Spending chains and Sankey diagrams

by Alan Hutchison

Published on Matches in the dark 18th October 2018 · Updated 20th November 2020

Understand spending chains and you understand a fair chunk of Modern Monetary Theory. When the government spends into the economy it initiates a sequence of financial flows in the non-government sector. The first recipient of the spending is likely to re-spend some or all of it and subsequent recipients will do the same, and so on. That’s a spending chain.

At first glance it looks as if the money will bounce around the economy forever and if that were the case the government would have to stop spending or inflation would soon result. Fortunately, there are two things which stop the money being used indefinitely: tax and savings.

The best way to understand this is with the aid of a Sankey diagram.[1] Here’s an example:

What we see here are the financial flows which result from the government creating £1,000 and spending it into the economy. The best way to understand the diagram is to assume that money only exists in the form of serial-numbered cash and that the diagram tracks how £1,000 worth of freshly minted notes issued by government travels through the economy.

The state money enters on the left and flows rightwards, getting all sorts of stuff done along the way and generating income for households and firms. The recipients of the spending are represented by vertical bars — called ‘nodes’ in a Sankey diagram. The taller the node, the higher the income.

The diagram may look a bit complicated in the middle, but it’s the extremities we need to focus on and they are quite simple. The start and end of any collection of spending chains is always going to look very much like this one, no matter how complicated it gets in the middle and no matter how long the chains get.

The chains start as the government spending enters the economy on the left. Each chain ends (on the right) at one of two nodes: tax or savings. At any given moment in time, the money originally spent by the government can be in one of two states: it has either been taxed away and destroyed or it is waiting to be spent. It cannot be anything else.

The unspent money can be money which is intended to be spent soon (such as cash in a wallet) or money which won’t be spent for a while (such as savings in an ISA).

Our diagram illustrates a set of very short chains and only half of the unspent money is in the form of long-term savings. If we continued to follow the chains we would see more money taxed away and less in unspent money, but a greater proportion of the unspent money would be in long-term savings.

The important thing to note is that the sum of the two end points — tax and savings — exactly equals the initial government spending. In this case, £1,000 of government spending is matched by £432 in tax and £568 in savings and other unspent money. This is an example of an accounting identity: a financial relationship which is true by definition and is true whichever way you look at it.

If we extend the chain for a much longer period — a year, for example — then the middle section is going to get extremely complicated and will have many more nodes. But the end will still have just the two nodes. Furthermore, most of the money will have been taxed away by the end of the year and spending will have all but stopped. And the bit which hasn’t been taxed away will be in long term savings, rather than in wallets.

And if we extend the model even further by injecting £800 billion on the left (which is how much the state creates and spends into the economy each year) it’s going to get very complicated indeed. The diagram would have to include all 66 million people living in the UK and the 5.7 million businesses which operate here. It would also have to include all the credit extended by the financial sector and all the foreign entities which interact with the UK and its currency. So, all the loans we take out and all the stuff we import from China would have to be accounted for, as would the German car companies which accrue Sterling savings when we buy their products.

Crucially, this mammoth Sankey diagram would highlight the initial target of most government spending: the public sector. The result would be a graphic demonstration (in the literal sense) of how the UK economy depends on public sector spending.

Clearly, it would be foolish to try and draw such a diagram.[2] But if it were possible then there would still be only two nodes at the end: tax and savings. And at the end of the year more than 90% of the £800 billion would have been taxed away and destroyed, with the few percent that’s left being the amount that we (and the Chinese and the Germans) have added to our stock of Sterling savings.

So, you can see that the scary ‘budget deficit’, which is the difference between the amount that the government spends in a particular period and the amount that is taxed away, is just a pejorative term that the mainstream uses for the amount we add to our savings. The deficit is a flow of funds from government into non-government financial assets. Not so scary now, is it?

For a country like the UK, savings are created by government spending and cannot be created by anything else.

