GCOE Discussion Paper Series
Global COE Program

Human Behavior and Socioeconomic Dynamics
Discussion Paper No.30

The Keynesian Multiplier Effect Reconsidered

Yoshiyasu Ono

January 2009GCOE Secretariat
Graduate School of Economics

OSAKA UNIVERSITY

1-7 Machikaneyama, Toyonaka, Osaka, 560-0043, Japan

December 2008

The Keynesian Multiplier Effect Reconsideredby

Yoshiyasu Ono*
Osaka University

Abstract
The Keynesian multiplier effect is reinterpreted and several issues that may have misledassessments of the effect of fiscal spending are discussed. It is shown that even in the textbook
Keynesian framework some transfer policy ‘reduces’ aggregate demand and that public works
spending may completely crowd out private consumption. Useless public works are found tobe equivalent to transfers although they increase accounting national income more thantransfers do. The net effect of fiscal spending on national benefits is explored and shown toequal only the direct benefit created by the spending.
JEL classification: E12, E62, E01
Keywords: the multiplier effect, public works, unemployment benefits, national income
accounting.
Address: Institute of Social and Economic Research, Osaka University, 6-1, Mihogaoka,
Ibaraki, Osaka, 567-0047, JAPAN*This is a substantially revised version of ISER Discussion Paper No.0673, October 2006. I am indebted to M.
Ogaki for his very stimulative suggestion. Comments and suggestions by H. Kojima, N. Matsushima, K. Takii and
A. Shibata are particularly valuable. I also thank C. Freedman, S. Ikeda, J. Itaya, R. Murota, K. Ogawa and Y.
Sugimoto for discussions. This research is financially supported by the Grants-in-Aid for Scientific Research,
JSPS, Japan.

Facing the financial crisis triggered by the US subprime loan problem in 2008, many
countries, including the USA, EU countries and Japan, have started to reaffirm the importanceof fiscal expansion. Since the neoclassical macroeconomics takes it as yielding crowding out
and gives no reason that supports it as a stimulus, most policy makers still rely on theconventional Keynesian multiplier model as a theoretical basis. This paper reinterprets theimplication of the multiplier effect and discusses some issues that may have misled
understanding of it.
By extending the multiplier model to the case where there are people with different
marginal propensities to consume this paper shows that public works spending may completely
crowd out private consumption even in the standard Keynesian setting. Government transfers,
such as unemployment relief expenditure, lump-sum benefits adopted by Japan’s K. Obuchi
administration in 1999, and tax rebates implemented by the US G. Bush administration in
2001, are shown to be equivalent to useless public works.1 It is also found that the benefit ofpublic works spending tends to be exaggerated under the present national accounting.

1. Reinterpreting the Multiplier EffectThis section starts the analysis by replicating the Keynesian multiplier effect, where
private investment is ignored for simplicity. Since disposable income Yd equals revenues fromfiscal spending G and consumption demand C minus tax payments T,
Yd = G + C − T,consumption C satisfies
C = F(G + C − T),(1)where F(.) represents the consumption function.2 Note that (1) is valid whether fiscal spending
G implies government purchases or transfers. National Income Y is thenY = αG + C,

(2)

where
α = 1 for government purchases,
α = 0 for transfers.
(1) and (2) reproduce the standard multiplier effect:

1

The T. Aso administration in Japan also proposes uniform benefits in 2008.

2

F(.) is used so as to distinguish between consumption level C and the consumption function.

1(3)

dY/dG = α + dC/dG,

(4)

where
dC/dG = F′/(1 − F′) under a loan budget,
dC/dG = dC/dG|dT = dG = 0 under a balanced budget.

(5)

The first term of (4), α, is interpreted as the government demand effect. It is the direct
effect of fiscal spending on income and hence satisfies (3). The second term, dC/dG, isinterpreted as the transfer effect. It exhibits the effect on household consumption provoked byfiscal payments. Note that there is no difference in the transfer effect between unemployment
benefits, public works, government purchases and so on since household behavior is the sameafter the payments are received. It only depends on the distribution of the payments.
In order to explore the implication of the transfer effect, (5) is modified so that it can treat
the case where there are two groups of people and their marginal propensities to consume differ
from each other. Let Fi represent the consumption function of group i (for i = 1, 2), aggregate
consumption C is
C = F1(σ1C + G1 − T1) + F2(σ2C + G2 − T2), where σ1 + σ2 = 1.

