GCOE Discussion Paper Series
Global COE Program

Human Behavior and Socioeconomic Dynamics
Discussion Paper No.36

Market Size and Entrepreneurship

Yasuhiro Sato, Takatoshi Tabuchi, and Kazuhiro Yamamoto

February 2009GCOE Secretariat
Graduate School of Economics

OSAKA UNIVERSITY

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

Market Size and Entrepreneurship
Yasuhiro Sato∗

Takatoshi Tabuchi†

Kazuhiro Yamamoto ‡February 20, 2009

Abstract
In order to examine the impacts of market size on entrepreneurship, we estimate
a monopolistic competition model that involves entrepreneurial decision by using dataon Japanese prefectures. Our results show that a larger market size measured by the
population density leads to higher incentive of people to become entrepreneurs. a 10
percent increase in the population density increases the share of people who wish to
become entrepreneurs by 2 percent. In contrast, the self-employment ratio is lower in
prefectures with higher population density, which suggests that the market size has
diﬀerent impacts on the entrepreneurship in diﬀerent stages.

JEL Classification: J62, L26, R12.
Keywords: market size, entrepreneurship, density economies, market expansion∗

Graduate School of Economics, Osaka University (Japan); E-mail: ysato@econ.osaka-u.ac.jp
Faculty of Economics, University of Tokyo (Japan); E-mail: ttabuchi@e.u-tokyo.ac.jp‡
Graduate School of Economics, Osaka University, (Japan); E-mail: yamamoto@econ.osaka-u.ac.jp†

1

Introduction

We often observe that the distribution of entrepreneurial activities is not equally distributed
across space, and big cities, such as New York, London, and Tokyo, look to have higher entrepreneurship than other cities. What makes the diﬀerence in entrepreneurship across space?
In answering this question, we focus on the regional market size and the entrepreneurship.
More precisely, the aim of this paper is to investigate empirically how the size of a region(the size of a home market) is associated with entrepreneurship in determining the spatial distribution of entrepreneurship in Japan. For this purpose, building on new economic
geography pioneered by Krugman [12], we first develop a monopolistic competition model
involving entrepreneurship decision by workers. We then estimate the relationship.
Under imperfect competition, an increase in the home market size has two opposing
eﬀects on firms’ profits. Both positive and negative eﬀects aﬀect the decision of (potential)
entrepreneurs whether or not to start a new business. Positive eﬀects come from density
economies as evidenced by Ciccone and Hall [4] and Ciccone [3], and market expansion asshown by Krugman [11] as the home market eﬀect. On the other hand, a negative eﬀect
stems from competition among firms. If the positive eﬀects dominate the negative one,entrepreneurs would establish a new firm in a large market.
In order to examine which is the dominant eﬀect, we estimate the relationship between themarket size and entrepreneurship, that are derived from the developed model. In estimation,
we use two indices of entrepreneurship: the share of potential entrepreneurs and the share ofself-employment. The former is the share of people who wish to start up a new business inthose who are either employed but want to change careers or not engaged in work but wantto find a job. We consider this to represent the ex ante entrepreneurship and show the degreeof incentive of people to start up a new business. The latter is the share of self-employedworkers in the total employed workers, and we interpret this as the ex post entrepreneurship.
We use the population density as the index of the market size, and investigate how it isassociated with the ex ante/ex post entrepreneurship. Our results show that the population
density is positively related to the ex ante entrepreneurship. For large prefectures, such as
Tokyo and Osaka, a 10 percent increase in the population density increases the share of ex1

