OSIPP Discussion Paper : DP-2004-E-002

Fiscal Policy and Entrepreneurship
May 7, 2004
Katsuya Takii
Associate Professor, Osaka School of International Public Policy(OSIPP)【キーワード】E62.
【要約】This paper reexamines the effect of expansionary fiscal
policy on real GDP in the presence of entrepreneurship, which isdefined as firms' activities to predict and adapt to changes in
consumers' tastes. As government expenditure cannot reflectchanges in consumers' tastes, it weakens the social role of thefirms' ability to process local information for predicting thechanges.
Hence, government expenditure cannot perfectly
substitute for private consumption. It is shown that expansionary
fiscal policy can lower real GDP when idiosyncratic risk and thesubstitutability of goods are large, and when firms have a strong
ability to predict changes in consumer tastes. In addition, thispaper shows that expansionary fiscal policy discourages firms
from investing in activities that aid prediction in the short run.
However, expansionary fiscal policy does not influence investmentin prediction ability in the long run.
I would like to thank Akihisa Shibata and Takashi Unayama for
helpful comments.

I also wish to thank seminar participants at

the Contract Theory Workshop, the Kansai Macroeconomics
Workshop, and the Monthly Macroeconomics Seminar in Seoul.
Financial support from the Japanese Ministry of Education,
Culture, Sports, Science and Technology (the Grant-in-Aid for
Scientific Research) is gratefully acknowledged. Osaka School ofInternational
PublicPolicy,Osaka
University,
1-31,
Machikaneyama, Toyonaka, Osaka, 560-0043, Japan. Tel:
81-6-6850-5631, E-mail: takii@osipp.osaka-u.ac.jp1

1

Introduction

Macroeconomics is considered the study of the economy as a whole and attempts to
explain the behavior of aggregate statistics. Since the study of macroeconomics began, extensive research has been conducted to find stable relationships among several
aggregate statistics on the assumptions that idiosyncratic changes in an economy, andagents’ adaptation to the changes, do not influence the behavior of aggregate statistics. It is hoped that once a stable structure of the economy is found, governments
may be able to control their economies using fiscal or monetary policy.
Hayek (1945) is known to be an opponent of central planning based on statistical information. He emphasizes the economic importance of “the knowledge of theparticular circumstances of time and place”:“If we can agree that the economic problem of society is mainly one of rapid adaptation to changes in the particular circumstances of time and place, it would seem tofollow that the ultimate decisions must be left to the people who are familiar withthese circumstances, who know directly of the relevant changes and of the resources
immediately available to meet them.”

Kirzner (1973) calls the agents who adapt to idiosyncratic changes entrepreneurs, andargues that the absence of entrepreneurs in the neoclassical framework means thatimportant aspects of the real economy are missed.
In this paper, I aim to model entrepreneurship, defined as firms’ activities topredict and adapt to idiosyncratic changes in consumers’ taste, in a general equilibrium model. I examine how the consideration of entrepreneurship changes theconsequences of expansionary fiscal policy. I argue that the absence of entrepreneurship in macroeconomics makes researchers overrate the eﬀectiveness of expansionary2

fiscal policy.
More specifically, I extend Startz’s (1989) model and include idiosyncratic taste
shocks, to which firms must adapt. In Startz’s model, large government expenditure
partially crowds out private consumption, but increases real GDP. The existence ofpartial crowding out generates a trade oﬀ between private consumption and government expenditure. In this paper, I show that expansionary fiscal policy can lower
real GDP because the existence of entrepreneurship makes it diﬃcult for government
expenditure to substitute for private consumption.
The logic is explained as follows. When consumers’ tastes alter, private demand
shifts to reflect the changes. However, as the government is not aware of the changes
due to a lack of local information, a welfare-maximizing government cannot change
its demand. Hence, firms that provide goods for consumers must adapt to changes
in demand by processing local information, but firms that provide goods to the government do not have to adapt. It is shown that firms’ aggressive adaptation makes
markets more competitive, causing the aggregate price for private consumption to
drop. Hence, when government expenditure partially crowds out private consumption, expansionary fiscal policy forces people to consume relatively expensive goods.
Thus, expansionary fiscal policy can lower real GDP when there is entrepreneurship.
It is shown that the multiplier of expansionary fiscal policy is a decreasing functionof the level of idiosyncratic risk, the substitutability of goods and the firms’ ability to
predict the changes in consumer tastes. Hence, the multiplier is likely to be negativeif these three factors are large. A rise in idiosyncratic risk increases the importanceof prediction, whereas a rise in the substitutability of goods makes demand moresensitive to changes in tastes. Hence, both increase the benefits from adapting tochanges by processing local information. On the other hand, an increase in firms’
prediction abilities allows firms to correctly adapt to changes. Thus, a rise in all3three factors increases the beneficial eﬀects of private consumption on real GDP andmakes it more diﬃcult for government expenditure to substitute for it.
In addition, in this paper I investigate how fiscal policy influences firms’ investments in prediction ability.

