Tag Archives: stock flow coherent models

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New Bank Of England Paper On The Financial Balances Model For The United Kingdom

Stephen Kinsella is out with a new paper with co-authors Stephen Burgess, Oliver Burrows, Antoine Godin, and Stephen Millard published by the Bank of England.

From the paper:

Our paper makes two contributions to the literature. First, we develop, estimate, and calibrate the model itself from first principles as well as describing the stock-flow consistent database we construct to validate the model; as far as we know, we are the first to develop such a sophisticated SFC model of the UK economy in recent years.4 And second, we impose several scenarios on the model to test its usefulness as a medium-term scenario analysis tool. The approach we propose to use links decisions about real variables to credit creation in the financial sector and decisions about asset allocation among investors. It was developed in the 1980s and 1990s by James Tobin on the one hand, and Wynne Godley and co-authors on the other, and is known as the ‘stock-flow consistent’ (SFC) approach. The approach is best described in Godley and Lavoie (2012) and Caverzasi and Godin (2015) and underpins the models of Barwell and Burrows (2011), Greiff et al. (2011), and Caiani et al. (2014a,b). Dos Santos (2006) describes how SFC models incorporate detailed accounting constraints typically found in systems of national accounts. SFC models allow us to build a framework for the model where every flow comes from somewhere in the economy and goes somewhere, and sectoral savings/borrowings and capital gains/losses add or subtract from stocks of wealth/debt, following Copeland (1949). Accounting constraints allow us to identify relationships between sectoral transactions in the short and long run. The addition of accounting constraints is crucial, as one aspect of the economy we would like to model is the way it might react differently when policies such as fiscal consolidations are imposed slowly or quickly

4 Such models were popular in the past; for example Davis (1987a, 1987b) developed a rudimentary stock flow consistent model of the UK economy.

[The title of this page is the link]

Simon Wren-Lewis On Wynne Godley’s Models

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

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

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

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

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

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

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

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

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

Economics Without Mathematics?

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Recently, Noah Smith wrote an article for Bloomberg View, titled Economics Without Math Is Trendy, But It Doesn’t Add Up.

Smith’s attitude is the following:

  1. Heterodox economics is vague and neoclassical economists are mathematical geniuses.
  2. Heterodox authors somehow manage to sneak in some model of the economy.

How about something opposite? That stock flow consistent/coherent models come close to describing the real world and neoclassical models don’t even start in the right foot? The usage of mathematics in neoclassical economics looks silly to me to say the least. Heterodox authors on the other hand have made important breakthroughs with stock-flow consistent models. In these models, the description of how stocks and flows affect each other leading to macrodynamics describing the real world is obtained.

Neoclassical models (which the phrase I use for the “new consensus”) not only doesn’t have anything as mathematical as this but it fails in the first place to identify the correct tools to describe economic behaviour.

Morris Copeland writing in Social Accounting For Moneyflows in Flow-of-Funds Analysis: A Handbook for Practitioners (1996) [article originally published in 1949] said:

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

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

Morris Copeland’s work is what led the U.S. flow of funds which is published by the Federal Reserve every quarter. National accounts have also improved since their first version to incorporate Copeland’s ideas. See the 2008 SNA and the Balance of Payments And International Investment Position Manual, Sixth Edition for example.

Apart from stock-flow consistent/coherent models, models of the economy don’t even come close to describing the economy, because they miss the most important aspect: flow of funds.

So Goldman Sachs’ chief economist, Jan Hatzius for example uses this approach. See his paper The Private Sector Deficit Meets The GSFCI : A Financial Balances Model Of The US Economy, Global Economics Paper No. 98, Goldman Sachs, Sep 18, 2003.

So it is not that neoclassical economists have great mathematical tools. It’s that by failing to incorporate the framework of flow of funds, they are showing their incompetence in mathematical reasoning.

A Short Note On George Soros’ Principle Of Reflexivity

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There’s a nice paper by George Soros from 2014, titled Fallibility, Reflexivity, And The Human Uncertainty Principle in which he gives a good alternative description of financial markets. It’s a kind of a review article of his own ideas he has developed over the years. This is in sharp contrast to the “efficient market hypothesis”.

Here I wanted to discuss just one aspect. In section 4.1 of the paper, Soros says:

Let me state the three key concepts of my approach, fallibility, reflexivity, and the human uncertainty principle as they apply to the financial markets …

…

Second, reflexivity. Instead of playing a purely passive role in reflecting an underlying reality, financial markets also have an active role: they can affect the future earnings flows they are supposed to reflect. That is the point that behavioral economists have missed. Behavioral economics focuses on only half of the reflexive process: cognitive fallibility leading to the mispricing of assets; they do not concern themselves with the effects that mispricing can have on the fundamentals.

