Posts Tagged 'conservation laws'

Keynes and Accounting Identities

In a post earlier this week, Michael Pettis was kind enough to refer to a passage from Ralph Hawtrey’s review of Keynes’s General Theory, which I had quoted in an earlier post, criticizing Keynes’s reliance on accounting identities to refute the neoclassical proposition that it is the rate of interest which equilibrates savings and investment. Here’s what Pettis wrote:

Keynes, who besides being one of the most intelligent people of the 20th century was also so ferociously logical (and these two qualities do not necessarily overlap) that he was almost certainly incapable of making a logical mistake or of forgetting accounting identities. Not everyone appreciated his logic. For example his also-brilliant contemporary (but perhaps less than absolutely logical), Ralph Hawtrey, was “sharply critical of Keynes’s tendency to argue from definitions rather than from causal relationships”, according to FTC economist David Glasner, whose gem of a blog, Uneasy Money, is dedicated to reviving interest in the work of Ralph Hawtrey. In a recent entry Glasner quotes Hawtrey:

[A]n essential step in [Keynes’s] train of reasoning is the proposition that investment and saving are necessarily equal. That proposition Mr. Keynes never really establishes; he evades the necessity doing so by defining investment and saving as different names for the same thing. He so defines income to be the same thing as output, and therefore, if investment is the excess of output over consumption, and saving is the excess of income over consumption, the two are identical. Identity so established cannot prove anything. The idea that a tendency for investment and saving to become different has to be counteracted by an expansion or contraction of the total of incomes is an absurdity; such a tendency cannot strain the economic system, it can only strain Mr. Keynes’s vocabulary.

This is a very typical criticism of certain kinds of logical thinking in economics, and of course it misses the point because Keynes is not arguing from definition. It is certainly true that “identity so established cannot prove anything”, if by that we mean creating or supporting a hypothesis, but Keynes does not use identities to prove any creation. He uses them for at least two reasons. First, because accounting identities cannot be violated, any model or hypothesis whose logical corollaries or conclusions implicitly violate an accounting identity is automatically wrong, and the model can be safely ignored. Second, and much more usefully, even when accounting identities have not been explicitly violated, by identifying the relevant identities we can make explicit the sometimes very fuzzy assumptions that are implicit to the model an analyst is using, and focus the discussion, appropriately, on these assumptions.

I agree with Pettis that Keynes had an extraordinary mind, but even great minds are capable of making mistakes, and I don’t think Keynes was an exception. And on the specific topic of Keynes’s use of the accounting identity that expenditure must equal income and savings must equal investment, I think that the context of Keynes’s discussion of that identity makes it clear that Keynes was not simply invoking the identity to prevent some logical slipup, as Pettis suggests, but was using it to deny the neoclassical Fisherian theory of interest which says that the rate of interest represents the intertemporal rate of substitution between present and future goods in consumption and the rate of transformation between present and future goods in production. Or, in less rigorous terminology, the rate of interest reflects the marginal rate of time preference and the marginal rate of productivity of capital. In its place, Keynes wanted to substitute a pure monetary or liquidity-preference theory of the rate of interest.

Keynes tried to show that the neoclassical theory could not possibly be right, inasmuch as, according to the theory, the equilibrium rate of interest is the rate that equilibrates the supply of with the demand for loanable funds. Keynes argued that because investment and savings are identically equal, savings and investment could not determine the rate of interest. But Keynes then turned right around and said that actually the equality of savings and investment determines the level of income. Well, if savings and investment are identically equal, so that the rate of interest can’t be determined by equilibrating the market for loanable funds, it is equally impossible for savings and investment to determine the level of income.

Keynes was unable to distinguish the necessary accounting identity of savings and investment from the contingent equality of savings and investment as an equilibrium condition. For savings and investment to determine the level of income, there must be some alternative definition of savings and investment that allows them to be unequal except at equilibrium. But if there are alternative definitions of savings and investment that allow those magnitudes to be unequal out of equilibrium — and there must be such alternative definitions if the equality of savings and investment determines the level of income — there is no reason why the equality of savings and investment could not be an equilibrium condition for the rate of interest. So Keynes’s attempt to refute the neoclassical theory of interest failed. That was Hawtrey’s criticism of Keynes’s use of the savings-investment accounting identity.

Pettis goes on to cite Keynes’s criticism of the Versailles Treaty in The Economic Consequences of the Peace as another example of Keynes’s adroit use of accounting identities to expose fallacious thinking.

