CIGS Working Paper Series No. 17-003E

Regional Business Cycle and Growth
Features of Japan

Masaru Inaba
Kansai University/The Canon Institute for Global Studies
Keisuke Otsu
University of Kent/The Canon Institute for Global Studies

March, 2017

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Regional Business Cycle and Growth Featuresof Japan∗
Masaru Inaba†
Kansai University and CIGS
Keisuke Otsu‡
University of Kent and CIGS
March 6, 2017

Abstract
We study the features of regional business cycles and growth inJapan. We find evidence of unconditional convergence over the 19552008 period. For the 1975-2008 period, we find evidence of convergence conditional on TFP gap, population growth, private investment
rate and TFP growth. We also find that the consumption-output
correlation puzzle exists, which implies that the idiosyncratic income
shocks are not shared among prefectures and regions. Our analysis
implies that frictions in financial markets are responsible for the low
consumption risk-sharing among prefectures.

Keywords: Japanese Economy; Regional Convergence; Regional Business
Cycle Synchronization
JEL Codes: E01; E32; O47∗
The authors are grateful to Etsuro Shioji for his insightful comments. We thank Steve
Ambler and Christian Zimmerman for their guidance on our empirical analysis. We also
thank participants of the 2015 Japanese Economic Association Meeting and workshops at
the University of Kent, University of Tokyo and Development Bank of Japan. Both authors
acknowledge supported by JSPS KAKENHI Grant Number 16H03626. Otsu acknowledges
the financial support by Grant-in-aid from the Japan Center for Economic Research. Inaba
acknowledges the financial support by the Nomura Foundation.
†
Faculty of Economics, Kansai University, 3-3-35 Yamate Suita Osaka 564-8680 Japan.
E-mail: imasaru@kansai-u.ac.jp.
‡
School of Economics and MaGHiC, University of Kent, Canterbury, Kent, CT2 7EP,
UK. E-mail.: K.Otsu@kent.ac.uk.

11Introduction

The postwar Japanese economy has been studied extensively due to its peculiar experience of the postwar rapid growth, bubble economy in the 1980s
and lost decade in the 1990s. In this paper we analyze the regional featuresof the Japanese economy during this period. In specific, we study the regional convergence of income and business cycle comovements among the 47
prefectures over the 1955-2008 period.
Japanese regional convergence has been studied by Barro and Sala-iMartin (1992) and Shioji (2001). Barro and Sala-i-Martin (1992) find strong
evidence of regional convergence over the 1930-1987 period. Shioji (2001)
study the convergence of Japanese prefectures over the 1965-1995 period andfind that regional public infrastructure capital stock had a modest eﬀect onregional growth. In this paper, we focus on the 1955-2008 period and find evidence of unconditional convergence during the entire period and conditional
convergence over the 1975-2008 period.
Regional business cycle features of Japan has been studied by Artis andOkubo (2011) and van Wincoop (1995). Artis and Okubo (2011) find that
prefecture pairs with similar industrial structures and shorter distance tend
to have higher business cycle synchronization over the 1955-1995 period. In
this paper, we focus on the 1975-2008 period and find similar relationshipbetween distance and business cycle synchronization. Moreover, van Wincoop (1995) finds that the consumption-output puzzle discussed in international macroeconomic literature such as Backus, Kehoe and Kydland (1992)
and Baxter and Crucicni (1995) exists in Japanese prefecture level over the
1975-1988 period. We find that this puzzle holds also over the 1975-2008
period. We further decompose consumption risk-sharing into contributionsof the inter-prefectural capital market, government transfer and the financial
market following Nakakuki and Fujiki (2005) and find that financial market
imperfection might be playing a role in the low cross-prefecture consumption
risk-sharing.
The remainder of the paper is organized as follows. In section 2 we
describe the data facts. In section 3 we conduct quantitative analysis on
regional convergence and comovement. Section 4 concludes the paper.

2

Data

In this section, we present summary statistics of the expenditure, production
and income statistics components of GDP. The main data set we use is the
ESRI data set on Japanese prefectural income and product accounts over the
1955-2008 period. The original data sets are compiled in several sub-periods,
1955-1975, 1975-1999, 1990-2009, 2000-2012 due to the change in the SNA
basis and reference years for regional price deflators. We choose to terminate
our data sample period at 2008 in order to avoid the eﬀects of the 2008/2009
financial crisis and the 2011 earthquake.
All data are converted into 2000 constant price per capita levels. Constant price data are constructed by dividing nominal variables with the GDP2deflator. In order to connect the data for the entire period, we splice thenominal variables and GDP deflators using the overlapping years. We use
prefectural population data obtained from the Labor Force Survey in order
to construct per capita data.
For presentation purposes, we define 9 areas: Hokkaido, Tohoku, Kanto,
Chubu, Kinki, Chugoku, Shikoku, Kyushu, Okinawa. The Tohoku area
consists of 6 prefectures: Aomori, Iwate, Miyagi, Akita, Yamagata andFukushima. The Kanto area consists of 7 prefectures: Ibaraki, Tochigi,
Gunma, Saitama, Chiba, Tokyo and Kanagawa. The Chubu area consists of
9 prefectures: Niigata, Toyama, Ishikawa, Fukui, Yamanashi, Nagano, Gifu,
Shizuoka and Aichi. The Kinki area consists of 7 prefectures: Mie, Shiga,
Kyoto, Osaka, Hyogo, Nara and Wakayama. The Chugoku area consistsof 5 prefectures: Tottori, Shimane, Okayama, Hiroshima, and Yamaguchi.
The Shikoku area consists of 4 prefectures: Tokushima, Kagawa, Ehime andKochi. The Kyushu area consists of 7 prefectures: Fukuoka, Saga, Nagasaki,
Kumamoto, Oita, Miyazaki, and Kagoshima. Hokkaido and Okinawa areareas that consist of single prefectures.

2.1

Regional Output

Table 1 presents the features of per capita regional output over the 19552008 period. The first column presents the average level of regional GDP
relative to the national level. The regional income in the Kanto area isclearly much higher than other regions at 1.190 while that of Okinawa is
0.626. The variation between the richest and the poorest prefecture is quite
large ranging from 1.764 in Tokyo to 0.626 in Okinawa. We also computethe simple average of all per capita prefecture GDP relative to the national
level which turns out to be 0.888. This implies that the income distribution
among prefectures are skewed with one very rich and large prefecture, Tokyo,
and a lot of relatively poor prefectures.
The second column presents the average per capita regional real GDP
growth rate. The national output growth was 3.85% where Tohoku area
was the highest at 4.28% and Hokkaido area was the lowest at 3.30%. At
the prefecture level, Nagano was the highest at 4.71% and Wakayama was
the lowest at 2.86%. The simple average of all prefectures is 3.97%, whichis slightly higher than the national aggregate growth rate. This is because
large prefectures such as Tokyo, Osaka, Kanagawa and Hyogo are growing
relatively slow and are bringing down the national aggregate growth rate.
The third column presents the correlation between HP filtered regional
output and national output.1 Kanto area has the highest correlation coefficient at 0.964 while Okinawa area has the lowest at 0.045 which is clearlyan outlier. At the prefecture level, Mie has the highest correlation at 0.924
while Okinawa has by far the lowest correlation.
Finally, the fourth column presents the standard deviation of the HP
filtered per capita regional real GDP relative to that of the national level.
The national output standard deviation was 2.99% where the Kanto area was
1

Throughout this paper we set the smoothing parameter to 100 for HP filtering.

3

the most volatile at 1.135 and the Tohoku area was the least volatile at 0.858
relative to the national volatility respectively. At the prefecture level, Shiga
was the most volatile while Kochi was the least volatile where the ratios are
1.705 and 0.842 respectively.
Figure 1 plots the Gini coeﬃcient computed from prefecture per capita
GDP and private consumption levels over time. This figure shows that interprefecture income inequality declined quite dramatically during the rapid
growth period falling from 0.14 in 1955 to 0.08 in 1975. Therefore, we findstrong evidence of the so-called σ-convergence during the 1955-1975 period.
However, the Gini coeﬃcient temporary rises during the late 1980s and remains thereafter higher relative to the 1975 level.