Although, in neoclassical economics, it is difficult to see how this is the case, it is easy in stock-flow coherent macro models. Without writing equations, let’s see how this works.

  1. A rise in expectations of equity prices will lead to a rise in the actual value of equity prices.
  2. Higher equity prices implies holding gains (capital gains) for the holders ultimately households.
  3. This raises consumption (and purchases of houses) as households are richer.
  4. This rise in domestic demand raises output as producers will produce more to meet the demand.
  5. Higher production means higher profits.
  6. A boom in financial markets also leads to a rise in firms’ capital formation (“investment”). Investment is self-financing as investment expenditure for one firm is a source of revenue for another.

Of course, there are feedback effects as well and this may become a bubble which goes bust, but this is the basic mechanism by which reflexivity works.

Although this appears simple, this cannot happen in neoclassical economics because the “production function” is at the heart of it.

Back to Soros. In the paper, he has a nice chart with an explanation of it.

George Soros - Stock Prices Affecting Fundamentals

Soros explains:

A typical market boom– bust. In the initial stage (AB), a new positive earning trend is not yet recognized. Then comes a period of acceleration (BC) when the trend is recognized and reinforced by expectations. A period of testing may intervene when either earnings or expectations waiver (CD). If the positive trend and bias survive the testing, both emerge stronger. Conviction develops and is no longer shaken by a setback in earnings (DE). The gap between expectations and reality becomes wider (EF) until the moment of truth arrives when reality can no longer sustain the exaggerated expectations and the bias is recognized as such (F). A twilight period ensues when people continue to play the game although they no longer believe in it (FG). Eventually a crossover point (G) is reached when the trend turns down and prices lose their last prop. This leads to a catastrophic downward acceleration (GH) commonly known as the crash. The pessimism becomes over done, earnings stabilize, and prices recover somewhat (HI).

Of course, it’s more complicated. There can be other factors leading to the fall of both equities and earnings. But importantly, the fall in equity prices can—via the wealth effect and a fall in firms’ capital formation (“investment”)—lead to a fall in earnings.

George Soros’ criticism of neoclassical economics is great and he’s quite correct in getting an important causality. His description however lacks a mechanism. This can be provided with a demand-led stock-flow coherent behavioural model without any production function.

Marc Lavoie Lectures On Post-Keynesian Economics And Stock-Flow Consistent Modeling

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There are two wonderful lectures by Marc Lavoie given at the UMKC two years ago. I had seen them that time but forgot to post it on my blog.

Likely you might have seen it, but if not, here they are.

Lecture 1: Essentials of Heterodox And Post-Keynesian Economics

Slides

Marc Lavoie - Essentials Of Heterodox And Post-Keynesian Economics

Click picture to view the video on YouTube.

Lecture 2: Workshop on stock-flow consistent modeling

Slides

Marc Lavoie - Workshop On Stock-Flow Consistent Modeling

Click picture to view the video on YouTube.

UK Poorer?

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The commentary after the EU Referendum has moved into a consensus from economists claiming that “Brexit” will make the UK poorer. So we hear it from Paul Krugman:

Yes, Brexit will make Britain poorer

Krugman’s thoughts are also echoed by Simon-Wren Lewis. First SWL claims that:

Calculating the size of this effect is an exercise in trade economics not macroeconomics

I don’t understand this. Calculation is both an exercise in trade economics and macroeconomics. So in stock-flow consistent models of the open economy, you see such a thing. It’s both macroeconomics and trade. Trade is automatically incorporated in a macroeconomic model.

This is not just a minor point in semantics. In stock-flow-consistent models, one cannot avoid some parts and talk of the rest. One is forced to incorporate trade, not just in goods and services but also financial assets. Something which models which SWL uses isn’t sophisticated enough to handle.

Moving on, SWL claims that the UK’s exit from the EU makes the UK poorer. He says:

This decline in trade leads to a loss in productivity which makes UK citizens poorer over the medium term. It also means that the real value of sterling has to fall to make up for the fall in net exports. Other things being equal, this fall in sterling will happen immediately, as indeed it already has. This will make people poorer immediately, because imported goods cost more. But here the macroeconomics gets complicated. The hit to trade from leaving the single market will evolve gradually, but the fall in sterling is immediate. (The reason is something economists call UIP.) That means that trading firms might get a short term competitiveness boost, even though this will evaporate in the medium term. This may or may not be enough to compensate for the short term impact of rising prices on consumption spending.