Before moving on, it’s worth seeing how long-winded a words-only version of the information contained in the diagram would be. Here’s a stab at it (feel free to skip this bit):

• The Government creates £1,000 out of thin air and spends it into the economy by paying Roger and Rita £400 each and Penny and Peter £100 each;
• These transactions and all subsequent transactions attract tax at a rate of 20%;
• Penny and Peter are poor. Of the £80 each has after paying £20 tax they are only able to add £10 to their Savings. They each spend their remaining £70 at Aldi;
• Roger and Rita are rich. They each save £100, pay £80 tax and spend £140 at Waitrose. They are also members of a Golf Club, where each spends £80;
• Aldi uses the £140 income from Penny and Peter to pay £20 each to two employees (Alice and Andrew) and purchase £60 worth of vegetables from Farmer Brown. After paying £28 tax, Aldi declares £12 as post-tax profit (which is just another name for corporate savings);
• Waitrose uses the £280 income from Roger and Rita to pay £15 each to four employees (William, Wanda, Wendy and Walter) and buy £140 worth of vegetables from Farmer Brown. After paying £56 in tax, Waitrose declares the remaining £24 as profit;
• The Golf Club has very few employees and it pays Outsourcing plc £100 to supply four workers. The Golf Club declares £28 as profit after it has paid £32 in tax;
• Outsourcing plc use the Golf Club payment to pay four zero-hours employees (Olga, Oscar, Owen and Olivia) £15 each. It pays £20 tax and the remaining £20 is declared as profit;
• Farmer Brown uses the payments from Aldi and Waitrose to pay four farm workers (Betty, Barbara, Bernard and Bob) £30 each. Brown pays £40 tax and she puts the £40 left over into her pension pot.
• Alice and Andrew, the Aldi employees, each pay £4 tax and at this stage in the spending chain have not spent any of their income. The unspent £16 is classed as savings (even although they may spend it quite soon).
• William, Wanda, Wendy and Walter, the Waitrose employees, each pay £3 tax and have unspent income (savings) of £12.
• Betty, Barbara, Bernard and Bob, who work for Farmer Brown, each pay £6 tax and have unspent income (savings) of £24
• Olga, Oscar, Owen and Olivia, the Outsourcing plc employees who work at the Golf Club, each pay £3 tax and have unspent income (savings) of £12.
• At the end of the chain £432 of the original government spending has been taxed away and £568 remains as savings and other unspent money. When added together they equal the original £1,000 government spending.

Anyone who doesn’t believe the accounting identity expressed in that last point should get out a calculator and tot up the numbers.

There’s much more that a Sankey diagram can tell us about the economy. For a start, it illustrates neatly a concept which appears in economics textbooks called the fiscal multiplier — the relationship between government spending and the resulting increase in national income. In our very limited model, the £1,000 worth of government spending has generated income for firms and households amounting to £2,160, giving a fiscal multiplier of 2.16.

There is much debate about the precise value of the multiplier, but one thing is certain: it is heavily dependent on the initial target of government spending. A recent research paper found that the average fiscal multiplier across the European Union is 1.6, but the fiscal multiplier for healthcare spending is 4.3.[3]

For spending on the military, the research found that the multiplier was a staggering −9.8. It’s a negative figure for defence spending because most of it is on imported equipment (imports do not add to national income). That and the fact that most defence equipment tends to lie idle (a good thing in terms of not killing people, but bad for the economy).[4]

Conversely, staff costs are the single largest area of spending for a healthcare system like the NHS and because most staff are not particularly well paid — nurses and cleaners, for example — all that government money is re-spent rather than saved.[5] That triggers millions of spending chains and gives a thumping great boost to the economy. That and the fact that the NHS keeps the UK workforce healthy and productive.

Most of the spending chains initiated by spending into the public sector result from spending on healthcare.[6] The NHS is the great engine which drives the UK economy.

Here’s one thing that recent Chancellors of the Exchequer never seem to mention: The fiscal multiplier engine has a reverse gear. Take £1 million out of the NHS and you take £4.3 million out of the economy. That’s what austerity is really about.

Two more textbook concepts are made visible by the diagram: the marginal propensity to save (MPS) and the marginal propensity to consume (MPC). These define the proportion of an increase in disposable income (after tax) a person is likely to either save or spend on consumption.[7] The MPC is the flip-side of the MPS: MPC = 1 − MPS.

