The Fatal Flaw of the Keynesian Multiplier Theory

May 17, 2012

The Failure of the New Economics, 1959, Henry Hazlitt. Chapter XI

“THE MULTIPLIER”

1. The Magic of It

Let us try to find in plainer language what it is that Keynes is saying here. He explains on the next page: “It follows, therefore, that, if the consumption psychology of the community is such that they will choose to consume, e.g. nine-tenths of an increment of income, then the multiplier k is 10; and the total employment caused by (e.g.) increased public works will be ten times the primary employment provided by the public works themselves” (pp. 116-117).
What Keynes is saying, among other things, is that the more a community spends of its income, and the less it saves, the faster will its real income grow! Nor do the implications of its own logic frighten him. If a community spends none of its additional income (from, say, the increased public works), but saves all of it, then the public works will give only the additional employment that they themselves provide, and that will be the end of it. But if a community spends all of the additional income provided by the public works, then the multiplier is infinity. This would mean that a small expenditure on public works would increase income without limit, provided only that the community was not poisoned by the presence of savers.
Keynes does not hesitate to accept this deduction, but he accepts it in a peculiar form. “If, on the other hand, they [the community] seek to consume the whole of any increment of income, there will be no point of stability and prices will rise without limit” … But just how did prices get into it? The “propensity to consume,” and “the multiplier,” we have been assured up to this point, are expressed in terms of “wage-units,” which, Keynes assures us, means “real” terms and not money terms. — (p. 137)

2. Not Fixed or Predictable

Let us try to look at one probable origin of the concept. If a community’s income, by definition, is equal to what it consumes plus what it invests, and if that community spends nine-tenths of its income on consumption and invests one-tenth, then its income must be ten times as great as its investment. If it spends nineteen-twentieths on consumption and invests one-twentieth, then its income must be twenty times as great as its investment. If it spends ninety-nine-hundredths of its income on consumption and invests the remaining one-hundredth, then its income must be a hundred times its investment. And so ad infinitum.
These things are true simply because they are different ways of saying the same thing. The ordinary man in the street would understand this. But suppose you have a subtle man, trained in mathematics. He will then see that, given the fraction of the community’s income that goes into investment, the income itself can mathematically be called a “function” of that fraction. If investment is one-tenth of income, income will be ten times investment, etc. Then, by some wild leap, this “functional” and purely formal or terminological relationship is confused with a causal relationship. Next, the causal relationship is stood on its head and the amazing conclusion emerges that the greater the proportion of income spent, and the smaller the fraction that represents investment, the more this investment must “multiply” itself to create the total income! — (p. 139)

3. “Saving” and “Investment” Again

One fallacy in the “multiplier” that is alone sufficient to discredit it completely is the assumption that the entire fraction of a community’s income that is not “consumed” is hoarded; that no part of this unconsumed income is invested. — (p. 146)

4. “Investment” Means Government Spending

Ruritania is a Keynesian country that has a national income of $10 billion and consumes only $9 billion. Therefore it has a propensity to consume of 9/10. But as in some way it manages to “save” 10 per cent of its income without “investing” the 10 per cent in anything at all, it has unemployment of 10 per cent. Then the Keynesian government comes to the rescue by spending, not $1 billion, but only $100 million on “investment.” For as the “multiplier” is 10 (because Keynes has written out a mathematical formula which makes it 10 when the marginal propensity to consume is 9/10), this $100 million dollars worth of direct new employment somehow multiplies itself to $1 billion of total new employment to “fill the gap,” and lo! “full employment” is achieved.
(Expressing this in terms of employment, we might say: When the propensity to consume of Ruritania is 9/10, then, unless something is done about it, only 9 million of Ruritania’s working force of 10 million are employed. It is then simply necessary to spend enough to employ directly 100,000 more persons, and their spending, in turn, will ensure a total additional employment of 1 million.)
The question I am raising here is simply why such a relationship between the marginal propensity to consume and the multiplier is supposed to hold. Is it some inevitable mathematical deduction? If so, its causal inevitability somehow escapes me. Is it an empirical generalization from actual experience? Then why doesn’t Keynes condescend to offer even the slightest statistical verification? We have already seen that investment, strictly speaking, is irrelevant to the “multiplier” — that any extra spending on anything will do. We have already illustrated this by dividing commodities into those beginning with the letters from A to W, and those beginning with the letters X, Y, and Z. But a still further reductio ad absurdum is possible. Here is a far more potent multiplier, and on Keynesian grounds there can be no objection to it. Let Y equal the income of the whole community. Let R equal your (the reader’s) income. Let V equal the income of everybody of Y; whereas your income is the active, volatile, uncertain element in the social income. Let us say the equation arrived at is:
V = .99999 Y Then, Y = .99999 Y + R .00001 Y = R Y = 100,000 R
Thus we see that your own personal multiplier is far more powerful than the investment multiplier. To increase social income and thereby cure depression and unemployment, it is only necessary for the government to print a certain number of dollars and give them to you. Your spending will prime the pump for an increase in the national income 100,000 times as great as the amount of your spending itself.
The final criticism of the multiplier that must be made is so basic that it almost makes all the others unnecessary. This is that the multiplier, and the whole unemployment that it is supposed to cure, is based on the tacit assumption of inflexible prices and inflexible wages. Once we assume flexibility in prices and wages, and full responsiveness to the forces of the market, the whole Keynesian system dissolves into thin air. — (pp. 150-151)