It is shown that expansionary fiscal policy lowers in-vestment in the short run, but does not influence it in the long run. In the shortrun, expansionary fiscal policy crowds out private consumption, which reduces thebenefits from investment in prediction ability.

However, as firms’ profits are kept

to zero in the long run due to entries and exits, a reduction in demand does notchange the benefits from investment in the long run.

Hence, expansionary fiscal

policy does not influence investment. It is shown that two demand-side factors–thelevel of idiosyncratic risk and the substitutability of goods–are the most important
determinants of the level of prediction ability in the long run.
Although this paper was stimulated by ideas in Hayek (1945) and Kirzner (1973), I
do not attempt to formulate the theories of these economists. As their arguments are
based on disequilibrium analysis, it is impossible to integrate them into an equilibrium
model. However, as Rosen (1997) argues, I believe that there are gains from trade
between Austrian and neoclassical economics.

In this paper, therefore, I attempt

to focus on the aspects of Hayek’s and Kirzner’s arguments that can be expressed inan equilibrium model in order to address a neglected issue in the literature of fiscal
policy1 .
This approach deserves more attention as recent micro evidence suggests that theadaptation to idiosyncratic shocks has significant economic impacts. Davis and Haltiwanger (1999) review the literature and insist that unobserved idiosyncratic factors
play a dominant role in explaining the redistribution of workers.

Hubbard (2003)

finds that advanced on-board computers significantly increase capacity utilization in
1

Interesting recent reviews of literature related to fiscal policy can be found in Chari and Kehoe(1999), Auerbach (2002), and Bénassy (2002).

4the trucking industry by improving dispatchers’ ability to make resource-allocation
decisions.

The evidence suggests that the investigation of entrepreneurship is an

important neglected area in macroeconomics.
A similar role for entrepreneurs was previously examined in a general equilibrium
framework by Holmes and Schmitz (1990) and Takii (2003c)2 . Holmes and Schmitz(1990) emphasize the importance of the division of labor between entrepreneurs andmanagers.

Takii (2003c) investigates the eﬀect of entrepreneurship on the totalfactor productivity in an economy. However, no paper examines a trade-oﬀ between
entrepreneurship and expansionary fiscal policy.
This paper is organized as follows. In the following section, I set up the model.
In Section 3, I analyze the eﬀect of expansionary fiscal policy on real GDP. It isshown that the eﬀect could be negative.

In Section 4, I identify the factors that

influence the magnitude of the multiplier of expansionary fiscal policy. In Section 5,
I investigate the eﬀect of expansionary fiscal policy on firms’ investments in prediction
ability. Section 6 concludes the paper.

2

The ModelThis section sets up the model that enables me to analyze the eﬀect of entrepreneurship on the multiplier of expansionary fiscal policy. The model is based on Startz(1989).

I add idiosyncratic taste shocks, to which firms must adapt, to a slightly

modified version of Startz’s model (1989). This modeling strategy is undertaken toclarify how the consideration of entrepreneurship changes the results in the previous
literature.
2

The diﬀerent roles of entrepreneurs are incorporated into equilibrium analysis by Kihlstrom andLaﬀont (1979) with respect to risk bearing, by Schmitz (1989) with respect to imitation, and by
Aghion and Howitt (1992) with respect to innovation.

5

Household: There are identical representative households in an economy, and total
population is normalized to be one.

It is assumed that the households’ utilities

depend on a bundle of goods purchased by the household, ci ( C goods ), a bundleof goods provided by the government, gi (G goods ), and leisure L:
U = θ log C + ξ log G + (1 − θ − ξ) log L,"R nwhere C =

"R n

#1

zi cαi di α
,
n1−α
c

c

#1

zi giα di α
G =
,
n1−α
g
1
α = 1 − ∈ (0, 1) .
ρgThe parameters θ and ξ are assumed to be between zero and one. They measure
the relative weights that agents place on C goods and G goods, respectively. The
parameter ρ is the measure of the elasticity of substitution. As α is assumed to be
between zero and one, ρ is greater than 1. This means that the goods are imperfect
substitutes. The variables nc and ng measure the varieties of C goods and G goods,
respectively.

or n1−α, are included in each subutility in
The denominators, n1−αcgorder to eliminate the positive taste for variety, as assumed in Startz (1989). The
random variables, zi , represent changes in tastes for each good and are identicallyand independently distributed (i.i.d).

