The Effects of Public Finance System and Public Educational Expenditure on Human Capital
Distribution in the Tokai Region: Simulation in a Six-Period Overlapping Generations Model∗
Yuko Shindo∗∗, Yamaguchi Prefectural University
Hideya Kato, Nagoya Keizai University
Mitsuyoshi Yanagihara, Nagoya University
Tsuyoshi Shinozaki, Tohoku Gakuin University
1. Introduction(million yen)This paper investigates the effects of public finance system and public education expenditure on
economic growth in three prefectures in the Tokai region, Aichi, Gifu and Mie, in a six-periodoverlapping generations model of endogenous growth fueled by human capital accumulation.
Japan has experienced high economic growth from the 1970s to the early 1990s and prolonged
economic
Figure 1. Regional GDP (nominal)
recession to date.
Figure 1 shows
250,000,000
Hokkaido&
the GDP levels ofTohoku
Japan’sseven
200,000,000
Kanto
regions, Hokkaido
Chubu
and
Tohoku,150,000,000
Kanto,
Chubu,
Kinki
Kinki, Chugoku,
100,000,000
Chugoku
Shikoku,
andKyushu,
from
Shikoku
50,000,000
1996 to 2008.
KyushuThereexists01996 1998 2000 2002 2004 2006 2008
divergence among
Source: Kenmin Keizai Keisan FY2008
regions.
TheKanto region has achieved the highest GDP level, while the Chugoku and Shikoku regions have caught
relatively the low GDP levels. In addition, despite the severe economic recession since the mid-1990s,the Chubu region had benefited the remarkable economic performance for the last 10 years. The GDP
level became very close to Kansai, the second largest region, by 2008.
Per capita GDP in the three prefecture of Aichi, Gifu and Mie located in the Chubu region, which isoften referred as the Tokai region, is shown in Figure 2. Per capita GDP of Aichi and Mie have grown
faster than that of national average until the Lehman shock in 2008. The main reason for such success ismainly based on export-oriented automobile industry such as Toyota and its affiliated factories in Aichi
and the growth of industrial complexes in Mie.

∗This research was supported by Grant-in-Aid for Asian CORE Program and Grant-in-Aid for Scientific Research (C)No.20530151 of Japan Society for the Promotion of Science (JSPS), and CASIO Science promotion Foundation.
∗∗Corresponding author: shindo@yamaguchi-pu.ac.jp
1Table 1 showstheeducation
3,800
expenditure andthecollege
3,600
entrance rate of
3,400
2009 high school
Gifu
graduates in the3,200
Tokai region. Mie
Aichi
3,000spendson
Mie
education
2,800
comparatively
Nationhigher than other2,600
1996
1998
2000
2002
2004
2006
2008
two prefectures.
Source: Kenmin Keizai Keisan FY2008
On the other hand,
Aichi and Gifu have higher college entrance rate than the national average ratio. It is reasonable to saythat the higher GDP levels in the Tokai region are derived from the higher levels of human resources inthe prefectures.
1,000 yen

Figure. 2 Per capita GDP

Table 1. Ratio of education expenditure to local government expenditure in 2010 and college entrance rate in 2009
Education
expenditure

Ratio of persons who advanced toschools of higher grade
MaleFemale

Gifu

25%

55%

55%

Aichi

25%

58%

60%

Mie

27%

50%

53%

Nation

N/A

52%

56%

Source: Japan Statistical Yearbook 2011& each prefectural government websites

Besides physical capital accumulation, human capital accumulation is assured to be one of the main
sources of economic growth. This paper attempts to explain how the education expenditure affects thegrowth rate from a macroeconomic viewpoint by carrying out the calibration in Tokai’s threeprefectures. More concretely, we will analyze the growth paths in these prefectures. To capture theregional economy as realistically as possible, we use the six-period overlapping generations model of
Shindo (2009) which is the extension of Bouzahzah et.al. (2002) and apply actual regional economic
data to capture the heterogeneity of regions.
The initial application of the overlapping generations model to the numerical analysis is conducted byAuerback and Kotlikoff (1987) to study the effects of public policies. Later, Docquier and Michel(1999) and Fougère and Mérette (1999) analyze the effect of education on human capital accumulation
or economic growth in European countries and in seven OECD countries, respectively. Uemura (2001),
Sadahiro and Shimasawa (2002), Shimasawa (2004) and Tatibanaki, Okamoto, Kawade, Hatano,Miyazato, Shima and Ishihara (2006) among many others study Japanese policies including education.
2However, except Ban (2007), there are only a few analyses which capture the heterogeneity of regionsin the country.
Our main finding is that even though the efficiency in education and the education expenditure are
not very high compared to other two prefectures, Mie achieves the highest growth in the long run. This
attributes to the small amount of the debt issue.
2. The Model
The model is constructed based on Shindo (2009). The difference is the number of the region, that is,there are three regions in this paper. Each region has perfectly competitive markets of goods, labor andcapital. We assume that all the markets are closed, that is, the goods, labor and capital are all immobilefor analytical convenience. Please refer to the full paper for details.
3. Calibration
In this section, we set parameters and find the steady growth paths or long-run equilibria of Aichi,
Gifu and Mie which replicate the actual data.
3.1 Parameter settingFirst, we set parameters along the lines of Bouzahzah et al. (2002) and Shindo (2009). The data that
we use are from 1998 to 2007. The parameter values are summarized in Table 2.
Based on these parameter values, we obtain equilibrium values in the steady growth paths of the threeprefectures. To begin with, normalizing h1 as one for analytical convenience, we obtain the capitalstock levels per efficient labor unit in the initial period, k 0* , as 1.176 for Aichi, 0.958 for Gifu and 1.069
for Mie. We then obtain the equilibrium values of the other endogenous variables and the human capital,
or economic growth rates. These values are listed in Table 3 in the next subsection. Finally, we change
the exogenous parameters of education investment, ψ , to check robustness.
Table 2. Parameter values
AichiGifuMie