The diagram indicates that there is inequality of MPS in the system because Rita and Roger (the two rich people) are able to save a greater proportion of their income than Penny and Peter (the two poor people).

The desire to save may be in all the textbooks, but they never follow the logic to a conclusion which shows the relationship between savings and the ‘deficit’. Explain this relationship to a mainstream economist and they will say that this is just another way of expressing the MPS and that there is ‘nothing new in MMT’.

A striking feature of the diagram is that it shows quite clearly that spending precedes taxation; that taxes do not fund spending; that all government spending is new money; that tax destroys money; and, most importantly, that government spending creates net financial assets in the non-government sector.

The perception of most politicians, commentators and the wider public is that none of this is true. Their beliefs are based on the existence of a feedback loop between tax and spending. Our Sankey diagram does not have a feedback loop because the feedback loop doesn’t exist in the real world.

There are, however, convoluted accounting structures which a lot of people interpret as evidence for tax and borrowing funding spending. But look what happens when we apply to our diagram the feedback loops implied by this thinking.

Admittedly, I have just plonked my original and very short spending chain diagram into this, so the proportion of tax to borrowing is way off. But the diagram still shows the absurdity of mainstream thinking and it should be quite clear that we have run into a chicken and egg situation. Which came first? The initial spending or the tax and borrowing?

There is also no mechanism here for the government to increase its spending and, just to stand still, the government would have to use all our savings, including all the unspent cash in our wallets.

The mainstream solution to the conundrum is to bring the financial sector into the picture and say that credit generates the tax which funds the government’s spending. But this doesn’t explain where savings come from because the actions of the financial sector cancel each other out somewhere in the middle of the diagram. All the assets created by banks, for example, are exactly matched by liabilities, all the loans create corresponding deposits, for every borrower there is a lender, and so on. All bank credit sums to zero.

The trouble with the ‘banks create all the money’ idea is that net financial assets cannot, in aggregate, come from bank loans. We have to pay off the loans (together with the interest they are subject to). We can’t save loans, but we can save government spending.

I have also built a few things into the spending chains which point to problems with the way the economy is structured. The most obvious is the inclusion of Outsourcing plc, the agency which provides workers for the Golf Club. For clarity, let’s redraw the diagram so that it only shows the spending chains which lead to Olga, Oscar, Owen and Olivia, the outsourced workers.

The problem with outsourcing

There are many problems with the outsourcing model and there is no need to rehearse them here. But there is one thing that most people don’t notice and which the diagram makes obvious: an extra £20 is removed from the system by taxation. It’s money which could have gone to the workers and because they are likely to be low paid (and pay little or no tax) it’s money they can keep. This highlights one of the problems with corporation tax.

Then there is the £20 profit the outsourcing agency extracts from the system. This is money which will likely go to shareholders and which could also have gone to the workers. If the Golf Club employed the workers directly there is every chance that each could be earning a £25 share of the original £1,000 government spending, rather than just £15.

There are also two hints about automation and efficient business models which I will look at in more detail another day. First, the supermarkets, Aldi and Waitrose, have very different business models and this is reflected in the diagram: Aldi has fewer staff per shop than Waitrose, but pays them much more (it’s the same for Lidl).[8] There are many reasons why Aldi and Lidl are doing so well and one of them is that they understand the proper role for automation: there are no self-service checkouts in Aldi; there are lots in Waitrose.

Second, Farmer Brown’s employees are paid very well and that’s because she, like Aldi and Lidl, understands automation. She has invested in agricultural automation and as a result is able to pay her workers a good wage. She has no need for cheap labour from Eastern Europe.

Sankey diagrams are great at visualising the relationship between spending, tax and savings, but they are not so good at providing a visual distinction between stocks and flows. It may be tempting to think that the start and end points represent stocks of money — that a stock of government money flows to a stock of tax and a stock of savings. The start and end points actually represent flows.

The total for tax, for example, is just the sum of all the tax which flowed out of the system during the period under investigation. The money which was taxed away ceased to exist at the moment it was taxed. Don’t think that the money still exists at the end of the diagram. The tax node is there simply as a mechanism for adding up all the financial assets which were destroyed.