The incorporation of zi in subutility is themain departure from Startz’s (1989) model.
Representative households maximize their utility functions by choosing ci and L
subject to the budget constraint:
Z nc

pci ci di = Π + (N − L) − T,where pci is the price of the ith C good, Π is capital income, N is the total amountof available labor in this household, and T is lump sum taxes.
6

The wage rate isassumed to be 1. Hence, N − L represents labor income.
Demand functions for C goods and leisure are easily derived, as follows:
Ã

! 1

"

#

α
zi 1−α 1−αθ Π+N −T
Pc
, ∀i,
ci =
pci
1−ξ
nc
1−θ−ξ
[Π + N − T ] ,L =1−ξ

where Pc =θ[Π + N − T ]
1−ξ





R nc

α
α−1

1
1−α

pci zi
nc

 α−1

di 

(1)
(2)

α



.

and 1−θ−ξ[Π + N − T ] are the amounts of expenditure allocated1−ξ

to the purchases of C goods and leisure, respectively.

Because of the log linear

specification of the utility function, the allocated expenditure is independent of theprice index, Pc . This simplifies the analysis below. Note that the demand functions
depend on the realization of the random variables, zi . Hence, a firm must adapt tothe changes in tastes when production takes place.

Government: A government purchases G goods and transfers them to households.
Following Startz (1989), it is assumed that re-trading G goods is prohibited. The
government is assumed to maximize the expected value of log G subject to its budget
constraint:

max
g
i

s.t. T =

Z ng

Z



log

ÃR n

zi giα di
n1−α
g

g

pgi gi di,!1 α qz (zi ) dzi ,where pgi is the price of the ith G good and qz (zi ) is a marginal density functionof zi .

Without loss of generality, the distribution function of zi is assumed to becontinuous. The main diﬀerence between the households’ decisions and the government’s decisions is that the government cannot observe changes in tastes due to the7lack of local information.

As the attention of a human being is limited, it is im-

possible for a decision-maker to observe all information on shifting consumer tastes
for individual goods. Hence, the government must maximize the expected value ofhouseholds’ utility. Of course, in reality, politicians would seek to satisfy their own
interests. However, my assumption of a benevolent government assists in identifying
the problems caused by the lack of local information.
As zi has an i.i.d. distribution and gi must be independently chosen due to thelack of information,

R ng

zi giα di =R ng e αRz g di, where z e = z q (z ) dz .
i z

iis no random component for this maximization problem.

iiHence, there

The following demand

function is easily derived:
gi =

Ã

ze
pgi

R

where Pg = 

ng

! 1

1−α

α
1−α

Pg
α

Ã

!

T
, ∀i,
ng
1

 α−1

(pgi ) α−1 (z e ) 1−α di 
ng

(3)

α

.

Note that the demand for G goods does not have any random components. As thegovernment guarantees the amount of demand, firms do not need to adapt to changes
in demand.

C-goods firm: Each variety of C goods and G goods is produced by a single firm.
A C-goods firm must make two decisions: it must choose how much it produces, andwhat the price of its product is. The timing of decisions is as follows. (1) A taste
shock, zi , occurs. (2) A firm, i, observes a noisy signal, si , and infers the realized zi .
(3) The firm produces non-storable goods, ci . (4) The firm discovers what the true
zi is. (5) The firm sets its price, pci .
Let us first consider how the firms set their prices. As it is assumed that goods
cannot be stored, the optimal strategy is for the firms to set the highest possible price8

PricePc
Demand Function

Cs

C goodFigure 1: The Pricing Decision (the picture shows that the highest possible pricethe firm can set when the firm has already produced cs is determined by the inverse
demand curve.)
at which they can sell all the products they have already produced3 . Assume thatfirms know the households’ demand function and that they have already produced
csi units of the goods. The optimal price for the firm i is derived from the inverse
demand function, which is depicted by Figure 1:
pci = zi (csi )α−1 Pcα"θ Π+N −T
1−ξ
nc

#1−α

.

Note that given this price, pci , the demand for the good always equals the supply of
the good: ci = csi . Hence, I use ci to denote the amount of supplied goods as well.

When the firm makes its production decision, it must predict the changes in tastes.
It knows that the price will be set on the inverse demand function no matter what3

When α ∈ (0, 1) in the utility function of consumers, it is not optimal for the firm to throw the

product away in order to keep the price high.

9the realization is. Hence, the firm’s problem is specified by the following equation.
½

s.t. pcihwhere E [pci |si ] =hqz/s(zi |si )

