A System Dynamics A pproach to Regional Income Disparities
Takayuki Yamashita
Department of Economics
Shizuoka University
Ohya 836, Suruga-ku, Shizuoka City, 422-8529, Japan
e-mail: yamashita.takayuki@ shizuoka.ac.jp
Abstract
The excess concentration of population and industry in the Tokyo Metropolitan is now
activating arguments on regional income disparities in Japan. From the statistical
investigation, regional income disparities have a close relation with the balance of
payments. Incomes in the trade-deficit regions are lower than those in the trade-surplus
regions. Based on the system dynamics approach, this study develops a regional economic
model under interregional trade and examines how the money inflow from exports brings the
economic growth. The two regions model clarifies significant results by mutual
dependency. The issue of regional disparities in the standard of living is a common hotly
debated topic in many countries. Findings of this study are valuable to reconsider the public
policy to correct those disparities.
Keyword : regional disparities, macroeconomic model, balance of payments
1. Introduction
The issue of regional disparities in the standard of living and quality of life has been debated
in recent decades. According to the statistical finding by Kuznets (1955), inequality in the
distribution of income increases in the early stage of development but decreases in the long
terms. According to the neo-classical economic growth model, every region within a single
country will converge the similar steady state. Regional disparities must be diminishing.
There is a growing number of attempts to assess the question of regional convergence.
Economic growth raises an average income but often widens the income disparities
within the country. Although nearly a quarter century has passed since the Maastricht Treaty
was signed, regional disparities in income are still raising economics and political issues in
European countries. Regional disparities are seen in the North America.
In Japan, the regional income inequality was high in the prewar period and tumed to
decrease in the postwar high economic growth period (from 1950s to 1970s). Recently, the
bankruptcy of Yibari City! and the excess concentration of population in the Tokyo
1 Yibari is a city in Hokkaido. The city was founded on April 1, 1943 as a coal mining town. When the
1
Metropolitan? are re-activating arguments on regional disparities. These arguments invoke
social unrest. Based on the Annual Report on Prefectural Accounts, we calculated the
coefficient of variation (CV) for per capita income for the 47 prefectures’ (Figure 1). CV
represents the ratio of the standard deviation to the mean, and it is a useful statistic for
comparing the degree of variation from one data series to another. A high value indicates a
large disparity.
0.3
0.25
——
0.1
0.05
Eee eee
19 otro OMOHOANHK OA XYTEbOnRHAN
Wow oC OSKEFTEEFEBDHDAHAAAARASESSTSEH
ror PADBARAAAARBARARSSSSES
ae eA ae eA HPA RPAH ASP AHA AAR AAN
— Coefficient of Variation
Figure 1. Coefficient of variation of per capita income (47 pref.)
Source: Economic and Social Research Institute (Cabinet Office), Annual Report on Prefectural Accounts.
CV was decreasing in the second decade of high economic growth period (from 1962 to
1973), indicating that income equality had been achieved. The Japanese post-war economic
miracle created the equality of income as well as the growth of income. However, CV has
risen since the recovery from “Lost Decade” (from 1991 to 2000), showing the income
inequality has increased.
The regional economy is connected to each other through exports and imports. Exports
increase monetary flows which are necessary for the regional economy to grow, whereas
imports decrease monetary flows in the regional economy. The economic performance of
regional economy is closely related to the balance of payments.
Figure 2 shows the relationship between the percentage of the balance of payments in the
mines were operating, Yibari had as many as 116,908 people. With the closing of the mines in the 1980s, an
attempt was made to convert the economic base to tourism, but few visitors came. In 2007 the city went
bankrupt with ¥358 billion financial loss. City services has been severely cut and Yabari has only 9,968
people in 2013.
2 According to Global Metro Monitor 2014 by the Brookings Institution, Tokyo is the world’s largest metropolitan with
US$1,616,792 GDP and 37,027,800 Population. The third part of GDP and population of Japan concentrate in Tokyo.
hitp://www.brooking 015/01/22-global-met
3 Prefectures are the main subdivisions of Japan, consisting of 47 prefectures, or 1 “to” (#8), 1 “do” (él), 2 “fu (JF), and 43
“ken” (J&). Tokyo-to is a metropolitan.
gross prefectural product (GPP) and per capita income of the 47 prefectures in fiscal 2012*.
The value for correlation coefficient is 0.808, and there is a significant correlation between
those two variables. Per capita incomes in the favorable balance of payments are high, and
per capita incomes in the unfavorable balance of payments are low. The national average of
the percentage of the balance of payments in GPP was 6.26% and per capita income was
4,299 thousand yen’. Tokyo, Aichi, Shizuoka, and Shiga Prefectures exceed the average
with both variables. These four prefectures are the representative base in Japanese
manufacturing industry. This finding is a piece of evidence that the manufacturing industry
is the engine of growth known as Kaldor’s growth laws®.
