The first rule of Post-Keynesian Economics is: You do not talk make accounting mistakes. The second rule of Post-Keynesian Economics is: You do not talk make accounting mistakes.
– Anonymous.
Jason Smith—who is a physicist—but writes a blog in Macroeconomics, wonders how equations in the simplest stock-flow consistent model given in the textbook Monetary Economics written by Wynne Godley and Marc Lavoie make any sense from a dimensional analysis viewpoint.
He says he
seem[s] to have found a major flaw.
He sees the equation:
ΔH = G – T
and wonders where the time dimensions are. For, H is the stock of money and hence has no time dimension, whereas the right hand side has flows and has time dimensions of inverse of time. For example if the US government spends $4 tn in one year, G is $4 tn/year.
In continuous time, the above equation is:
dH/dt = G – T
So how are these two equations the same?
Perhaps, Jason is not familiar with difference equations. He instead seems to prefer:
τ·ΔH = G – T
Well that’s just wrong if τ is anything different from 1, as a matter of accounting.
Now moving on to time scales, it is true that in difference equations some time scale is implicit. But it doesn’t mean the methodology itself is wrong. Many physicists for example set all constants to 1 and then talk of numbers which are dimensionless.
So if a relativist sets “c=1”, i.e, the speed of light to 1, all velocities are in relation to the speed of light. So if somebody says the speed is 0.004, he/she means the speed is 0.004 times the speed of light.
But Jason Smith says:
Where does this time scale come from over which the adjustment happens? There is some decay constant (half life). It’s never specified (more on scales here and here). If you think this unspecified time scale doesn’t matter, then we can take Δt →lp and the adjustment happens instantaneously. Every model would achieve its steady state in the Planck time.
That’s not true. String theorists for example set the parameter α’ = 1. But nobody ever claims that macroscopic adjustments happen at Planckian length scales or time scales.
Coming back to economics, there’s nothing wrong in
ΔH = G – T
There’s an implicit time scale yes, such as a day, or a month, or a year, or even an infinitesimal. But parameters change accordingly. So in G&L models we have the consumption function
C = α1 ·YD + α2 ·W
where C is household consumption, YD, the disposable income and W, the household wealth.
Let’s say I start with a time period of 1 year for simplicity. α2 might be 0.4. But if I choose a time period of 1 quarter, α2 will correspondingly change to 0.1. In English: if households consume of 4/10th of their wealth in one year, they consume in 1/10th one quarter.
So if we were to model using a time scale of a quarter instead of a year, α2 will change accordingly.
But the equation
ΔH = G – T
won’t change because it is an accounting identity!
It’s the difference equation version of the differential equation:
dH/dt = G – T
Physicists can pontificate on economic matters. I myself know string theory well. But boy, they shouldn’t make mathematical errors and embarrass themselves!
In other words, accounting identities can be written as accounting identities in difference equations. What changes is values of parameters when one chooses a time scale for difference equations.
Wynne Godley’s model is touched by genius. In fact according to one of the reviewers of Monetary Economics, Lance Taylor says that it is out of choice that Wynne Godley chose a difference equation framework. They can be changed to differential equations and we’ll obtain the same underlying dynamics.
Godley has always preferred to work in discrete time, responding to the way the data are presented.
Question: is the equation ΔH = G – T consistent with dimensional analysis?
Answer: Yes. H is the stock of money at the end of previous period. ΔH is the change in stock of money in a period. G and T are the government expenditure and tax revenues in that period. So H, ΔH, G and T have no times dimensions in difference equations. All are in the unit of account. Such as $10tn, $400bn, $4 tn, $3.6tn. Time dynamics is captured by model parameters.
In G&L’s book Monetary Economics, in Appendix 3 of Chapter 3, there’s a mean-lag theorem, which tells you the mean lag between two equilibrium (defined as a state where stock/flow ratios have stabilized):
it is:
[(1 − α1)/α2 ]· [(1 – θ)/θ]
where θ is the tax rate.
So, in the model, assuming a value of 0.6 for α1, 0.4 for α2, and 0.2 for θ we have the mean-lag equal to 4.
Let’s assume that time period is yearly. This means the mean lag is 4 years.