Unfortunately that is not all that happens in the short term. Uncertainty about future arrangements will hold back investment, and it may also add to the depreciation in sterling. For this and other reasons the short term impact on aggregate demand is likely to be negative, although measuring its size is difficult. We then need to think about whether the MPC will raise or cut interest rates. The National Institute’s analysis is very readable on all this.

[underlying: mine]

So the claim that it will make the UK poorer. In effect, SWL’s model is telling him that real GDP will fall as well as real wealth as well fall in real household expenditure. There are several ways in which it happens. Productivity falls. Fall in productivity leads to a less than rapid increase in production. Consumer prices rising means lower real expenditure and so on.

Now, in Kaldorian story the causalities in the real story of actual economic dynamics are almost reverse than the ones presented above. Faced will less free trade, the UK government is less constrained to expand domestic demand and output. It can protect its manufacturing industry. Rising production leads to rising productivity, reverse of what is implied by SWL’s model. True, imported goods will be costlier, but it also reduces import penetration which allows domestic demand to be expanded and hence output and hence real national income and household income so that consumers are more than compensated for imports being made more expensive.

Of course, all this depends on whether the UK government reduces austerity and expands domestic demand. But some effects can be seen, although uncertain. This is because the foreign trade multiplier is improving and the fiscal policy multiplier improves, even if the fiscal stance is not changed. Higher wages if immigration is controlled also provides a boost to demand.

At any rate, the important point in this post is that the remain campaign’s economics is a model which is completely erroneous about causalities and how economies work.

We Don’t Need No Helicopters … Hey! Economists! Leave Fiscal Policy Alone

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A lot has been written on helicopter money recently. Most of them bad with a few exceptions such as one by JKH.

In my opinion, the main reason economists come up with stories such as “helicopter money” etc. is that it is difficult in standard economic theory to introduce money.

Few quotes from Mervyn King’s book The End of Alchemy: Money, Banking, and the Future of the Global Economy:

But my experience at the Bank also revealed the inadequacies of the ‘models’ – whether verbal descriptions or mathematical equations  – used by economists to explain swings in total spending and production. In particular such models say nothing about the importance of money and banks and the panoply of financial markets that feature prominently in newspapers and on our television screens. Is there a fundamental weakness in the intellectual economic framework underpinning contemporary thinking? [p 7]

For over two centuries, economists have struggled to provide a rigorous theoretical basis for the role of money, and have largely failed. It is a striking fact that as as economics has become more and more sophisticated, it has had less and less to say about money… As the emininent Cambridge economist, and late Professor Frank Hahn, wrote: ‘the most serious challenge that the existence of money poses to the theorist is this: the best developed model of the economy cannot find room for it’.

Why is modern economics unable to explain why money exists? It is the result of a particular view of competitive markets. Adam Smith’s ‘invisible hand’ …

… Money has no place in an economy with the grand auction. [pp 78-80]

But the ex-Bank of England governor perhaps never worked with stock flow consistent models. The advantage of these models is that what money is and how it is created is central to the question of how economies work. The framework used in stock flow consistent models is not new exactly. What’s new in stock-flow consistent models is the behavioural analysis on top of the existing framework the system of national accounts and flow of funds. As Morris Copeland, who formulated the flow of funds accounts of the U.S. economy said:

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

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

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

So what do we mean by helicopter money and it is really needed or useful? For that we need to go into a bit into some behavioural equations in stock-flow consistent models. One way is to use a somewhat simplified notation from Tobin’s nobel prize lecture Money and Finance in the Macroeconomic Process. In Tobin’s analysis, the government’s fiscal deficit is financed by high-powered money and government bonds:

G – T = ΔH + ΔB

ΔH = γH·(G – T)

ΔB = γB·(G – T)

 γH + γB = 1

0 ≤  γH, γB  ≤ 1

So the deficit is financed by “high-powered money” (H) and government bonds (B) in proportion γH and γB

Now it is important to go into a bit of technicalities. Prior to 2008, central banks implemented monetary policy by a corridor system. After 2008, when the financial system needed to be rescued and later when central banks started the large scale asset purchase program (“QE”), central banks shifted to a floor system.

Although economics textbooks keep claiming that the central bank “controls the money supply”, in reality they are just setting interest rates.

In the corridor system, there are three important rates:

  1. The deposit rate: The rate at which central banks pay interest on banks’ deposits (reserves) with them,
  2. The target rate: The rate which the central bank is targeting, and is typically the rate at which banks borrow from each other, overnight, at the end of the day.
  3. The lending rate: The rate at which the central bank will lend to banks overnight.