Tokyo
| Shizuoka Alcht
Per capta GPP (1,000Yen)
a
°
S
S
5,000
4 4 4 * in i 4 4
+ + + -—4 :
4,000 Kagoshima ¢ . o %o ¢ o*
Okinwa |} Hees 7% le
= ‘ ro “eo a
3,000 » * +
Nara
2,000 4
1,000 +
0
-30 -20 -10 0 10 20 30
Balance of payments/GPP (%)
Figure 2. Balance of payments and per capita gross prefectural product (47 pref.)
Source: Economic and Social Research Institute (Cabinet Office), Annual Report on Prefectural Accounts, fiscal 2012.
The purpose of this paper is to examine how the imbalance of interregional trade raises
the regional income disparities and to explore the way to compensate those differences.
System dynamics is applied in this study for the following reasons:
(1) Since Forrester’s pioneering work (1969), the system dynamics has been certified as a
powerful approach to investigate the regional issues.
(2) The flexibility in the model building makes us focus on the issue that the standard
economic model cannot handle.
(3) The structure-based approach of system dynamics works well for elucidating a
4 The gross regional product is called as the gross prefectural product in prefectural accounts.
5 Atthe time of writing, 1 US dollar equals 107 Yen, and 1 Euro equals 122 Yen.
© The first law is that the growth of the GDP is positively related to the growth of the manufacturing sector.
3
phenomenon with limited information. It is hard to obtain a reliable econometric result
when data is little. The structure-based approach gives us the ability to explore such a
phenomenon.
Interregional trade is quite complex because many regions involve. In a simple
approach, the volume of regional production is explained by the volume export from that
region to the other region or the rest of the country. The basic model is explained in the next
section. After that, two-way trade model is proposed.
2. Regional Keynesian model
This section gives the one region model. Demand-oriented approaches to the economic
growth emphasize the role of exports. Exports differ from the other components of demand
in two respects. Firstly, exports are primal way to increase monetary inflow in a local
economy (North [1955]). Secondary, exports are the only autonomous component of
demand in an economic system, in the sense of demand emanating from the outside the
system (Thirlwall [2002]).
The export activity is the engine of economic growth. Income originally eared by the
export sector is spent and re-spent locally, creating additional income through the multiplier.
This idea is expressed regarding employment or incomes. The simplest way to model this
idea is called exports base model or economic base model’. The income version of
economic base model resembles a Keynesian approach of a regional economy’.
The standard Keynesian aggregate demand expression can be applied to a region as
Ef =Ci +1f+Gi+Xf-Mf (1)
where E; represents regional expenditure, C; represents regional consumption, I; is
regional investment, G; is regional government spending, X; are regional exports, and
M; are regional imports in period t.
Consumption expenditure is a stable component of regional expenditure. Consumption
expenditure function is assumed as a Keynesian type function in which the level of
consumption depends on regional income.
OP=e'Vy (2)
where c‘is regional marginal propensity to consume (MPC) and Y ‘is gross regional product
(GRP).
Regional investment is assumed to be exogenous.
ret" (3)
7 According to Andrews (1953), the export base concept dates back to Robert Haig in 1928 and the export base theory was
developed by Homer Hoyt in the 1930s for city planning. Economic version of the export base model was developed by
Richard Andrews, Douglas North, and Charles Tiebout, independently.
8 There are many attempts to model system dynamics version of the Keynesian macroeconomic model. Among them, Low
(1980) was helpful to understand standard thought in system dynamics context.
4
Regional government spending is assumed to be exogenous’.
G,=G" (4)
In the export-base methodology, regional exports are assumed to be exogenous.
X,=x" (5)
Regional imports expenditure function is given as
Mi =m'C/4+n'X/ (6)
where m'‘is regional marginal propensity to import for consumption (MPMC) and n'is
regional marginal propensity to import for exports production (MPMP).
In the case of regional accounts, the definition of imports is expenditure on anything
which is purchased from outside of the region, as well as outside of the country. A large part
of regional imports are intermediate goods because there are extensive and deep supply chains
within a country. This point is a major difference between the regional and national
income-expenditure frameworks. Consequently, imports share of GRP is far larger than that
of GDP. Although imports function is usually a function dependent on GDP only in the
national model, the level of regional imports is dependent on regional exports as well as
regional consumption. This formulation fits a regional data much better than the standard
imports function!”
The regional economy is in equilibrium when income equals total expenditure.
