KEO Discussion Paper No. 172

Spatially Uneven Pace of Deindustrialization
Within a Country
Kozo Kiyota
Keio Economic Observatory, Keio University

Spatially Uneven Pace of Deindustrialization
Within a Country*
Kozo Kiyota†
Keio University, RIETI, and TCER
July 22, 2022

Abstract
The declining share of manufacturing value-added, often referred to as “deindustrialization,” is fast becoming a major concern for policymakers and academic
researchers, especially in high-income countries. When compared with countrylevel analysis, however, regional-level analyses of deindustrialization within a country are limited. This paper empirically examines how and why the patterns ofdeindustrialization are uneven across regions within a country. The analysis builds
upon the neoclassical trade model and uses regional-level data in Japan where both
detailed output and input data are available at the regional and industry levels forboth manufacturing and nonmanufacturing industries over the last four decades.
One of the major findings is that the large variation in deindustrialization withina country is attributable to differences in productivity and price changes across regions. In contrast, the effect of the slowdown in capital accumulation, partly fromthe expansion of foreign direct investment or offshoring, commonly appears not in
specific regions but across regions. The effect of spatial interdependence is also not
only statistically significant but also nonnegligible in terms of its magnitude.
Key words: deindustrialization, region, neoclassical trade model, productivity,
spatial interdependence
JEL classification codes: F11, F14, R12* The author benefited from helpful comments on earlier drafts by Flora Bellone, Theresa Greaney,
Takatoshi Ito, Yasusada Murata, Kentaro Nakajima, Toshihiro Okubo, Justin Pierce, Peter Schott, Nori
Tarui, two anonymous referees, and seminar participants at Columbia University, Keio University, andthe University of Hawai‘i. The author gratefully acknowledges the financial support of the Japan Society
for the Promotion of Science (JSPS) Grants-in-Aid (JP19H01475, JP19H00598, JP22H00063). The usual
disclaimer applies.
†
E-mail: kiyota@keio.jp

1

Introduction

The declining share of manufacturing value-added, often referred to as “deindustrialization,” is fast becoming a major concern for policymakers and academic researchers(e.g., Rodrik, 2016; Bernard, Smeets, and Warzynski, 2017).1 One reason for this is that“many observers and policy makers believe future economic hopes rest in importantpart on fostering new manufacturing industries” (Rodrik, 2016, p. 2). In this context,
Redding (2002) and Nickell, Redding, and Swaffield (2008) examined the specialization dynamics of manufacturing production across countries. Redding (2002) foundthat factor endowments play an important role in the long-run patterns of specialization in Organisation for Economic Cooperation and Development (OECD) countries,
while Nickell, Redding, and Swaffield (2008) concluded that the more rapid decline in
the manufacturing share of gross domestic product (GDP) in the UK and the US thanin Germany and Japan is explained by the patters of total factor productivity (TFP) andchanges in the relative price of manufactured and nonmanufactured goods.
It is also a concern that manufacturing in some regions within a country decline
more rapidly than in others, with recent studies suggesting that factor markets should
be defined at the local rather than the national level. For example, Autor, Dorn, andHanson (2013) argued that labor mobility across states is surprisingly low even in the
US. Dix-Carneiro (2019) pointed out that the adjustment of capital across regions is also
slow in Brazil because depreciation is low and new investments are gradually directed
toward regions that are less affected by trade shocks. An important implication of thesestudies is that because factor adjustment across regions is slow, industrial structure
could diversify across regions within a country and therefore the pace of deindustrialization may be uneven across regions.2 This is important because regional heterogeneity could lead to unintended distributional consequences of various national policies,
such as trade liberalization.
When compared to country-level analysis, the regional-level analysis of deindustrialization within a country remains limited. One reason is that to investigate deindustri1

Deindustrialization is also represented by the declining share of manufacturing in employment. For
example, see, Rodrik (2016).
2
Bernard, Redding, and Schott (2013) found that factor price equalization does not hold across regionsin the US. They also revealed that regional wage differentials are closely related to regional industrial
structure.

