascertain that it is a comprehensive account of the sources and uses of all flows to and from the sector and then reading across each row to find the counterpart of each transaction by one sector in that of another. Note that all sources of funds in a sectoral account take a plus sign, while the uses of these funds take a minus sign. Any transaction involving an incoming flow, the proceeds of a sale or the receipts of some monetary flow, thus takes a positive sign; a transaction involving an outgoing flow must take a negative sign. Uses of funds, outlays, can be either the purchase of consumption goods or the purchase (or acquisition) of a financial asset. The signs attached to the ‘flow of funds’ entries which appear below the horizontal bold line are strongly counter-intuitive since the acquisition of a financial asset that would add to the existing stock of asset, say, money, by the household sector, is described with a negative sign. But all is made clear so soon as one recalls that this acquisition of money balances constitutes an outgoing transaction flow, that is, a use of funds.

So the government expenditure G has a minus sign because it is a use of funds and its sources are taxes, net issuance of bills and central bank profits.

The sources of funds for the production sector (abbreviated “firms”) is retained earnings (or undistributed profits, called FU), loans from banks and the issuance of equities and also sales (the consumption by households), government purchase of goods and investment itself because producers create tangible capital for themselves as a whole.

Now compare signs in the two matrices – equities are a source of funds for firms and hence has a positive sign in the transactions flow matrix but equities are also liabilities and hence the stock of equities appears with a negative sign in the balance sheet matrix.

Similarly, borrowing via loans are a source of funds for households and hence the positive sign in Table 2 while in Table 1 it appears with a minus sign.

For banks, making loans is a use of funds and taking deposits a source of funds. Hence minus and plus respectively in Table 2.

Also, the equities and loans in Table 2 are flows whereas in Table 1 they are stocks. Hence in Table 2, we have “Δ Loans” or change in loans, whereas in Table 1 its simply “Loans”.

Once we have a beginning of period balance sheet matrix and the transactions flow matrix, how do we construct the end of the period balance sheet matrix? I will leave this question for another post because I will have to introduce capital/holding gains and something called a full integration matrix. Before that I will have another post on real numbers taken from statistical releases to get more a intuitive feel for the balance sheet matrix.

The three matrices (the transactions flow matrix, the balance sheet matrix and the full integration matrix) go into the heart of “how money is created”. For this to be seen in detail, I will have to go into “monetary circuits” using transaction flows and that is the topic of yet another post. If you really understand how loans make deposits, the two tables should set you into a dynamical view of the whole process – a description completely different than the chimerical money multiplier model.

Updated: 21 April 2012 (Minor Typos Corrected)

The Transactions Flow Matrix

Why is GDP defined as C+I+G+… and how is it related to national income, expenditure etc and that of each sector of an economy such as that of households?

The following table (redrawn by myself) taken from the book Monetary Economics by Wynne Godley and Marc Lavoie gives an idea on how to go about measuring national income, product etc. The sample chapter (Contents, Chapter 1 & Index) from the publisher’s website has an introduction to the authors’ approach of studying Macroeconomics from a stock-flow consistent approach.

The table describes income and expenditures flows within an economy. Of course, as mentioned this is simplified and complications have to be added one by one. For example, there is no inventories, no external sector and households do not purchase a house etc. However, the above construction shows an easy way of building up and thinking about how funds flow between different ‘sectors’ of an economy. The reader who is new to this way of thinking should pay attention to the signs attached to each entry. For example, households receive wages and it is a source of funds for them and hence the positive sign. When they are consuming, they use funds and hence the first row in the table with the item consumption has a negative sign for households. For businesses, this a source of funds and hence positive. Another item which may be unfamiliar is the capital account of businesses. Firms purchase capital goods for their production and the sale of these goods comes from the same sector and hence one need for this column.

Even at this simplified form, there are a lot which are not known from the above table. What form does saving take? How does the government finance its excess of expenditure over income (i.e., deficit)? How do firms pay for wages and get funds to do the investment etc. To see this, we need a transactions flow matrix which I had discussed previously in my post Financial Crisis And Flow Of Funds from a not-so-pedagogic perspective. It is a foxy trick.

A few things before going into this. First notice that from the matrix,

C + I + G = Y = WB + F

So in our simplified example, gross domestic product is the sum of expenditures on goods and services and at the same time the sum of incomes paid for the production of goods and services.