Similarly, the savings node adds up all the financial assets which were created during the period. They flowed into and increased the existing stock of wealth held by the non-government sector, but that stock is not shown anywhere in the diagram. And because the deficit is the evil twin of savings, the deficit is also a flow — one which adds to the stock of government debt.[9]

As for government spending, it’s a flow too — one which was created out of thin air — and the government node tots up all the instances of the state injecting new money into the system. The diagram is not saying that the spending has to happen all at once and even the imaginary £800 billion Sankey monster described above would still have only one government node.

Having said all that, I wish there was a stock of tax — a temporary one — because I quite like the idea of the government saving up all the cash it taxes away from us and piling it up in Parliament Square for an annual Tax Bonfire each November. That would certainly silence the ‘taxes fund spending’ ideologues and is much more civilized than burning the effigy of a seventeenth century explosives expert.

Anyway, however you look at the economy, a model which fails to account fully for stocks and flows is faulty — it won’t be Stock-Flow Consistent.[10] As Michał Kalecki told Joan Robinson in 1936:

“I have found out what economics is; it is the science of confusing stocks with flows.”[11]

Modern Monetary Theory does not confuse stocks with flows.

Notes:

1. Sankey diagrams are named after Irish-born Matthew Henry Phineas Riall Sankey who used one in 1898 to map the energy flows in a steam engine. See Sankey Diagram, Wikipedia. They may look complicated, but are surprisingly easy to create using free online tools. My favourites are SankeyMATIC and Google Sankey Diagrams. If you paste the contents of this text file into SankeyMATIC you will get a close approximation to the diagram shown here.  If you are comfortable with Javascript, here is one built with Google Sankey. The nice thing about SankeyMATIC is that it understands Stock-Flow Consistency and will warn you if your numbers don’t add up.
2. A Sankey diagram would probably be the wrong approach because the standard implementations don’t handle reverse flows very well — Betty wouldn’t be able to buy anything from Aldi or Waitrose. A Chord Diagram would be a better solution. See Chord Diagram, Wikipedia.
3. See Does investment in the health sector promote or inhibit economic growth?, Aaron Reeves et al, 23 September 2013, Globalization and Health. In the interests of open debate, I feel I also need to point you to a very different conclusion from the Centre for Economic Performance at LSE which claims that the fiscal multiplier is zero for countries which, like the UK, have floating currencies (but high for those which peg their currency) and that the fiscal multiplier is zero for ‘high-debt’ countries. See How Big (Small?) are Fiscal Multipliers? [PDF], Ethan Ilzetzki et al, CEP Discussion Paper No 1016, October 2010, LSE.
4. However, focusing on fiscal multipliers may not take into account all the benefits to the economy of the research and development carried out under the guise of military spending. The US leads the world in many areas of technological development because of massive spending on subsidised R&D and it makes the spending more palatable to the public by hiding it in the military budget.
5. According the IFS ‘Pay is the single largest cost of delivering healthcare, accounting for around two thirds of NHS spending.’ See Securing the future: funding health and social care to the 2030s [PDF], Anita Charlesworth and Paul Johnson, May 2018, Institute for Fiscal Studies.
6. At around 19% of total government spending, healthcare is the biggest component of spending into the public sector. Assuming the 4.3 EU average healthcare multiplier applies to the UK, then the £148 billion spent on healthcare generates £611 billion in national income. The multiplier for education is much higher at 7.6, but as education spending is £42 billion it only generates £319 billion. Spending figures are for 2018-2019. See Table 6.4, Public Expenditure: Statistical Analyses 2018 [PDF], July 2018, HMT.
7. We’re assuming here that the amounts shown in the diagram don’t represent an individual’s total income. If they did then the diagram would be showing us the Average Propensity to Save and the Average Propensity to Consume.
8. See Aldi to become highest-paying supermarket in the UK…, 5 January 2017, Independent.
9. The ‘evil twin’ idea is amusing, but should be used with caution. The deficit is neither good nor bad.
10. See Stock-flow consistent macro models, Bill Mitchell, 8 September 2009.
11. Quoted by Joan Robinson. See Shedding Darkness, 1 September 1982, Cambridge Journal of Economics.