1

alization (i.e., the declining share of manufacturing value-added), economists need not
only information on manufacturing but also on nonmanufacturing to compute industry shares. In other words, the analysis of the patterns of manufacturing specialization
across regions within a country is not necessarily able to directly address deindustrialization within a country. Nonetheless, some studies have addressed this issue. Redding
and Vera-Martin (2006) examined the patterns of specialization for 45 regions in seven
European countries; however, their regional classification is not sufficiently detailed tofocus on a single country. Murakami (2015) and Dauth and Suedekum (2016) investigated the regional heterogeneity of deindustrialization in Japan and Germany, respectively. Murakami (2015) pointed out that migration and urbanization affected deindustrialization in Japan prior to 1970.3 For their part, Dauth and Suedekum (2016) foundthat deindustrialization was driven by the increase in international trade.4 While thesestudies present insightful results with significant contributions to the literature, theirempirical analyses do not necessarily connect to the underlying theoretical models inthe sense that the regression equations in Murakami (2015) and Dauth and Suedekum(2016) are not directly derived from theory.
This paper cements research gaps discussed above and also addresses these issues, focusing on Japan where both output and input data are available at detailed
regional and industry levels for both manufacturing and non-manufacturing industries between 1972 and 2012.5 Like other high-income countries, Japan has experienced shrinking manufacturing employment and falling manufacturing value-added
as a share of total over the last four decades. Panel A in Figure 1 plots the level andshare of manufacturing employment from 1972 to 2012. As shown, manufacturing
employment peaked at well over 15 million workers in 1992 and then fell by nearly
35 percent over the next 20 years. Similarly, the share of manufacturing employment
in total employment declined continuously over the same period, from 25.6 percent
in 1972 to just 15.9 percent in 2012. Panel B in Figure 1 plots the level and share ofmanufacturing value-added (current prices) over the same period. As shown, manu3

However, the migration rate in Japan declined after 1970, which is detailed in Section 2.3.
In addition to these factors, some theoretical and simulation studies in new economic geographysuggest that the decline in transportation costs could affect deindustrialization (e.g., Murata, 2008; Desmet
and Rossi-Hansberg, 2014) or spatial inequality in incomes (e.g., Allen and Arkolakis, 2014). However, tothe best of our knowledge, empirical studies have yet to confirm a clear relationship between these factors
across regions within a country.
5
Section 2 explains the data used in this paper in more detail.
4

2

facturing value-added peaked at 123.3 trillion yen in 1991, falling to only 86.5 trillion
yen by 2012, while its total value-added share gradually declined from 35.5 percent in1972 to just 20.8 percent in 2012.6
However, this deindustrialization pattern is not common across prefectures within
Japan.7 Figure 2 illustrates the share of manufacturing value-added in 1972 and 2012by prefectures, which are sorted from left to right based on their manufacturing sharesin 1972. If a percentage point decline is common across prefectures, the line exhibitsa parallel downward shift. If the decline is proportional, the line depicts a smaller
downward shift in the prefectures on the left and a larger downward shift in the prefectures on the right. Panel A of Figure 2 presents, however, neither of these patterns
and the decline in the share of manufacturing value-added differs markedly across prefectures within the country. Consequently, even though Japanese manufacturing faces
deindustrialization on average, there are a few prefectures in which the share of manufacturing value-added has increased. In other words, deindustrialization is spatially
uneven within the country.
Panel B of Figure 2 presents this pattern on a map of Japan. Colors are based on thequartile of the changes in the share of manufacturing value-added, which corresponds
to the vertical difference between 1972 and 2012 in Figure 2 for each prefecture (i.e.,the change from 1972 to 2012 for each prefecture). A darker color indicates a larger
decline. This figure shows that rapid deindustrialization is not randomly distributed
across prefectures and is concentrated in two major metropolitan areas: Tokyo andOsaka. This also implies that deindustrialization may be spatially interdependent.8
Drawing on this background, this paper empirically examines how and why deindustrialization patterns can vary across regions within a country. Our theoretical andempirical approach is based on a series of works by Redding and colleagues (Redding,
2002; Redding and Vera-Martin, 2006; Nickel, Redding, and Swaffield, 2008) that analyzed cross-country specialization patterns according to neoclassical trade theory. An
advantage of the use of a trade model is that it enables us to analyze the changes in theshare of value-added across sectors simultaneously in a simple way. The contribution
6

The value-added per capita increased from 2.190 in 1972 to 9.591 in 2005 and then declined to 8.675 in
2012.
7Japan consists of 47 administrative regions. Each region is officially called a “prefecture.” Hereafter,
this paper freely interchanges the terms “region” and “prefecture.”
8
Formal tests of spatial interdependence will be provided in Section 3.