¾

ci
i
A
"
#1−α
θ Π+N −Tα−1 α= zi ci Pc
1−ξnc

E h [pci |si ] ci −π (si ) = max
c
Z

(4)

h
pci qz/s(zi |si ) dzi ,h(si |zi ) qz (zi )
qs/z
= R h
qs/z (si |zi ) qz (zi ) dzi

hand A measures the productivity of the firm and qs/z
(si |zi ) is a conditional densityh(zi |si ) isfunction of si given the realization of zi . The last equation shows that qz/s

a posterior density of zi having observed si .
hNote that qs/z
(si |zi ) depends on h, which measures the firms’ ability to predictthe changes in households’ tastes. If the firm can accurately predict the realizationof zi , the firm has a likelihood function endowed with high h and is considered tohave precise knowledge about the nature of shifting tastes for a particular good. As
the knowledge makes it possible for the firms to adequately adapt to the changes, theparameter, h, can be interpreted as the index of firms’ entrepreneurial ability. The
ordering of h is mathematically defined later.
The solution to the profit-maximization problem reveals that the price has to beequal to a constant markup, α1 , times marginal cost, A1 , on average:p (zi , si ) ≡ pci =where E h (zi |si ) =Rzi,αAE h (zi |si )(5)hzi qz/s(zi |si ) dzi . Note that the actual price deviates from theconstant mark-up rule due to firms’ misunderstanding the changes in tastes, E h (zzii |si ) .
When the firm discovers the true zi , it realizes that zi diﬀers from the predicted value.
If the realized zi is greater than the predicted one, E h (zi |si ), then the firms can set ahigher price than the mark-up rule. If zi is lower than E h (zi |si ), then the firm must
set a lower price. Hence, E h (zzii |si ) can be interpreted as the measure of “a wonderful10

surprise”4 .

G-goods firm: G-goods firms have the same technology as C-goods firms, but thedemand for goods is guaranteed by the government. Hence, when the firms decide
how much they produce, the prices of the goods are automatically determined fromthe government’s inverse demand function. The G-goods firms’ problem is written
as:

π gi
s.t. pgi

½

¾

gi
= max
pgi gi −,giAÃ !1−αTe α−1 α= z gi Pg
.
ng

(6)

As there is no random variable on the inverse demand function, there is nothing topredict. Hence, the price is set at exactly the markup, α1 , times marginal cost A1 :
pgi =

1
.
αA

(7)

Capital-Market Clearing Condition: It is assumed that a capital market isperfectly competitive and that entrepreneurs can hedge their own risk. Hence, thefollowing capital-market clearing condition must be satisfied:Π = nc4·Z¸π (si ) qsh (si ) dsi − F (h) + ng [π g − Fg ] ,(8)Kirzner (1997) points out that entrepreneurs correct their decisions during the equilibrative

market process because the decision-makers discover their earlier errors. Thus, discovery is always
accompanied by a sense of “surprise”. Of course, his emphasis is on “ unthought-of knowledge”,
which diﬀers from the “known ignorance” in this paper. However, I believe that a careful examination of entrepreneurial discovery based on “known ignorance” clarifies the benefits and the limitsof the neoclassical framework, which is part of the purpose of this paper.

11where qsh (si ) =R hqs/z (si |zi ) qz (zi ) dzi , and F (h) and Fg are fixed costs for the pro-duction of C goods and G goods, respectively.
Fixed cost can be interpreted as the cost of employing management groups andanalysts, the importance of which is emphasized by Chandler (1990).

The fixed

costs, F (h) and Fg , may diﬀer as C-goods firms must employ professional analysts
in order to predict the changes in tastes. Hence, the natural assumption would be
F (h) ≥ Fg .
Equilibrium: The market equilibrium in the short run is formally defined as follows.
Definition 1 The market equilibrium in the short run is {c (·) , L, gi , p (·, ·) , pg , π (·) , π g , Π},which satisfies the following conditions:
1. Households maximize their utility: equations (1) and (2).
2. A government maximizes households’ expected utility: equation (3 ).
3. C-goods firms and G-goods firms maximize their own profits: equations (4), (5),(6) and (7).
4. The capital market is cleared: equation (8).
The labor market clearing condition is omitted from the definition of the market
equilibrium because of Walras’s law.

The market equilibrium in the short run isdefined with a given nc and ng . The zero profit conditions that determine nc and ng
will be introduced later to define the market equilibrium in the long run.

The Expected Revenue in the Equilibrium: Substituting the profit-maximizing
prices of the C-goods firm and the G-goods firm into the demand functions, the12expected revenues of the firms are derived as follows:1αα

E h [p (zi , si ) c (si )] = [z (h)] 1−α (αA) 1−α Pc1−α1ααpg g = [z e ] 1−α (αA) 1−α Pg1−αh1where z (h) = E h E h [zi |si ] 1−αRi1−αθ Π+N −T
,
1−ξ
nc

T
,
ng

(9)
(10)

,
h

1

i

h
(si |zi ) qz (zi ) dzi dsi and E h E h [zi |si ] 1−α =and E h [p (zi , si ) c (si )] = p (zi , si ) c (si ) qs/z

R hR

i 1

h
zi qz/s(zi |si ) dzi 1−α qsh (si ) dsi .

The structure of the expected revenue between the C-goods firm and that of the

G-goods firm is similar.

The main diﬀerence is that the expected revenue of the

C-goods firm is aﬀected by h through z (h) , whereas that of the G-goods firm isnot. It is shown below that z (h) is an increasing function of h. This means that
if entrepreneurs have greater ability to predict changes in tastes, they can expect
to obtain more revenue.

