Last week I wrote a series of posts (starting with this and ending with this) that were mainly motivated by a single objective: to show how taking the accounting identity between savings and investment seriously can get someone, even a very fine economist, into serious trouble. That, I suggested, is what happened to Scott Sumner when, in a post about whether a temporary increase in government spending and taxes would increase GDP, he relied on the accounting identity between savings and investment to conclude that a reduction in savings necessarily leads to a reduction in investment. Trying to trace Scott’s mistake to misuse of an accounting identity led me a little further than I anticipated into the substance of the argument about how a temporary increase in government spending and taxes affects GDP, an argument that I am still not quite satisfied with, but which – you can relax — I am not going to discuss in this post. My aim in this post is merely to respond to one of Scott’s rejoinders to me, which is that he was just relying on a proposition – the identity of savings and investment – that is taught in just about every macro textbook, including textbooks by Paul Krugman and Greg Mankiw, two of the current heavyweights of the profession. If so, Scott observed, my argument is not really with him, but with the entire profession.
No doubt about it, Scott has a point, though I think that most textbooks and most economists have an intuitive understanding that the accounting identity is basically a fudge, and therefore, unlike Scott, generally do not rely on it for any substantive conclusions. The way that most textbooks try to handle the identity is to say that the identity really just refers to realized (ex post) saving and investment which must be equal, while planned (ex ante) investment and planned (ex ante) saving may not be equal, with the difference between planned investment and planned saving corresponding to unplanned investment (accumulation) of inventories. Equilibrium is determined by the equality of planned investment and planned saving, and any disequilibrium (corresponding to a divergence between planned saving and planned investment) is reflected in unplanned inventory accumulation (either positive or negative) which ensures that the identity between realized investment and realized saving is always satisfied. The usual fudge distinguishing between planned and realized investment and saving and postulating that unplanned inventory investment is what accounts for any difference between planned investment and saving is itself problematic, but it at least puts one on notice that there is a difference between an equilibrium condition and an accounting identity, while nevertheless erroneously suggesting that the accounting identity has some economic significance.
Not entirely coincidentally, Scott having got started on this topic by responding to a post by Paul Krugman, Krugman himself weighed in on the subject of accounting identities last week, enthusiastically citing a post by Noah Smith warning about the misuse of accounting identities in arguments about economics. Now the truth is that there is not too much in Krugman’s post that I disagree with, but there are certain verbal slips or misstatements that betray the confusion between accounting identities and equilibrium conditions that I am trying to get people to recognize and to stay away from. While avoiding any substantive error, Krugman perpetuates the confusion, thus contributing unwittingly to the very problem that motivated his post. Thus, his confusion is not just annoying to compulsive grammarians like me; it is also unnecessary and easily avoidable, and creates the potential for more serious mistakes by the unwary. So there is really no excuse for continuing to pay lip service to the supposed identity between savings and investment, regardless of how deeply entrenched it has become as the result of many decades of unthinking, rote repetition on the part of textbook writers.
What he’s referring to, I assume, is arguments like “since savings equals investment, fiscal stimulus can’t affect overall spending”, or “since the current account balance is equal to the difference between domestic saving and domestic investment, exchange rates can’t affect trade”. The first argument is, more or less, Say’s Law and/or the Treasury view. The second argument is what John Williamson called the doctrine of immaculate transfer.
This is pretty straightforward, though I don’t care for the examples that Krugman gives, displaying a conventional misunderstanding of Say’s Law. But Say’s Law is a whole topic unto itself. Nor can the Treasury view be dismissed as nothing more than the misapplication of an accounting identity. So I’m just going to ignore those two specific examples for purposes of this discussion. Back to Krugman.
Why are such arguments so misleading? Noah doesn’t fully explain, so let me put in a further word. As I see it, economic explanations pretty much always have to involve micromotives and macrobehavior (the title of a book by Tom Schelling). That is, when we tell economic stories, they normally involve describing how the actions of individuals, driven by individual motives (and maybe, though not necessarily, by rational self-interest), add up to interesting behavior at the aggregate level.
Again, nothing to argue with there, though the verb “add up” has just faintest whiff of an identity insinuating itself into the discussion.
And the key point is that individuals in general [as opposed to those strange creatures called economists who do care about "aggregate accounting identities?] neither know nor care about aggregate accounting identities.
Ok, now we are starting to have a problem. Individuals in general neither know nor care about aggregate accounting identities. Does that mean that those strange creatures called economist should know or care about aggregate accounting identities? I have yet to hear any cogent reason why they should.