ante entrepreneurs by around 2 percent. In contrast, the population density is negatively
related to the ex post entrepreneurship. Thus, the market size has opposite impacts onentrepreneurship in diﬀerent phases.
There are several studies that showed the relationship between the market size and entrepreneurship. According to Berry and Reiss [2], empirical studies based on micro data showedthat there are thresholds of regional population size that enables firms to establish themselves as going concerns, and firm entry is high in regions with large population size. Similar
results on the relationship between regional population size and firm entry are obtained by
Reynolds et al. [15], who showed that higher growth of regional population leads to higher
birth rate of firms. Harada [9] used data on workers who wish to start up a business andshowed that workers are more likely to become entrepreneurs in regions with larger grossprefectural domestic product. Rosenthal and Strange [16] showed that entrepreneurship ishigher in districts with higher employment density using data on new establishments in the
New York Metropolitan Area. Glaeser and Kerr [8] measured entrepreneurship by new establishments that are independent from existing firms and showed that new entrants are likely
to be drawn to areas with high overall levels of customers and suppliers, and strongly drawn
to areas with many smaller suppliers. However, in the results of Glaeser [7] who adopted
the self-employment rate and average firm size as indices of entrepreneurship, employment
density aﬀects entrepreneurship only insignificantly.
The novelty of our paper lies in the following two points. First, we measure entrepreneurship by the share of potential entrepreneurs as well as the share of self-employment.
This enables us to see if the market size is associated with the entrepreneurship in diﬀerent
stages of entrepreneurship, i.e., ex ante and ex post. Second, we consider the possibility of
non-linearity and non-monotonicity in the relationship between the market size and entrepreneurship, which allows flexibility in capturing this relationship. This is in contrast to theexisting studies mentioned above, most of which assume the linearity and monotonicity.
The remainder of the paper is organized as follows. Section 2 presents a model of new
economic geography with entrepreneurship and characterizes entrepreneur formation. Section
3 analyzes the entrepreneur formation and investigates the positive eﬀects arising from density
economies and market expansion. It provides a set of empirical results by using Japanese2prefectural-base data. Section 4 checks robustness of these results by diﬀerent methods of
estimations. Section 5 concludes and suggests future research directions.

2

Basic ModelIn this section, we present a simple new economic geography model involving entrepreneurshipin order to examine how the market size aﬀects entrepreneurship.
There are two goods in a region. The first good is homogeneous. Consumers have apositive initial endowment of this good which is also produced using labor as the only input
under constant returns to scale and perfect competition. This good can be traded freely andis chosen as the numéraire. The other good is a horizontally diﬀerentiated product, which issupplied by using labor under increasing returns to scale and monopolistic competition.1
There is a mass of individuals, L, who move between the two sectors according to the wage
diﬀerential given later. As in Ottaviano, Tabuchi, and Thisse [14], consumers’ preferences
are identical across individuals and are described by the following utility function of thequasi-linear form:
U =α

Z n
0

β
q(v)dv −2Z nγ(q(v)) dv −
2
0
2

∙Z n
0

q(v)dv¸2+ q0 ,

where q(v) is the quantity of variety v, n is the mass of varieties, q0 is the quantity of thenuméraire, and α, β, and γ are positive parameters. The budget constraint of an individualis given by

Z np(v)q(v)dv + q0 = q 0 + w,

0

where p(v) is the price of variety v, w is the individual’s wage, and q 0 is the initial endowment,
which is supposed to be suﬃciently large to ensure the positive demand of the numéraire.
Maximizing the utility subject to the budget constraint yields the individual demandq(v) =
where P =1Rn0αβ + γP1− p(v),β (β + γn) βp(v)dv is the price index.

This good may be services which consist of a continuum of varieties without export to the rest of theworld.

3

Turning to the supply side, technology in the homogeneous good sector requires one unitof labor in order to produce one unit of output. Due to this numéraire with costless trade,the equilibrium wage of the sector is always one.
In the diﬀerentiated good sector, each firm supplies a single variety under increasing
returns to scale so that n is also regarded as the number of firms. The fixed requirement oflabor is one and the marginal requirement of labor is normalized to zero without much lossof generality.
Each firm chooses a price p(v) that maximizes its profit:
π(v) = [p(v) − τ (D)] q(v)L − w,

(1)

where τ (D) is the marginal costs of production, which include the distribution costs involving
the retail and wholesale costs within the region. A higher density would lead to lower marginal
costs because of greater Marshallian externalities, such as knowledge spillover and laborpooling or because of lower distribution costs. We assume τ is decreasing in the population
density D in order to capture such density economies. It is well known in urban economics(Alonso [1]) that the average population density in a city is positively associated with city
size, and hence, the density economies may be regarded as agglomeration economies accruing
from the high density or large size of a city. This implies that the population density is highin regions involving large cities, where agglomeration economies as well as density economies
are large.
Because firms are symmetric with respect to production technologies, they charge thesame price in equilibrium, and thus, we drop v hereafter. This is given byp=αβ + τ (D) (β + γn).
2β + γnPlugging the price into (1), the profit made by a firm is rewritten as follows:π=[α − τ (D)]2 βL− w.
(2β + γn)2

Under free entry of firms, this profit equals zero so that the equilibrium wage in the diﬀerentiated good sector is determined asw=[α − τ (D)]2 βL.
(2β + γn)24(2)

We follow existing microeconomic studies of the formation of entrepreneurship by assuming that individuals choose to become either a worker employed by an entrepreneur or anentrepreneur employing workers. Because the equilibrium wage in the homogeneous good
sector is one, the arbitrage between the two sectors by individuals requires thatw = 1.

