Accounting Identities and the Implicit Theory of Inertia

Animals can be divided into Carnivores and Non-Carnivores: A = C + NC. Therefore, if we add some wolves to an island of sheep, the number of animals on that island will increase.

It's easy to see why that argument might not be right. Wolves kill sheep. But if you didn't know that fact about wolves and sheep, the argument looks very appealing. But the equation A = C + NC tells us absolutely nothing about the world; it's an accounting identity that is true by definition. The only thing it tells you is how I have chosen to divide up the world into parts. And I can choose an infinite number of different ways to divide the world up into parts.

Here are two more examples:

1. Y = C + I + G + X - M. Therefore an increase in Government spending will increase GDP.

2. Y = C + S + T. Therefore an increase in Taxes will increase GDP.

My guess is that you are much more uncomfortable with the second of those two examples than the first. You have probably seen the first argument before, but have probably not seen the second. But they are both equally correct accounting identities and are both equally rubbish arguments.

How can a purely arbitrary choice of which accounting identity I write down make any difference at all to how we think about the world?

I call it "The Implicit Theory of Inertia": We assume a thing will keep on doing the same as it would otherwise have done, unless you give me a good reason why it wouldn't. The onus is on you to explain why more wolves would mean fewer sheep, and unless you give me a good reason I will assume that the number of sheep stays the same (or keeps growing or declining at the same rate) regardless of the number of wolves. You need the force of a good argument to overcome the assumed inertia of things. So by choosing one accounting identity over another, I am dividing the world up into one set of things rather than another, and then exploiting your Implicit Theory of Inertia to rig the argument in my favour.

Sadly, we don't just fool other people when we write down accounting identities to divide the world up one way rather than another. We fool ourselves too.

Theorising starts when we write down the variables.

Comments

[marcus nunes]

That´s why, again, it´s better called GDP=Gross Deceptive Partitioning!

[Michael Clifford]

Do you think the MMT obsession with the sectoral balances paradigm falls victim to this problem as well?

[Gavin Moodie]

I apologise for this naive question. Mightn't I believe that Y = C + I + G + X - M is true because the government finances its increased spending from borrowing which it never repays?

[Nick Rowe]

marcus: ;-)

Michael: It seems to me to be a particular problem with some of the more naive followers of MMT, but I think the more sophisticated economists aren't much worse in this than the rest of us. I don't think any of us are immune. MV=PY for example is another case where we need to be careful.

Gavin: Y = C + I + G + X - M is always true, regardless of how the government finances its spending. It would still be true in a world where all government spending was on police used to enforce the ban on producing goods (wolves and sheep). We divide all output (Y) into goods sold to consumers, firms, government, foreigners, remembering to subtract the goods that households firms and governments buy from foreigners.

[Gavin Moodie]

Great, thanx Nick.

[louis]

There's nothing to dispute in the post itself, Nick is very right about accounting identities and how people misuse them to infer causality.
Perhaps there is something to salvage in argument 1 though - a similar sounding argument that is less wrong, or what people have in their minds that lets them accept the flawed reasoning. I think you start by moving away from Y and replacing it with AD. A budgeted increase to govt deficit should increase AD in a given year; it should represent a rightward shift in the curve. Same if a large business/industry in a small economy were to initiate a large investment project (a worthwhile oil sands initiative?). We can see the government budget, it is large relative to the size of the economy, and spending levels are largely planned in advance. Granted, if the CB is doing its job (and has the power monetarists expect it to have) this increase in AD will have no effect on Y. But most of the time people who argue for larger deficits start from an assumption of a general glut and AD < Ybar.

[Michael Clifford]

Nick:

I think in an old post (or perhaps on Twitter), you said that MV=PY is an accounting identity when V is actual velocity, but an equilibrium condition when V is desired velocity. I think that's one way we could avoid reasoning from an identity.

I only ask because I used to believe that sectoral balances was the main model guiding MMT, but after reading more of their professional writings and less of the Twitter rants put out by their followers, I don't think that's the case anymore (Functional Finance seems to be their guidebook). The argument that the mechanical relationship between government deficits and net private saving is an economically useful concept is still dubious, though, and I think you might feel the same way given the emphasis you put on the difference between saving money (purchasing assets) and an excess demand for money (holding money).

[Andy Harless]

Are they equally rubbish arguments? As you point out, they're using a cognitive bias to sneak in behavioral assumptions. I would argue that if your argument is sneaking in vaguely reasonable behavioral assumptions (that exogenous changes in G won't affect C, I, or X-M), it is a less rubbish argument than one that sneaks in obviously insane ones (that exogenous changes in T won't affect C+S).

[Jeremy Fox]

Ecologists, evolutionary biologists, and statisticians also have accounting identities, though we don't call them that. Some of them often are misinterpreted (others are rarely misinterpreted). But they're never misinterpreted in the specific way that seems to be so common in economics. So whatever's going on here--Nick's implicit theory of inertia or something else--it's an affliction specific to economics.