2.2

Regional Expenditure

The ESRI data set provides annual data of regional expenditure on final
consumption and investment of both the household and the government.
Table 2 presents the average regional expenditure shares of GDP for private
consumption, private investment, public consumption, and public investment
over the 1955-2008 period. The national private consumption share is 0.486
where the regional shares range from 0.542 in the Hokkaido area to 0.467
in the Kanto area. At the prefecture level, Nara has the highest share at
0.688 while Tokyo has the lowest at 0.375. The national private investment
share is 0.222 where the regional shares range from 0.250 in the Okinawa
area to 0.183 in the Hokkaido area. At the prefecture level, the highest is
0.332 in Ibaraki and the lowest is 0.181 in Tokyo. The national government
consumption share is 0.151 where the regional shares range from 0.267 in
the Okinawa area to 0.124 in the Kanto area. At the prefecture level, thehighest is 0.267 in Okinawa and the lowest is 0.096 in Aichi. The national
government investment share is 0.075 where the regional shares range from
0.129 in the Hokkaido area to 0.059 in the Kanto area. At the prefecturelevel, the highest is 0.159 in Fukui and the lowest is 0.052 in Tokyo. It turns
out that the expenditure shares of the four expenditure components in Tokyo
are significantly lower than those at the national level and add up to only
72.4% of its GDP. In other words, domestic absorption in Tokyo is less thanits GDP, which implies that Tokyo is a net exporter of goods and services.
Table 3 presents the intra-regional comovement of the expenditure components. Table 3a lists the intra-regional HP-filtered correlation of output
with its expenditure components over the 1955-2008 period. The first column
shows the intra-regional correlation between output and private consumption. The national aggregate correlation is 0.489 showing that consumption
is procyclical at the national level. At the regional level, the Okinawa area
has the highest correlation at 0.633 while the Hokkaido area has the lowest
at 0.043. At the prefecture level, the correlation ranges from 0.817 in Gunma
to -0.044 in Aichi. The second column shows the intra-regional correlation
between output and private investment. The national aggregate correlation
is 0.727 showing high procyclicality of investment. At the regional level,
the Chubu area has the highest correlation at 0.769 while the Okinawa area
has the lowest correlation at 0.072. At the prefecture level, the correlation4

ranges from 0.806 in Aichi to 0.072 in Okinawa. The third column shows
the correlation between output and government consumption. The national
aggregate correlation is 0.081. At the regional level, the Kyushu area has thehighest correlation at 0.424 while the Kanto area has the lowest correlation
at -0.024. At the prefecture level, Miyazaki has the highest at 0.638 andAichi has the lowest at -0.177. The fourth column shows the intra-regionalcorrelation between output and government investment. The national aggregate correlation is 0.193. At the regional level, the Kyushu area has thehighest correlation at 0.552 and Chubu has the lowest at -0.051. At the prefecture level, Tokushima has the highest correlation at 0.606 and Aichi has
the lowest at -0.139.
Table 3b shows the HP-filtered standard deviation of each expenditurecomponent relative to that of output over the 1955-2008 period. The firstcolumn shows the standard deviation of private consumption relative to thatof output. The national aggregate ratio is 0.565 ranging from 1.541 in the
Okinawa area and 0.518 in the Kanto area. At the prefecture level, Okinawa
has by far the highest ratio while Hiroshima has the lowest correlation at
0.513. A ratio larger than 1 is puzzling because standard business cycle
theory will predict consumption smoothing in response to income shocks.
The result implies that there are forces in Okinawa that prevent eﬃcientconsumption smoothing such as financial frictions. The relative volatility ofprivate investment to that of output is much higher than that of consumption
to output with the national aggregate ratio at 3.373. At the regional level,
the Chugoku area has the highest ratio at 3.549 while the Hokkaido area has
the lowest ratio at 2.692. At the prefecture level, Ibaraki has the highest
ratio at 4.235 while Chiba has the lowest ratio at 2.223. Consumption is lessvolatile and investment is more volatile than output at the government level
as well. The third column shows that the ratio of the standard deviation of
government consumption to that of output is 0.864 at the national aggregate
level. At the regional level, the Okinawa area has the highest ratio at 1.316
while the Hokkaido area has the lowest ratio at 0.762. At the prefecture level,
Fukui has the highest ratio at 1.746 while Saitama has the lowest ratio at
0.610. The fourth column shows that the standard deviation of government
investment relative to that of output is 2.020 at the national level. At theregional level, the Okinawa area has the highest ratio at 4.044 while the
Chubu area has the lowest ratio at 1.929. At the prefecture level, Niigata
has the highest ratio at 4.413 while Aichi has the lowest ratio at 1.459.
Table 4 presents the comovement between regional and national expenditure components. Table 4a presents the HP filtered correlation of each regional expenditure component with its national aggregate counterpart. The
first column shows the correlation of regional consumption and national consumption. At the regional level the Chubu area has the highest correlation at
0.919 while the Okinawa area has the lowest at 0.202. At the prefecture level,
Fukui has the highest correlation at 0.856 while Okinawa has the lowest. The
average of the correlation coeﬃcients of all prefectures is 0.609. The second
column presents the correlation between regional and national private investment ranging from 0.986 in the Chubu area to 0.572 in the Okinawa area. At
the prefecture level, Osaka has the highest correlation at 0.974 while Aomori

5has the lowest at 0.539. The average of all prefectures is 0.815. The thirdcolumn presents the correlation between regional and national government
consumption ranging from 0.869 in the Chubu area to 0.206 in the Okinawa
area. At the prefecture level, Miyagi has the highest correlation at 0.835
while Shiga has the lowest at 0.108. The average of all prefectures is 0.585.
The fourth column presents the correlation between regional and national
government investment ranging from 0.918 in the Chubu area to 0.289 in the
Okinawa area. At the prefecture level, Oita has the highest correlation at
0.796 while Kagawa has the lowest at 0.210. The average of all prefectures
is 0.575.
Table 4b presents the HP-filtered volatility of each regional expenditurecomponent relative to that of their national counterpart. The first column
reports the standard deviation of regional consumption relative to that of
the national consumption ranging from 2.861 in the Okinawa area to 1.041
in the Kanto area. At the prefecture level, Okinawa has the highest relative
volatility while Tokyo has the lowest at 1.126. The average of all prefectures is1.677 showing much greater volatility at the prefecture level compared to thenational aggregate, which implies negative covariance of consumption acrossprefectures. The second column reports the standard deviation of regional
private investment relative to that of national investment which ranges from1.149 in the Kanto area to 0.738 in the Tohoku area. At the prefecturelevel, Ibaraki has the highest at 1.660 while Kagoshima has the lowest at
0.627. The average of all prefectures is 1.043. The third column reports thestandard deviation of regional government consumption relative to that ofnational government consumption which ranges from 1.598 in the Okinawa
area to 1.001 in the Chubu area. At the prefecture level, Wakayama has
the highest at 2.199 while Saitama has the lowest at 0.849. The average ofall prefectures is 1.498. The fourth column reports the standard deviationof regional government investment relative to that of national investment
ranging from 2.099 in the Okinawa area to 1.027 in the Chubu area. At theprefecture level, Kagawa has the highest at 2.681 while Aichi has the lowest
at 1.039. The average of all prefectures is 1.701.

2.3

Regional Income

In this section we utilize the ESRI regional income statistics to compute thelabor income share and capital depreciation rate for each region. The labor
income share is defined as1−θ =employees compensation + 0.5 × indirect business tax + 0.8 × mixed income.
GDPfollowing Hayashi and Prescott (2002).2 The capital depreciation rate isdefined as
fixed capital depreciation.
δ=net capital stock2

The details of the construction of the labor income share is described in the data
appendix.

6

The first column in Table 8 reports the average labor income share overthe 1975-2008 period. The data shows that the average labor income shareis 0.593 at the national level where the regional levels range from 0.635 in
the Hokkaido area to 0.540 in Okinawa area. The prefecture shares range
from 0.645 in Tokyo to 0.489 in Shiga. Figure 2 plots the labor income shareover the 1975-2009 period. This figure shows that the labor income share has
been falling throughout the 1975-1990 period followed by an increase during
the 1990s in all regions. After 2000 the labor income share has been declining
until it sharply rises in 2008 in most regions.
The second column shows the correlation between the HP filtered labor
income share and the HP filtered output over the 1975-2008 period. The
correlation for the national level is -0.715 where that for regional levels varyfrom -0.716 for the Kanto area to 0.010 for the Shikoku area. Ehime has
the highest positive correlation at 0.115 while Yamanashi has the highest
negative correlation at -0.828. The countercyclical labor income share isconsistent with the observation in the US by Young (2004) and Hansen andPrescott (2005).
The third column in Table 8 reports the average capital depreciation
rate over the 1975-2008 period. The national average is 0.077 ranging from
0.087 in the Tohoku area to 0.066 in the Kinki area. The prefecture level
depreciation rates range from 0.109 in Kumamoto to 0.046% in Mie. Figure
3 plots the capital depreciation rate over the 1975-2008 period. This figure
shows that the depreciation rate has been falling until the mid 1980s andthen has gradually increased. Aggregate depreciation rate should decline
when investment on fixed assets that depreciate slower such as structure
increases relative to those that depreciate faster such as intangible assets.
One potential explanation of the evolution of the depreciation rate is thatthe share of investment in structure increased during the late 1970s and thatof intangible assets, equipment and machinery increased after the 1980s. In
order to assess this hypothesis, further analysis of fixed investment by typesof assets is needed.
The fourth column shows the correlation between the HP filtered depreciation rate and the HP filtered output over the 1975-2008 period. The
correlation at the national level is 0.489 where the regional correlation ranges
from 0.620 in the Kanto area to 0.317 in the Kinki area. At the prefecturelevel, Saitama has the highest correlation at 0.773 while Hyogo has the lowest
at -0.185. The average of the prefecture level correlation is 0.415 indicatingprocyclical depreciation rate on the average.

