Discussion Paper No. 673

FALLACY OF THE MULTIPLIER EFFECT:CORRECTING THE INCOME ANALYSIS

Yoshiyasu Ono

October 2006

The Institute of Social and Economic Research
Osaka University
6-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan

October 2006

Fallacy of the Multiplier Effect: Correcting the Income Analysis
byYoshiyasu Ono*
Osaka University

Abstract
Although the Keynesian multiplier effect of public works is criticized for lack of a
microeconomic foundation, it is still taught in most undergraduate courses and believed to be
useful for policy makers. However, it has a serious fallacy even if we accept the consumptionfunction. This note shows that useless public works is equivalent to unemployment relief
expenditure in the presence of unemployment and that the argument on the multiplier effectseriously misleads the present national accounting and thereby distorts evaluation of publicworks. A correction of the textbook explanation on the income analysis is also provided.
JEL classification: E12, E62, E01
Keywords: multiplier effect, consumption function, national income account.
Address: Institute of Social and Economic Research, Osaka University, 6-1, Mihogaoka,
Ibaraki, Osaka, 567-0047, JAPANE-mail: ono@iser.osaka-u.ac.jp*Professor, Institute of Social and Economic Research. The author is particularly indebted to N. Matsushimaand K. Takii for their very helpful comments and discussions. He also thanks S. Ikeda, J. Itaya, K. Ogawa and Y.
Sugimoto for useful comments. This research is financially supported by the Grants-in-Aid for Scientific
Research, JSPS, Japan.

Although the Keynesian multiplier effect is criticized for lack of a microeconomic
foundation, it has still been taught as a standard macroeconomic theory in most undergraduate
courses. The criticism against it is mainly from lack of consideration on the intertemporalbudget constraint --i.e., even loan expenditure generates no spillover effect on consumption
once the intertemporal budget equation is taken into account. However, it is rather acceptedthat public works expenditure under a balanced budget increases the national income by its
own size --i.e., the multiplier under a balanced budget equals one.1 Since this property is
independent of what is produced, it is believed that even useless public works is better thanunemployment relief expenditure since the latter is a mere redistribution and hence does notincrease the national income.2
This note shows that useless public works under a balanced budget is equivalent tounemployment relief expenditure whether the rational consumer behavior or the Keynesian
consumption function is assumed --i.e., the balanced-budget multiplier is economicallymeaningless. Moreover, it provides an alternative income analysis that corrects the problem. A
problem of the present national accounting owing to this misunderstanding is also pointed out.

1. Unemployment Relief Expenditure vs. Useless Public WorksFirst, suppose useless public works in which only labor services are used and compare its
effect with that of unemployment relief expenditure. In the case of unemployment relief
expenditure a government collects money as the unemployment insurance premium or a tax
and pays unemployment allowance to the unemployed. In the case of ‘useless’ public works
under a balanced budget the government collects taxes, hires the unemployed, leaves themdoing nothing substantial and pays salaries to them. Thus, these two are exactly the sameexcept under what name money is paid, viz. unemployment allowance or salaries. They areboth mere redistributions without producing anything and hence the disposable income of theprivate sector remains unchanged, generating no effect on the national product.
The same logic applies to general public works in which some commodities such asconcrete are required. A riverbank reinforcement project may be an example. Since salary1

See e.g. Stiglitz (1997, pp.775-776) and Mankiw (2003, pp.264-265). It is called Haavelmo’s theorem, as
mentioned by Moene and Rodseth (1991).
2Keynes (p.127, 1936) himself states that even useless public works is better than unemployment relief
expenditure since it creates new demand.

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payment on labor services has the same effect as mentioned above, I focus on the effect of
payment on concrete. Since concrete is produced of gravel and limestone, the payment is fully
distributed to miners and haulers. Thus, it is equivalent to unemployment allowance to them aslong as they would be unemployed without the project. The same logic applies to any
commodity demand by public works, such as trucks, machineries, etc. Thus, in general, theeffect of useless public works under a balanced budget is the same as that of unemployment
relief expenditure.3

Proposition 1: Useless public works under a balanced budget is equivalent to unemployment
relief expenditure.

There are two things worth noting. First, since the total disposable income does not varyand nothing useful is produced in both cases, the above property is valid regardless of which
consumer behavior is assumed, the Keynesian consumption function or neoclassical rational
behavior. Second, since the above result is valid in the case of a useless public works project, if
it is of some use then it increases the national product by its resultant value. Thus, the following
proposition obtains:

Proposition 2: Public works under a balanced budget generates no spillover effect on thenational income. It raises the national product exactly by the value that it directly produces–i.e., the balanced-budget multiplier of public works with respect to the national productequals its efficiency rate.

2. Correction of Textbook Explanation on the Effect of Public Works
Why does the multiplier effect of public works seem to generate a different effect fromthat of unemployment relief expenditure in the Keynesian model? In most textbooks thisproperty is described as follows:y = c(y − t + z) + g + i,3(1)There is a slight difference between useless public works and unemployment relief expenditure. The former
hires people and hence reduces the deflationary gap in the labor market while the latter does not. A reduction in
deflation makes it less advantageous for consumers to hold money than to consmue now and hence stimulates
consumption. See Ono (2001) for this effect of public works in the steady state where persistent stagnation arises.