Talented entrepreneurs produce more when they can set

high prices, and produce less when they must set low prices. Hence, the correlation
between the price and output is high.

That is why they expect to receive a highrevenue. To formally prove this intuition, we need the following assumption.

Assumption: Assume that h is ordered by the informativeness, in the sense of Blackwell (1953).

That is, h1 ≥ h2 if and only if there exists a nonnegative function

φ (s2i |s1i ), which satisfies the following three relations:Z³

Z

φ s2i |s1i ds2i = 1, a.e. ∀s1i ,Z

φ s2i |s1i ds1i ∈ (0, ∞) , a.e. ∀s2i .

´

1

³

´

³

´

³

´

2

³

´

h
h
φ s2i |s1i qs/z
s1i |zi ds1i = qs/z
s2i |zi , a.e. ∀zi , ∀s2i

Blackwell (1953) proves that if h is ordered by this criterion, information structure h1 brings higher ex-ante utility than information structure h2 for any utility
13

function.

Using Blackwell’s (1953) definition of informativeness, it is shown thatz (h) is increasing in h.

Lemma 2 If h is ordered by the informativeness in the sense of Blackwell (1953),
then z (h) is increasing in h and z (h) ≥ z e for any h.
1hProof. As E h [zi |si ] 1−α is convex in E h [zi |si ] and E h [zi |si ] is convex in qz/s
(zi |si ),1hE h [zi |si ] 1−α is convex in qz/s
(zi |si ). From Theorem 2 in DeGroot (1970, p.436), theresult is immediate.
Using the above lemma, the expected revenue of the C-goods firm is increasing
in h. However, consumers allocate a constant amount of expenditure to C goods,θ[Π + N − T ].
1−ξHence, the expenditure on C goods is independent of h. As theexpenditure must be equal to the total expected revenue of the C-goods sector in
equilibrium, the price must be adjusted. That is, the firms’ aggressive adaptation to
the changes in tastes would raise competition in the market, and, therefore, the priceindex of C goods would drop. It is shown that Pc and Pg are decreasing in z (h) andz e , respectively:
Pc =
Pg =

1
1

,

1

.

αAz (h) α1αA (z e ) α

The equations show that the price index for C goods is lower than the price index
for G goods. Because of high competition in the C-goods market, the price index of
C goods is lower than that for G goods.
Substituting the price indexes into equations (9) and (10), the expected revenue
in the equilibrium is independent of h:
14

E h [p (zi , si ) c (si )] =pg g =

θ(Π + N − T )
(1−ξ)

nc

,

T
.
ng

The equation shows that the expected revenues of C-goods and G-goods firms in theequilibrium are equivalent to the expenditure allocated to those goods per firm. As
the total expenditure on C goods is independent of h, the expected revenue is also
independent of h in the equilibrium.

The benefits of strong prediction ability arealways cancelled out by a rise in competition.
Of course, if the utility function is not log linear in C, G, and L, the total expenditure on C goods is aﬀected by the relative price of C goods and G goods. A
reduction in Pc raises the total expenditure on C goods and the expected revenue
in the equilibrium. The log linear specification eliminates this additional eﬀect andmakes my analysis simpler.

3

The Multiplier and Prediction Ability

In this section, the eﬀect of expansionary fiscal policy on real GDP is examined.
In particular, I am interested in how firms’ ability to predict the changes in tastes
aﬀects the multiplier of government expenditure. It is shown that the multiplier canbe negative.

Real GDP: Real GDP consists of real private consumption and real government
expenditure:Y≡

nc E h [p (zi , si ) c (si )] ng pg g
+
,
Pc
Pg
15

=

θ
(Π + N − T )
(1−ξ)

Pc

+

T
,
Pg

= C + G.
The above equation shows that the definition of real GDP equals the sum of subutility
from C goods and G goods. Note that as ngPpgg g = G, G is equivalent to real government expenditure. Although G is treated as endogenous in this paper, as G = PTg ,and Pg and T are exogenous, G can be also considered as a policy instrument5 .
Hence, there are two possible policy instruments: real government expenditure, G,or nominal government expenditure, T . Following Startz (1989), G is chosen to be asuitable policy instrument. The choice of policy instrument does not aﬀect the mainarguments below.

Wealth Eﬀect:6 Because monopoly prices exceed marginal costs, an increase ingovernment expenditure raises aggregate profits:Π=(1 − α) θN − (1 − ξ) (nc F (h) + ng Fg ) + (1−ξ−θ)(1−α)
G1eαA(z ) α

1 − ξ − (1 − α) θ.

Using this equation, after-tax wealth, Π + N − T , is solved as a function of G:
Π+N −T =5·(1 − ξ) N −¸G
1 − (nc F (h) + ng Fg )A(z e ) α

1 − ξ − (1 − α) θ.