A case in point is The Economic Consequences of the Peace, the heart of whose argument rests on one of those accounting identities that are both obvious and easily ignored. When Keynes wrote the book, several members of the Entente – dominated by England, France, and the United States – were determined to force Germany to make reparations payments that were extraordinarily high relative to the economy’s productive capacity. They also demanded, especially France, conditions that would protect them from Germany’s export prowess (including the expropriation of coal mines, trains, rails, and capital equipment) while they rebuilt their shattered manufacturing capacity and infrastructure.

The argument Keynes made in objecting to these policies demands was based on a very simple accounting identity, namely that the balance of payments for any country must balance, i.e. it must always add to zero. The various demands made by France, Belgium, England and the other countries that had been ravaged by war were mutually contradictory when expressed in balance of payments terms, and if this wasn’t obvious to the former belligerents, it should be once they were reminded of the identity that required outflows to be perfectly matched by inflows.

In principle, I have no problem with such a use of accounting identities. There’s nothing wrong with pointing out the logical inconsistency between wanting Germany to pay reparations and being unwilling to accept payment in anything but gold. Using an accounting identity in this way is akin to using the law of conservation of energy to point out that perpetual motion is impossible. However, essentially the same argument could be made using an equilibrium condition for the balance of payments instead of an identity. The difference is that the accounting identity tells you nothing about how the system evolves over time. For that you need a behavioral theory that explains how the system adjusts when the equilibrium conditions are not satisfied. Accounting identities and conservation laws don’t give you any information about how the system adjusts when it is out of equilibrium. So as Pettis goes on to elaborate on Keynes’s analysis of the reparations issue, one or more behavioral theories must be tacitly called upon to explain how the international system would adjust to a balance-of-payments disequilibrium.

If Germany had to make substantial reparation payments, Keynes explained, Germany’s capital account would tend towards a massive deficit. The accounting identity made clear that there were only three possible ways that together could resolve the capital account imbalance. First, Germany could draw down against its gold supply, liquidate its foreign assets, and sell domestic assets to foreigners, including art, real estate, and factories. The problem here was that Germany simply did not have anywhere near enough gold or transferable assets left after it had paid for the war, and it was hard to imagine any sustainable way of liquidating real estate. This option was always a non-starter.

Second, Germany could run massive current account surpluses to match the reparations payments. The obvious problem here, of course, was that this was unacceptable to the belligerents, especially France, because it meant that German manufacturing would displace their own, both at home and among their export clients. Finally, Germany could borrow every year an amount equal to its annual capital and current account deficits. For a few years during the heyday of the 1920s bubble, Germany was able to do just this, borrowing more than half of its reparation payments from the US markets, but much of this borrowing occurred because the great hyperinflation of the early 1920s had wiped out the country’s debt burden. But as German debt grew once again after the hyperinflation, so did the reluctance to continue to fund reparations payments. It should have been obvious anyway that American banks would never accept funding the full amount of the reparations bill.

What the Entente wanted, in other words, required an unrealistic resolution of the need to balance inflows and outflows. Keynes resorted to accounting identities not to generate a model of reparations, but rather to show that the existing model implicit in the negotiations was contradictory. The identity should have made it clear that because of assumptions about what Germany could and couldn’t do, the global economy in the 1920s was being built around a set of imbalances whose smooth resolution required a set of circumstances that were either logically inconsistent or unsustainable. For that reason they would necessarily be resolved in a very disruptive way, one that required out of arithmetical necessity a substantial number of sovereign defaults. Of course this is what happened.

Actually, if it had not been for the insane Bank of France and the misguided attempt by the Fed to burst the supposed stock-market bubble, the international system could have continued for a long time, perhaps indefinitely, with US banks lending enough to Germany to prevent default until rapid economic growth in the US and western Europe enabled the Germans to service their debt and persuaded the French to allow the Germans to do so via an export surplus. Instead, the insane Bank of France, with the unwitting cooperation of the clueless (following Benjamin Strong’s untimely demise) Federal Reserve precipitated a worldwide deflation that triggered that debt-deflationary downward spiral that we call the Great Depression.

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About Me

David Glasner
Washington, DC

I am an economist in the Washington DC area. My research and writing has been mostly on monetary economics and policy and the history of economics. In my book Free Banking and Monetary Reform, I argued for a non-Monetarist non-Keynesian approach to monetary policy, based on a theory of a competitive supply of money. Over the years, I have become increasingly impressed by the similarities between my approach and that of R. G. Hawtrey and hope to bring Hawtrey's unduly neglected contributions to the attention of a wider audience.

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