There are many complications but the above is for simplicity. Typically the target rate is mid-way between the lower (deposit rate) and the higher (lending rate).

In the floor system, the government and the central bank cannot set the overnight at the target rate if the central bank doesn’t supply as much reserves as demanded by banks. Else the interest rate will fall to the deposit rate or rise to the lending rate. In a system with a “reserve-requirement”, banks will need an amount of reserves deposited at the central bank equal to a fraction of deposits of non-banks at banks.

So,

H = ρ·M

where M is deposits of non-banks at banks and ρ is the reserve requirement. In stock-flow consistent models, M is endogenous and cannot be set by the central bank. Hence H is also endogenous.

In the floor system, the target rate is the rate at which the central bank pays interest on deposits. Hence the name “floor”. There are some additional complications for the Eurosystem, but let’s not go into that and work in this simplification.

In the floor system, the central bank and the government can decide the proportions in which deficit is financed between high powered money  and government bonds. However since deposits are endogenous the relation between high powered money and deposits no longer holds.

In short,

In a corridor system, γH and γB are endogenous, M is endogenous and H = ρ·M. In a floor system, γH and γB can be made exogenous, M is endogenous and H ≠ ρ·M. M is not controlled by the central bank or the government in either cases and is determined by asset allocation decisions of the non-bank sector.

Of course, the government deficit G – T itself is endogenous and we should treat the government expenditure G and the tax-rates θ as exogenous not the deficit itself.

So we can give some meaning to “helicopter money”. It’s when the central bank is implementing monetary policy by a floor system and γH and γB are exogenous.

But this doesn’t end there. there are people such as Ben Bernanke who have even proposed that the central bank credit government’s account with some amount and let it spend. So this introduces a new variable and let’s call it Gcb.

So we have a corridor system with variables G and θ versus a floor system with variables G’, G’cb, θ,  γ’H and γ’B

The question then is how is the latter more superior. Surely the output or GDP of an economy is different in the two cases. However people constantly arguing the case for “helicopter money” are in the illusion that the latter case is somewhat superior. Why for example isn’t the vanilla case of a corridor system with higher government expenditure worse than “helicopter money”.

Also it effectively reduces to a fiscal expansion combined with a large scale asset purchase program of the central bank (“QE”). I described QE’s effect here. Roughly it works by a wealth effect on output with some effect on investment via asset allocation.

To summarize, the effect on output by these crazy ways can be achieved by a higher fiscal expansion. There’s hardly a need to bring in helicopters. Some defenders say that it is faster but that just sounds like an excuse to not educate policymakers.

On The Blogs

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Two things caught my attention in the last two days.

First is the claim by Roger Farmer:

The Keynesian economics of the General Theory is static.

That’s the strangest critique of the GT I have ever seen. How is the GT static? John Maynard Keynes highlighted how a fall in the propensity to consume reduces output. His mechanism was quite dynamic. He was arguing that a fall in the propensity to consume will reduce consumption and hence firms’ sales and hence production and hence employment and hence consumption and so on. Keynes did not explicitly write down a mathematical model like as done for example in the book Monetary Economics by Wynne Godley and Marc Lavoie. But his arguments were quite dynamic in nature. So was his argument about how investment creates saving. And also the Keynesian multiplier. “Stock-flow consistent” models are quite close to Keynes’ spirit.

The second is this paragraph from Michael Pettis:

… This is one of the most fundamental errors that arise from a failure to understand the balance of payments mechanisms. As I explained four years ago in an article for Foreign Policy, “it may be correct to say that the role of the dollar allows Americans to consume beyond their means, but it is just as correct, and probably more so, to say that foreign accumulations of dollars force Americans to consume beyond their means.” As counter-intuitive as it may seem at first, the US does not need foreign capital because the US savings rate is low. The US savings rate is low because it must counterbalance foreign capital inflows, and this is true out of arithmetical necessity, as I showed in a May, 2014 blog entry (link broken: archive.is link).

Oh boy! That’s confusing accounting identities with behaviour. A simple way to show how inaccurate this is by using standard Keynesian analysis. Assume US households reduce the propensity to consume. This leads to a fall in output and income and hence a fall in imports and an increase in the current account balance of payments (assuming exports are exogenous to the model). This can be seen more precisely in a stock-flow consistent model.

Pettis’ arguments are in response to Stephen Roach’s recent article on US balance of payments and I discussed that recently here.  Both Roach and Pettis are incorrect.