Take the doctrine of immaculate transfer: if you want to claim that a rise in savings translates directly into a fall in the trade deficit, without any depreciation of the currency, you have to tell me how that rise in savings induces domestic consumers to buy fewer foreign goods, or foreign consumers to buy more domestic goods. Don’t tell me about how the identity must hold, tell me about the mechanism that induces the individual decisions that make it hold.
Here is where Krugman, after skating on the edge, finally slips up and begins to talk nonsense — very subtle nonsense, but nonsense nonetheless. What does it mean to say that an identity must hold? It means that, by the very meaning of the terms that one is using, the identity of which one is speaking must be true. It is inconceivable that an identity would not hold. If the difference between investment and savings (in an open economy) is defined to be identitically equal to the trade deficit, then talking about a mechanism that induces individual decisions to make it hold makes as much sense as saying that there must be a mechanism that induces individual decisions to make 2 + 2 equal 4. If, by the very meaning of the terms that I am using, the difference between investment and savings must equal the trade deficit (which, to repeat, is what it means to say that there is an identity between those magnitudes) there is no conceivable set of circumstances in which the two magnitudes would not be equal. If, in the very nature of things, two magnitudes could never possibly be different, it is nonsense to say that there is a mechanism of any kind (much less one describable in terms of the decisions of individual human beings) that operates to bring it about that the equality actually holds.
And once you do that, you realize that something else has to be happening — a slump in the economy, a depreciation of the real exchange rate, it depends on the circumstances, but it can’t be immaculate, with nothing moving to enforce the identity.
No, no! A thousand times no! If we are really talking about an identity, nothing has to be happening to enforce the identity. Identities don’t have to be enforced. Something that could not conceivably be otherwise requires nothing to prevent the inconceivable from happening.
When it comes to confusions about the macro implications of S=I, again the question is how the identity gets reflected in individual motives — is it via the interest rate, via changes in GDP, or what?
There are no macro implications of an identity; an identity has no empirical implications of any kind — period, full stop. If S necessarily equals I, because they have been defined in such a way that they could not possibly be unequal, then there is no conceivable state of the world in which they are unequal. Obviously, if S and I are equal in every conceivable state of the world, the necessary identity between them cannot rule out any conceivable state of the world. That means that the identity between S and I has no empirical implications. It says nothing about what can or cannot be observed in the real world at either the micro or the macro level.
Accounting identities are important; in fact, they’re the law. But they should inform your stories about how people behave, not act as a substitute for behavioral analysis.
I don’t know what law Krugman is referring to, but usually laws of nature tell us that some conceivable observations are not possible. Accounting identities don’t tell us anything of the sort. They are merely express certain conventional meanings that we are assigning to specific terms that we are using. How an accounting identity that could not be inconsistent with any conceivable state of the world can inform anything is a mystery, but I heartily agree that an accounting identity cannot be “a substitute for behavioral analysis.”
I have been rather (perhaps overly) harsh in my criticism on Krugman, but not to show that I am smarter than he is, which I certainly am not, but to show how easily habitual ways of speaking about macro lead to (easily rectifiable) nonsense statements. The problem is not any real misunderstanding on his part. Indeed, I would be surprised if, should he ever read this, he did not immediately realize that he had been expressing himself sloppily. The point is that macroeconomists have gotten into a lot of bad habits in describing their models and in failing to distinguish properly between accounting identities, which are theoretically unimportant, and equilibrium conditions, which are essential. Everything that Krugman said would have made sense if he had properly distinguished between accounting identities and equilibrium conditions rather than mix them up as he did, and as textbooks have been doing for three generations.
Savings and investment are equal in equilibrium, because that equality is a necessary and sufficient condition for the existence of an equilibrium. If so, being out of equilibrium means that savings and investment are not equal. So if we think that a real economy is ever out of equilibrium, one way to test for the existence of disequilibrium would be to see if actual savings and actual investment are unequal, notwithstanding the presumed accounting identity between savings and investment. That accounting identity is a product of the special definitions assigned to savings and investment by national income accounting practices, not by the meaning that our theory of national income assigns to those terms.
PS I will once again mention (having done so in previous posts on accounting identities) that all the essential points I am making in this post are derived from the really outstanding and unfortunately not very widely known paper by Richard G. Lipsey, “The Foundations of the Theory of National Income” originally published in Essays in Honour of Lord Robbins and reprinted in Macroeconomic Theory and Policy: Selected Essays of Richard G. Lipsey.