Chapter XIV

“LIQUIDITY PREFERENCE”

2. Money is a Productive Asset

Before we go on to explain the theoretical reasons why Keynes’s liquidity-preference theory is wrong, we must first point out that it is clearly wrong. It goes directly contrary to the facts that it presumes to explain. If Keynes’s theory were right, then short-term interest rates would be highest precisely at the bottom of a depression, because they would have to be especially high then to overcome the individual’s reluctance to part with cash — to “reward” him for “parting with liquidity.” But it is precisely in a depression, when everything is dragging bottom, that short-term interest rates are lowest. And if Keynes’s liquidity-preference were right, short-term interest rates would be lowest in a recovery and at the peak of a boom, because confidence would be highest then, everybody would be wishing to invest in “things” rather than in money, and liquidity or cash preference would be so low that only a very small “reward” would be necessary to overcome it. But it is precisely in a recovery and at the peak of a boom that short-term interest rates are highest.4 See Appendix D, p. 448. — (p. 192) (see also Huerta de Soto’s explanation of the ABCT)

Dissent on Keynes: A Critical Appraisal of Keynesian Economics, 1992, Mark Skousen.

Chapter 4 : The Myths of the Multiplier and the Accelerator, 1992, by Jeffrey M. Herbener.

Multiplier

Keynes ignored this complexity in social action and assumed a precise, fixed multiplier process. Keynes described his multiplier as follows:
“In given circumstances a definite ratio, to be called the multiplier, can be established between income and investment, subject to certain simplifications, between the total employment and the employment directly employed on investment. This further step is an integral part of our theory of employment, since it establishes a precise relationship, given the propensity to consume, between aggregate employment and income and the rate of investment.” (Keynes 1936: 113 [emphases added])
Furthermore, he claimed that the MPC (Marginal Propensity to Consume) “is of considerable importance because it tells us how the next increment of output will have to be divided between consumption and investment” (ibid.: 115 [emphasis added]). The multiplier (k) equals 1/1-MPC, and thus, he concluded, “it tells us that, when there is an increment of aggregate investment, income will increase by an amount which is k times the increment of investment” (ibid, [emphasis added]).
To use k in support of “public works,” the multiplier must have the mathematical precision Keynes gives it (ibid.: 116). Yet this precision leads to logical absurdities. Three absurd cases exist, corresponding to three violations of Keynes’s pronouncement that 0 < MPC < 1. As shown above, there is no accounting principle that the MPC be bound in this way, and there is ample evidence that the MPC is not so bound (see Table 4.1).

One absurdity exists when the MPC = 1 since, in this case, k is infinitely large. Thus, any additional expenditure on “public works” would end scarcity! Keynes tried to avoid this absurdity by claiming that “prices will rise without limit” (ibid.: 117). This was nothing but a rhetorical trick since Keynes had defined his theory in real terms (wage-units). If prices are important in his equations, then he should put them in and explain their role in the multiplier process. Keynes could not do that because his entire theory falls apart as soon as changing relative prices are recognized (Hazlitt [1959] 1973: 288-318).

