Do government higher education expenditures affect more on economic growth or
disparity? 
Yuko Shindo
Abstract
The effects of government higher education expenditures on economic growth and
inequality were examined. A multi-regional, general equilibrium, overlapping
generations model with endogenous growth driven by human capital accumulations was
developed. The model is useful for policy makers to capture regional growth and
divergence. The model shows that the economy might grow faster in the whole country
because higher GDP levels may be attributed to higher levels of human resources in the
regions where the household preference over education and average human capital are
higher than the national average. However, the result also indicates that the economic
slowdown might occur in the long run because the education gap could widen in the
country. This suggests that decentralized governments require not only a positive
educational policy reform but central government also needs to set a policy that
redresses regional disparities.
Keywords: General Equilibrium Models, Economic growth, regional disparity,
education policy, higher education
JEL classifications: C68, D91, H75, I24

This work was supported by JSPS KAKENHI Grant Number 15K03521.
Faculty of Intercultural Studies, Yamaguchi Prefectural University; Corresponding author
Email: [email protected]

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1. Introduction
This paper investigates the effects of decentralization on economic growth and
disparity in a three-period overlapping generations (OLG) model of endogenous growth
fueled by human capital accumulation.
The distribution of human capital is geographically uneven around the world. Japan
is not an exception. Figure 1 indicates percentage of undergraduate enrollment from
high school by prefecture quinquennially from 1985 to 2015 in Japan. Although all
prefectures have steady increased in the share of tertiary-educated households over time,
urbanized prefectures tend to have a higher enrollment than rural prefectures because
both the quantity and the quality of universities are much better in the former
prefectures.
Figure 1. Percentage of undergraduate enrollment from high school by prefecture
Source: Gakko kihon chousa (2016)
Because human capital is mobile, the distribution of human capital across
prefectures becomes even more unequal. As Figure 2 shows, the urbanized prefectures
in Japan experience inflows of young people attending a university and finding a job
although other age groups are less likely to move to urban prefectures. According to the
2010 census, the fraction of households graduated from tertiary school at the top of the
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distribution, i.e. Tokyo is 2.7 times larger than at the bottom of the distribution, i.e.
Aomori.
Figure 2. Net inflow of people aged 18 and 22 in 2014 (person)
17,000
5,000
0
Tokyo
16,000
4,000
[CELLRANGE]
net inflow of people aged 22
3,000
Osaka
2,000
[CELLRANGE]
[CELLRANGE]
1,000
[CELLRANGE]
[CELLRANGE]
0
-3,000
-2,000
-1,000
0
1,000
2,000
[CELLRANGE]
Kyoto
[CELLRANGE]
[CELLRANGE]
[CELLRANGE]
3,000
4,000
11,000
5,000
12,000
6,000
-1,000
[CELLRANGE]
-2,000
net inflow of people aged 18
Source: Jumin kihon daichou jinkou idou houkoku (2014)
The trend of uneven geographic distribution of human capital may lead to persistent
regional economic growth difference. It is a well-known fact that education not only
reflects earnings of households but also benefit others. Thus, it is critical to assess the
efficiency and equality of public investment in education. This paper shows how
household preference and average human capital affect regional economic growth
difference. Also we examine how local government policy is effective or ineffective for
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growth and why central government policy is needed for amending inequality.
2. Framework
Consider many regions in one country. Both physical capital and human capital are
perfectly mobile. We assume that the size of each generation is simply normalized to
unity.
The firms use physical capital,
and human capital,
to supply goods,
each period according to the following Cobb-Douglas technology:
,
in
(1)
where
and
are an exogenously given technology parameter and the output
elasticity of capital, respectively. Defining the capital stock and the output as
and , the aggregate production function in (1) is the one expressed in as
y t  Ak t . As the market is perfectly competitive, the profits of firms are assumed to be
zero. Thus,
, and
(2)
,
(3)
where
and
are wage rate and interest rate.
The households in region obtain utilities from their consumption of middle aged,
, and old,
, and education of their children,
.
,
(4)
where and are exogenously given time preference and parental altruism rate.
The individual budget constraint is written as:
, and
,
where
,
,
, and
(5)
(6)
are exogenously given income tax rate,
exogenously given central and local government education subsidies, savings, and
education spending.
4
The level of human capital of middle aged households depends on his parent’s
education spending during his childhood and intergenerational externality,
.
(7)
where is exogenously given output elasticity of human-capital formation.
By maximizing (4) subject to (5), (6) and (7), the optimal allocation of consumption
for the household is
(8)
The optimal investment in education for children is
(9)
From (5), (6), (8) and (9), we have
, and
(10)
.
(11)
Savings increase if the households are patient and/or uncommitted to education, and
decrease if they are impatient and/or committed to education. All prefecture receive the
same amount of the central government education expenditure, yet the amount of the
local government education expenditure depends on the prefectures.
The central government levies income taxes and share revenue with local
governments. The intertemporal budget constraints of the central and local government
are
, and
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(12)
,
where
,
,
and
(13)
are the central and local government revenues,
grants from the central government to the local governments and exogenously given
portion of local governments. The central and local government revenues are divided
into central and local government education subsidies and central and local other
government expenditures,
and
, respectively as
and
(14)
.
(15)
As labor market clears, the amount saved by middle aged in period t is equal to the
physical capital in period t+1 as
K t 1  H t st .
(16)
Finally, the equilibrium growth rate,
, is
.
(17)
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