(3)

Let e be the share of entrepreneurs in the diﬀerentiated good sector. Since the mass ofvarieties, n, is equal to the number of firms in the region, the labor market clearing implies
eL = n. Substituting this into (3) with (2), we can uniquely determine the entrepreneur
share by the following equation√[α − τ (D)] βL
1=.
2β + γeL(4)Let h be the area of inhabitable land so that L = hD holds. Then, we can rewrite (4) as afunction of the population density. Taking the logarithm of it, we havenopln (e) = ln [α − τ (D)] βhD − 2β − ln (γhD) .

(5)

The first term of the RHS in (5) is increasing in the population density D, whereas thesecond term is decreasing in D. Hence, as D increases, the first term has positive eﬀects on
the entrepreneur share e, whereas the second term has a negative eﬀect on e.
The positive eﬀect comes from two sources. One is the density economies, which aredescribed by changes in τ (D): increasing density reduces the marginal costs, enhances firms’
profits, and then encourages to be entrepreneurs. The other is the eﬀect of market expansion,√
which is represented by changes in βhD. Since increasing market size enlarges the amountsof sales for a given cost-price margin α − τ (D), raises profits, and augments the number ofentrepreneurs. The negative eﬀect is given by the second term of the RHS in (5). This
term expresses competition among firms because it involves the substitutability parameter γ.
Concentration of firms reduces firms’ revenues and profits due to the substitutability between
varieties, and thus discourages the incentive to become entrepreneurs in the diﬀerentiatedgood sector. Which eﬀect dominates the other is not clear a priori by theory. We therefore
resort to empirical analysis in order to reveal the overall eﬀect of market size on the formationof entrepreneurship.
5

3

Empirical analysis

3.1

Model specification

In order to obtain an explicit equation that can be estimated, we have to specify the functional
form of the distribution costs. We linearly approximates the distribution costs τ (D) asτ (D) = t0 − t1 D,
where t0 and t1 are positive constants. We assume α > t0 so that the diﬀerentiated good is
produced. Substituting this τ (D) into (5), we have the equation to be estimated as:2ln(e) = a0 − ln(D) −¡¢1ln (h) + ln −2h−1/2 + a1 D1/2 + a2 D3/2 ,2where a0 , a1 , and a2 are defined asµ ¶βa0 ≡ ln,γ

α − t0a1 ≡ √ ,β(6)t1
a2 ≡ √ .
β

As we saw in the previous section, the population density as a surrogate for the homemarket size has the positive and negative eﬀects on entrepreneurship. By estimating equation(6) using Japanese data, we investigate which eﬀect dominates.

3.2

Data and preliminary results

We use the data for years 1992, 1997 and 2002 on Japanese prefectures in order to estimate(6). For the data of entrepreneurship, we use two indices. One is the share ea of people whowish to start up a new business in those who are either employed but want to change careers
or not engaged in work but want to find a job. The other is the share ep of self-employment,
which is calculated by the ratio of the number of self-employed people to the number of people
in all jobs. All these data are taken from Employment Status Survey published by Ministryof International Aﬀairs and Communications of Japan. ea can be interpreted as the shareof ex ante (potentially new) entrepreneurs, whereas ep is considered as the share of ex post
2

We can also obtain this estimation equation by considering Cournot competition instead of monopolisticcompetition, which implies that our results are robust with respect to the type of imperfect competition. See
Appendix for this point.