2.4

Regional Production

Next, we assess the production factors: labor, capital and productivity. Total
factor productivity is computed using a standard Cobb-Douglas production
function
θiyi,t = Ai,t ki,tli,t 1−θi ,(1)where y is per capita GDP, k is per capita capital stock, l is per capita labor,and A is total factor productivity (TFP) for region i at time t. We assume7

that the labor income share 1 − θi is constant.3
The data for labor input is the total man hours series (employment times
hours worked per worker) from the R-JIP 2012 database which is available
for the 1970-2008 period. For capital stock, we use the perpetual inventory
method in order to construct the regional net capital stock series over the
1975-2008 period.4 The details of the computation is available in the appendix. The labor income share is computed from national income data overthe 1975-2008 period as described in the following sub-section.
Table 5 presents the average regional per capita production factors relative to the national level over the 1975-2008 period. The first column showsthat labor is relatively abundant in the Chubu area with a ratio of 1.076
while it is relatively scarce in the Okinawa area with a ratio of 0.851 relative to the national level respectively. At the prefecture level, Tokyo has
the highest per capita labor input with a ratio of 1.374 while the lowest is
in Nara with a ratio of 0.669. The average of all prefectures is 0.992. The
second column shows that capital stock is relatively abundant in the Chubu
area with a ratio of 1.208 while it is relatively scarce in the Okinawa areawith a ratio of 0.661. At the prefecture level, the highest per capita capitalis in Mie with a ratio of 1.722 and the lowest is in Kumamoto with a ratioof 0.617. The average of all prefectures is 0.942. The third column presents
the total factor productivity gaps between the regional and national levels
defined as( ) θi2+θ ( )1− θi2+θ
yi,t ktlt
dAi,t =.
yt ki,tli,tAt the regional level, the Kanto area has the highest relative TFP with aratio of 1.134 while the Okinawa area has the lowest with a ratio of 0.882.
At the prefecture level, Tokyo has the highest relative TFP with a ratio of
1.330 while Ibaraki has the lowest with a ratio of 0.784. The average of all
prefectures is 0.933.
Table 6 reports the intra-regional comovement of production factors overthe 1975-2008 period. Table 6a presents the intra-regional HP-filtered correlation of output with its production factors. The first column shows theintra-regional correlation between output and labor. The national aggregate
correlation is 0.643. At the regional level, the Kyushu area has the highest
correlation at 0.747 while the Okinawa area has the lowest at 0.159. At theprefecture level, Tochigi has the highest correlation at 0.727 while Tokushima
has the lowest at -0.089. The average of all prefectures is 0.383. The second column shows the intra-regional correlation between output and capitalstock. The national aggregate correlation is 0.428. At the regional level, theKyushu area has the highest correlation at 0.660 while the Okinawa area has
the lowest correlation at 0.166. At the prefecture level, Osaka has the highest correlation at 0.738 while Wakayama has the lowest correlation at -0.100.
3
Allowing time varying labor share proves problematic for TFP calculations, especially
its growth over time. The computation of the labor share is explained in the following
subsection.
4
The regional private capital stock data published by R-JIP and by ESRI are bothgross capital stock series.

8

The average of all prefectures is 0.298. Finally, the third column shows theintra-regional correlation between output and total factor productivity. The
national aggregate correlation is 0.829 showing high procyclicality of TFP.
At the regional level, the Kanto area has the highest correlation at 0.887
while the Shikoku area has the lowest correlation at 0.616. At the prefecturelevel, Osaka has the highest correlation at 0.957 while Kagoshima has thelowest correlation at 0.487. Therefore, TFP is procyclical at the prefecturelevel as well. The average of all prefectures is 0.813.
Table 6b reports the HP-filtered volatility of production factors relative
to that of output. The first column shows the standard deviation of labor
relative to that of output. The national aggregate volatility of labor relative
to output is 0.527. At the regional level, the Hokkaido area is the highest
at 1.114 while the Kanto area is the lowest at 0.433. At the prefecture level
Kagoshima is the highest at 1.328 while Osaka is the lowest at 0.351. The
average of all prefectures is 0.671. The second column shows the volatilityof capital relative to that of output which is 0.808 at the national level. At
the regional level, the Shikoku area has the highest ratio at 0.918 while the
Chubu area has the lowest at 0.694. At the prefecture level Kagoshima has
the highest at 1.170 while Wakayama has the lowest at 0.380. Finally, thethird column shows that the standard deviation of TFP relative to that of
output is 0.795 at the national level. At the regional level the Okinawa area
has the highest ratio at 1.084 while the Kyushu area has the lowest at 0.662.
At the prefecture level Kagoshima has the highest at 1.203 while Osaka has
the lowest at 0.701. The average of all prefectures is 0.940.
Table 7 reports the comovement between the regional and national production factors. Table 7a presents the HP-filtered correlation between regional and national production factors. The first column shows that the correlation between regional and national labor range from 0.962 in the Chubu
area to 0.528 in the Hokkaido area. At the prefecture level, Wakayama has
the highest at 0.922 while Nara has the lowest at 0.395. The average of thecorrelation of all prefectures is 0.749. The second column shows that the correlation between regional and national capital range from 0.986 in the Kinki
area to 0.559 in the Hokkaido area. At the prefecture level Kanagawa has thehighest correlation at 0.974 while Hokkaido has the lowest. The average ofall prefectures is 0.861. The third column shows that the correlation between
regional and national TFP is highest in the Kanto area at 0.953 while the
Hokkaido area is the lowest at 0.413. At the prefecture level, Mie has thehighest correlation at 0.872 while Kochi has the lowest at -0.092. The average of all prefectures is 0.583. The fourth column presents the correlation
between regional and national output over the 1975-2008 period to match thesample period of the production factors. At the regional level, the Chubu
area has the highest correlation at 0.957 while the Okinawa area has the lowest at 0.398. At the prefecture level, Mie has the highest correlation at 0.932
while Kochi has the lowest at 0.086. The order of the ranking is somewhat
diﬀerent from that for the 1955-2008 period. Moreover, the average of all
prefectures is 0.664 which is much lower than that of the 1955-2008 period,
0.731.
Table 7b reports the standard deviation of regional production factors

9relative to that of their national counterpart. The first column reports thestandard deviation of regional labor relative to that of the national laborwhich ranges from 1.643 in the Hokkaido area to 1.014 in the Kinki area. At
the prefecture level, Nagasaki has the highest ratio at 2.362 while Gifu has thelowest at 0.876. The average of all prefectures is 1.409. The second column
reports the standard deviation of regional capital stock relative to that ofnational capital stock which ranges from 1.209 in the Kanto area to 0.860
in the Kyushu area. At the prefecture level, Ibaraki has the highest ratio at
1.891 while Wakayama has the lowest at 0.651. The average of all prefectures
is 1.027. The third column reports the standard deviation of regional TFP
relative to that of national TFP which ranges from 1.347 in the Kanto area to0.745 in the Hokkaido area. At the prefecture level, Ibaraki has the highest
ratio at 2.071 while Hokkaido has the lowest. The average of all prefectures is
1.371. The fourth column reports the standard deviation of regional output
relative to that of national output over the 1975-2008 period to match thesample period of the production factors. At the regional level, the Kanto
area has the highest ratio at 1.209 while the Hokkaido area has the lowest at
0.777. At the prefecture level, Fukushima has the highest ratio at 1.696 while
Kagoshima has the lowest at 0.582. The average of all prefectures is 1.170
which is roughly the same as the 1955-2008 period. The relative volatility ofregional output is consistent with those for the 1955-2008 period.
We can also compare production eﬃciency across regions by the marginal
product of labor and capital which are defined as
mpli,t = (1 − θi )

yi,t
yi,t
, mpki,t = θi
li,t
ki,t

respectively.
The first column of Table 9 presents the regional marginal product of labor
relative to its national counterpart over the 1975-2008 period. At the regional
level, the Kanto area has the highest ratio at 1.159 while the Okinawa area
has the lowest at 0.720. At the prefecture level, Tokyo has by far the highest
ratio at 1.409 while Okinawa has the lowest. The average of all prefectures
is 0.891. The second column reports the regional marginal product of capital
relative to its national level. At the regional level, the Kanto area has thehighest ratio with a ratio of 1.105 while the Chugoku area has the lowest
at 0.901. At the prefecture level, Shiga has the highest ratio at 1.319 while
Ibaraki has the lowest at 0.619. The average of all prefectures is 0.995. Figure
4 plots the Gini coeﬃcients of MPL and MPK computed from prefecture level
data over time in order to highlight the regional misallocation of production
factors. Interestingly, after the 1990s the regional discrepancy in MPL has
been falling while that of the MPK has been rising. This figure implies thatthe misallocation of labor has been decreasing while that of capital has been
increasing.

