A new high performance hybrid car has recently been released by a Roring Motors, Inc. According to Managing Director Rory Robertson, the new “GoFlowMobile” ™© achieves unparalleled performance for a hybrid car, by applying a simple insight from economics to the hide-bound world of engineering.

Mr Robertson, an economist, took over the firm in a hostile private equity bid, because he saw an opportunity to bring economic thinking to bear on the vexed issue of designing the world’s fastest hybrid car.

“I read press report after press report about the company’s difficulties in producing a hybrid car that was as fast as a conventional one”, Mr Robertson explained, “and suddenly the light dawned: the designers were obsessed about all sorts of ratios that involved comparing stocks to flows!”

“As an experienced and well-trained economist, I knew that comparing a stock to a flow was a schoolboy error–like comparing apples with oranges, as Steve Keen does when he compares Debt levels to GDP. So I saw an opportunity to help them make a breakthrough, and I took it.”

Mr Robertson’s first directive on arrival at what used to be known as High Performance EcoMotors, was that no stock to flow ratios were to be used by the design team. Sure enough, in a short while the firm’s engineers achieved a dramatic breakthrough. The new GoFlowMobile achieved performance levels befitting a Ferrari, rather than the sluggish sedan-level performance that was the best achieved by established players like Toyota and Honda.

The technical details behind the car’s success are protected by numerous patents, but Petra Seller, our investigative reporter here at Fantasy Wheels, managed to find out what the key advance was, when she tracked down the company’s recently retired Chief Engineer.

Dr StrangeLove, who took advantage of an attractive voluntary redundancy package shortly before the release of the car, was willing to speak on condition that the location of the mine shaft where he now lives was kept secret.

“The car is so much faster than the opposition because it weighs so much less”, Dr StrangeLove explained. “And it weighs less because it has a 1 litre petrol tank.”

“The comparison of the volume of the fuel tank to the car’s rate of consumption of petrol was an obvious stock to flow comparison”, Dr StrangeLove explained. “When Mr Roberston freed me from the tyranny of schoolboy stock to flow comparisons, I was able to ignore this ratio and focus just on the flow issues.”

“With the same engine size consuming the same maximum amount of fuel per minute, but a far smaller tank, less petrol weight, far less tubing and so on, the car weighs over 200 kilos less than its predecessor. It is also more streamlined, with no need to design the car around a bulky fuel tank. So it goes 20 per cent faster with the same engine as in the previous model.”

When Petra asked about any drawbacks to this radical design, Dr StrangeLove took a while to compose himself before answering that drivers wouldn’t know about this problem until after they had purchased the car, because the car’s advertising also made no references to stock to flow comparisons.

“This also was a great efficiency. Whole pages of PR that used to extol the car’s range between refuelling stops were eliminated–since this number was also the result of comparing a stock to a flow”, Dr StrangeLove explained, while giggling slightly.

As his wheelchair retreated back into the mineshaft, Dr StrangeLove volunteered the closing remark that the car, having been inspired by economic theory, could do its bit to help to resolve the current economic crisis. “I believe there will be plenty of work for unemployed economists now”, he said, “explaining to motorists every 10 kilometres or so that stock to flow comparisons don’t matter.”

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OK, for those who don’t know where this came from, one irritation I’ve had to deal with when debating the financial crisis with neoclassical economists is the proposition that my comparison of the level of debt to GDP is erroneous, because I am comparing a stock (the outstanding level of debt) to a flow (GDP, which records the monetary value of output produced per year in an economy). I’ve had this said to me by an RBA Deputy Governor, as well as numerous economic commentators. Most recently, Rory Robertson repeated the same claim in a newletter, which Chris Joye reproduced in an article in the Business Spectator, Time to buy a dwelling?:

“Dr Steve Keen amongst others continues to make the schoolboy error of comparing debt to income (a stock to a flow — apples to oranges) and misses the main game. ”

Every time this furphy has been thrown my way, I’ve tried to explain why this specific ratio does matter. Anyone who is not an economist (a neoclassical economist, that is!) has got it almost instantly. But neoclassical economists, who know nothing about dynamic analysis, keep coming back with this “comparing a stock to a flow is like comparing apples to oranges” nonsense.

While one has to be very careful in dynamic analysis to differentiate stocks from flows, there are many, many times when the ratio between them matters. But getting that through to economists **who have no significant training in dynamics at all** proved simply impossible.

So I’ve given up on serious discussion: maybe satire might get the point through (sorry Rory, but in a schoolyard sense, you did ask for this one!). **Stock to flow comparisons matter because they tell you the capacity of your system to maintain a flow**. They abound in engineering, which is a discipline in which dynamic analysis is central.

Economists don’t get it because their discipline is still overwhelmingly dominated by static thinking.

An education in dynamic analysis starts with a course in what are known as “Ordinary Differential Equations”. You can’t graduate as an Engineer without having done at least a semester length course in them, and your career–if you work in design–is dominated by applying them to inventing new manufactured goods that (unlike the economy itself) actually work well almost all of the time.

The vast majority of economists, on the other hand, learn what little mathematics they know from other economists in courses on “Mathematical Methods for Economics”, or “Econometrics”, and the like. The vast majority of these courses–certainly at undergraduate level–teach some algebra and calculus (otherwise known as **differentiation**), but not **differential equations **(doing the latter requires knowledge of calculus and algebra, but differential equations are inherently more difficult than differentiation). The techniques economists learn are suited to optimisation, and equilibrium calculations, but are irrelevant to dynamics. Differential equations, on the other hand, are essential to the understanding of dynamic systems.