Output elasticity of capital ( α )

0.324

0.382

0.380

Technology parameter (A)

5.254

4.180

4.231

Capital depreciation rate ( δ )Time preference rate ( γ )

0.753

0.779

0.684

0.840

0.840

0.840

Intertemporal elasticity of substitution ( σ )

1.500

1.500

1.500

1.284

1.388

1.402

1.439

1.770

1.667

2

OJT/human capital depreciation in age group 2 ( θ )3

OJT/human capital depreciation in age group 3 ( θ )

3

4

1.421

1.711

1.617

51.015

1.043

0.873

OJT/human capital depreciation in age group 6 ( θ )

6

1.015

1.043

0.873

Human capital productivity ( ξ )

0.245

0.159

0.219

Parameter for education investment ( ψ )

0.128

0.221

0.041

Consumption tax rate ( τ c )

0.05

0.05

0.05

Wage income tax rate ( τ w )

0.379

0.444

0.399

Education subsidy rate ( ν )

0.019

0.162

0.027

Pension payment (p)

2.081

1.927

1.944

Retirement ratio ( ζ )

0.500

0.500

0.500

Other government expenditures (g)

0.270

0.054

0.324

OJT/human capital depreciation in age group 4 ( θ )OJT/human capital depreciation in age group 5 ( θ )3.2 Individual lifecycles on the steady growth paths
Figure 3 shows the consumption and asset level per effective labor unit in each age group. First, wecan see on the left-hand side figure that the consumption per efficient labor unit increases with ageing inall prefectures. This is because individuals accumulate human capital and smoothen the utility levels
throughout their lives. However, the consumption in Aichi is increasing faster than those in Mie andGifu. This reflects the fact that the rate of return to capital in Aichi is the lowest among three prefectures,as shown in Table 3. The reason is that output elasticity of capital in Aichi is the smallest and thus theproductivity of physical capital becomes low compared to those of other prefectures.
Assets are also increasing on the right-hand side figure until the individuals reach the fifth age group.
Because they accumulate human capital with age, their wage income increases and so do their assets. Inaddition, they need to save assets to cover their consumption after their retirement in the middle of thefifth age group. To maintain the highest level of consumption in Aichi, its assets are also the highest
among the three prefectures.
Figure 3. Individual lifecycles
Consumption per effective labor unit

Assets per effective labor unit
1015
Aichi

10Gifu5mil yen/10 yrs

mil yen/10 yrs

20

Mie

0

86

Aichi

4Gifu

2Mie01234

51

6

Age group

23Age group

44

56

Table 3. Steady State Values
Aichi

Gifu

Mie

Lifetime consumption per effective labor unit (mil yen/10 yrs)

41.63731.57122.987

Lifetime asset per effective labor unit (mil yen/10 yrs)

22.987

16.11919.908Human capital/economic growth rate (%/10 yrs)

1.158

1.075

1.183

Education subsidies per effective labor unit (mil yen/10 yrs)

0.001

0.008

0.001

Education time per capita (during 10 yrs)

0.033

0.033

0.012

Rate of return to capital (%/10 yrs)

0.773

0.860

0.858

Capital stock per effective labor unit (mil yen/10 yrs)

1.176

0.958

1.069

Assets per effective labor unit (mil yen/10 yrs)

2.740

2.066

1.996

Debt issues per effective labor unit (mil yen/10 yrs)

1.457

1.029

0.880

When we observe the effects of human capital/economic growth in the third row, Mie has the highest
rate. Therefore, we can forecast that the prefecture will be able to catch up to the consumption and asset
levels of Aichi in the long run although Mie is the lowest education time per capita among theprefectures in the initial steady growth path which is listed in the fifth row. On the contrary, the lowest
growth performance in Gifu which lacks adequate physical capital and human capital will lead to thelow growth performance.
The reason for Mie to achieve the highest growth rate is attributed from the smaller amount of thedebt issue listed at the bottom although the efficiency for education and the education subsidy rate are
not very high. This indicates that the debt issues by the local governments would crowd out the humancapital accumulation as well as the physical capital accumulation.
The interesting result of this simulation is that depending on the initial configuration of physicalcapital and the growth rate, each prefecture takes different growth paths. Especially, there are various
differences in exogenous variables such as output elasticity of capital and human capital productivity.
Although the effects of exogenous parameters significantly affect the simulation results, our model
offers some plausible explanations for the observed results.
4. Conclusion
The different public financial system and education expenditure lead to different growth paths in thethree prefectures in the Tokai region. In particular, we clarify that the debt issue may crowd out thehuman capital accumulation as well as physical capital accumulation. In spite of the positive values ofthe efficiency in education and the education subsidy rate, the negative effect of the debt would
dominate on the human capital accumulation. This indicates the importance of public financialmanagement. Still, we do not deny that the initial structure of physical capital and the initial growth ratestrongly affect the long-run growth path in each prefecture.
One of the limitations in our analysis is that we do not allow the factors of production to move acrossprefectures. We should modify the model more realistically. Another limitation is that we only analyze
the three prefectures. We should examine entire prefectures or at least all regions to grasp the structureof economic growth in Japan.
5Regardless of the limitations, this is a first step to capture the economic growth through education andto show the effect of governmental policy on the human capital accumulation.
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