103

Regional Growth and Convergence

3.1

Growth Accounting

The production function (1) can also be used for growth accounting. Deriving(1) with respect to time we get
·

·

·

·

yi,t
Ai,t
ki,t
li,t
=
+ θi
+ (1 − θi ) .
yi,t
Ai,t
ki,t
li,t

(2)

The right hand side decomposes output growth into the contribution of the
production factors.
Table 10 presents the regional growth accounting results over the 19752008 period. The numbers in each columns correspond to the average percapita output growth rate and the contributions of each production factor
to it, that is, the variables on the right hand side on (2). The results forthe national level show that labor was declining and reduced output growthby 0.25%. The declining labor is common across all regions except for the
Okinawa area and reflects the aging population and decline in labor participation rate. On the other hand, capital growth and TFP growth contributed
to output growth by 1.05% and 1.19% respectively.
At the regional level, the Chubu area has the highest regional growth rateof output at 2.28% which is led by capital accumulation which contributes
to 1.41%. The Tohoku area has the second highest output growth rate at
2.12% where both capital growth and TFP growth is higher than the national
average. The Hokkaido area has the lowest output growth rate at 1.68% andthe lowest labor and capital growth rate. At the prefecture level, Fukushima
and Nagano have the highest output growth rates at 2.74% and 2.74% which
are driven by the high TFP growth at 1.78% and 1.74% respectively. On theother hand, Wakayama has the lowest output growth rate at 0.77% where
its TFP growth rate is also the lowest at 0.11%. However, Hokkaido has an
output growth rate lower than the national level while its TFP growth rate
is much higher than the national level. Therefore the growth pattern is not
monotonic.

3.2

β−Convergence

In this section we investigate the existence of absolute convergence in output
levels also known as β-convergence. This concept considers convergence as anegative correlation between the growth in income over time and its initiallevel. According to a standard textbook Solow-Swan neoclassical growthmodel, countries who initially have low output due to low capital stock shouldgrow faster because of the high initial marginal product of capital.
3.2.1

Solow-Swan Model

Solow-Swan growth model is a dynamic model of capital accumulation. The
typical per capita capital law of motion looks like··

ki,t = pii,t − (δi + ni )ki,t ,11·where ni is population growth representing the capital dilution eﬀect. Assume that households save a fixed fraction of their income
si,t = φi yi,t .
Consider a closed economy so that savings is equal to investment:
pii,t = yi,t − ci,t − gi,t = si,t .
Finally, assume production function is (1) so that the capital law of motion
is
·
ki,t
·
θi −1
= φi Ai,t ki,tli,t 1−θi − (δi + ni ).
(3)ki,tAccording to the model, when the current capital stock level is low, themarginal product of capital is high. Thus, capital accumulation leads to rapid
growth in output, which increases investment until eventually the marginal
product of capital decreases as capital stock approaches its steady state.
In addition, a) high TFP leads to a higher steady state capital stock andthus should lead to higher growth during the transition towards the steadystate; b) high labor share (low capital share) increases the diminishing of themarginal product of capital and thus should lead to slower growth during thetransition; c) higher investment rate accelerates capital accumulation andhence leads to higher growth during the transition; d) higher depreciation
rate and population growth rate slows down the accumulation of per capita
capital stock and thus leads to lower growth during the transition.
3.2.2

Growth Regression

Empirical analysis on regional convergence goes back to Barro (1991) andMankiw, Romer and Weil (1992) who test absolute convergence among countries. The basic cross-section estimation equation isgi = α + βy0,i + γxi + εi ,(4)where g is the average GDP growth rate and y0 is the initial GDP level inregion i. The initial GDP is expressed as the ratio of regional per capita GDP
to national per capita GDP in the initial year. The economic intuition of
the Solow-Swan model explained above implies that the coeﬃcient β shouldbe negative. We further add control variables x to the regression according
to the model (3) where x consists of the average TFP gap, the labor share,
the capital depreciation rate, population growth rate, private investment to
GDP ratio, government investment to GDP ratio. Finally, considering the
growth accounting results, we also control for the diﬀerences in TFP growth
rates across prefectures.
Table 11 summarizes the regression results. First we run a regression for
the 1955-2008 period with no control variables which is reported as model
1. The coeﬃcient β is negative and significant at the 95% confidence level
and the R2 is 0.454. Therefore, we conclude that unconditional regional
convergence exists in Japan over the 1955-2008 period. In model 2 we add all12

control variables and find that the negative eﬀect of initial output is robust.
In addition, TFP gap, population growth, private investment rate and TFP
growth all have 95% significant eﬀects on growth as expected. Labor share,
capital depreciation and government investment rate do not have significant
eﬀects.
Next we focus on the 1975-2008 period in order to exclude the postwar
rapid growth period.5 The regression results in model 3 with no control variables show that for this period the initial output has no significant eﬀects on
output growth. Moreover the R2 is extremely low compared to that in model
1. Therefore, there is no evidence of unconditional convergence. However,when we add all control variables in model 4, the coeﬃcient on initial output
is negative and significant at the 90% level where the R2 increases to 0.699.
In addition, the TFP gap, population growth, private investment rate and
TFP growth are all significant at the 95% level. Therefore, we find evidenceof conditional convergence over the 1975-2008 period.

4

Regional Comovement and the Quantity Anomaly

In this section we analyze bilateral business cycle comovement patterns acrossprefectures. With 47 prefecture, we have 1081 pairs (47 × 46 ÷ 2) to analyze bilateral comovement patterns. We first focus on the cross-prefectural
correlation patterns and find that the so-called quantity anomaly holds inJapanese prefectures as shown in van Wincoop (1995). Second, we investigate sources of the degree of business cycle synchronization following Artisand Okubo (2011). Next, we focus on the components of risk-sharing between
prefectures following Nakakuki and Fujiki (2005).

4.1

Cross-Prefectural Correlation Patterns

Table 12 shows the mean bilateral correlation of all pairs for each variable
over the 1975-2008 period. The mean output correlation is 0.462. Consumption correlation is lower than output correlation at 0.264 while investment
correlation is higher at 0.642. Labor and capital correlation are higher than
output correlation at 0.575 and 0.759 respectively. Finally, TFP correlation
is lower than output correlation at 0.358. In sum, we find that for private
expenditure components
ρ(pci , pcj ) < ρ(yi , yj ) < ρ(pii , pij )and for production factors
ρ(zi , zj ) < ρ(yi , yj ) < ρ(li , lj ) < ρ(ki , kj ).
Therefore, the data shows the quantity anomaly a la Backus, Kehoe andKydland (1994):
ρ(pci , pcj ) < ρ(zi , zj ) < ρ(yi , yj )5

We run a Quandt-Andrews unknown breakpoint test and find that the output growth
has a trend break in 1974.

13

which is consistent with the findings of van Wincoop (1995) for the period
1974-1988.
We follow Ambler, Cardia and Zimmermann (2004) and conduct a GMM
analysis on the order of correlation. It turns out that, unlike their analysis
for 20 OECD countries, we cannot statistically reject the hypothesis thatρ(pci , pcj ) > ρ(yi , yj ),in the 47 prefectures in Japan at a 10 percent confidence level. However,78.35% of the total 1081 pairs in our sample are consistent with the quantity
anomaly:ρ(pci , pcj ) < ρ(yi , yj ).
Therefore, we consider that the quantity anomaly does exist within Japanprefectures.

4.2

Cross-Prefectural Business Cycle Synchronization

In this section, we investigate the sources of bilateral business cycle synchronization among Japanese prefectures in a simplified version of Artis andOkubo (2011). Instead of their GMM panel framework, we estimate thefollowing regression for the cross-section correlation of variable v:
ρ(vi , vj ) = α + βXij + εij
where X includes the bilateral geographical proximity, industrial similarity, and the size of the combined economy. In addition to their analysis ofcross-prefectural output correlation, we investigate the synchronization in
the fluctuations of consumption, investment, labor, capital and productivity.
For geographical proximity, we consider the distance which is measured
as the straight distance between the capital cities of each prefecture. We expect the pairs to have lower distance and are in the same region should havehigher bilateral business cycle synchronization. For industrial similarity, we
consider the absolute value of the logged capital income share ratio.6 We
expect this term to have a negative eﬀect on synchronization as it represents
the idiosyncrasies in industry composition which leads to idiosyncratic vulnerability to industry level shocks. Finally, the size of the combined economy
is defined as the product of the GDP shares of national GDP. We expect thisterm to be positive as the larger the economy the greater the intraindustry
trade we should expect according to the gravity model.
Table 13 presents results to a cross-section regression of several characteristics of the bilateral country pair on the correlation of each variable. The
first column shows the result for output. All variables are statistically significant and the coeﬃcients have the expected signs for output correlation.
Therefore, the main results of Artis and Okubo (2011) hold in our simplified

6

Artis and Okubo (2011) consider the per capita output diﬀerence as a proxy of industry
diﬀerences.