6

entrepreneurs. The population density Dpop is computed by the prefectural population L(Population Estimates published by Ministry of International Aﬀairs and Communications)divided by the inhabitable area H (Social Indicators by Prefecture published by Ministryof International Aﬀairs and Communications). Table 1 lists the summary statistics of thesevariables and Table 2 describes and sources of all variables.3[Insert Tables 1 and 2 around here]
In order to see the overall distributions of ea and ep across regions, we estimate theirdistribution by use of kernel density estimation. The estimated distributions of ea and ep
are drawn in Figures 1 and 2, respectively, where the horizontal axis represents the share ofentrepreneurs and the vertical one shows its density.4[Insert Figures 1 and 2 around here]
Note first that the entrepreneurship significantly varies across regions in each year: 5 to
11 percent with respect to ex ante entrepreneurs and 7 to 19 percent with respect to ex post
entrepreneurs. On average, the share of ex post entrepreneurs is higher than the share of ex
ante entrepreneurs. This would reflect the fact that the latter does not include those inherit
business from their parents. Second, both figures show that the distribution has shifted fromyear to year, which indicates that the entrepreneurship in all regions is aﬀected by changes
in the national economy as a whole. The decline of the Japanese economy during the 1990s
is thought to be the reason for this steady fall in the entrepreneurship.
Before estimating the equation (6), we provide some preliminary estimation of the relationship between the population density and the entrepreneurship. Table 3 shows theregression results in which the dependent variables are ln(ea ) and ln(ep ), and the independent variables are ln(Dpop ) and ln(Gd ), where Gd is the per capita GDP (National Accounts
3

The Hokkaido prefecture is the largest in terms of inhabitable area and contains one big city (Sapporo)and many small cities. Since the average density of Hokkaido does not represent its regional characteristics,
we have eliminated it from our sample, which leads to our sample size of forty-six prefectures times three
years.
4
We used the Silverman’s default bandwidth in the kernel estimation. See Härdle [10] for more details.

7

published by Department of National Accounts in Cabinet Oﬃce) that controls for the year
eﬀect.
[Insert Table 3 around here]
In Table 3, (1) and (4) represent the results estimated by OLS regression, regressions (2)and (5) by the fixed eﬀect model, and (3) and (6) by the random eﬀect model. From theHausman test, we can see that the random eﬀect model is shown to be more appropriate
than the fixed eﬀect one. These estimated results show that the ex ante entrepreneurship is
positively related to the population density, whereas the ex post entrepreneurship is negatively related to the population density. In what follows, we estimate (6) in order to analyze
in more detail on the relationship between the population density and the entrepreneurship.

3.3

Model for estimation

In the above preliminary regressions, we ignore several variables that are considered to aﬀect
the entry decision of entrepreneurs based on the literature of empirical studies of firm entry
in the tradition a la Orr [13].5 We therefore include the following control variables. First, weappend the per capita gross prefectural domestic product (GPDP) (Gp ), the year to year comparison of the per capita GPDP (gp = Gpt /Gpt−1 ), and the price-cost margin (M), which describe the overall economic conditions of the corresponding region. Gp represents the current
condition and gp indicates the future prospect. M is defined as M = (GPDP−intermediate
output−indirect tax less subsidies−compensation of employees)/GPDP, which is a proxy forprofitability of business in the region. Second, in order to control the diﬀerence in industry
structures, we add the shares of agriculture, manufacturing, and public sectors in the GPDP
(Sha , Shm , and Shp ). All the data for Gp , gp , M, Sha , Shm , and Shp are taken from Prefectural
Accounts published by Department of National Accounts in Cabinet Oﬃce. Third, we also
control the eﬀective job opening to job applicant ratio (V ), which is available in Monthly
Report of Public Employment Security Statistics published by Ministry of Health, Labourand Welfare. Table 1 provides the basic statistics of these variables, and Table 2 describes
and sources of all variables.
5

See Geroski [6] for **surveys** on empirical studies of firm entry.

8Introducing all these variables into (6), the equation to be estimated becomes
´
³
1
−1/2
1/2
3/2
ln(eit ) = a0 − ln(Dit ) − ln (hit ) + ln −2hit + a1 Dit + a2 Dit
2(7)+ b1 ln(Gpit ) + b2 ln(gpit ) + b3 ln(Mit ) + b4 ln(Shait )+ b5 ln(Shmit ) + b6 ln(Shpit ) + b7 ln(Vit ) + b8 ln(Gdt ) + uit ,where uit is the standard error term. We estimate this equation by the nonlinear least squares
method.