Shameless self-promotion: an overview of accounting identities in ecology and evolution: https://dynamicecology.wordpress.com/2016/06/06/in-praise-of-partitions-in-ecology-and-evolution/

I'm sure I've commented along the same lines here before, so apologies for repeating myself. I wish I had some new insight to offer, but I don't. I just continue to find it interesting and puzzling that different accounting identities in different fields seem to be prone to different misunderstandings (or to no misunderstanding in some cases).

[Nick Rowe]

louis: OK, but now you are putting forward an actual theory, not merely an accounting identity.

Michael: I tend to agree.

Andy: Suppose we have full monetary offset (in expectation, anyway), because the central bank is targeting inflation (or NGDP). Or we are up against a capacity constraint. Or just the standard Long Run assumption. It would be daft to think C+I+X-M wouldn't fall by a roughly offsetting amount when G rises. And if taxes are lump-sum, and people have a target level of consumption and saving for their old age (rapidly diminishing Marginal Utility of Consumption), it's quite reasonable to assume they will work more to produce more goods to pay increased taxes. Income effect on labour supply.

[Nick Rowe]

Jeremy: interesting observation. I don't know why economics would be different. If it were only non-economists making this sort of mistake about economics, I think I could explain it as a confusion between accounting and economics, since they might seem sorta the same, or at least closely related. But even though that might be part of it, I don't think that explains the whole thing.

Good post by the way. I think I understood most of it!

[Merijn Knibbe]

I was taught, and rightly so, that ex ante, the accounting identities do not hold. But ex post, they always and by necessity do, thanks to the essential properties of money and the national accounts estimating the monetary side of life. Which also means that they are only true for the nominal measurements, not for the deflated ones (at least not when one looks at more than one period). Meaning that when it comes to the accounts, a 50% increase in oil prices will have the same result as a 50% increase in imports of physical oil. Wile, going granular, a rise in nominal imports while nominal exports do not increase will, starting from a situation where the current account surplus is zero, inevitably lead to a negative current account and more inernational debt, even when the initial imports are financed by payables and receivables - in the end, someone will have to pay the payables and will have to borrow foreign currency. In the Eurozone it might even show up as a Target2 deficit. When thinking about the accounting identities, it's good to keep such ideas in mind. There is no such thing as a one sided transaction.

[Rainer Voss]

Animals can be divided into Carnivores and Non-Carnivores: A = C + NC. Therefore, if we add some wolves to an island of sheep, the number of animals on that island will increase.
Where do the wolves come from, falling from the sky ? If they come from somewhere else, there will be less sheep eaten there, which makes the equation valid, no ? Once they have eaten all sheep on the island they will die. This will not happen, because there is an equilibrium which determines how many wolves the sheep population on the island can sustain .... am I mistaken ?

Your argument is grossly off-track

[Nick Rowe]

Merijn: I partly agree and partly disagree.

"quantity of apples bought = quantity of apples sold" is a (valid) accounting identity, regardless of whether we measure apples in kilograms or in dollars (as long as we define and measure apples the same way on both sides). It's true in both a monetary exchange economy and in a barter economy.

But yes, "quantity of apples demanded = quantity of apples supplied" (or desired or planned or expected to buy/sell) is not an accounting identity. It's a market-clearing or equilibrium condition; a statement about the world that may be true or false.

[Ed Zimmer]

I think what's being missed here is that an equation expressing a relationship among variables is not very useful (and certainly cannot be counted on to reflect reality) unless all of the variables can be precisely defined and accurately measured. That's where most non-physical science equations fall apart. Just look at all the distorted derivations (and explanations) of sectoral balances that exist.

[Peter Dorman]

I too have been railing for years against the abuse of using accounting identities for the purpose of attributing causation: see, for instance, http://econospeak.blogspot.com/2016/12/the-identity-equals-causation-fallacy.html. The worst offender, in my opinion, is the claim that the components of net national savings “determine” the current account balance. It’s beyond weird.

One small step toward sanity I’ve advocated on my own blogsite is actually using three parallel lines to indicate identity rather than the two for equality. It should function as a mnemonic device to remind us that when we have an identity we lack the necessary degree of freedom for making a causal argument. (To say A causes B makes sense only if there is at least a logical possibility that B could be other than what A makes it be.)

As for the national income accounting identity and sheep/wolves, wolf predation plays the role that crowding out might play in fiscal policy. We have to channel our inner Farley Mowat and investigate how carnivorous these wolves actually are: do they decimate the poor sheep or just pick off the weak outlier now and then? It quickly gets empirical.