Second, if you want the actual numbers (for the United States), the place to get this from the Federal Reserve Statistical Release Z.1. In particular, tables F.6 and F.7 and the hyperlink directly takes you to the table.

Back to our question on what form does saving take and how do firms finance their activities etc. Below is the table I made using TeX (and taken from the same book, Chapter 1)

The questions asked also lead us naturally to the introduction of the banking sector and its importance in the process of production, and this sector was missing in Table 1. So we can now clearly see what form saving takes. For households, this is in the form of currency notes, bank deposits, government T-bills and firms’ equities. Apart from various complications added, you may have noticed that profits are assumed to be part distributed and part retained. Firms hence finance investment by retained earnings, loans from banks and by issuance of equities, here. The government finances its deficit (i.e., excess of outlays over receipts) by issuing currency notes and T-bills. We have merged the Central Bank and the Federal Government into one sector “Govt”, for simplicity (which is also the case for Table 1). The behavioural aspects are something different and it should not be assumed that the government can “control” its deficit and that it can choose the proportion of financing in the form of currency notes and bills.

Needless to say, the above transactions flow matrix is a simplified one. For example, you may immediately notice that there is no interest payments on loans and bills yet.

It should be noted here that the entries in the table are flows and hence you may see a lot of Δs. The reader who is relatively new to this should not fail to observe the signs attaching each entry. The negative sign in the entry for deposits for households may be confusing at first, but the self-consistency of the whole construction forces the signs on these entries.

It is worth emphasizing that the fact that all rows and columns sum to zero and this makes the whole construction very appealing. When I was trying to get myself introduced to economics about 3 years back, I browsed around the internet and quickly came across the transactions flow matrix – exactly what I was looking for!

This construction greatly simplifies visualizing flow of funds as compared to the Blue Book way of doing it. The following is the 2008 SNA way of maintaining national accounts and there is some additional effort one needs to visualize this without the usage of a transactions flow matrix!

(click to enlarge)

Updated: 21 April 2012 (Minor Typos Corrected)

Z.1, Q3-2011

The Federal Reserve released the Flow of Funds Accounts of the United States today.

The Flow of Funds Accounts provides one of the best snapshot of an economy. In an article appropriately titled ‘No one saw this coming’ – or did they? (see the full paper here), Dirk Bezemer correctly recognizes that the Economics profession’s ignorance of Flow of Funds had a big role to play in its inability to see a crisis coming. Bezemer says

We economists – and the policymakers who rely on us – ignore balance sheets and the flow of funds at our peril.

Of course, as Bezemer points out, there were exceptions. Post Keynesians were always aware of the flow of funds because monetary economy is a natural starting point in their theory. Wynne Godley and Marc Lavoie wrote a book (my favourite!) Monetary Economics: An Integrated Approach To Credit, Money, Income, Production and Wealth, Palgrave Macmillan, 2007, to unify Post Keynesian theory and the flow of funds approach, perhaps improving the presentation of the latter using something called the “transactions flow matrix”.

In my opinion, nobody even came close to Wynne Godley in not only predicting the crisis but the warning about the difficulties in resolving it.

One notable highlight of today’s Z.1 release was that

Household net worth—the difference between the value of assets and liabilities—was $57.4 trillion at the end of the third quarter, about $2.4 trillion less than at the end of the previous quarter.

A lot of readers will know about sectoral balances. How do we get that from Z.1? Table F.8 gives “Net Lending” of each sector of the economy. The difference in a sector’s income and expenditure is it’s “Net Lending”.

(click to expand, and click again to expand)

Before the crisis, the private sector had its income lower than expenditure and was financing the difference by borrowing from the other sectors. As the crisis hit, private sector expenditure retrenched – so you can see how the private sector has become a net lender from being a net borrower before the crisis. Because of this, the government’s borrowing increased from (line 49) $408.1bn in 2007 to $1,471.7bn in Q3 2011 (annualized). It was also due to a relaxation of fiscal policy during the crisis, in order to stimulate demand. The expenditure of the United States as a whole is higher than its income, and the difference is the current account deficit. This is financed by net borrowing from foreigners (line 42) – which was $446.7bn in Q3 2011 (annualized). This deficit was $715.9bn in 2007, bleeding demand at a massive scale from the US economy.