3.4

Results

Estimation results of (7) are reported in Table 4. Columns 1 and 2 lists the parameter
estimates for ex ante entrepreneurs and ex post entrepreneurs, respectively, when the abovementioned conditions are controlled for.
[Insert Table 4 around here][interpretations on the estimated coeﬃcients]
Using these estimated regression equations, we can simulate the elasticity (Dpop /e)(∂e/∂Dpop )of the entrepreneur share e with respect to the population density Dpop . Figure 3 provides
the simulation results for the relevant range of Dpop , when the elasticity is evaluated at themean of the inhabitable area h.
[Insert Figure 3 around here]
The horizontal axis represents the logarithm of Dpop , whereas the vertical axis describes
the elasticity. The solid curve shows the results for the ex ante entrepreneurs ea , and thedashed curve describes the results for the ex post entrepreneurs ep . We observe from thisfigure that the population density has a positive impact on the ex ante entrepreneurship. For
large prefectures, such as Tokyo and Osaka, a 10 percent increase in the population density
increases the share of ex ante entrepreneurs by around 2 percent. In contrast, the population
density is likely to have a negative impact on the ex post entrepreneurship. The ex ante
positive impact may suggest that high density is considered to be an entrepreneurial chance9to start business. High density would mean large and diversified cities, where innovation isfostered and new products are developed (Duranton and Puga [5]). However, the ex post
negative impact may indicate that high density turns out to be keen competition between
firms so that quite a few entrepreneurs get out of business.

3.5

Density economies or market expansion?

The population density has a positive eﬀect on the ex ante entrepreneurship. It also has
a positive eﬀect on the ex post entrepreneurship although the range of a negative eﬀect
dominates that of a positive eﬀect. As we discussed in section 2, such a positive eﬀect comesfrom two sources: density economies and market expansion. It is interesting to focus on thepositive eﬀect and investigate which of these two is the main source.
√
The positive eﬀect comes from changes in [α − τ (D)] βhD in (5). Therefore, we cancheck which of the two sources dominate by computing the derivative of this term with respect
to the population density D. That is, the positive eﬀect can be decomposed as follows:√opp[α − τ (D)] βh
d n
√
+
.
[α − τ (D)] βhD =t βhD|1 {z }
dD
2
D
|
{z
}
density economies
market expansion≡ A(D)≡ B(D)The relative strength of these two is given by
A(D)
2D
=
.
B(D)
(α − t0 ) /t1 + D
Because (α − t0 ) /t1 = a1 /a2 from (6), the estimates of this ratio can be obtained by Table
4. We then depict the ratio of A(Dpop )/B(Dpop ) for ex ante and ex post entrepreneurship in
Figure 4, respectively.
[Insert Figure 4 around here]
We observe that the market expansion is more important than the density economies
with respect to ex post entrepreneurship for a wide range of the population density. Thisis also true for ex ante entrepreneurship when the population density is low. This may
10

imply that the market expansion is crucial for regions with low density involving small cities,
while the density economies are insuﬃcient to start up new business in small cities for exante entrepreneurship. When the population density is high, the density economies are
more important than the market expansion for entrepreneurship. This may suggest that thedensity economies are at work for entrepreneurship in regions involving large cities, whereas
the market expansion is exhausted in such cities.

4

Robustness checks

In what follows, we conduct two diﬀerent estimations in order to check robustness of ourresults.

4.1

Nonparametric estimation

The analysis in the previous section may rely on the functional form of (6). This restriction,on the one hand, enables us to simulate the responses of entrepreneurship to changes in the
population density. However, on the other hand, it may be too simple to capture the true
relationship between the entrepreneurship and population density. We therefore do not assume the explicit functional form in estimating the relationship between the entrepreneurshipand population density. This can be done by estimating the mean of the entrepreneur shareconditioned on prefectural population density by Kernel estimation. More specifically, we
estimate the values of E(et | ln(Dpop )).6 Estimated conditional means are shown in Figure 5
with the ex ante entrepreneurs ea and in Figure 6 with the ex post entrepreneurs ep . Figures
5 and 6 verifies the findings obtained in the previous section.
[Insert Figures 5 and 6 around here]

4.2

Employment density

Thus far, we focus on the population density. Since the employment density may be more
important for entrepreneurs, we pursue this possibility. Replacing the population density
6

Again, we used the Silverman’s default bandwidth in the kernel estimation.

11

with the employment density, we have conducted the estimation of (7), and obtained theresults shown in Table 5. As before, the first and second columns describe the parameter
estimates using data of ex ante entrepreneurs ea and ex post entrepreneurs ep , respectively.
We can then compute the elasticities (D/e)(∂e/∂D) of the entrepreneur share with respect
to the market size by use of the parameter estimates. They are drawn in Figure 7.
[Insert Table 5 around here][Insert Figure 7 around here]
We confirms from Figure 7 that the employment density is positively (resp. negatively)
associated with the ex ante (resp. ex post) entrepreneurship. Since this result is similar tothat by Figure 3, we conclude that the impact of the employment density on entrepreneurship
does not diﬀer from that of the population density.