14

analysis.7 The second column shows that for consumption the industry specialization and size aﬀects in the same way of output. This can be considered
as an indirect eﬀect of these regressors through their eﬀects on income correlation.8 Interestingly, the eﬀect of distance is insignificant for consumption
correlation. The third column shows that distance and size aﬀect investment
correlation in the same direction as they aﬀect output correlation. However, the eﬀect of industry similarity is not significant. The fourth and fifth
column show that the eﬀect of industry similarity is not significant for labor and capital correlation as well. The distance negatively aﬀect labor andcapital correlation. While size positively aﬀects capital correlation, it negatively aﬀects labor correlation. Finally, distance and size aﬀect TFP in thesame direction as they aﬀect output correlation while the eﬀect of industry
similarity is insignificant.

4.3

Decomposition of Cross-Prefectural Risk-Sharing

Following Nakakuki and Fujiki (2005) we decompose regional GDP into several components:
y1it y2it y3it
y1it =
pcit ,(5)y2it y3it pcit
where y1it , y2it , y3it , pcit are per capita GDP, GNP, personal disposable income, and private consumption for prefecture i.9 The first term yy1it
stands2it
for income risk-sharing through the capital market as GNP adjusts for the
net factor payment transfers across prefectures. The second term yy2it
stands3it
for income risk-sharing through government transfers as personal disposable
income adjusts for government transfer across prefectures. The third term
Y3itstands for consumption risk-sharing across prefectures.
Cit
We estimate the consumption risk-sharing components via panel regressions
·

·

·

·

·

·

·

y1it − y2it = νKt + βK y1it + ϵKit ,·y1it − y3it = νKT t + βKT y1it + ϵK+T it ,·y1it − pcit = νKT Ct + βKT C y1it + ϵK+T +Cit ,where νjt correspond to the period fixed eﬀects. Consider the case in which
an increase in GDP has no eﬀect on GNP. The the coeﬃcient βK should be
7

Since we have a measure of TFP correlation, we could include it in the regression. In
fact, TFP correlation has a significant impact on output correlation in a simplle regression
ρ(yi , yj ) = 0.206 + 0.715 × ρ(zi , zj ) + εij ,(24.58)(35.40)with R2 = 0.537. However, as we show later, TFP correlation itself is aﬀected by distanceand size.
8
If we simply regress consumption correlation on income correlation we getρ(ci , cj ) = 0.052 + 0.461 × ρ(yi , yj ) + εij ,(2.927)(13.21)

with R2 = 0.138.
9
Regional disposable income is not directly available in the regional SNA database.
The detailed method of constructing this data is listed in the appendix.

15

equal to one. Therefore, the interpretation of the coeﬃcients is such that thehigher the β the stronger the risk-sharing.
Table 14 summarizes the regression results. We find that over the 19752008 period, the income risk-sharing through the capital market βK is 15.6%,
the income risk-sharing through the capital market and government transfer
βKT is 46.5% and these income risk-sharing plus the consumption risk-sharing
through the financial market βKT C is 69.6%.10 The marginal eﬀects of eachlevel of risk-sharing are simply the diﬀerences in the βs. This shows that mostof the prefectural risk-sharing is done by the government (βKT − βK = 30.9)
and that the financial market plays less of a role (βKT C − βKT = 23.1%).
This implies that the financial market imperfection might be responsible forthe low cross-prefectural consumption correlation.
In comparison to the results in Nakakuki and Fujiki (2005) for 19902001, our estimate of the total risk-sharing βKT C is lower (69.6% compared to
83.6%).11 The risk-sharing through capital markets βK is at a similar level totheirs (15.6% compared to 16.3%), the risk-sharing by the government βKT −βK is much higher (30.9% compared to 9.0%) and the risk-sharing throughfinancial markets βKT C − βKT is much lower (23.1% compared to 58.1%).
There are several reasons for this diﬀerence. First, we have a diﬀerent time
period. To check whether this has an eﬀect, we estimated the panel regression
coeﬃcients with the same period and found that the total risk-sharing is not
too diﬀerent from our original result (71.5% compared to 69.6%). Second,
they consider consumption as total final consumption expenditure of theprefecture whereas we only focus on private consumption. We estimated therisk-sharing of total consumption over the 1990-2001 period and found thatthe coeﬃcient slightly increases from our original result (75.2% comparedto 69.6%). However, it is still significantly lower than Nakakuki and Fujiki(2005). Finally, the SNA data has gone through a significant revision overtime and we are able to use a more complete data set than what was available
for Nakakuki and Fujiki (2005).12 Most importantly, there is much more
SNA income data available today which saved us the need to estimate theprefectural personal disposable income.

5

Conclusion

In this paper, we have gone over regional economic data in Japan over the
1955-2008 period. We find that the diﬀerence in per capita output levels
and growth rates across regions are quite high while inter-regional output
10
The total risk-sharing coeﬃcient βKT C is lower than that reported in Nakakuki andFujiki (2005), 82.2. This is because we have a longer estimation period and that the SNA
database recentlt made a significant revision which gave us more access to data that were
not available to them.
11
They report results for 68SNA data over the 1975-1999 period and 93SNA data overthe 1990-2001 period. Since our data set is predominantly based on 93SNA data, we only
compare our resutls with their 93SNA data results.
12
For instance, the SNA93 data has been extended in the past up to 1980. Furthermore,
there are much less missing values in our dataset than theirs. Therefore, we constructeda balanced panel whereas they use an unbalanced panel.

16

inequality decreased dramatically during the 1955-1975 period. In terms of
expenditure data, the cross-regional output correlation is higher than crossregional consumption correlation. In terms of production, labor misallocation
has been declining while capital misallocation has been increasing over the
1975-2008 period. In terms of income data, the income share of labor has
been declining during the 1975-1990 period, increasing during the 1990s anddeclining again in the 2000s in all regions while the depreciation rate has
declined during the late 1970s and persistently increased after 1980 in all
regions.
We have conducted basic growth accounting analysis and find that TFP
growth and capital accumulation are equally important in accounting for regional output growth. We also conduct a growth regression and find that
unconditional regional convergence exists in the 1955-2008 period but notduring the 1975-2008 period. However, conditional regional convergence does
exist during the 1975-2008 period controlling for the TFP gap, population
growth, private investment rate, and TFP growth. Future studies on post1975 Japanese growth should attempt to reveal the underlying reasons ofregional discrepancies in these control variables. In terms of the regional
business cycles, we find that the quantity anomaly holds in Japanese prefectures where on average the cross-prefectural correlation of output is higher
than that of consumption. We decompose risk-sharing components and findthat government transfers play a more important role in consumption risksharing than domestic financial markets. Future studies should investigate
sources of financial market imperfections that prevent cross-prefectural consumption risk-sharing.

References[1] Ambler, S., E. Cardia and C. Zimmermann, 2004, International businesscycles: What are the facts? Journal of Monetary Economics, 51,
pp.257-276.
[2] Artis, M. and T. Okubo, 2011, The intranational business cycle in Japan,
Oxford Economic Papers, 63, pp.111-133.
[3] Backus, D., P. Kehoe and F. Kydland, 1992, International Real Business
Cycles, Journal of Political Economy, 100 (4), pp.745-775.
[4] Baxter, M. and M. Crucicni, 1995, Business Cycles and the Asset
Structure of Foreign Trade, International Economic Review, 36 (4),pp.821-854.
[5] Barro, R., 1991, Economic Growth in a Cross Section of Countries,
Quarterly Journal of Economics, 106 (2), pp.407-443.
[6] Barro, R. and X. Sala-i-Martin, 1992, Regional Growth and Migration:
A Japan-United States Comparison, Journal of the Japanese andInternational Economies, 6, pp.312-346.
[7] Chari, V.V., P. Kehoe, and E. McGrattan, 2007, Business Cycle Accounting, Econometrica, vol.75 (3), pp.781-836.