(6)σi, Gi and Ti respectively denote group i’s share of income generated by consumption demandC, fiscal spending paid to group i, and taxes imposed on group i. Without loss of generality weassume1 ≥ F1′ > F2′ ≥ 0,

(7)

where group 2 is naturally considered to be richer than group 1. From (6),dC = [F1′d(G1 − T1) + F2′d(G2 − T2)]/{1 − [σ1F1′ + (1 − σ1)F2′]},(8)where d(Gi − Ti) stands for an increase in group i’s net receipt from fiscal spending. From (7)and (8), fiscal spending distributed to the poorer has a larger stimulative effect on aggregate
consumption C than that to the richer.
Fiscal spending may even reduce aggregate consumption under a balanced budget:dG − dT = d(G1 − T1) + d(G2 − T2) = 0.
In fact, (7) and (8) then givedC/d(G1 − T1)|dT = dG = (F1′ − F2′)/{1 − [σ1F1′ + (1 − σ1)F2′]} > 0,dC/d(G2 − T2)|dT = dG = − (F1′ − F2′)/{1 − [σ1F1′ + (1 − σ1)F2′]} < 0.

(9)

Since a pure transfer yields no government demand, i.e., α = 0 as shown in (3), from (2) and(9), a net redistribution from the poorer to the richer reduces aggregate consumption C andnational income Y. Unemployment compensation is a typical reverse example. Moreover, if the2

people of group 1 are unemployed (σ1 = 0) and spend all additional income on consumption(F1′ = 1), from (7) and (9)dC/d(G2 − T2)|dT = dG = − 1 if σ1 = 0 and F1′ = 1,

(10)i.e., if the government reduces unemployment benefits and redistributes the fund to theemployed, aggregate consumption C and national income Y decrease by the amount ofredistribution. Intuitively, since only people in group 2 are employed and hence the multiplieris 1/(1 − F2′), a decrease in the income of the unemployed yields a negative transfer effect ofwhich the magnitude is −F1′/(1 − F2′), where F1′ = 1, while an increase in the income of theemployed yields a positive transfer effect of which the magnitude is F2′/(1 − F2′). Thus, thetotal effect equals −1. Note that this property holds for any F2′ that satisfies (7).
From (3), (4) and (9), it is also shown that the multiplier effect of government purchases
can be less than 1. In particular, if the government reduces unemployment benefits and expands
commodity purchases, i.e.,dT1 = dT = dG = dG2, dT2 = dG1 = 0,then from (10)dC/dG = dC/d(G2 − T2)|dT = dG = − 1.
Therefore, from (2) and (3),dY/dG = 1 + dC/dG = 0,i.e., the multiplier effect on national income Y is zero. Unemployed people decrease
consumption and the government increases it by just that much.
In sum, the estimated income multiplier can be either negative or positive. This may be
why the effects on GDP of various fiscal expenditures are found to be significantly different in
the literature, depending on the composition of fiscal spending.3 The pattern of distribution
among different income classes that have different marginal propensities to consume is quite
important when comparing the demand-side effects of various fiscal expenditures on GDP,
while the difference of the purpose of fiscal spending, e.g., productive vs. non-productive
expenditures, current vs. capital expenditures, etc., is important on the supply side.4

3

Gupta et al. (2005) give an extensive survey of the literature on this issue.

4

Aschauer (1989) shows that public expenditures on nonmilitary public capital contribute to productivity
significantly more than those on military capital. Devarajan, Swaroop and Zou (1996) find that in developing
countries current expenditures stimulate growth more than capital expenditures and conclude that those countries
may spend too much on public capital.

32. Benefit of Fiscal Spending
The transfer effect exhibits not only the magnitude of demand creation but also the actual
benefit that people receive from consumption since they spend income on consumption after
recognizing it as worthy. In contrast, the government demand effect does not necessarily
represent actual benefits since fiscal spending is not determined on the utility basis. Thissection returns to the original model, where (5) is valid, and examines the effects of various
types of fiscal spending on national benefit B.
Let θ denote the direct benefit-cost ratio of fiscal spending, total benefit B is
B = θG + C,
and the multiplier effect on total benefit B is
dB/dG = θ + dC/dG,(11)

where dC/dG is given by (5). If fiscal spending G is a transfer payment, such as unemployment
benefits and tax rebates, θ equals zero and hence the effect on total benefit B consists of only
the transfer effect, as is consistent with (3) and (4). In the case of useless public works θ again
equals 0. Therefore, useless public works are equivalent to unemployment benefits, although inthe standard multiplier theory they are considered to be more stimulative than unemployment
benefits since they create demand.5
The equivalence between unemployment benefits and useless public works is intuitively
explained as follows. Unemployment benefits are directly paid to unemployed people without
making them work. In the case of useless public works the government hires them, makes them
do nothing substantial and pays salaries to them. Thus, these two are the same except for thepretext of the payment, viz. unemployment benefits or salaries.6 The same logic applies to thecase in which some commodities, e.g. concrete, are purchased. Concrete is produced of gravel
and limestone and the payment is distributed to miners and haulers –i.e., purchasing concrete isequivalent to paying unemployment benefits to them.
The multiplier effect of public works spending (or government purchases) is shown to belarger than that of a transfer payment by (3) and (4) since not the benefit, but the amount, ofspending is focused on.7 The national accounting system follows such convention and public

5

See Keynes (p.127, 1936) and the textbook by Itoh (2001, p.61) for such statements.