5

Concluding remarks

This paper explored how the market size aﬀects entrepreneurship. Our results show thata larger market stimulates ex ante entrepreneurship and gives workers stronger incentives
to start up a new business, but leads to lower ratio of self-employment, i.e., lower ex post
entrepreneurs. Moreover, the eﬀect of market density economies is important in encouraging
people to be entrepreneurs ex ante especially in large cities. In contrast, with respect tothe self-employment ratio, the eﬀect of market expansion dominates the eﬀect of density
economies in general and these two positive eﬀects are smaller than the negative eﬀect. Thismay be due to the fierce competition among firms in the large market ex post.
The current analysis cannot provide the reason why the market size has diﬀerent impacts
on entrepreneurship in diﬀerent stages. By exploiting micro-data on firms, we may be able
to find the reason. In particular, it would be useful to work on data regarding firm turnovers.
This is an important direction of future research.

12

References[1] Alonso, W., 1964, Location and Land Use, Cambridge, MA, Harvard University Press.
[2] Berry, S. and P. Reiss, 2007, Empirical models of entry and market structure, in: M.
Armstrong and R. Porter (eds.), Handbook of Industrial Organization, Volume III, Amsterdam, North-Holland.
[3] Ciccone, A., 2002, Agglomeration eﬀects in Europe, European Economic Review 46,
213-227.
[4] Ciccone, A. and R.E. Hall, 1996, Productivity and the density of economic activity,
American Economic Review 86, 54-70.
[5] Duranton, G. and D. Puga, 2001, Nursery Cities: Urban diversity, process innovation,and the life cycle of products, American Economic Review 91, 1454-1477.
[6] Geroski, P.A., 1995, What do we know about entry, International Journal of Industrial
Organization 13, 421-440.
[7] Glaeser, E.L., 2007, Entrepreneurship and the city, NBER Working Paper 13551.
[8] Glaeser, E.L. and W.R. Kerr, 2008, Local industrial conditions and entrepreneurship:
How much of the spatial distribution can we explain?, NBER Working Paper 14407.
[9] Harada, N., 2005, Potential entrepreneurship in Japan, Small Business Economics 25,
293-304.
[10] Härdle, W., 1990, Applied Nonparametric Regression, Cambridge, Cambridge University
Press.
[11] Krugman, P.R., 1980, Scale economies, product diﬀerentiation, and the pattern of trade,
American Economic Review 70, 950-959.
[12] Krugman, P.R., 1991, Increasing returns and economic geography, Journal of Political
Economy 99, 483-499.

13

[13] Orr, D., 1974, The determinants of entry: A study of the Canadian manufacturingindustries, Review of Economics and Statistics 56, 58-66.
[14] Ottaviano, G., T. Tabuchi and J.-F. Thisse, 2002, Agglomeration and trade revisited,
International Economic Review 43, 409-436.
[15] Reynolds, P.D., B. Miller and W.R. Maki, 1995, Explaining regional variation in businessbirths and deaths: U.S. 1976-88, Small Business Economics 7, 389-407.
[16] Rosenthal, S.S. and W.C. Strange, 2005, The geography of entrepreneurship in the New
York metropolitan area, Federal Reserve Bank of New York Economic Policy Review 11,
29-53.

Appendix: A Cournot competition model with entrepreneurship
In this appendix, we show a diﬀerent model with Cournot competition yields the same
estimation equation.
The utility function is quasi-linear with respect to the homogeneous good x
U = αx −β 2
x + q0 ,2

where α and β are positive parameters. Given the budget constraint w + q 0 = px + q0 , where
p is the price of x, the inverted demand function is
p=α−β

nx
.
L

Firms are competing a la Cournot. The good market clearing requires Lx =Pn

v=1 xv ,where xv is the good supplied by firm v, and hence, the inverted demand function that firms
face is given by
p=α−β

µPn

v=1 xiL¶.