Ye = Er (7)
Figure 3 shows the basic idea of the regional macroeconomic model.
GRP ——————— GRP 1)
+
Aggregate + ,
expenditure“ ———-C onsumption
+
+7 +
{ os )
(me Imports
Government +
spending
Figure 3. Basic regional macroeconomic model
Exports
Equations from (1) to (7) give the difference equation.
"G6 iture is treated as an variable in many studies.
10 For more details, see Yamashita [2016]
Yf =1'+G7+(-n")Xf+c'(l-m')Y,, (8)
The equilibrium level of income remains what it is in the static model. Since Y,"
forall t in equilibrium, then
1 +6" +(l-n')x? (9)
1-c'(1-m'‘)
y"
3. Exporter region and importer region
Among 47 prefectures, Shizuoka prefecture is modelled as a net exporter region and
Kagoshima Prefecture as a net importer region!!. These two prefectures have a tight
economic relationship. Shizuoka Prefecture has been renowned for Japanese tea as well as
for manufacturing. Shizuoka tea has been ranking first in crop acreage, production, and
shipping. However, the amount of tea leaf is not enough for production, Shizuoka Prefecture
is now ranking first in imports of tea leaf. Kagoshima Prefecture is a major supplier of tea
leaf. Shizuoka Prefecture offers technical guidance in tea farming to Kagoshima Prefecture,
and people exchange is active!*. Shizuoka Prefecture is a major production area of not only
Japanese tea but also manufacturing products. Shizuoka is ranking first in production of
motorcycles, musical instruments, medical appliances, and fishing boats. Those
manufacturing products are sold in Kagoshima Prefecture. Table 1 summarize the brief
comparison of two prefectures.
Table 1. Data for prefectures
Real GPP, Real Exports, Real Imports, Real per capita
2012 2009 2009 Population, on 7
(million yen, (million yen, _ (million yen, 2012 x 4
2007 base) 2007 base) 2007 base) 007 Bass Me
Shizuoka 15,798,754 15,011,812 13,187,180 3,734,540 4,550
Kagosh 5,921,187 2,425,744 3,038,643 1,689,641 3,504
Source: Economic and Social Research Institute (Cabinet Office), Annual Report on Prefectural Accounts, fiscal 2012.
The official statistics of exports and imports have not been published since 2010.
Based on the Annual Report on Prefectural Accounts, we simulated the regional
macroeconomic model for Shizuoka Prefecture from 1975 to 2012 fiscal!*. The vertical axis
in Figure 4 indicates billion yen. Simulated values fit historical data.
11 In this paper, we call the region with the favorable balance of payments as exporter region, and the region with the
unfavorable balance of payments as importer region.
12 Mt Fuji Shizuoka Airport has a Shizuoka-K agoshima airline.
13 The value of MPC is obtained from calibration. The values of MPMC and MPMP are obtained from regression analysis
because those values give good estimations, System dynamics and ics have pectively as Meadows
(1980) explained.
6
20,000
15,000
10,000
5000
0
1975 1979 1983 1987 1991 1995 1999 2003 2007 2011
Time (Y ear)
GRP : Model Shizuoka —————— GRP : Real Shizuoka
Figure 4. Shizuoka model
Figure 5 shows a simulation of Kagoshima Prefecture from 1975 to 2012 fiscal.
7000
5250
3500
1750
0
1975 1979 1983 1987 1991 1995 1999 2003 2007 2011
Time (Y ear)
GRP : Real Kagoshima
GRP : Model Kagoshima
Figure 5. Kagoshima model
4. Two-region model
This section expands the one-region model to the two-region model. Exports from a
particular region are imports into another region. Shizuoka Prefecture (r=1) and
Kagoshima Prefecture (r =2) are mutually depending through exports and imports (Figure 6).
Export by region 1 Export by region 2
= +
u Consumption 2
0 ion
Consumption 1 ae
+ \t +/ +
Import by region 1 Import by region 2
Figure 6. Interregional trade model
The following equation is assumed to connect two regions.
Xi=a+fM), ixj (9)
The variable ‘1 to 2’ named after money flow from region | to region 2 and ‘2 to 1’ vice versa.
Regression analysis estimated parameters because constant terms were needed to consider
trade with other regions.
A considerable number of regional studies assume exports as an exogenous variable.
Exports are autonomous or uncontrollable. Figure 7 shows the simultaneous simulation
under fixed parameters X'=X 4. and M'=M4.. Under the fixed volume of trade,
GRPs in both regions declined.