At graduate level, economists sometimes gain basic knowledge of differential equations, but in the courses I have seen, this stops at what are known as second order linear equations. Many of the economists who teach mathematical methods to other economists don’t know anything above this level either. But the interesting, real-world-relevant stuff starts with nonlinear equations, especially higher-order ones (with 3 or more interacting variables).

As a result, comments like Rory’s–that by comparing a stock to a flow I am comparing apples to oranges–look sophisticated to other economists, and might befuddle people with no mathematical training. But in fact, they betray that economists aren’t even equipped to understand dynamic analysis–something that is rather absurd since the economy is clearly dynamic.

This is one of the main reasons why they understand the economy so poorly–and why they didn’t see this crisis coming, whereas I did (and for the record, I did introductory and advanced courses in differential equations with the UNSW Department of Mathematics while completing my PhD in economics).

I’ll finish with one more piece of dynamic analysis. A technique that is drummed into engineers is dimensional analysis: looking at what sort of number results by comparing the dimensions of variables to each other, rather than their values. Let’s apply this to the car example above, and my Debt to GDP comparison, to see whether the resulting dimensions makes sense. If so, they would be relevant considerations in whether one should buy a car, and in how you assess the health of an economy. If not, they could justly be ignored.

The ratio of a car’s fuel tank size to the engine’s fuel consumption (at a given speed) is a comparison of litres to litres per minute. The resulting ratio is minutes:

Litres/Litres/Minute = Minutes

The stock to flow comparison of a car’s petrol tank to its usage of petrol per minute therefore tells you how long you will get between refuelling stops from a given car driven at a given speed. I would suggest you don’t buy a car to which the value of that ratio is “3 minutes”, no matter how fast it might travel in the meantime.

The ratio of Debt to GDP is a comparison of dollars to dollars per year. The resulting ratio is years:

Dollars/Dollars/Year = Years

Does this matter when assessing the health of an economy? You betcha. Especially when that economy has been booming along on an orgy of debt-financed speculative spending. The ratio tells you how many years it would take to reduce debt to zero, if all of GDP were devoted to doing that.

Now of course it won’t be, and of course any attempt to do so would backfire because, with all income being directed at debt repayment, the economy would collapse for want of effective demand and GDP itself would fall and… **hey, isn’t that what’s actually happening?**

Not because all of income is being directed at debt repayment, of course–that is impossible–but because rather than spending being augmented by additional borrowing, spending is now less than income as individuals (both firms and households) struggle to repay debts.

That is an instance of where I have correctly applied dimensional analysis to add a flow to the rate of change of a stock: I regard aggregate spending in the economy as the sum of GDP (a flow) plus the change in debt (also a flow). Add the two, and you get the actual sum spend in the economy–aggregate demand (conventional economists, who are misled into regarding money and debt as irrelevant to the performance of the real economy, don’t consider the change in debt in their models).

The ratio of the change in debt to aggregate demand yields a dimensionless number that tells you how much of aggregate demand is debt financed. Since debt finance can turn on a dime–it can go from expanding to contracting virtually overnight–this ratio can tell you more about where the economy is headed than virtually any other indicator.

**IF**, that is, that “apples to oranges” comparison of debt to GDP returns a large number–because then changes in debt will also be much, much larger than changes in GDP. If, on the other hand, that number is very small–as it was back in the 1960s–then changes in GDP will be larger than changes in debt, and the latter will have little influence on overall economic activity.

The power of this indicator is obvious when you look at the correlation between this ratio (Annual Change in Debt/[Annual Change in Debt plus GDP]) and the unemployment rate. Back in the 1960s, when the Debt to GDP ratio was low (80–100% in the USA, and between 25–30% in Australia), there was no particular correlation. Now, with extremely high debt to GDP ratios (297% in the USA, 159% in Australia [down from a peak of 165%, but I expect it will rise again in the near future]) the correlation is overwhelming.

The causal mechanism behind this is that, when the debt contribution to demand drops in a country with a high Debt to GDP ratio, aggregate demand collapses. Unemployment rises soon after. The process is well under way in the USA–which is why de-leveraging is now the key force driving economic activity there. And it is starting in Australia:

It won’t end with debt to GDP levels of zero of course (I’ve seen it said that I am anti-debt, and that’s nonsense: I am anti-debt when it finances asset price speculation, but recognise the legitimate role of debt in financing investment and the working capital needs of firms). But will will end with debt levels substantially below current ones, and if we let that process occur “naturally”, it will take many many years to complete. And unemployment will go through the roof.

It will also quite probably start with an **increase** in the debt to GDP ratio, as has recently happened in the USA. America’s ratio has jumped sharply from 290% three months ago to 296.7% in the most recent Flow of Funds data (published by the Federal Reserve last week).

The reason is, of course, that though the rate of growth of debt has plummeted, both real output and prices are falling in the USA, and at rates that haven’t been seen since the last Great Depression. The same phenomenon drove the debt to GDP ratio in the USA from 176% at the end of 1929 to a peak of 238% in the depths of the Depression in 1932.

Today, the USA has only begun the process of debt-deleveraging and deflation, and it has a debt to GDP ratio of almost 300%. That implies the process of returning to a “a ‘good financial society’ in which the tendency by businesses and bankers to engage in speculative finance is constrained” (quoting Hyman Minsky) may take a good deal longer than it did in 1930.

Yes Rory, sometimes stock to flow comparisons do matter.

(Any economist who wants to learn a lot about differential equations should buy a copy of Differential Equations and Their Applications : An Introduction to Applied Mathematics by Martin Braun. It’s an extremely well written and engaging introduction to an area that should be a foundational study for economists, but is neglected by a discipline that is still locked in a 19th century, pre-dynamic mindset.)

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