If G is chosen to be a policy instrument, T must be considered as an endogenous variable. Thismeans that the government is assumed to minimize T , provided that it guarantees the subutility G
to representative consumers. The solution is the same.
6
The wealth eﬀect that operates through an increase in profits is considered the reason for theKeynesian multiplier eﬀect [ex. Silvestre (1989)]. Unayama, Otaki, and Saito (2000) and Bénassy(2002) point out that, in fact, the real reason for output expansion in response to expansionary
fiscal policy is the negative wealth eﬀect: as a rise in tax reduces agents’ wealth, agents consume
leisure less and work more. The argument in this paper does not depend on the reason for GDP
expansion.

16

The equation shows that an increase in government expenditure lowers after-tax
wealth. Hence, it lowers private consumption. This brings about a trade oﬀ between
government expenditure, G, and private consumption, C.

Fiscal Policy: Substituting the derived after-tax wealth into the definition of realGDP, real GDP in the short run is shown to be a function of government expenditure.
Proposition 3 Real GDP in the short run, Y S , can be expressed as a function ofreal government expenditure, G:
Y S = is + ms G,
where ms =isµ(1 − ξ − θ) + αθ 1 −

³

z(h)
ze

´1¶
α

,
1 − ξ − (1 − α) θ1αAθ [N − (nc F (h) + ng Fg )]z (h) α .
=[1 − ξ − (1 − α) θ]

If z (h) = z e , which can be interpreted as the case of no entrepreneurial activity,
then the result is the same as Startz (1989) and ms is always positive.
if z (h) > z e , ms can be negative.

However,That is, if there are entrepreneurial activities,

large government expenditure can lower real GDP. Note that if z (h) > z e , thenPc < Pg . As large government expenditure partially crowds out private consumption,
households must spend more on relatively expensive goods. Hence, large government
expenditure can lower real GDP.
Note that because z 0 (h) > 0, an improvement in the firms’ ability to predict thechanges in tastes lowers the multiplier. That is, active entrepreneurial activities canweaken the eﬀect of expansionary fiscal policy.
Now, let us consider the eﬀectiveness of expansionary fiscal policy in the longrun. In the long run, firms enter the market as long as expected profits are positive.
Expected profits are zero in the long-run equilibrium:E h [π (si )] = F (h) ,17

π g = Fg ,where E h [π (si )] =R

π (si ) qsh (si ) dsi .

Substituting the zero profit conditions into

equation (8), Π = 0. Using this result, real GDP in the long run is derived from thedefinition of real GDP.
Proposition 4 Real GDP in the long run, Y L , can be expressed as a function of real
government expenditure, G:
Y L = il + ml G,
where ml =
il

1−ξ−θ

³

1−ξ

z(h)
ze

´1

α

,

1

θNαAz (h) α=.
(1 − ξ)The results are qualitatively the same as those for the short run: if there is noentrepreneurial activity (z (h) = z e ), then ml is positive, as in Startz (1989), whereas if
entrepreneurial activities are present (z (h) > z e ), then ml can be negative. However,
the magnitude of the multiplier is diﬀerent between the long run and the short run:θ (1 − α) (1 − ξ − θ)
ml − ms = −[1 − ξ − (1 − α) θ] (1 − ξ)

Ã

z (h)
ze

!1

α

< 0.

This result also appeared in Startz (1989). However, there are two new observations.

First, the diﬀerence is larger when z (h) is larger.

That is, when firms

have a strong ability to predict changes in tastes, the multiplier in the long run issubstantially lower than that in the short run. Second, as ml can be negative, it ispossible that even when expansionary fiscal policy raises real GDP in the short run,it can be the source of long-run stagnation.

18

4

Idiosyncratic Risk and Substitutability

In this section, I make a further assumption on the information structure in order
to identify the conditions that influence the multiplier of expansionary fiscal policy.
It is shown that the level of idiosyncratic risk, the substitutability of goods, and theprediction ability are the key parameters influencing the multiplier.
I assume that log zi comprises a predictable component µ and an unpredictablecomponent ui :log z = µ + ui
where ui is normally distributed with a mean of 0 and a variance of σ 2u . It is assumed
that the unpredictable component ui summarizes unexpected changes in tastes. The
firms cannot observe ui before making production decisions, but they can observe thesignal si :si = ui + εi
where εi is normally distributed with a mean of 0 and a variance of σ 2ε (h).

Notethat the variance of the noise term diﬀers when the firms’ prediction ability diﬀers.
The following measure to capture the firms’ ability to predict the change in consumer tastes, ui , is suggested by Takii (2003a).
Definition 5 The measure of the firms’ ability to predict changes in tastes, u, (thefirms’ prediction ability), is defined by:h=1−
where V ar (u|s) =

R³

R

R

V ar (u|s) qsh (s) ds,
σ 2u

u − uqzh (z|s) dz´2qzh (z|s) dz and u = log z − µ.