20,000
15,000
10,000
0
2012 2014 2016 2018 2020 2022 2024 2026 2028 2030 2032
Time (Y ear)
GRP 1: Curent ——+—-+—1— GRP 2: Curent —2—-2—2—2
Figure 7. Simulation under fixed exports and imports
Figure 8 shows the simulation under endogenous imports and exports. Trade increased
GRP in the net exporter region. Although GRP in the net importer region slightly declined,
GRP was higher than that before the trade.
20,000
15,000
10,000
5000 |
0
2012 2014 2016 2018 2020 2022 2024 2026 2028 2030 2032
Time (Y ear)
GRP 1:Curent ——+—_1—_1— GRP 2 :Curent —2——2—2—2
Figure 8. Simulation under interdependent exports
Methodologically, economic base analysis views the region as if it were a small nation
and uses notions of comparative advantage from international trade theory. On the other
hand, this two-region showed trade gains without production specialization. Trade gains
arose from the economic growth.
5. Public policy for regional disparities
Now let us examine a policy to correct the income disparity between two prefectures.
Trade is a beneficial activity for both regions, but cannot compensate the regional disparity by
itself. There are many arguments on the regional disparities. Some argue that scaling back
of public works be a cause of current income disparity.
There are two policy options: national govemment spending transferred into the net
exporter region or the net importer region to increase public works and services. One
example was the industrial areas in Tokyo, Aichi, and Gifu Prefectures invested heavily by the
Japanese government in the 1950s; the other was local areas invested by the local allocation
tax in the 1990s'*. It is important to use a numerical simulation to choose right choice.
Assume that national government transfers 500 billion yen for the region 1 or the region
2 from 2017 to 2020. An increase in the local government expenditure affects not only this
region but also the trading partner. Figure 9 shows the simulation result that 500 billion yen
was transferred into the rich exporter region 1. The vertical axis indicates billion yen.
mee Att Lee
15,000
10,000
5000
0
2012 2014 2016 2018 2020 2022 2024 2026 2028 2030 2032
Time (Y ear)
GRP 1:Curent ——1—_1—_1.— GRP 2:Curent —2—2—2—2
Figure 9. Supplementary budget for the region 1
A 4-year increase in intraregional demand improved the gross regional product of region
14 Heavy investment on 1964 Tokyo Olympic made Tokyo Prefecture grow rapidly. So there is an argument that stadiums
of 2020 Tokyo Olympic should be decentralised to the outside of Tokyo.
10
1. Although this growth towed region 2 slightly, it did not correct the income gap.
Figure 10 shows the simulation result that 500 billion yen was transferred into the poor
importer region 2. A 4-year increase in intraregional demand improved GRP of region 2,
although it narrowed income gaps during just 2 years. An increase of intraregional demand
of region 2 put region 1 on the growth path.
20,000 PEL erry 7 |
15,000
10,000
5000 ba Lo) te ear
0
2012 2014 2016 2018 2020 2022 2024 2026 2028 2030 2032
Time (Y ear)
GRP 1 :Curent ——z—z—3— GRP 2:Cument —2—2—2—2
Figure 10. Supplementary budget for the region 1
The government spending in the net importer region improved the net exporter region
more than the same spending in the net exporter region. These results suggest that
government spending should be heavily invested in the poor importer region to correct the
regional income gap.
6. Conclusion
According to the neo-classical growth theory, every region within a single country will
converge the similar steady state. According to the international trade theory, factor prices
will be equalised. However, there remain the regional income disparities even in the highly
advanced economies and income disparities often poses policy issues. We must investigate
the nature and the origin of regional disparities precisely. System dynamics approach is a
helpful method to examine this unsolved problem. Findings of this paper are summarised as
follows:
1) The imbalance of the balance of payments is the source of regional income disparities.
However, participating in interregional trade is beneficial to net importer regions as well as
the net exporter regions.
2) Reginal imports are affected by its exports as well as its consumption. This feedback
mechanism is a source of regional economic growth. Although a considerable number of
11
regional studies and system dynamics studies assume exports as an exogenous variable, rise
and fall of exports cause by imports are keys to regional income growth.
3) Connecting exports and imports are a simple but an effective idea to examine the
interregional trade. The flexibility of system dynamics helps us to model the feedback
mechanism. System dynamics approach also makes us observe the dynamic inflow and
outflow of income with accuracy.
4) Redistribution of national government spending is effective to correct regional income
disparities when it is invested in the poor importer regions. Government spending in the net
importer region improves the importer region and reduces the income gap while it creates
economic growth of the exporter region.
These years, many local governments in net importer regions promote sightseeing tours
as a growth strategy. However, there are not many success examples. Public works are
effective solutions to correct income gap. It is necessary to investigate other policy options
such as private investment and immigration. Further studies are needed.
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