There are two more tables I see closely. The first is the net income payments from the rest of the world, which surprisingly remains positive, leading to a lot of literature about “dark matter”. (More on that some other time). This, according to the Z.1 is the “net receipts from foreigners of interest, corporate profits, and employee compensation”.

 The Levy Institute has been tracking this since 1994. Here’s a latest graph (from their March 2011 analysis)

There are discrepancies between BEA and Fed data. The other table which I rush to check, whenever the flow of funds data is released is the United States’ net indebtedness to the rest of the world – L.107:

which at the end of Q3 was $3,616bn, or 24% of GDP.

There’s a new table – L.108, Financial Business – which actually appeared first time in the previous release (Q2). This sector had $64,299bn in assets and $60,457bn of liabilities at the end of Q3!

Of course, I look at all the tables at some time or the other. Highly recommended.

Financial Crisis And Flow Of Funds

Marc Lavoie forwarded me the European Central Bank’s Monthly Bulletin, October 2011 which has a section on TARGET2 and the European monetary system. I have had good discussions with him on emails to nail the TARGET2 operations so it is good to see the conclusions being verified in publications. I am waiting to write a long blog post on TARGET2 and trying to collect sources I can quote/link and I came across a section on flow of funds in the same article. It appears on page 99 (page 100 of the pdf) and is titled The Financial Crisis In The Light Of Euro Area Accounts: A Flow-Of-Funds Perspective. 

The article has this chart which will be very familiar to readers because it has been in the Levy Institute’s Strategic Prospects since many years.

There are some differences in terminologies. Wynne Godley (and Francis Cripps) started using NAFA (Net Accumulation/Acquisition of Financial Assets) to denote a sector’s surplus in the 1970s and Levy Institute has continued using this. Modern national accountants use Net Lending (by a sector) and split this into Net Acquisition of Financial Assets and Net Incurrence/Acquisition/Increase of/of/in Liabilities and take the difference. Levy’s authors also use Net Lending but as Net Lending to a Sector – e.g., Net Lending to Households.

The article also presents this table (termed Transactions Flow Matrix by Wynne Godley – his greatest trick)

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and has this description:

The sectoral accounts present the accounts of institutional sectors in a coherent and integrated way, linking – similar to the way in which profit and loss, cash flows and balance sheet statements are linked in business accounting  – uses/expenditure, resources/revenue, financial flows and their accumulation into balance sheets from one period to the next.To this effect, all units in the economy are classified in one of the four institutional sectors (i.e. households, non-financial corporations, financial corporations and general government). Their accounts are presented using identical classifications and accounting rules (those of ESA 95), in a manner such that each transaction/asset reported by one unit will be symmetrically reported by the counterpart unit (at least in principle). Accordingly, the sectoral accounts present the data with three constraints: each sector must be in balance vertically (e.g. the excess of expenditure on revenue must be equal to financing); all sectors must add up horizontally (e.g. all wages paid by sectors must be earned by households); and transactions in assets/liabilities plus holding gains/losses and other changes in the volume of assets/liabilities must be consistent with changes in balance sheets (stock-flow consistency). The sectoral accounts are commonly presented in a matrix form, with sectors in columns and transactions/instruments in rows, with horizontal and vertical totals adding up (see the example in the table).

The first five rows of the table show the expenditure and revenues of each of the sectors (broken down into types of expenditure/revenue). In row 6, the difference between revenue and expenditure (the surplus/deficit) is shown.

The notions of revenue and expenditure are close to, but generally less encompassing than, the more traditional national account concepts of resources and uses. Income can then be defined as revenue (except capital transfers received) minus expenditure other than final consumption and capital expenditure (capital formation and capital transfers paid). For corporations, income corresponds to retained earnings. Savings is the excess of income over final consumption.

Surpluses/deficits are then associated with transactions in financial assets and liabilities in each sector. This is shown in rows 7 to 10. The bottom part of the table shows the stocks of assets and liabilities, which result from the accumulation of transactions and other flows. This table is extremely simplified (e.g. omitting an explicit presentation of the stock of non-financial assets).