3

Figure 1: Manufacturing Employment and Value-Added in Japan, 1972–2012
Panel A: Level and share of total employment
18.0

16.0

30.0%

Level (left)

Share (right)
25.0%

20.0%

12.0

10.0
15.0%
8.0

10.0%

6.0

Share of manufacturing employment (%)

Number of workers (millions)

14.0

4.0
5.0%

0.0

1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012

2.0

0.0%

Panel B: Level and share of total value-added
Level (left)

Share (right)

35.0%

120.0

Value-added (trillion yen, current prices)

40.0%

30.0%
100.0
25.0%
80.0
20.0%
60.0
15.0%
40.0
10.0%

20.0

1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012

0.0

5.0%

Notes: Manufacturing value-added based on current prices.
Source: Research Institute of Economy, Trade, and Industry (RIETI) (2017) R-JIP Database.

4

0.0%

Share of manufacturing value-added (%)

140.0

Figure 2: Share of Manufacturing Value-Added in 1991 and 2012 by Prefecture
Panel A: Share of manufacturing value-added
60%

1972

Share of manufacturing value-added (%)

50%

2012
JAPAN
35.5%

40%

30%

20%

10%

Aomori
Kagoshima
Kochi
Akita
Kumamoto
Miyazaki
Hokkaido
Okinawa
ShimaneIwate
Yamagata
Oita
NagasakiMiyagi
Saga
Yamanashi
Tokushima
Fukushima
Fukuoka
Tottori
Nara
KagawaNiigataFukui
NaganoIshikawa
Ehime
Tokyo
Toyama
JAPAN
Gifu
Osaka
Hiroshima
Gumma
Kyoto
Yamaguchi
Shiga
IbarakiTochigi
Okayama
Chiba
Shizuoka
Hyogo
SaitamaAichi
Mie
Wakayama
Kanagawa

0%

JAPAN
20.8%

Panel B: Changes in the share of manufacturing value-added

Notes: In Panel A, JAPAN is the average of Japan. Manufacturing value-added is based on current prices.
Colors relate to the quartile of the changes in the share of manufacturing GDP, with darker colors indicating larger declines. The Japanese map data are from https://gadm.org/.
Source: RIETI (2017) R-JIP Database.

5

of this study is twofold. First, the analysis considers the spatial interdependence ofdeindustrialization across regions using spatial econometric techniques and the framework of general equilibrium analysis. In this paper, spatial interdependence means thespatial correlation of production (e.g., through agglomeration externalities) and that ofrandom shocks between prefectures.9 Second, the paper quantifies the contribution of
the factors that could potentially affect deindustrialization.
The major findings of this paper are threefold. First, the large variation in deindustrialization within a country is attributable to differences in productivity and pricechanges across prefectures. This suggests that prefectures with manufacturing industries that face sharp price declines and/or exhibit slower productivity growth are more
likely to deindustrialize. Second, the effect of a slowdown in capital accumulation,
partly because of the expansion of foreign direct investment (FDI) or offshoring, does
not appear in individual prefectures, but is common across prefectures. Finally, theeffect of spatial interdependence is not only statistically significant, but also nonnegligible in terms of magnitude.
The remainder of the paper is organized as follows. Section 2 explains the analyticalframework, discussing the theoretical model, data, and econometric concerns. Section
3 presents the results of the baseline model and Section 3 discusses the results of alternative models. Drawing on these estimation results, Section 4 examines the economic
magnitude of these results, the changes in industry composition within manufacturing, and the price changes. The final section summarizes the findings and presents
their implications.

2

Analytical Framework

2.1

Theoretical backgroundOur theoretical framework follows Redding (2002) by drawing on the neoclassical theory of trade and production (Dixit and Norman, 1980). More specifically, the analysis
focuses on production rather than trade. One of the advantages of this model is that
9

In this paper, production is measured by the value-added (net output). Section 2.3 presents a formal
definition.