6

They are equivalent also from the viewpoint of distribution in the present example.

7

Alesina and Perotti (1997), Alesina et al. (1998), Kneller et al. (1999) and von Hagen and Strauch (2001)
empirically examine fiscal consolidations in OECD countries and find that reductions in transfers tend to be more4

works spending is in its entirety added to national income regardless of its benefit, whereas atransfer payment is not counted. Thus, the effect of public works spending tends to be
exaggerated.8 The conventional result is valid on the benefit basis only if fiscal spending
creates the same benefit as the cost (i.e., θ = 1). Even if not so, however, public works spending
is still more beneficial than a transfer payment as long as it yields some direct benefit (θ > 0).

3. Some Extensions and Conclusion
In the absence of fiscal illusion the Ricardian equivalence holds and disposable income Yd
must be calculated on the permanent basis, implying that T = G in (1). From (5), the transfer
effect (except the redistribution effect given by (9)) is null and only the government demand
effect arises, whether under a balanced budget or a loan budget. Therefore, from (4) and (11),dY/dG = 1, dB/dG = θ,i.e., the effect of government purchases on accounting national income is 1 whereas the effecton national benefit equals the benefit directly created by them.
In the presence of fiscal illusion the transfer effect, dC/dG, is given by the first equation of(5) under a loan budget. In this case, however, the fiscal deficit must be redeemed in the future
and then a negative transfer effect with the same present-value magnitude arises. Thus, aftercancelling out the costs and benefits intertemporally we come to a quite simple conclusion:“The net effect of fiscal spending on national benefit consists of its direct benefit
and the redistribution effect only, regardless of the budget system or the type offiscal spending.”
Transfer payments and useless public works yield only the redistribution effect, which can beeither positive or negative.
There are still some aspects that are ignored here. If there is some disutility of working,useless public works are inferior to transfers.9 Another difference arises through the inflation
effect. Public works create new labor demand and reduce the deflationary gap in the labor

successful than reductions in public investment --i.e., the former contract national income less than the latter.
Gupta et al. (2005) show the same tendency in developing countries.
8

Kuznets (1948) expresses concern about the part of government purchases in national income accounting
from another viewpoint. Although they are uniformly regarded as final consumption, in reality they may be used
for intermediate goods and then are duplicated in calculating national income.
9

Keynes (p.128, 1936) states that labor may have a positive utility for people who have been longunemployed, which makes public works superior to transfers.

5market while transfers do not. The reduction in deflation makes it less advantageous for
consumers to hold money than to consume and hence stimulates consumption.10 Anyway, thesefactors are not taken into account in the conventional Keynesian framework.

REFERENCES

Alesina, A., and R. Perotti. (1997) “Fiscal Adjustments in OECD Countries: Composition andMacroeconomic Effects.” IMF Staff Papers, 92, 571-89.
Alesina, A., R. Perotti, and J. Tavares. (1998) “The Political Economy of Fiscal Adjustments.”
Brookings Papers on Economic Activity, 1, 197-248.
Aschauer, D. A. (1989) “Is Public Expenditure Productive?” Journal of Monetary Economics,
23, 177-200.
Devarajan, S., V. Swaroop and H. Zou. (1996) “The Composition of Public Expenditure andEconomic Growth.” Journal of Monetary Economics, 37, 313-44.
Itoh, M. (2001) Nyumon Keizaigaku (Introductory Economics), 2nd edition. Tokyo: Tokyo:
Nihon Hyoronsha.
Gupta, S., B. Clements, E. Baldacci and C. Mulas-Granados. (2005) “Fiscal Policy,
Expenditure Composition, and Growth in Low-income Countries.” Journal ofInternationl Money and Finance, 24, 441-63.
Keynes, John M. (1936) The General Theory of Employment, Interest and Money. London:
Macmillan.
Kneller, R., M. Bleaney and N. Gemmell. (1999) “Fiscal Policy and Growth: Evidence from
OECD Countries.” Journal of Public Economics, 74, 171-90.
Kuznets, S. (1948) “National Income: A New Version.” Review of Economics and Statistics,
30, 105-24.
Ono, Y. (1994) Money, Interest, and Stagnation. Oxford, UK: Clarendon Press.
Ono, Y. (2001) “A Reinterpretation of Chapter 17 of Keynes’s General Theory: Effective
Demand Shortage Under Dynamic Optimization.” International Economic Review, 42,
207-36.
von Hagen, J., and R. Strauch (2001) “Fiscal Consolidations: Quality, Economic Conditions,and Success.” Public Choice, 109, 327-46.
10

See Ono (1994, 2001) for this effect of public works spending in the steady state with persistent stagnation.

6