In producing good x, the marginal labor requirement is given by τ (D) = t0 − t1 D so that
there are density or agglomeration economies. The profit of firm v is described as
π v = (p − τ (D)w)xv .
14

(A1)

Solving the first-order condition for the profit maximization, we get the equilibrium output
and profit asx=L(α − t0 + t1 D)
β(n + 1)andπ=

L (α − t0 + t1 D)2,β(n + 1)2(A2)

where subscript v is dropped due to the identical production technologies. Because thenumber of firms is equal to the number of entrepreneurs, n = eL holds. Plugging thisrelation and (A2) into (A1) with w = 1 and π(v) = 0, we have
¶
µ
1
1
1/2
3/2
ln(e) = − ln(D) − ln(h) + ln − 1/2 + a1 D + a2 D,2hwhich is the same estimation equation as (6) except the constant terms. We therefore conclude that all the results obtained in this paper are valid for the Cournot competition model.

15

ea
ep
L
H
Dpop
E
Dem
Gp
gp
M
Sha
Shm
Shp
V
Gd

Mean
0.08050.133
2616.02147.6
1387.11371.1725.8
3393.91.00
0.241
0.0279
0.246
0.109
0.839
3973.0

Std Dev0.01410.02402457.0981.2
1622.61327.5875.8
769.0
0.01820.02540.02000.08550.03040.374
109.0

Minimum
0.05440.0710
612
832.6
372.7
314.6
181.0
2165.90.960
0.178
0.000526
0.04880.05800.230
3887.7

Table 1. Summary statistics

Maximum
0.118
0.191
12219
4562.88753.76677.04838.67242.81.06
0.322
0.0898
0.502
0.203
1.91
4126.4

Sha
Shm
Shp
V

Description
share of people who wish
to start up a businessshare of self-employment
number of employed workers (in thousands)
employment density
prefectural population (in thousands)
population density
inhabitable area (km2 )per capita GPDP
(in thousand yen)year to year comparison of Gp
price-cost margin=(GPDP−intermediate
output−indirect tax less subsidies−compensation of employees)/GPDP
share of agriculture in the GPDP
shares of manufacturing in GPDP
share of public sectors in the GPDP
active job opening to job applicant ratio

Gd

per capita GDP (in thousand yen)

ea
ep
E
Dem
L
Dpop
H
Gp
gp
M

Table 2. Description and sources of variables

SourceEmployment Status Survey= 1000 × E/HPopulation Estimates= 1000 × L/H
Social Indicators by Prefecture

Prefectural Accounts

Monthly Report of Public
Employment Security Statistics
National Accounts

dependent variableln(Dpop )ln(Gd )
const.

ln(ea )
(1)
0.0951∗∗∗(0.0202)0.753(0.514)−9.43∗∗(4.26)
NoNo

fixed eﬀect
random eﬀect
p-vale of Hausman test
R2
0.15

Table 3. Preliminary estimation(2)−0.577(1.27)
0.874(0.593)

Yes
No
0.36

(3)
0.0949∗∗∗(0.0244)0.753∗(0.442)−9.43∗∗∗(3.66)
No
Yes
0.87
0.15

ln(ep )
(4)
−0.158∗∗∗(0.0187)−0.223(0.476)0.919(3.95)
No
No
0.34

(5)
−0.114(0.727)−0.230(0.337)

Yes
No
0.81

(6)
−0.158∗∗∗(0.0274)−0.223(0.311)0.919(2.58)
No
Yes
0.95
0.34

dependent variable ln(ea )a0−5.35(4.25)
a1
0.00312∗∗∗(0.210 × 10−3 )a20.850 × 10−6∗∗∗(0.170 × 10−6 )b1−0.114(0.169)b2−0.170(0.743)b3
0.299∗∗(0.142)b4
0.140∗∗∗(0.0451)b5−0.135∗∗(0.0566)b6−0.539∗∗∗(0.174)b7
0.173∗∗∗(0.0444)b8
2.00∗∗∗(0.522)
2
R
0.46
N
138

ln(ep )
9.72∗∗∗(3.25)
0.00365∗∗∗(0.000206)
0.526 × 10−6∗∗∗(0.116 × 10−6 )−0.0125(0.123)0.803(0.565)−0.215∗∗(0.109)0.165∗∗∗(0.0353)−0.117∗∗(0.0461)−0.140(0.132)0.0892∗∗∗(0.0334)
0.166(0.398)0.70
138

Table 4. Results for entrepreneurship
Note: Standard errors are in parentheses. Significance levels: ∗ = 10%, ∗∗ = 5%, ∗ ∗∗ = 1%.