6

it requires no assumptions about consumer preferences.10 The analysis in this paper isthus consistent with a wider range of forms of consumer preferences, which affects the
production structure through prices.11
Another advantage of neoclassical theory is that it enables us to analyze the changes
in the share of value-added across sectors simultaneously in a simple manner.12 Morespecifically, the theory allows us to identify the determinants of deindustrializationin the general equilibrium framework and derive an econometric specification withproducer optimization. The theory translates the fall in manufacturing and the risein the services sector into the contribution of relative prices, productivity, and factor
endowments as follows.
Index regions by z ∈ {1, ..., Z}; industries by j ∈ {1, ..., N }; factors of production byi ∈ {1, ..., M }; and time t. Assume that production occurs under perfect competitionand constant returns to scale.13 Let yzjt and vzjt be the output and factor inputs ofindustry j in region z in year t. Assume that technology differences are represented by
Hicks-neutral region–industry–time technology.14
In this setting, the revenue function takes the form r(ϕzt pzt , vzt ), where ϕzt and pzt
are the vectors of the productivity parameter and relative prices of region z in year t;
and vzt is factor endowment in region z in year t. Assume that the revenue function isapproximated as a translog form that provides an arbitrarily close local approximation
10

Indeed, the central predictions of the Heckscher–Ohlin model are for producer equilibrium, as threeof the Heckscher–Ohlin model’s four key theorems (i.e., Rybczynski, Stolper–Samuelson, and factor priceequalization) require no assumptions about consumer preferences.
11
Recent studies have pointed out the importance of nonhomothetic preferences as a determinant of thesectoral composition in value-added. For example, see Matsuyama (2019).
12
In recent years, studies such as Allen and Arkolakis (2014) have developed quantitative spatial modelsof trade. While their frameworks are precise and sophisticated, they are also complicated; therefore, they
are not easy to implement. This paper attempts to present a simple alternative approach, although we
acknowledge that the framework has several shortcomings.
13
While these assumptions are restrictive, they are helpful when formulating a general equilibrium
trade model. For example, see, Eaton–Kortum model (Eaton and Kortum, 2002) which develops a multicountry, multisector general equilibrium Ricardian model.
14
The introduction of the productivity parameter allows us to control for Ricardian technology differences across regions. For details, see Morrow (2010).

7

to the true underlying revenue function:
1 XX
βjk ln(ϕzjt pzjt ) ln(ϕzkt pzkt )
2
j
j
k
X
1 XX
δih ln vzit ln vzht+
δ0i ln vzit +
2
i
i
h
XX
+
γji ln(ϕzjt pzjt ) ln(vzit ),(1)ln r(ϕzt pzt , vzt ) = β00 +jX

β0j ln ϕzjt pzjt +iwhere j, k ∈ {1, ..., N } index industries and i, h ∈ {1, ..., M } index factors. Assume
further that the symmetry of the cross effects (i.e., βjk = βkj and δih = δih ∀j, k, i, h)PPP
and linear homogeneity of degree one in v and p (i.e., j β0j = 1, j δ0j = 1, j βjk =PP0, i δ0j = 0, and i γij = 0).
In the model, firms maximize profits, taking producer prices as given. Because under perfect competition, domestic producer prices equal foreign producer prices plus
tariffs and transportation costs, producer prices include the effects of tariffs and transportation costs. Differentiating the revenue function with respect to the log of pzjt andadding the error term εzjt , we obtain the following general equilibrium relationship between the share of industry j in region z’s GDP in year t and relative prices, technology,
and factor endowments:
pzjt yzjt (ϕzt pzt , vzt )+ εzjtr(ϕzt pzt , vzt )XX= β0j +
βjk ln ϕzkt pzkt +γij ln vzit + εzjt ,szjt ≡

where

(2)

i

k

15 Standard microeconomic theory suggests that the effect of ownj szjt = 1.

P

sector price-productivity is positive (i.e., βjj > 0) because it increases revenue. In
contrast, the effect of other-sector price productivity is undetermined a priori because it
depends upon the complementarity/substitutability between industries. Trade theory
suggests that γij > 0 if industry j is factor i-intensive. The magnitude of the coefficientcannot be determined a priori and thus clarified by the empirical analysis. In the matrix
form, equation (2) is written as:

sjt = βj Xjt + jt ,15

For the derivation of equation (2), see Appendix A.