If instead, we were to use quarterly time periods, α2 would be 0.1 and the mean lag evaluates to 16, i.e., sixteen quarters, which is 4 years, same as before.
So there is really no inconsistency in stock-flow consistent models.
tl;dr summary: In difference equations, there’s nothing wrong with equations such as ΔH = G – T. It is an accounting identity. By a choice of a time scale, one implicity chooses a time scale for parameter values. What’s wrong? Jason Smith would obtain the same results as the simplest Godley/Lavoie model if he were to work in continuous time and write equations such as dH/dt = G – T. I will leave it to him as an exercise!
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:
Income and Expenditure Flows
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:
NL = NAFA – NIL
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:
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.
… 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).
Example
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
$
Assets
200
Nonfinancial Assets Deposits Equities
0 30 170
Liabilities and Net Worth
200
Loans Net Worth
0 200
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
$
Assets
675
Nonfinancial Assets Deposits Equities
500 20 155
Liabilities and Net Worth
675
Loans Net Worth
450 225
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.
There are two new books in honour of Wynne Godley and they are out now
The first one – edited by Marc Lavoie and Gennaro Zezza – has selected articles and papers by Wynne Godley, and carefully chosen.
It’s available at amazon.co.uk, but not yet on amazon.com
Here’s the book’s website on Palgrave Macmillan. The book also contains the full bibliography of Godley’s papers, books, working papers, memoranda (such as to the UK expenditure committee), magazine/newspaper articles, letters to the editor etc.
Here’s a picture I took of Marc at Levy Institute in May when he was deciding on the cover.
The is second book written in honour of Wynne Godley contains proceeding of the conference held in May at the Levy Institute (the same place the above photograph was taken)
The death of Wynne Godley silences a forceful and very often critical voice in macroeconomics. Wynne’s own strong view, that although his work was representative of the non-mainstream Keynesian approach to economics and especially economic policy was important nevertheless, has been confirmed time and time again as evidenced in the fortunes of the UK, US and Eurozone economies. His writings, reflecting the sharpness of his mind and intellectual integrity, have had a considerable impact on macroeconomics and have aroused the interest of scholars, economic journalists and policymakers in both mainstream and alternative thought. In a review of Wynne’s last book with Marc Lavoie (2007), Lance Taylor had this to say: ‘Wynne’s important contributions are foxy – brilliant innovations… that feed into the architecture of his models’
I also like Wynne’s stand on the current account imbalance of the United States:
Bibow finds that Godley’s diagnosis of the looming economic and financial difficulties ahead of their occurrence was prescient with regard to US domestic developments – a theme that came up in the chapters by Wray and Galbraith. But Bibow takes issue with Wynne’s assessment of the US external balance being unsustainable. He notes that the US investment position and income flows are more or less in balance and he attributes this phenomenon to the safety of the US Treasury securities and the dollar functioning as the reserve currency.
Dimitri then says
Even if this is so, it cannot continue indefinitely, Wynne would have replied.
Kevin O’Rourke of Oxford University has a post on Project Syndicate, correctly titled A Summit to the Death, in which he nicely summarizes the recent EU “summit to end all summits” held at Brussels. He says
With this in mind, the most obvious point about the recent summit is that the “fiscal stability union” that it proposed is nothing of the sort. Rather than creating an inter-regional insurance mechanism involving counter-cyclical transfers, the version on offer would constitutionalize pro-cyclical adjustment in recession-hit countries, with no countervailing measures to boost demand elsewhere in the eurozone. Describing this as a “fiscal union,” as some have done, constitutes a near-Orwellian abuse of language.
As, FT Alphaville put it appropriately, “Do you believe in Merkels?”
It’s a dark age for Macroeconomics, as Paul Krugman put it – except for a few like Stephen Kinsella (from the Univesity of Limerick, Ireland), who is taking up the challenge of making stock-flow coherent models more practical and using them to come up with policy proposals, scenarios under different policies, etc for the Irish economy. Here’s an interview by INET
This blog post is about the Great Recession, the imbalances which led to it, the use of Keynesian principles by governments of all nations to prevent a deep implosion and how and why the Keynesian mini-revolution didn’t last long. Suddenly, nobody is asking Are We Keynesians Now? and the economics profession has lost lines of communications with governments. Like a Guns ‘N Roses song that goes
What we’ve got here is failure to communicate, some men you just can’t reach.