This measure implies that the firms accurately predict u when on average they
reduce the conditional variance, having observed si . To compare ability in diﬀerent

19environments,
ance of ui .

R

V ar (u|s) qsh (s) ds is divided by σ 2u , which is the unconditional vari-

The measure h ranges from 0 to 1.

If the firms perfectly predict thechanges, h = 1, whereas if the firms do not predict the changes at all, h = 0.
Using the definition of h, the variance of the noise term is endogenously determined
as follows:(1 − h) σ 2u.
h

σ 2ε (h) =(11)As expected, when the firms more accurately predict unexpected changes, the varianceof the noise term is smaller. When h = 1, the variance is 0, whereas when h = 0,
the variance is infinite.
Given this definition, it is shown that:z (h) = z e exp
1
where ρ = 1−α.

(ρ − 1) σ 2u h
,
2

(12)

The equation shows that the marginal value of prediction ability

is larger if risk is large and goods are more substitutable. If goods are more substitutable, demand is more sensitive to the changes in tastes, from equation (1). Hence,
it is more important for the firms to predict the changes.
Substituting equation (12) into the definitions of ms and ml , the following proposition is derived.
Proposition 6 Both the multipliers in the short run and long run are decreasingin the level of idiosyncratic risk, σ 2u , the substitutability of goods, ρ and the firms’
prediction ability h:
ms =

³

´ ³

2

´

1 − ξ − θ − 1 − ρ1 θ exp ρσ2u h − 1
1 − ξ − ρθ

,

(13)

2

ml

1 − ξ − θ exp ρσ2u h
.
=
1−ξ
20

(14)

Note that because the multipliers are decreasing in risk, the substitutability ofgoods and the firms’ prediction ability, the multipliers are likely to be negative if
the three factors are large. A rise in idiosyncratic risk increases the importance ofprediction, and a rise in the substitutability of goods makes demand more sensitive
to changes in tastes. Hence, both increase the benefits from adapting to changes
by processing local information. On the other hand, an increase in firms’ prediction
abilities allows firms to correctly adapt to changes. Thus, a rise in all three factors
increases the beneficial eﬀects of private consumption on real GDP and makes it morediﬃcult for government expenditure to substitute for it.

5

Investment in Prediction Ability

An increase in government expenditure may have a further detrimental eﬀect on theeconomy: it may discourage investment in prediction ability.

This section asks adiﬀerent question than the previous section did, focusing on how expansionary fiscal
policy aﬀects firms’ investment in prediction ability.
Suppose that C-goods firms can invest in their management staﬀ and choose thelevel of prediction ability before starting their businesses.
max E h [π (si )] − F (h) ,hhE [π (si )] =

h³

´

iρ−1

1 − ρ1 Aθ Π+N−T
Pcρ−1 1−ξncρ(z e )ρ exp

ρ (ρ − 1) σ 2u h.
2Assume that the convexity of the F function is strong enough to satisfy the second
order condition. That is, F 00 (h) >hi
ρ(ρ−1)σ2u 2 h
E (π (si )) for any E h (π (si )) in the22uequilibrium. Moreover, it is assumed that F 0 (0) < ρ(ρ−1)σE 0 (π (si )) and F 0 (1) >2

ρ(ρ−1)σ 2u 1
E (π (si )).
2

These two conditions guarantee that the solution is interior in21[0, 1]. Hence, the optimal h satisfies:0

F (h) =

ρ (ρ − 1) σ 2u h
E (π (si )) .
2

The firms’ investment in prediction ability can be analyzed by examining E h (π (si ))in the short run and in the long run.

Prediction ability in the short run: In the short run, the number of firms does
not change and profits are positive.

Hence, the expected profits depend on the

demand for C goods:

F 0 (h) =θ (Π + N − T )=(1 − ξ)(ρ − 1) σ 2u θ (Π + N − T ),2
nc (1 − ξ)
"

θ N−

G

ρ

A(z e ) ρ−1#− (F (h) nc + Fg ng )1 − ξ − ρθ.