8(3)

where sjt is the GDP share of industry j in year t, and Xjt is a matrix of regressors
including factor endowments. This equation is the basis of the regression analysis.
P
Note that because j szjt = 1 and with parameter restrictions only N − 1 equations
can be estimated.

2.2

Data

2.2.1

Source and classifications

Before discussing the econometric specification, we explain the data used in the analysis, being the 2017 Regional-level Japan Industrial Productivity (R-JIP) Database from1972 to 2012.16 This is a regional-level version of the Japan Industrial Productivity
Database, which provides annual information on capital and labor inputs, as does the
National Bureau of Economic Research manufacturing database. There are two notablefeatures of this database. First, the information is available at the prefecture–industry
level. Second, the data include both manufacturing and nonmanufacturing sectors in
47 administrative prefectures in Japan from 1970 to 2012 for 13 manufacturing industries and 10 nonmanufacturing industries.17 The local market is defined using thisprefecture classification.18 Note that a “prefecture” in Japan corresponds to a “state” inthe US. The sample period commences with the return of the Okinawa prefecture by
the US to Japan in 1972.
Following Nickell, Redding, and Swaffield (2008), industries are aggregated into
five sectors: Agriculture (j = 1), Manufacturing (j = 2), Other production (j = 3),
Business services (j = 4), and Other services (j = 5).19 Given that deindustrialization is concerned with the decline in the share of aggregate manufacturing in GDP, themanufacturing sector is considered as a whole, along with aggregates of the other major sectors. The Other production sector comprises mining, utilities, and construction.
The services sector is divided into Business services and Other services because financial and business services are likely to be more tradable than other services, which may
16

Available at https://www.rieti.go.jp/en/database/r-jip.html
See Table B1 in Appendix B for the prefecture classification.
18
The local market can be defined not only by the administrative classification but also by the commuting zone. However, “most of the workers work in the prefecture where they live” (Taniguchi, 2019, p. 3).
Therefore, the definition of factor markets at the prefecture level may have some validity.
19
See Table B2 in Appendix B for the industry classification. The original industry category is the “industry” while the aggregate industry category is the “sector.”
17

9

lead to different price movement patterns between prefectures.

2.2.2

GDP shares

The model yields predictions for the share of the current value-added price of eachsector in current price share of GDP. Hence, the current price share of GDP is the dependent variable. Table 1 presents the change in the share of sectoral GDP.20 This table
presents the arithmetic mean values across prefectures, showing that the average shareof manufacturing value-added (∆s2 ) declined in the period from 1972 to 2012. It is alsointeresting to note that all sectors except for Business services exhibit declining shares.
The remaining variables are detailed in Section 3.
Table 1: Summary Statistics: Arithmetic Mean Change Across Prefectures, 1972–2012
Mean S.D. Minimum Maximum∆s1-0.067 0.035-0.137-0.002∆s2-0.083 0.081-0.3310.051∆s3-0.040 0.026-0.0970.012∆s4-0.006 0.011-0.0390.018∆s50.197 0.045
0.131
0.348
∆ ln(ϕ1 p1 ) 1.173 0.269
0.506
1.764
∆ ln(ϕ2 p2 ) 1.967 0.355
1.230
2.755
∆ ln(ϕ3 p3 ) 1.746 0.258
1.346
2.379
∆ ln(ϕ4 p4 ) 1.675 0.174
1.107
2.092
∆ ln(ϕ5 p5 ) 2.352 0.169
1.938
2.874
∆ ln(K/L) 1.604 0.237
1.058
2.094
Notes: ∆sj presents the changes in the share of sector j’s GDP; ∆(ϕj pj ) indicates the changes in thelog of the product of productivity and price of sector j; and j = 1, 2, 3, 4, 5 correspond to Agriculture,
Manufacturing, Other production, Business services, and Other services, respectively.
Source: RIETI (2017) R-JIP Database.