Even more damaging is the case where the MPC exceeds one (see Table 4.1). In this case, the multiplier is negative! But Keynes claimed that more spending always means more prosperity, not less. The final case is no less absurd. If the MPC is negative (see Table 4.1), then k will be a positive fraction. Thus, an increase in spending for “public works” gets partially consumed somewhere in the aggregate economy. But Keynes claimed that failure to spend leads to recession. His formula does not concur, nor can it be reconciled with his verbal pronouncements. Keynesians cannot have it both ways: either they must give up mathematical precision (rendering the theory null) or they must reconcile these absurdities with general economic theory (not possible).
Furthermore, granting that a multiplier exists, why should it equal 1/1-MPC? Why does the MPC determine additional spending in response to changing income? Even Keynes assumed that, when income increases, some of the additional saved funds go into investment spending. Since this additional investment is reacting to income, it should be included with the MPC. Moreover, given Keynes’s accounting assumptions (Y = C + I), all spending comes out of income. Thus, no source of funds exists to initiate the multiplier process except hoards (or fiat money). This result applies with equal force to government expenditures. There is no reason to treat them as initiating the multiplier process since they must also come out of income. Finally, there is no direction of cause and effect in the equation. And his system of equations (Y = C + I; C = a + bY; I = d) is recursive, that is, it is impossible to tell, mathematically, which variable changes first and which ones follow.
Even if these criticisms could be overcome, the multiplier could not be initiated without assuming unemployed resources and inflexible wages and prices (Hazlitt [1959] 1973: 149-52). Without unemployed resources, any increased spending in one area must draw resources out of other production. This process normally takes place even in the face of “unemployed” resources. Thus, a positive multiplier process in the industry receiving the spending would be offset by a negative multiplier process in the receding industry. More generally, even if created money stimulates production temporarily, it does so only by drawing resources out of some (previously preferred) alternative. In Keynesian terms, we might call these alternatives hoards of capital (excess capacity) or hoards of labor (leisure).
Finally, hoarding of money (lack of spending, for Keynes) cannot cause a multiplier effect in the absence of inflexible wages and prices. With flexibility, the only effect of hoarding money (an increase in money demand) or dispersing money (a decline in money demand) is a change in the general level of market prices. Because of this flexibility, any amount of money serves the entire medium of exchange function (Rothbard [1962] 1970: 661-719). Assuming wage and price inflexibility assumes away the desire individuals have to cooperate through the market. Prices and wages are terms of contracts used by individuals to bring about this cooperation. Even if the wage and price components of these contracts are inflexible, they may have other, flexible components. Employers could reduce fringe benefits or increase work loads to effectively circumvent fixed money wages, and suppliers could use rebates or giveaways to put flexibility into prices. — (pp. 78-79)

The Critics of Keynesian Economics, 1960, Henry Hazlitt.

Mr. Keynes’ “General Theory”, 1937, by Etienne Mantoux.