17[8] Fujiki, H. and M. Nakakuki, 2005, Asymmetric Shocks and Regional
Risk Sharing: Evidence from Japan, Monetary and Economic Studies, 23 (2), pp.31-60.
[9] Hansen, G. and E. Prescott, 2005, Capacity constraints, asymmetries,
and the business cycle, Review of Economic Dynamics, 8 (4), pp.850865.
[10] Hayashi, F. and E. Prescott, 2002, The 1990s in Japan: A Lost Decade,
Review of Economic Dynamics, 5 (1), pp.206-235.
[11] Kalemli-Ozcan, S., B. E. Sorensen and O. Yosha, 2003, Risk Sharing
and Industrial Specialization: Regional and International Evidence,
American Economic Review, 93 (3), pp.903-918.
[12] Mankiw, N., D. Romer and D. Weil, 1992, A Contribution to the Empirics of Economic Growth, Quarterly Journal of Economics, 107 (2),pp.407-437.
[13] Shioji, E., 2001, Public Capital and Economic Growth: A Convergence
Approach, Journal of Economic Growth, 6, pp.205-227.
[14] van Wincoop, E., 1995, Regional Risksharing, European Economic Review, 37, pp.1545-1567.
[15] Young, A., 2004, Labor share’s fluctuations, biased technical change,
and the business cycle, Review of Economic Dynamics, 7 (4), pp.916931.

18

A

Data Appendix

A.1

Net Capital Stock

We consider net private capital stock as a sum of private firm fixed assets(manufacturing firm fixed assets + non-manufacturing firm fixed assets +intangible fixed assets), and private inventory stocks. In order to computethe net capital stock series over the 1975-2008 period, we use the perpetualinventory method which is based on the net capital accumulation equation
Kt+1 = Kt + P It − Dt
where K is the net private capital stock, P I is the private investment and D
is the private depreciation of the capital stock.
The benchmark capital stock level for 1975 is constructed as follows.
We use the ESRI Prefecture Private Capital Stock data for the benchmark
regional private firm fixed asset. For the benchmark private inventory stock,
we use the Private and Public Sector Balance Sheet data. Since only thenational private inventory stock data is available, we allocate the stock toeach prefecture using the relative size of private firm capital stock to construct
the benchmark regional private inventory stock. The value of benchmark
regional private capital stock is converted into constant 2000 prices using theregional GDP deflator.
Once we pin down the initial capital stock level, we can use the capital accumulation equation and annual flow data to construct the regional net
capital stock series. The regional private investment is available directly fromthe expenditure data. We obtain regional private depreciation as the diﬀerence between total depreciation and the depreciation for government service
providers using the ESRI Prefecture Gross Domestic Product by Economic
Activity and Factor Income data. Both series are converted into constant2000 price series using the regional GDP deflator. The capital depreciation
rate can be computed by dividing the regional private depreciation by theconstructed net capital stock.

A.2

Labor Income Share

The labor income share is constructed following Hayashi and Prescott (2002).
They define labor income as the sum of compensation of employees, half ofindirect business tax, and 80% of mixed income. Part of indirect businesstaxes paid by the firms is considered as the contribution of labor to production extracted from the government. ”For lack of good alternatives” theychoose to split the taxes equally between labor and capital income. They
define mixed income as the ”operating surplus in the nonhousing componentof the noncorporate sector” of which 80% is assumed to be labor income.
The compensation of employees and indirect business taxes (‘tax on production and imports’) are available at the prefecture level in the Prefecture
Gross Domestic Product by Economic Activity and Factor Income data.
However, mixed income is not available independently as it is reported as19‘operating surplus and mixed income’. In order to construct the mixed income series, we first use the Prefecture Residents Income data to computethe ratio of mixed income to the sum of operating surplus and mixed incomeof the residents:
mixed income
proprietors income - imputed rent=.
mixed income + operating surplus
nonfirm property income + business income
Then we multiply the prefecture domestic operating surplus and mixed income by this ratio to construct the prefecture domestic mixed income series.
Finally, the constructed labor income series is divided by regional GDP
to compute the labor income share. In terms of national income accounting,labor income, capital income and depreciation will add up to GDP where
capital income is defined as the sum of corporate operating surplus, half ofindirect business tax, 20% of mixed income, and imputed rent.

A.3

Disposable Income

The definition of the prefectural personal disposable income corresponding
to Prefecture Economic Accounts is,prefectural personal disposable income= prefectural disposable income (household)+ prefectural disposable income (non-profit institutions serving households)− employers’ contribution to social security.
For missing data, we follow Nakakuki and Fujiki (2005) and use Household
Survey data to estimate them. The main assumption is that the ratio of”disposable income” to ”gross income” net of ”social security receipt” inthe Household Survey should be equal to the ratio of prefectural incomeof the household and non-profit institutions serving the households net of
employers social security contribution to prefectural disposable income ofhouseholds and non-profit institutions serving household net of employers’social security contribution in the Prefecture Economic Accounts. Then we
can estimate the missing prefectural personal disposable income asprefectural personal disposable income= [prefectural income (household)+ prefectural income (non-profit institutions serving households)−employers’ contribution to social security]
×disposable income ÷ [gross income − social security receipt].
Further details can be provided by authors upon request.

20

B

Tables and Figures

Table 1. Summary Statistics of Regional Output: 1955-2008
y i /yg(y i )
corr(y i , y)std(y i )/std(y)National
Hokkaido
Tohoku
Kanto
Chubu
Kinki
Chugoku
Shikoku
KyushuOkinawa
Average
1
2
3
..
.

1.000
0.962
0.858
1.135
1.075
1.134
1.043
1.020
0.914
1.048
1.165
Shiga
1.705
Chiba
1.592
Mie
1.554
..
..
.
.

45
46
47

1.000
0.932
0.792
1.190
1.071
0.966
0.920
0.824
0.799
0.626
0.887
Tokyo
1.764
Osaka
1.195
Aichi
1.140
..
..
.
.
Kumamoto 0.694
Kagoshima 0.689
Okinawa
0.626

3.85%
3.30%
4.28%
3.61%
4.09%
3.47%
3.99%
3.84%
3.96%
4.26%
3.97%
Nagano4.71%
Fukushima 4.65%
Yamanashi 4.57%
..
..
.
.

1.000
0.760
0.712
0.964
0.955
0.958
0.933
0.857
0.877
0.045
0.731
Mie
0.924
Chiba
0.915
Saitama 0.902
..
..
.
.

Nara
Hyogo
Wakayama

Saga
Aomori
Okinawa

3.23%
3.17%
2.86%

0.429
0.387
0.045

Kagoshima
Niigata
Kochi

Table 2. GDP Share of Expenditures (%): 1955-2008

National
Hokkaido
Tohoku
Kanto
Chubu
Kinki
Chugoku
Shikoku
KyushuOkinawa
Average
1
2
3
..
.
45
46
47

PrivateConsumption
Investment
48.6
22.2
54.2
18.3
53.4
21.6
46.7
21.6
47.6
23.2
49.4
23.2
47.4
23.4
51.4
21.3
49.7
22.3
53.3
25.0
51.4
22.7
Nara
68.8
Ibaraki
33.2
Saitama 64.1
Mie
31.4
Chiba
64.1
Hyogo
27.5
..
..
..
..
.
.
.
.

Government
Consumption
Investment
15.1
7.5
21.7
12.9
20.6
10.7
12.4
5.9
13.6
7.8
13.3
6.4
17.1
8.6
19.8
9.4
21.1
8.9
26.7
11.5
18.2
11.5
Okinawa 26.7
Fukui
15.9
Nagasaki 25.9 Shimane 14.8
Tottori
25.6
Iwate
14.1
..
..
..
..
.
.
.
.

Tochigi
Fukuoka
Tokyo

Osaka
Kanagawa
Aichi

44.2
43.5
37.5

Tottori
Hokkaido
Tokyo

21

18.6
18.3
18.1

11.5
11.4
9.6

Shizuoka
Osaka
Tokyo

5.5
5.5
5.2

0.892
0.844
0.842

Table 3a. Intra-Regional Expenditure Correlation with Output: 1955-2008ii
i
i
corr(pc , y i )corr(pi , y i )corr(gc , y i )corr(gi , y i )National
Hokkaido
Tohoku
Kanto
Chubu
Kinki
Chugoku
Shikoku
KyushuOkinawa
Average
1
2
3
..
.
45
46
47

0.489
0.043
0.577
0.510
0.512
0.334
0.548
0.589
0.496
0.633
0.467
Gunma
0.817
Mie
0.712
Fukushima 0.699
..
..
.
.

0.727
0.540
0.651
0.765
0.769
0.650
0.670
0.620
0.588
0.072
0.577
Aichi
0.806
Miyagi
0.749
Kagawa 0.742
..
..
.
.

0.081
0.409
0.298
-0.024
0.037
0.142
0.060
0.244
0.424
0.412
0.234
Miyazaki
0.638
Nagasaki
0.632
Fukui
0.499
..
..
.
.

0.193
0.163
0.132
0.126
-0.051
0.426
0.325
0.343
0.552
0.404
0.212
Tokushima 0.606
Hyogo
0.606
Saga
0.557
..
..
.
.