dependent variable ln(ea )a0−4.63(4.26)
a1
0.00420∗∗∗(0.000275)
a2
0.244 × 10−5∗∗∗(0.449 × 10−6 )b1−0.0850(0.162)b2−0.153(0.730)b3
0.309∗∗(0.141)b4
0.161∗∗∗(0.0438)b5−0.126∗∗(0.0545)b6−0.504∗∗∗(0.168)b7
0.153∗∗∗(0.0419)b8
1.83∗∗∗(0.525)
2
R
0.47
N
138

ln(ep )
9.31∗∗∗(3.31)
0.00504∗∗∗(0.000280)
0.141 × 10−5∗∗∗(0.302 × 10−6 )−0.0186(0.117)0.798(0.564)−0.215∗∗(0.109)0.168∗∗∗(0.0345)−0.114∗∗(0.0454)−0.145(0.130)0.0823∗∗(0.0323)0.145(0.405)0.70
138

Table 5. Robustness check: employment density
Note: Standard errors are in parentheses. Significance levels: ∗ = 10%, ∗∗ = 5%, ∗ ∗∗ = 1%.

kernel density estimation of the share (ea) of ex ante entreprenuers
60

EA1992 × EA
EA2002 × EA

EA1997 × EA

50

40

30

20

10

0.055

0.060

0.065

0.070

0.075

0.080

0.085

0.090

0.095

0.100

0.105

0.110

0.115

Figure 1: Kernel density estimation of the share (ea ) of ex ante entreprenuers

20.0

kernel density estimation of the share (ep) of ex post entrepreneurs
EP1992 × EP
EP2002 × EP

EP1997 × EP

17.5

15.0

12.5

10.0

7.5

5.0

2.5

0.07

0.08

0.09

0.10

0.11

0.12

0.13

0.14

0.15

0.16

0.17

0.18

0.19

Figure 2: Kernel density estimation of the share (ep ) of ex post entrepreneurs

Dpop eiei  Dpop
0.3
Dpop ea

0.2

ea  Dpop
0.1
lnDpop 
6.5
0.1
0.2

7.0

7.5

8.0

8.5

9.0

Dpop ep
ep  Dpop

0.3
Figure 3: Simulated elasticity of ex ante/ex post entrepreneurship with respect to the
population density. The solid curve represents (Dpop /ea )(∂ea /∂Dpop ) and the dashedcurve represents (Dpop /ep )(∂ep /∂Dpop ).

ADpop BDpop 
1.4
1.2
1.0
0.8
ADpop 
0.6

BDpop 

for eaADpop 

0.4

BDpop 

0.2

for eplnDpop 

6.0

6.5

7.0

7.5

8.0

8.5

9.0

Figure 4: Relative importance of density economies to market expansion. The solid
curve represents the case of ex ante entrepreneurship and the dashed curve represents
the case of ex post entrepreneurship.

0.110kernel estimation of the conditional mean of ea (=E(ea|ln(Dpop))

0.105

EEA1992 × LNDPOPEEA2002 × LNDPOPEEA1997 × LNDPOP

6.25

7.00

0.100
0.095
0.090
0.085
0.080
0.075
0.070
0.065

6.00

6.50

6.75

7.25

7.50

7.75

8.00

8.25

8.50

8.75

9.00

Figure 5: Kernel estimation of the conditional mean of ea (= E(ea | ln(Dpop )))0.16

kernel estimation of the conditional mean of ep (=E(ep|ln(Dpop))
EEP1992 × LNDPOP
EEP2002 × LNDPOP

EEP1997 × LNDPOP

6.25

7.00

0.15

0.14

0.13

0.12

0.11

0.10

6.00

6.50

6.75

7.25

7.50

7.75

8.00

8.25

8.50

8.75

9.00

Figure 6: Kernel estimation of the conditional mean of ep (= E(ep | ln(Dpop )))Dem eiei  Dem
0.3
0.2

Dem eaea  Dem

0.1

6.5
0.1
0.2

7.0

7.5

8.0

8.5

9.0

lnDem 

Dem ep
ep  Dem0.3
Figure 7: Robustness check. Simulated elasticity of ex ante/ex post entrepreneurship with respect to the employment density. The solid curve represents(Dem /ea )(∂ea /∂Dem ) and the dashed curve represents (Dem /ep )(∂ep /∂Dem ).