Balance of payments is important and in my opinion, the most important thing in Economics. Michael Pettis gets the attention because he realizes the importance of balance of payments in the economic dynamics of the world. However looked more closely, many of his arguments appear vacuous.

Discrete Time Or Continuous Time?

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There is always some debate by people on how continuous time is better modelling. A James Tobin quote from his Nobel Lecture comes to mind.

Macroeconomic Modeling Strategy: Continuous or Discrete Time

The issues just discussed are related to the modeling of time. The equations introduced above count time in discrete periods of equal finite length. Within any period, each variable assumes one and only one value. In particular, clearing of asset markets determines one set of asset prices per period. From one period to the next asset stocks jump by finite amounts. Therefore the demands and supplies for these jumps affect asset prices and other variables within the period, the more so the greater the length of the period. They will also, of course, influence the solutions in subsequent periods.

The same modeling strategy can be used with continuous time. The specific saving functions, as well as the total saving function, then tell the rate at which savers want to be increasing their stocks of particular assets and of total wealth. They will reflect both the continuous execution of long run saving and portfolio plans and the speeds of adjustment of stocks to deviations from these plans that arise because of surprises, news, and altered circumstances or preferences.

Either representation of time in economic dynamics is an unrealistic abstraction. We know by common observation that some variables, notably prices in organized markets, move virtually continuously. Others remain fixed for periods of varying length. Some decisions by economic agents are reconsidered daily or hourly, while others are reviewed at intervals of a year or longer except when extraordinary events compel revisions. It would be desirable in principle to allow for differences among variables in frequencies of change and even to make those frequencies endogenous. But at present models of such realism seem beyond the power of our analytic tools. Moreover, many statistical data are available only for arbitrary finite periods.

Representation of economies as systems of simultaneous equations always strains credibility. But it takes extraordinary suspension of disbelief to imagine that the economy solves and re-solves such systems every microsecond. Even with modern computers the task of the Walrasian Auctioneer, and of the market participants who provide demand and supply schedules, would be impossible. Economic interdependence is the feature of economic life and we as professional economists seek to understand and explain. Simultaneous equations systems are a convenient representation of interdependence, but it is more persuasive to think of the economic processes that solve them as taking time than as working instantaneously.

In any event, a model of short-run determination of macroeconomic activity must be regarded as referring to a slice of time, whether thick or paper thin, and as embedded in a dynamic process in which flows alter stocks, which in turn condition subsequent flows.

Subscripting Helps!

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The accounting identities equating aggregate expenditures to production and of both to incomes at market prices are inescapable, no matter which variety of Keynesian or classical economics you espouse. I tell students that respect for identities is the first piece of wisdom that distinguishes economists from others who expiate on economics. The second? … Identities say nothing about causation.

– James Tobin, 1997, p. 300, ‘Comment’, in B.D. Bernheim and J.B. Shoven (eds), National Saving and Economic Performance, Chicago: University of Chicago Press.

This is a continuation of my post Stock-Flow Inconsistent? which was a reply to Jason Smith’s blog post More like stock-flow inconsistent on his blog Information Transfer Economics. If you had checked my post before around noon UTC yesterday, you might want to check the updated version.

Jason Smith also has updated his post and proposes a new equation:

ΔH = Γ·(G – T)

(incorrect equation)

Now, that’s quite wrong because it violates rules of accounting.

Morever, Jason Smith insists that it is a behavioral equation.

A lot of clarity can be achieved if one uses subscripts, so that things are clearer.

So we have two equations:

ΔH = G – T

dH/dt = G – T

Although these two are related, they are not exactly the same: the former is in a difference equation form and the latter in the differential equation form. The G in the former has no time dimensions and the G in the latter has time dimension equal to –1. The G in the former is total expenditure in a period, the G in the latter is a rate. 

Since stock-flow consistent models are written typically in difference equations, rather than differential equations, let us avoid subscripts for difference equations for the former and use it for latter.

So it is better to write the equations as:

ΔH = G – T

dHcontinuous/dt = Gcontinuous – Tcontinuous

Each time step in the formalism of difference equations is Δt and hence

G = Gcontinuous ·Δt

T = Tcontinuous ·Δt

Hcontinuous = H

So,

ΔH/Δt = Gcontinuous – Tcontinuous

(approximately)

Or,

ΔH/ Δt = G/Δt – T/Δt

Or,

ΔH = G – T

So instead of reaching the correct equation which is:

ΔH= Δt · (Gcontinuous – Tcontinuous)

Jason reaches the equation:

ΔH = Γ·(G – T)

(incorrect equation)

But

ΔH = G – T

as it is an accounting identity in the model!