Wakayama
Hokkaido
Osaka

Oita
NagasakiOkinawa

Kanagawa
Gifu
Aichi

KagawaShizuoka
Aichi

00092
0.043
-0.044

0.260
0.240
0.072

-0.102-0.118-0.177-0.058-0.075-0.139

Table 3b. Intra-Regional Expenditure Volatility relative to Output: 1955-2008
std(pci )/std(y i )std(pii )/std(y i )std(gci )/std(y i ) std(gii )/std(y i )National
Hokkaido
Tohoku
Kanto
Chubu
Kinki
Chugoku
Shikoku
KyushuOkinawa
Average
1
2
3
..
.
45
46
47

0.565
0.813
0.877
0.518
0.592
0.603
0.615
0.685
0.824
1.541
0.829
Okinawa 1.541
Akita 1.174
Kumamoto 1.169
..
..
.
.
Aichi 0.576
Tokyo 0.535
Hiroshima 0.513

3.373
2.692
2.900
3.413
3.300
3.302
3.549
3.245
2.926
2.983
3.041
Ibaraki 4.235
Fukui 4.187
Kochi 3.957
..
..
.
.
Kagoshima
Miyazaki
Chiba

22

2.371
2.271
2.223

0.864
0.762
1.061
1.184
0.804
1.138
0.976
0.891
0.985
1.316
1.130
Fukui 1.746
Gunma 1.731
Akita 1.545
..
..
.
.
Tokushima
Mie
Saitama

0.639
0.612
0.610

2.020
2.343
2.722
2.237
1.929
2.422
2.794
2.591
2.499
4.044
3.018
Niigata 4.413
Kagawa 4.308
Fukui 4.269
..
..
.
.
Fukuoka
Shiga
Aichi

2.256
1.755
1.459

Table 4a. Expenditure Correlation with National Aggregate: 1955-2008
corr(pci , c)corr(pii , i)corr(gci , gc)corr(gii , gi)
Hokkaido
Tohoku
Kanto
Chubu
Kinki
Chugoku
Shikoku
KyushuOkinawa
Average
1
2
3
..
.

0.619
0.782
0.848
0.919
0.860
0.834
0.760
0.813
0.202
0.609
Fukui
Yamaguchi
Chiba
..
.

45
46
47

Oita
Shiga
Okinawa

0.856
0.837
0.830
..
.

0.769
0.859
0.979
0.986
0.985
0.953
0.918
0.922
0.572
0.815
Osaka
0.974
Saitama 0.948
Shizuoka 0.946
..
..
.
.

0.463
0.813
0.865
0.869
0.868
0.859
0.780
0.678
0.206
0.585
Miyagi
0.835
Hyogo
0.825
Yamaguchi 0.801
..
..
.
.

Oita
Aichi
Saga
..
.

0.796
0.777
0.769
..
.

0.389
0.387
0.202

Akita
Okinawa
Aomori

Okinawa
Nagasaki
Shiga

Fukui
Okinawa
Kagawa

0.329
0.289
0.210

0.607
0.572
0.539

0.206
0.170
0.108

0.659
0.725
0.860
0.918
0.863
0.765
0.659
0.823
0.289
0.575

Table 4b. Expenditure Volatility relative to National Aggregate: 1955-2008
std(pci )/std(pc)std(pii )/std(pi)std(gci )/std(gc)std(gii )/std(gi)Hokkaido
Tohoku
Kanto
Chubu
Kinki
Chugoku
Shikoku
KyushuOkinawa
Average
1
2
3
..
.
45
46
47

1.384
1.332
1.041
1.127
1.212
1.137
1.238
1.334
2.861
1.677
Okinawa 2.861
Nagasaki 2.353
Mie
2.304
..
..
.
.

0.767
0.738
1.149
1.051
1.110
1.098
0.981
0.793
0.927
1.043
Ibaraki
1.660
Shiga
1.358
Hiroshima 1.338
..
..
.
.

0.849
1.054
1.557
1.001
1.493
1.179
1.052
1.042
1.598
1.498
Wakayama 2.199
Gunma
2.169
Tokyo
2.121
..
..
.
.

1.116
1.157
1.257
1.027
1.360
1.443
1.308
1.131
2.099
1.701
Kagawa2.681
Yamanashi 2.189
Nagasaki
2.120
..
..
.
.

Miyagi
Hiroshima
Tokyo

Saga
Aomori
Kagoshima

Tottori
Tokushima
Hokkaido

Kagoshima
Hokkaido
Aichi

1.186
1.155
1.126

23

0.753
0.744
0.627

1.014
0.888
0.849

1.363
1.116
1.039

Table 5. Production Factor relative to National Aggregate: 1975-2008
Hokkaido
Tohoku
Kanto
Chubu
Kinki
Chugoku
Shikoku
KyushuOkinawa
Average
1
2
3
..
.
45
46
47

Labor
0.979
1.020
1.004
1.076
0.943
1.021
0.994
0.958
0.851
0.992
Tokyo
1.374
Nagano 1.101
Fukui
1.097
..
..
.
.
Chiba
Saitama
Nara

0.740
0.738
0.669

Capital
0.861
0.782
1.045
1.208
0.963
1.066
0.872
0.841
0.661
0.942
Mie
1.722
Ibaraki
1.596
Hyogo
1.339
..
..
.
.
Nara
SaitamaKumamoto

0.626
0.618
0.617

TFP
0.961
0.912
1.134
0.974
0.963
0.905
0.879
0.901
0.882
0.933
Tokyo
Saitama
Shiga
..
.

1.330
1.096
1.074
..
.

Wakayama
Mie
Ibaraki

0.796
0.790
0.784

Table 6a. Intra-Regional Factor Correlation with Output: 1975-2008ii
i
corr(l , y i )corr(k , y i )corr(z , y i )National
Hokkaido
Tohoku
Kanto
Chubu
Kinki
Chugoku
Shikoku
KyushuOkinawa
Average
1
2
3
..
.
45
46
47

0.643
0.518
0.605
0.504
0.684
0.725
0.540
0.358
0.747
0.159
0.383
Tochigi
0.727
Aichi
0.679
Saitama
0.666
..
..
.
.

0.428
0.510
0.375
0.259
0.366
0.569
0.335
0.584
0.660
0.166
0.298
Osaka
0.738
Kagawa0.698
Fukuoka
0.636
..
..
.
.

0.829
0.613
0.756
0.887
0.863
0.884
0.818
0.616
0.718
0.800
0.813
Osaka
0.957
Tochigi
0.937
Kanagawa 0.926
..
..
.
.

Kyoto
Wakayama
Tokushima

Shizuoka
Fukui
Wakayama

Kochi
NagasakiKagoshima

0.039-0.012-0.08924-0.035-0.090-0.100

0.602
0.544
0.487

Table 6b. Intra-Regional Factor Volatility relative to Output
std(li )/std(y i )std(k i )/std(y i )std(z i )/std(y i )National
Hokkaido
Tohoku
Kanto
Chubu
Kinki
Chugoku
Shikoku
KyushuOkinawa
Average
1
2
3
..
.
45
46
47

0.527
1.114
0.691
0.433
0.512
0.463
0.603
0.959
0.728
0.800
0.671
Kagoshima 1.328
Nagasaki
1.142
Kochi
1.117
..
..
.
.

0.808
0.898
0.811
0.808
0.694
0.768
0.693
0.918
0.752
0.844
0.729
Kagoshima 1.170
Ibaraki
1.014
Gifu
0.961
..
..
.
.

Fukushima
Nara
Osaka

TochigiToyamaWakayama

0.419
0.407
0.351

0.479
0.453
0.380

0.795
0.762
0.833
0.885
0.799
0.704
0.872
0.936
0.662
1.084
0.940
Kagoshima 1.203
Fukui
1.177
Yamanashi 1.131
..
..
.
.
Saga
Iwate
Osaka

0.752
0.723
0.701

Table 7a. Factor Correlation with National Aggregate: 1975-2008
corr(li , l)corr(k i , k)corr(z i , z)
Hokkaido
Tohoku
Kanto
Chubu
Kinki
Chugoku
Shikoku
KyushuOkinawa
Average
1
2
3
..
.
45
46
47

0.693
0.906
0.905
0.962
0.944
0.869
0.871
0.831
0.528
0.749
Wakayama 0.922
Fukushima 0.906
Kagawa
0.904
..
..
.
.
Okinawa
Saga
Nara

0.528
0.471
0.395

0.559
0.910
0.985
0.970
0.986
0.936
0.967
0.948
0.762
0.861
Kanagawa 0.974
Osaka
0.972
Kyoto
0.967
..
..
.
.
Kumamoto 0.669
Shimane0.623
Hokkaido 0.559

25

corr(y i , y)

0.413
0.764
0.953
0.946
0.820
0.879
0.486
0.765
0.499
0.583
Mie
0.872
Tokyo
0.855
Shizuoka 0.826
..
..
.
.

0.687
0.816
0.945
0.957
0.907
0.929
0.613
0.777
0.398
0.664
Mie
0.932
Hiroshima 0.909
Aichi
0.888
..
..
.
.