My recommendation when faced with an accounting identity is to recognize that we are describing a single entity, however we choose to slice it. Change the entity and the components will change such that the identity continues to hold. At most we can identify more “active” components in the sense that the forces operating to alter the system work most immediately through those components—but they are still just conduits for causal forces operating externally, and there is no temporal or causal relationship between changes in these components and changes in the other ones. This is what I argued for current account balances in the article I wrote for Challenge many years ago. (I concluded that, based on the empirical evidence available at that time, the primary determinants of changes in the current account-net national savings system came from the trade side. But that doesn’t mean the trade account “causes” net national savings! See https://www.jstor.org/stable/i40032476)

As to why economists are so prone to this logical error, I suspect it has something to do with political or ideological proclivities. Economists often become attached to a particular policy or narrative and their misuse of accounting identities feels right to them because it reinforces their priors. I definitely think the near-universal misuse of the net national savings-current account identity fits that mold. As soon as you endogenize the macro aggregates the simple comparative advantage world of trade theory has to be qualified. Economists don’t want to do that, so they interpret the identity as saying that net national savings, as a separate entity, “determines” the current account, and by implication trade, account, returning us to that nice, tidy comparative advantage world. (FWIW, I gravitate toward an IPE understanding of international economic relations. Countries are structurally inclined toward chronic surpluses or deficits due to deeply embedded traits that operate on both components of the identity. Detailed knowledge of how they work is necessary to explain/forecast changes in the surplus/deficit and net national savings position, which are the same thing.)

[Nick Rowe]

Ed: lots of concepts are very useful despite being a bit fuzzy around the edges of their definition. "Species" is one example. Wittgenstein IIRC gave "bald" vs "hirsute" as another. "Planet" might be another, if I remember the Pluto controversy.

Peter: we are very much in agreement! I just did a Tweet saying that the Canadian Trade deficit must equal non-Canadian National Saving minus non-Canadian Investment, so it must be caused by damned foreigners, and has nothing to do with Canada! I too like to use the triple lines for an identity, but the trouble is that mathematicians use the regular = for what we would call identities.

[Jacques René Giguère]

Trade balance is the difference between the two savings. Of course those damn foreigners are responsible for all our trouble. Let’s invade them. When we are united, the difference will disappear. Ok we’ll need equalization payments but at last the whole world will be Canadian. Poor sods.

[bernard11]

The point is that these are not equations in the sense of the value of a dependent variable being calculated from some variables that move independently of each other. The "independent" variables are not independent - if one changes for some reason it is likely that others will change as well - so the whole idea that you can shove one around and have it affect only the dependent variable is wrong.

Change G and all else changes as well.

Increase T and C and S change.

[Merijn Knibbe]

Dear Nick,

your statement about apples sold is apples bought is true. For a single product. It's not true for monetary aggregates consisting of products with variable relative prices. And different bundles of products (investment goods, exports, imports, consumption goods) with time varying variable prices. Consider double deflation which, in case of an input which gets much cheaper and is used a lot more (artificial fertilizer was a case in point, computers another) using yesterdecades prices to value inputs might yield negative value added even when nominal value added is clearly positive. The accounting identities are only true when one calculates them in current prices. Neoclassical macro tries to get arround this by assuming a coconut economy woth one complex but stable good: coconuts. When apples are introduced in this economy, you will, however, get in trouble. Using nominal values however enables you to model a macro economy where new goods and services are introduced (even when more attention should be given to things like the rise of suburbia and its consequences for the concept of intermediate use of gasoline). We do have to embrace the bottom up aggregated economy. No coconut economy and fundamentally flawed examples. Money exists because there are multiple goods and services and persons and times and changing relative prices. Our examples will have to be monetary.

[Frances Woolley]

Nick nice post! I think I would turn to behavioural economics to explain what your Implicit Theory of Inertia - concepts like anchoring (we tend to use whatever we're given as a reference point to evaluate other things, which is why restaurants have ridiculously expensive wines on their menus (wow! $50 a bottle is cheap!) or salience (people focus on what's right in front of them). Are economists more prone to this than other scholars? I think old school economists, i.e. those of us who were educated prior to the profession's shift to empiricism, have a tendency to try to explain things with mathematical theorizing. And a lot of mathematical theorizing is basically taking some objective function, combining it with a accounting identities and auxilliary assumptions, and doing the math. Hence our special relationship with accounting identities!

[Henry Rech]

Nick,

For once I am very happy to have read one of your posts - normally I haven't the brains to make sense of your analogies which generally leave me in excruciating mental knots. This one I get (well, I think I do).

Regarding accounting identities as evidence for a particular behaviourial relationship from which outcomes can be worked ex ante, is always vexing to me.

The most consistent abusers of macro identities, it seems to me, are the MMTers. They can't be told enough.

[Nick Rowe]

Merijn: Since:
apples bought = apples sold,
it is also true that:
apples bought x any random price of apples I make up = apples sold x that same price I just made up.

It works for bananas too.

And if A=a and B=b, then A+B=a+b too, as we can add apples and bananas any way we like, as long as we do it the same way on both sides of the bought=sold identity.

Frances: Thanks! Hmmm. You might be onto something with anchoring.

Henry: thanks. Sounds like you get it.

[Henry Rech]

Frances,

"concepts like anchoring.....or salience..."

I would venture to say it's more like intellectual or ideological "venality".

Economists are no different than most people.

We've decided what we want to prove and we work backwards to do it.

It's all over economics.