Are we moreover to assume that reduction of nominal wages is in no case an effective means of combatting unemployment? This is where those celebrated “expectations” came in. The volume of employment depends, at all events, on the sums that entrepreneurs have decided to invest in production. These in turn depend only indirectly on prices existing at the time; for it is the entrepreneurs’ expectations that determine the volume of sums to be invested; a decline in wages, opening up the prospect of a further decline, will not serve to increase the demand for labor (p. 263). It is upon probable consumption expenditures that the expectations are based. These future expenditures, or the “effective demand,” correspond to the point of intersection of the entrepreneurs’ over-all supply and demand functions (expressed in “anticipated” prices). Keynes gives the name of “propensity to consume” to the ratio of consumption expenditures to the total income of the community (the marginal propensity dC/dY — being (p. 115) the ratio of infinitesimal increments of the two variables). Now the volume of employment is controlled by that of investments. What part, then, is played by the propensity to consume?
This brings us to the multiplier theory, under which Keynes merely develops some reflections due to R. F. Kahn on the incremental effects of a capital investment. Obviously the movements of capital entailed by investing a certain sum devoted, say, to the execution of a given public works program, will not be confined to the original sum, and a certain amount of additional investments will result, after a varying interval of time, from that initial outlay. The sums invested will more or less rapidly permeate the structure of production, first leading to expenditures among enterprises, and later, when they reach the consumer through payment of wages or other income, causing a demand for consumption goods, which in turn will step up demand for intermediate goods, and so on.
Most analyses of this highly complex phenomenon assume, as we have seen, that all the factors of production are employed. In that case a new investment can only have the effect, in production as a whole, of transferring factors from one branch to another, most often from the consumption goods to the production goods market. It then becomes difficult to speak of net secondary effects of the initial investment, since their addition does not go to augment total output. Kahn’s multiplier measured the ratio of the immediate increment of employment, due to a given investment, to the total increment. Keynes here defines his investment multiplier as the ratio of the total increment of income brought about by a given increment of investments, to this original increment (Y income, I investment, multiplier k = ΔY/ΔI).
One might first point out that it is very hard to tell what moment to choose for evaluating the final result Y. The interval between the initial outlay and the time when the money invested reaches consumers is not only highly variable, but scarcely amenable to averaging without recourse to some concept like the “Austrian” theory’s “period of production” — apparently not very congenial to Keynes (p. 76). His “period of production” (p. 287), defined in terms of the time elapsed before increased demand for a given product expresses itself in a diminished elasticity of employment, looks very much like a petitio principii. But the effects of the multiplier, approximate as they are, are indubitable. Far more debatable is the function making the multiplier depend on the propensity to consume. The latter is equal, by definition, to 1 – 1/k, since income is divided between consumption expenditures and investment expenditures.
Given the definition of the multiplier, the propensity to consume therefore becomes equal to 1 – 1/k, which amounts to saying that as the propensity to consume approaches unity, meaning if the community applies the totality of its income to consumption expenditures, the secondary effects of a primary investment would approach infinity. Remarkable! Back in 1933, Keynes thought the multiplier, in Great Britain, was slightly greater than 2. It is altogether reasonable to use a term such as the “multiplier” to express a fact patent to everyone; one may go on to regard the proportion of income devoted to consumption as an independent function; lastly, it is quite permissible to make a certain function, called the “multiplier,” depend by definition on a certain variable called the “propensity to consume.” It is another matter to turn this formal relationship into a causal relationship. — (p. 107-109)
Is not this policy likely to beget inflation pure and simple, and present us once more with the excesses that have characterized all great crises, and that were indulged in con molto brio during the last? For Keynes, apparently, there can be no inflation so long as there is not full employment. “It is when an acceleration of demand cannot significantly increase the volume of employment, and expresses itself merely in rising prices, that we can speak of true inflation.” England, with its 1,570,000 unemployed, is therefore approaching this limit today in his opinion, since prices (especially the cost of living) have been accelerating alarmingly for the past year (though much progress is still to be made in the “distressed areas” before true inflation need be feared). In that case one may wonder what is really meant by “full employment”! If Keynes considers that rising prices are a sufficient sign to serve as the criterion, many of the unwillingly unemployed may not agree with him. At any rate, this might put the famous “irreducible minimum” pretty high. — (p. 122)

Money, Bank Credit, and Economic Cycles, 2009, Jesús Huerta de Soto.

Chapter 7 : A Critique of Monetarist and Keynesian Theories

Criticism of the Keynesian Multiplier

Indeed the multiplier indicates that any increase in credit expansion will cause a rise in real national income equal to the reciprocal of the marginal propensity to save (one minus the marginal propensity to consume). Hence according to Keynesian logic, the less people save, the more real income will grow. … Credit expansion will stimulate investment that will drive up the price of the factors of production and bring about a subsequent, more-than-proportional increase in the price of consumer goods and services. Even if gross income in money terms rises as a result of the injection of new money created by the banking system, the multiplier, owing to its mechanical and macroeconomic nature, is inadequate to depict the disruptive microeconomic effects credit expansion always exerts on the productive structure. Consequently the multiplier masks the widespread malinvestment of resources which in the long run impoverishes society as a whole (rather than enriching it, as Keynes alleges). We agree with Gottfried Haberler when he concludes that the multiplier …
“turns out to be not an empirical statement which tells us something about the real world, but a purely analytical statement about the consistent use of an arbitrarily chosen terminology — a statement which does not explain anything about reality. . . . Mr. Keynes’ central theoretical idea about the relationships between the propensity to consume and the multiplier, which is destined to give shape and strength to those observations, turns out to be not an empirical statement which tells us something interesting about the real world, but a barren algebraic relation which no appeal to facts can either confirm or disprove.” — (pp. 559-560)
Short-term unemployment can only be eliminated through “active” policies if workers and unions let themselves be deceived by the money illusion, and thus maintain nominal salaries constant in an inflationary atmosphere of soaring consumer prices. Experience has shown that the Keynesian remedy for unemployment (the reduction of real wages through increases in the general price level) has failed: workers have learned to demand raises which at least compensate them for decreases in the purchasing power of their money. Therefore the expansion of credit and effective demand, an action Keynesians supported, has gradually ceased to be a useful tool for generating employment. It has also entailed a cost: increasingly grave distortions of the productive structure. In fact a stage of deep depression combined with high inflation (stagflation) followed the crisis of the late seventies and was the empirical episode which most contributed to the invalidation of all Keynesian theory. — (p. 562)

Meng Hu on HBD and Austrian Economics

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