Saga
Ibaraki
Kochi

Kagoshima
Wakayama
Kochi

0.288
0.231
-0.092

0.334
0.308
0.086

Table 7b. Factor Volatility relative to National Aggregate: 1975-2008
std(li )/std(l)std(k i )/std(k)std(z i )/std(z)std(y i )/std(y)Hokkaido
Tohoku
Kanto
Chubu
Kinki
Chugoku
Shikoku
KyushuOkinawa
Average
1
2
3
..
.
45
46
47

1.643
1.309
0.994
1.042
1.014
1.149
1.513
1.278
1.270
1.409
Nagasaki 2.362
Kochi
1.984
Ehime
1.947
..
..
.
.

0.863
1.001
1.209
0.921
1.096
0.861
0.944
0.860
0.874
1.027
Ibaraki
1.891
Hyogo
1.567
Nara
1.540
..
..
.
.

0.745
1.046
1.347
1.079
1.023
1.102
0.979
0.771
1.142
1.371
Ibaraki
2.071
Wakayama 1.930
Fukushima 1.876
..
..
.
.

0.777
0.998
1.209
1.072
1.154
1.004
0.831
0.925
0.837
1.170
Fukushima 1.696
Hyogo
1.626
Aichi
1.561
..
..
.
.

Gunma
Osaka
Gifu

OkayamaToyamaWakayama

MiyazakiKagoshima
Hokkaido

Fukui
Hokkaido
Kagoshima

0.967
0.881
0.876

0.726
0.673
0.651

0.914
0.881
0.745

0.816
0.777
0.582

Table 8. Income Statistics: 1975-2008

National
Hokkaido
Tohoku
Kanto
Chubu
Kinki
Chugoku
Shikoku
KyushuOkinawa

Labor Income Share
Levelcorr(1 − θi , yi )0.593
-0.7150.635-0.4190.584-0.3920.597-0.7160.586-0.6940.592-0.6860.588-0.610
0.588
0.010
0.591
-0.6180.540-0.243

Capital Depreciation
Ratecorr(δ i , yi )
0.077
0.489
0.073
0.551
0.087
0.396
0.083
0.620
0.079
0.543
0.066
0.317
0.069
0.541
0.075
0.338
0.077
0.334
0.083
0.438

1
2
3
..
.

Tokyo
Kochi
Hokkaido
..
.

0.645
0.635
0.635
..
.

Yamanashi
SaitamaShizuoka..
.

-0.828-0.738-0.732..
.

SaitamaKumamoto
Chiba
..
.

0.094
0.094
0.085
..
.

Saitama
Yamanashi
Chiba
..
.

0.773
0.745
0.718
..
.

45
46
47

Chiba
Ehime
Shiga

0.537
0.529
0.489

Saga
Kochi
Ehime

0.022
0.099
0.115

IbarakiWakayama
Mie

0.045
0.045
0.043

NaganoKagoshima
Hyogo

0.017
-0.055-0.18526

Table 9. Eﬃciency relative to National Aggregate: 1975-2008
Hokkaido
Tohoku
Kanto
Chubu
Kinki
Chugoku
Shikoku
KyushuOkinawa

MPL
0.978
0.804
1.159
1.008
0.969
0.913
0.825
0.852
0.720

MPK
0.935
1.090
1.098
0.928
0.955
0.894
0.963
0.978
1.151

Labor Wedge
1.047
1.103
0.954
1.081
0.991
1.012
1.071
0.959
0.932

Capital Wedge
1.006
0.997
0.946
1.132
0.933
1.062
0.995
1.041
0.873

National

0.891

1.010

1.046

1.016

1
2
3
..
.

Tokyo
Osaka
Kanagawa
..
.

1.409
1.120
1.086
..
.

Saitama
Ishikawa
Shiga
..
.

1.350
1.319
1.299
..
.

Akita
Tottori
Niigata
..
.

1.238
1.228
1.200
..
.

IbarakiMie
Yamaguchi
..
.

1.311
1.284
1.139
..
.

45
46
47

Ehime
Aomori
Okinawa

0.751
0.742
0.720

Wakayama
Mie
Ibaraki

0.667
0.604
0.600

Nara
AomoriFukuoka

0.877
0.876
0.836

Okinawa
Ishikawa
Shiga

0.873
0.858
0.842

Table 10. Growth Accounting (%): 1975-2008
National
Hokkaido
Tohoku
Kanto
Chubu
Kinki
Chugoku
Shikoku
KyushuOkinawa
1
2
3
..
.
45
46
47

Output
1.99
1.68
2.12
1.93
2.28
1.72
1.89
1.75
1.96
1.84
Fukushima 2.74
Nagano
2.68
Shiga
2.57
..
..
.
.

Labor
-0.25
-0.39
-0.28
-0.22
-0.23
-0.30
-0.31
-0.25
-0.22
0.02
Nagasaki
0.05
Okinawa
0.02
Saga
-0.07
..
..
.
.

Capital
1.19
0.83
1.34
1.10
1.55
0.96
1.10
1.11
1.30
1.28
Mie
1.86
Ibaraki
1.79
Aomori
1.58
..
..
.
.

TFP
1.05
1.24
1.05
1.06
0.96
1.06
1.10
0.89
0.89
0.53
NaganoFukushima
Iwate
..
.

1.62
1.57
1.47
..
.

Fukuoka
Kochi
Wakayama

Hokkaido
NaganoTokushima

Hokkaido
Fukui
Chiba

AomoriMie
Wakayama

0.46
0.45
0.02

1.53
1.27
0.77

27

-0.39
-0.40
-0.41

0.83
0.77
0.69

Table 11. Growth Regression

Constant
InitialOutput
TFP
Gap
Labor
Share
CapitalDepreciation
Population
GrowthPrivateInvestment
Government
Investment
TFP
GrowthGrowth 1955-2008
(1)
(2)
0.049
**
0.013
(32.027)(1.013)-0.011** -0.014(-6.260)(-5.217)
0.023(2.187)0.012(0.989)-0.029(-0.527)-0.300(-3.089)
0.051(2.714)-0.022(-1.160)
0.428(3.764)
0.454
0.707

R2
Table 12. Average Correlation
Output0.462
Consumption 0.264
Investment
0.642
Labor
0.575
Capital
0.759
TFP
0.358

28

**
**

**
**

**

Growth 1975-2008
(3)
(4)
0.023
** -0.013(7.401)(-1.052)-0.004-0.009(-1.152)(-2.249)
0.023(2.254)-0.007(-0.617)-0.018(-0.396)-0.505(-3.032)
0.104(4.195)-0.012(-0.637)0.709(6.708)
0.007
0.650

**
**

**
**

**

29

R2

Industry
Similarity
OutputSizeDistance

Constant

Output1.051**(23.40)-7.86E-05 **(-4.876)-0.291**(-2.350)0.143**(12.29)0.146

Consumption
0.601**(10.27)-3.43E-05(-1.634)-1.017**(-6.300)
0.070**(4.588)0.051

Table 13. Comovement Regression
Investment
0.924**(27.68)-7.44E-05 **(-6.214)0.052(0.564)0.067**(7.675)
0.088

Labor
0.344
**
(8.951)-8.96E-05 **(-6.494)-0.084(-0.795)-0.076**(-7.626)
0.079

Capital
0.913**(28.74)-6.79E-05 **(-5.956)
0.094(1.073)0.034**(4.078)0.049

Productivity
0.566**(11.53)-7.70E-05 **(-4.364)0.069(0.512)0.046**(3.643)0.029

Table 14. Decomposition of Risk-Sharing
Capital Market +Government +Financial Market
Constant
GDP
GrowthR2-0.0040∗∗(-32.61)
0.1557∗∗(31.03)0.635-0.0056∗∗(-16.90)0.4649∗∗(35.97)0.645

30-0.0146∗∗(-46.64)0.6956∗∗(69.42)0.801

Figure 1. Inequality
0.16

0.14

0.12

Gini Coefficient

0.1

0.08

0.06

0.04

0.02

0
1955

1960

1965

1970

1975

1980

1985

1990

1995

2000

2005

Figure 2. Labor Income Share
0.7

0.65

0.6

0.55

0.5

0.45
1975

1980
National

Hokkaido

1985
Tohoku

1990
Kanto

Chubu

1995
Kinki

Chugoku

2000
Shikoku

2005
KyushuOkinawaFigure 3. Depreciation Rate
10%

9%

8%

7%

6%

5%

4%
1975

1980
National

Hokkaido

1985
Tohoku

1990
Kanto

Chubu

1995
Kinki

Chugoku

2000
Shikoku

2005
KyushuOkinawaFigure 4. Misallocation
0.12

0.11

0.1

Gini Coefficient

0.09

0.08

0.07

0.06

0.05

0.04
1975

1980

1985

1990
MPL

1995
MPK

2000

2005