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where y is income, z is unemployment allowance, c is the consumption function that depends
on disposable income y − t + z, and g is public works spending. Without any loss of the present
analysis investment i is assumed to be fixed. Under a balanced budget:g + z = t,(2)

from (1) it is immediately found thatdy /dg⏐z = 0 = 1, dy/dz⏐g = 0 = 0,-- i.e., the balanced-budget multiplier equals 1 whereas that of unemployment allowance iszero.
The fallacy comes from a confusion of public works expenditure and the value of its
product. The private sector sells products and receives income that equals consumption c plus
investment i. In addition, it pays tax t and receives either income from government spending gor unemployment allowance z. Thus, disposable income yd is
yd = c + i + g + z − t.

(3)dConsumption c depends on y and hencec = c(yd).

(4)
v

The value of the national product, denoted by y , is the sum total of consumption c,investment i and the value of the public works product θg where θ represents the efficiency rateof g. Thus, yv is given by
yv = c + i + θg.

(5)Note that θ equals zero if the public works is useless.
From (2), (3) and (4) one has
yd = c(yd) + i,
showing that neither z nor g has any effect on disposable income yd:
dyd/dg = 0, dyd/dz = 0.

(6)

Since (2), (3) and (5) imply
yv − θg = yd,from (4) and (5) yv satisfies
yv = c(yv − θg) + i + θg.
From this equation one finds
dyv/dg = θ, dyv/dz = 0.

3(7)Equations (6) and (7) imply proposition 2. In particular, if the project is of no use (i.e., θ = 0), it
affects neither disposable income yd nor national product yv and hence is equivalent tounemployment relief expenditure, as stated in proposition 1.
The first equation of (7) shows that a public works project is worth carrying out as long as
the value of its product is positive (θ > 0). Note that it is still true even if the value is less thanthe expenditure (θ < 1). It is in sharp contrast to the neoclassical case --i.e., under full
employment if θ is less than 1, the public works project reduces the national product since its
spending exactly exhibits its opportunity cost. In the presence of unemployment, in contrast, it
is not an opportunity cost but a costless transfer since the workers should be unemployed
without it.

3. Conclusion: The Present National Income Accounting May Mislead
Policy Decision
In standard textbooks it is taught that in the presence of unemployment public works raises
the national income by creating new demand whereas unemployment relief expenditure does
not since it is a mere redistribution. Since this property is independent of what is produced bypublic works, even useless public works is believed to be better than unemployment reliefexpenditure. This note shows that it is a fallacy and that such public works is equivalent tounemployment relief expenditure whether the rational consumer behavior or the Keynesian
consumption function is assumed.
The fallacy comes from a confusion between the spending and the produced value of
public works, and the present national income accounting is also distorted by the confusion. In
the present national accounting if a government collects money under the name ofunemployment insurance premium and transfers it to the unemployed as unemployment
allowance, it adds nothing to the national income. However, if it collects money under thename of tax payment and transfers it as payroll for public works, the amount is added to thenational income. Thus, the level of the multiplier calculated under the present national income
accounting is meaningless when considering the national product. It is because the present
accounting implicitly assumes that the value of public works equals its cost. In reality,however, useless public works is a mere redistribution and equivalent to unemployment reliefexpenditure. Therefore, public works must be evaluated as the value of its product in thenational income accounting.
4Such a correction can also apply to the case of full employment. An increase in public
works crowds out private usage of production factors and increases the national product by thevalue of its product. In the present accounting system public works is evaluated not by thevalue of its product but by the expenditure level and hence the national product does not varyeven if it is of no use. If it is evaluated by the value of its product (which is zero in the presentcase), however, the national product decreases by the expenditure level, showing correctly thecrowding-out effect.
Finally, it is to be noted that the results obtained under a balanced budget can also apply tothe case of loan expenditure if the intertemporal budget equation is taken into account. It isbecause the Ricardian equivalence holds and hence there is no difference between
balanced-budget expenditure and loan expenditure. Thus, any property based on the multipliereffect is a fallacy even in the presence of unemployment. Nevertheless, public works of someuse is worth doing even if the value of its product is less than the expenditure.

5References

Keynes, John M., The General Theory of Employment, Interest and Money, London:Macmillan, 1936.
Mankiw, N. Gregory, Macroeconomics, 5th ed., New York: Worth, 2003.
Moene, Karl Ove, and Asbjorn Rodseth, "Nobel Laureate: Trygve Haavelmo", Journal ofEconomic Perspectives, vol.5, Summer 1991, 175-192.
Ono, Y., "A Reinterpretation of Chapter 17 of Keynes’s General Theory: Effective Demand
Shortage Under Dynamic Optimization," International Economic Review, vol.42,February 2001, 207-236.
Stiglitz, Joseff E., Economics, 2nd ed., New York: Norton, 1997.

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