Will it take another crisis to revive Keynesianism? While, the author is a die-hard Keynesian, he believes that fiscal policy alone cannot resolve the crisis. Governments are aware of this but government officials give only vague replies when taken to task.
The blog in general is/will be about an approach which has roots in the New Cambridge approach to studying economies and how it can be applied to find political economic solutions to put the world in a sustainable path of growth and achieve full employment. It is also about about the Post-Keynesian theory of Endogenous Money and the Stock Flow Coherent Approach. Using the blogosphere as a medium to satiate my crave to put forth my understanding of how economies work, I aim to make a difference. Post-Keynesians emphasize that monetary economies function differently from the chimerical neoclassical story and money cannot but be endogenous. I plan to take the reader into how the monetary and financial system works, the role of various sectors (individuals and institutions) in a demand-led process, their behaviour and what can be done to reverse sectoral imbalances that have built up.
Why Keynesianism was short-lived in the Great Recession is a difficult question to tackle in a single post. Before the 1970s, for many years, the world was run using Keynesian principles and suddenly it fell apart. To me, the situation right now is very reminiscent of what went on during the 70s and the 80s (I am not that old!).
Francis Cripps wrote this brilliantly in a 1983 article What Is Wrong With Monetarism [1]
The conclusion which has to be drawn is that, if a modern economic system is to function properly, a mechanism is required for the management of aggregate demand. Now it happens that the need for management of aggregate demand within a closed national economy can be met rather easily. It is easily met because national economies have an institution called the state which is unique in that it has virtually unlimited powers of credit creation or borrowing (or would have within a closed national economy). Keynesians gave up at this point, thinking that once the need for demand management had been pointed out, and the possibility for demand management by a national government had been understood, the problem of demand management was solved once and for all. Unfortunately, there is no such thing as the state in the contemporary international economy at the international level and the absence of the state as such at the international level is, I believe, a sufficient explanation of why the world economy has run into serious problems of recession …
… The important point is rather that in an international economy the possibilities of national demand management are strictly limited. They are limited by problems of balance of payments adjustment and international finance. Governments that wish to regulate national demand so as to sustain full employment run into problems of increasing trade deficits and, in economics with liberal exchange regimes, loss or confidence and outflows of capital. It is actual or potential balance of payments crises which have been decisive in breaking the habit or Keynesian demand management at the national level. Many national governments are still trying but they are trying under difficulties and they are frightened of balance of payments problems that would result if they tried too hard.
Further, as Francis Cripps concluded, in that brilliant article,
… [U]ntil the economists in our society get around to tackling this problem, we risk being stuck with periods of long recession, even if we are occasionally and accidentally favoured with periods of world boom.
In the book From Keynesianism To Monetarism: The Evolution Of UK Macroeconometric Models [2], Peter Kenway writes:
… There is, however, a greater sense in which the development of the Cambridge Group in that period is more important than the model that came to represent them. That sense stems from the historical significance of those ideas…. the ideas were therefore more ‘anti-Keynesian’ than ‘Keynesian’… what makes the anti-Keynesian views of the 1970s Cambridge Economic Policy Group so significant is that they grew out of the very heart of Keynesianism itself …
… On the one hand, as far as the goals it espoused are concerned, of full employment, of steady growth and of government’s responsibility to pursue these ends, the Group’s commitment to Keynesianism never wavered. But on the other hand, as far as the practice of Keynesianism was concerned, and especially the conceptualization of the reasons for the increasing and evident failure of that practice, the Policy Group not only was part of, but in some respects actually led the revolution against Keynesianism in the UK …
(No) Conclusion
Think my blog posts should be short, but this being the introduction needed to longer. Come back for some Kaldorian Monetary Economics!
References
Francis Cripps, What Is Wrong With Monetarism, pp 55-68, Monetarism Economic Crisis And The Third World, ed. Karel Jansen, Frank Cass, 1983.
Peter Kenway, p 92, From Keynesianism To Monetarism: The Evolution Of UK Macroeconometric Models, Routledge, 1994 (2011 reprint).