Applying the implicit function theorem to the first order condition, h is derived as afunction of G, σ 2u and ρ in the short run:
Proposition 7 Prediction ability in the short run, hs , is decreasing in G and increasing in σ 2u :
³

´

³

´

³

´

hs ≡ H s G, σ 2u , ρ , HGs G, σ 2u , ρ < 0, Hσs G, σ 2u , ρ > 0.
The proposition shows that large government expenditure discourages investmentin prediction ability whereas large idiosyncratic risk requires prediction ability. Because of the crowding- out eﬀect, private demand is lower when the government
spends more. This lowers the firms’ incentives to invest in prediction ability. Strong
uncertainty about taste shocks requires that firms have more ability to predict tastechanges. This increases the firms’ incentives to invest in h.
22

The eﬀect of substitutability of goods is ambiguous. On the one hand, the more
substitutable goods are, the more sensitive demand is to changes in tastes. Hence,the substitutability of goods increases the importance of prediction ability. On theother hand, however, strong substitutability of goods reduces the monopoly rents offirms and, therefore, reduces the expected profits of the firms in the equilibrium. Thiseﬀect discourages firms from investing in prediction ability. However, the following
corollary shows that the first eﬀect dominates the second eﬀect in my model, if the
expected taste shocks are normalized to be 1.
Corollary 8 Prediction ability in the short run, hs , is increasing in ρ if z e = 1:³´

If z e = 1, Hρs G, σ 2u , ρ > 0.
Note that proposition 6 shows that the multiplier is decreasing in firms’ prediction
ability. Hence, the results in proposition 7 and corollary 8 reinforce the results inproposition 6: an increase in risk and substitutability of goods reduces the economic
eﬀectiveness of expansionary fiscal policy.

Prediction ability in the long run: Eventually, entries and exits occur andE h (π (si )) = F (h) is satisfied in the long run:F 0 (h) =ρ (ρ − 1) σ 2u
F (h) .
2This means that changes in demand cannot aﬀect the investment decisions in thelong run. The implicit function theorem proves that h is increasing in σ 2u and ρ inthe long run.
Proposition 9 Firms’ prediction ability in the long run, hl , is increasing in σ 2u and
ρ:
³

´

³

´

³

´

hl ≡ H l σ 2u , ρ , Hσl σ 2u , ρ > 0, Hρl σ 2u , ρ > 0.
23

Note that government expenditure does not influence firms’ prediction ability inthe long run. The only important variables that influence prediction ability from thedemand side are the level of idiosyncratic risk and the substitutability of goods.
Evidence that risk requires prediction ability is found by Takii (2003a, 2003b) indiﬀerent contexts. Although there is no evidence about the substitutability of goods
and prediction ability, casual observations indicate that prediction ability is highly
demanded in financial markets, in which, I believe, goods are greatly substitutable.

6

Conclusion

This paper reexamines the eﬀectiveness of expansionary fiscal policy in the presence ofentrepreneurship. It is shown that the budget-balancing multiplier can be negative
when idiosyncratic risk, substitutability of goods, and prediction ability are large.
In addition, it is shown that expansionary fiscal policy discourages investment inprediction ability in the short run, but does not aﬀect it in the long run.
Two remarks on this paper are required. First, my analysis is not valid either
when crowding out does not occur or when aggregate shocks are more important thanidiosyncratic shocks. If there is no crowding out, there is no trade oﬀ between private
consumption and government expenditure. Therefore, there is no trade oﬀ between
entrepreneurship and central planning.
If aggregate shocks are more important than idiosyncratic shocks, then it would
not be diﬃcult for government to access information7 .

The comparison between

aggregate shocks and idiosyncratic shocks reminds us that Hayek (1945) compares
the relative importance of diﬀerent kinds of knowledge - scientific knowledge and theknowledge of the particular circumstances of time and place.
7

This paper implies

Bénassy (2001) shows that the optimal fiscal policy is activist even if government is less informed

about aggregate shocks.

24that the eﬀectiveness of expansionary fiscal policy may depend on the answers to
the questions raised by Hayek (1945). Note that, as mentioned in the Introduction,
recent micro evidence emphasizes the importance of unobserved idiosyncratic factors
explaining the redistribution of workers. It suggests that a quantitative examinationof the model would be fruitful8 .

Although I have chosen to work with a static

model to clarify the main intuition in this paper, for the quantitative exercise, themodel should be extended to a standard dynamic model in order to incorporate
the eﬀects of intertemporal substitution, capital accumulation, and government-debt
accumulation. This extension is the next interesting challenge.
Second, the model in this paper aimed to examine the eﬀect of expansionary fiscal
policy on real GDP, but did not attempt to examine the optimal size of government
expenditure. In this sense, the result of this paper cannot be judged from a normative point of view.

The log linear specification of my utility function allows us toignore how the relative price between C and G goods influences the demand for C
goods. This assumption assists in clarifying the intuition of my analysis by eliminating auxiliary eﬀects. However, the same assumption requires that I ignore how
the relative price aﬀects the optimal size of government expenditure. As the eﬀectof entrepreneurship is summarized by the price index, the assumptions are fairly restrictive for examining the optimal size of government expenditure. This is an issue
that needs to be analyzed separately. That task is also left for future research.
8

Of course, these exercises might underestimate the role of entrepreneurship that is emphasized by

Kirzner (1997), as a statistical distribution can only measure Knightian risk faced by entrepreneurs.
Nonetheless, I believe that the quantitative exercise can at least provide a lower bound about theeﬀect of entrepreneurship.

25

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