2.2.3

Productivity

This paper measures productivity using a superlative index number measure of TFP(for example, see, Nishimura, Nakajima, and Kiyota, 2005) for the following reasons.
First, it is derived under the neoclassical model’s assumptions of constant returns toscale and perfect competition. It is thus consistent with the theoretical framework inthis paper. Second, although much progress has been made on estimating production
20

Summary statistics for the share of GDP and other variables are in Table B3 in Appendix B. Note thatby definition, sectoral GDP includes sectoral exports while excluding sectoral imports. The analysis thus
accounts for international trade. Note also that the changes in the share of manufacturing value-added inTable 1 is the arithmetic mean of the changes across prefectures. The change in Panel B in Figure 1 is theshare of manufacturing value-added in Japan as a whole.

10

functions over the past decade (e.g., Dobbelaere and Kiyota, 2018; Gandhi, Navarro,
and Rivers, 2020), that framework requires large cross-sectional variations (i.e., large
sample sizes for a given time) and thus is usually unable to be applied to sector-level
data (i.e., small sample).
Approximating constant returns to scale production technology with a translog
functional form, this superlative index number evaluates productivity in each prefecture and year relative to a hypothetical average prefecture in the sector. Based on theavailability of the data, we use real value-added for output Y , and capital K and labor
L for inputs and set 2000 as the benchmark year (i.e., ln ϕzjt = 0 if t = 2000). Thismeans that TFP is measured relative to the hypothetical average prefecture in 2000.
More detailed explanations are in Appendix C.

2.2.4

Output, factor inputs, and prices

Output is defined as real value-added. Prices are measured with value-added deflators.
The deflator is an index of sector j in prefecture z in year t relative to their value in thesame prefecture in 2000 (i.e., 2000 constant prices), and thus takes the value of one in2000 in all prefectures. This deflator provides information on changes in nominal prices
in a particular prefecture–sector over time. Although the deflator does not capture
the level of prices across prefectures and sectors in 2000, the econometric specification
captures the level of prices in 2000 using a prefecture–sector fixed effect as described
below.
In the 2017 R-JIP Database, two factors are available at the prefecture–industry
level: capital (K) and labor (L), which correspond to the inputs of the production function (equation (C1) in Appendix C) and the endowments (vzit ) in equation (2). Capitalstock is defined as the net real capital stock, and the unit of measurement is one million
Japanese yen (2000 constant prices). The capital stock primarily consists of machinery and buildings, but not land. Labor is measured by hours worked (i.e., number ofworkers multiplied by working hours per worker divided by 1,000).21 All inputs wereidentified at the workplace.
Total cost is defined as wL+rK. The price of the capital (r) is the user cost of capital
21

In the 2017 R-JIP Database, labor is not disaggregated by skills or tasks. For a detailed explanation,
see Tokui, Makino, Fukao, Miyagawa, Arai, Arai, Inui, Kawasaki, Kodama, and Noguchi (2013).

11

that differs across industries but is identical across prefectures at the sector level. The
price of labor (w) is the average wage at the prefecture–sector level. TFP is computed
using the information on output, inputs, and prices (i.e., based on equation (C1) inAppendix C). Prefecture endowments are also computed by aggregating prefecture–
sector capital and labor (hours worked) at the prefecture level. Before proceeding to
the estimation, the next subsection discusses some of the econometric challenges.
One concern is the effects of Japanese outward FDI (or offshoring) on deindustrialization. Note that the expansion of FDI would lead to a decline in domestic capitalstock (Kzt ). In that sense, we consider the effects of FDI through the changes in capitalstock. Another concern may be the effects of an aging and declining population, leading to a decline in the domestic labor force (Lzt ). This analysis accounts for the effects
of aging and a declining population through the changes in the labor force.