The excess of revenue over expenditure is the net lending/net borrowing (i.e. financial surplus/ deficit), a key indicator of the sectoral accounts. Typically, a household’s revenue will exceed its expenditure. Households are thus providers of net lending to the rest of the economy. Non-financial corporations typically do not cover their expenditure by revenue, as they finance at least part of their non-financial investments by funds from other sectors in addition to internal funds. Non-financial corporations are thus typically net borrowers. Governments are also often net borrowers. If the net lending provided by households is not sufficient to cover the net borrowing of the other sectors, the economy as a whole has a net borrowing position vis-à-vis the rest of the world. Deviations from this typical constellation were apparent in several euro area countries before the crisis, in particular, with extremely elevated residential investment that resulted in households becoming net borrowers (as has been the case in the United States).

The adding-up constraints in the accounts require that any (ex ante) increase in the financial balance of one sector is matched by a reduction in the financial balances of other sectors. The accounting framework does not, however, indicate by which mechanism this reduction will be brought about, or which mechanisms are at play. The EAA makes it possible to track changes in net lending in the different sectors of the economy. It also specifies the financial instruments affected and shows how the transactions and valuation changes leave a lasting effect on the balance sheets of the sectors.

The article is worth a read.

The Bank of England also had a similar article recently but before: Growing Fragilities – Balance Sheets In The Great Moderation by Richard Barwell and Oliver Burrows and quotes the work of G&L (Godley and Lavoie). It also has a similar matrix as the ECB’s article.

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Godley and Lavoie build a series of closed accounting frameworks based on the system of National Accounts, which encompass: the standard national income flows, such as wages and consumption; the counterpart financing flows, such as bank loans and deposits; and stocks of physical and financial assets and liabilities. This framework lends itself to representation in a set of matrices. The first matrix captures flow variables (Table A.1). The columns represent the sectors of the economy and the rows represent the markets in which they interact. The matrix has two important properties. Each sector’s resources and uses columns provide their budget constraint — the sums must equal to ensure that all funds they receive are accounted for. And each row must also sum to zero, to ensure that each market clears — that is, the supply of a particular asset must be matched by purchases of that asset, to ensure that no funds go astray.

The table can usefully be split in two, with the top half covering the standard income and expenditure flows and the bottom half covering financing flows. The two halves of the table are linked together by each sector’s ‘net lending balance’, or ‘financial surplus’. The net lending balance can be used to summarise each sector’s income and expenditure flows as the difference between the amount the sector spends on consumption and physical investment and the amount that it receives in income. This difference must be met by financing flows — either borrowing or the sale of financial assets. In national accounts terminology, a sector’s net lending balance (NL) must equal its net acquisition of financial assets (NAFA) less its net acquisition of liabilities (NAFL). Across sectors, the net lending balances have to sum to zero, as all funds borrowed by one sector must ultimately come from another.

While it is useful to split the table for accounting purposes into income and expenditure flows and financing flows, it is important to note that the acquisition of financial assets and liabilities is not necessarily determined purely by imbalances between income and desired expenditure. Sectoral balance sheets can adjust for other reasons. Agents may want to borrow money to purchase assets, simultaneously acquiring financial assets and liabilities. And on occasion agents may want to shrink the size of their balance sheets, selling off financial assets to pay off financial liabilities. Finally, some agents may default on their debt obligations, which will involve a revision in the financial assets and liabilities of both debtor and creditor. At an aggregate level, simultaneous expansion of a sector’s assets and liabilities invariably represents one set of underlying agents taking on assets whilst the other takes on liabilities. The household sector provides an important example. If a young household takes a mortgage to buy a house from an old household, the sector in aggregate simultaneously acquires a liability (the young household’s mortgage) and an asset (the deposit created for the young household to pay to the old household).

All of these activities — leveraging up, deleveraging and default — involve NAFA and NAFL moving in lockstep. The net lending identity still holds: the gap between income and expenditure determines the difference between NAFA and NAFL. But the absolute size of the NAFA and NAFL flows is determined by agents’ actions in financial markets. The second table captures the balance sheet positions of each sector. The balance sheet matrix is updated over time using data on the acquisition of assets and liabilities from the transaction flows matrix, and revaluation effects to asset positions. Proceeding in this manner, balance sheets always balance across sectors, flows of funds are always accounted for over time and the impact of flows of funds on balance sheets is always recorded.

Again, good article!

The first time a proper transactions flow matrix appeared was in a 1996 Levy institute paper by Wynne Godley:  Money, Finance And National Income Determination – An Integrated Approach.

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James Tobin et al. had something similar – almost but not quite in A Model Of US Financial And Nonfinancial Economic Behavior :

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