2.3

Econometric issues

2.3.1

Regression equations and estimation

There are four concerns in estimating equation (2). First, equation (2) forms a system
of N − 1 equations reflecting the general equilibrium relationship between variables.
Noting the cross-equation symmetry constraints, the error terms across equations may
be contemporaneously correlated; therefore, it is necessary to use a systems estimator.
To address this issue, we select Zellner’s method for seemingly unrelated regression(SUR) equations, because of the following reasons. The one is that SUR can consider
the correlation of error terms in the system of equations. The other is that it enables us
to impose constraints on the parameters between the equations in a simple way. No
other estimation method appears to address these concerns simultaneously.22 Owing
to the parameter restrictions, we drop Other services from the estimation.
Second, as discussed earlier, deindustrialization may also be spatially interdependent. For example, suppose that an automobile company locates in one prefecture with
automotive parts provided by other firms located in either the same or neighboring prefectures through vertical linkages. If production of the automobile company declines
for some reason (e.g., the global financial crisis), the production of parts in other pre22

SUR is often used in estimating the system of equations. For example, see, Cicerone, McCann, andVenhorst (2020).

12fectures may also decline through backward linkages. In that case, deindustrialization
between prefectures will indicate positive correlation. In contrast, some manufacturing activities in one prefecture may move to another neighboring prefecture to avoid
high land prices. Then, deindustrialization between prefectures will show a negative
correlation. Moreover, unobserved shocks may be correlated because of geographicalproximity. However, such spatial interdependence is not captured in the theoreticalmodel in this paper.
To address the issue of spatial interdependence while simplifying the theoreticalframework, we employ spatial econometric techniques. Indeed, such spatial econometric issues are not new in the literature on international trade.23 The value-added inthis study is to extend the analysis by introducing spatial econometric techniques andSUR simultaneously, which is novel in the trade literature.
Note that there are several forms of spatial dependence. For example, spatial correlation can be controlled for by including the spatial lag of the dependent variable
as an additional independent variable when some part of the total variation in deindustrialization would be explained by each prefecture’s dependence on its neighbors.
Alternatively, spatial lag can be included as an error term when the error of an observation affects the error of its neighbors. More generally, spatial lags can be included asboth an independent variable and as an error term. For the choice of spatial form, we
employ the Lagrange multiplier test proposed by Mur, López, and Herrera (2010).24
Third, the initial industrial structure attributable to various factors, such as infrastructure and policies following WWII, may also affect the results. Noting that the initial
sectoral structure is constant throughout the period, we control for this effect by introducing a prefecture–sector fixed effect, αzj . This fixed effect also captures the timeinvariant prefecture–sector effects such as hysteresis.25
Finally, both factor prices and TFP are potentially endogenous because they may
be correlated with unobserved demand and/or supply shocks. In addition, factors
23

For example, see, Baldwin and Jaimovich (2012) for the analysis of free trade agreements.
Another popular test for spatial autocorrelation is Moran’s I test which investigates the correlationsof a variable among nearby locations in space. However, as pointed out by Bivand, Millo, and Piras(2021), Moran’s I provides no guidance in choosing between alternative models (e.g., a model with aspatial autoregressive term or spatial errors). Therefore, we employ the Lagrange multiplier test rather
than Moran’s I test.
25
While the prefecture–sector fixed effect controls for the time-invariant (e.g., initial) structure between
sectors, it does not control for the time-invariant structure within each sector. We address this in Section
4.2.
24

13

are mobile across prefectures. Therefore, the demand-side effect may lead to reverse
causality between the sectoral share of GDP and factor endowments. However, unlike
country–industry-level data, it is not easy to find valid instruments at the prefecture–
sector level for both nonmanufacturing and manufacturing over the period.26 Even
if we could find some valid instruments, it is difficult to combine the instrumental
variable approach with SUR and spatial interdependence simultaneously because the
SUR itself is “structural” in the sense that it forms a system of equations that reflect
the general equilibrium relationships between variables. While we acknowledge theimportance of endogeneity, we place more weight on the general equilibrium as well
as spatial aspects given the difficulty in identifying appropriate instruments and thegrowing importance of general equilibrium (e.g., Allen and Arkolakis, 2014).
Fortunately, labor mobility across prefectures is not high in Japan. This alleviates
some concern about the demand-side effects. Nevertheless, there remains a concern
about the effects of unobserved demand and/or supply shocks, which we control forby introducing a sector–period fixed effect, αjτ , where the period is defined as the 5year interval (i.e., τ = 1972–1976, 1977–1981, etc.).27
Note that even though the use of a year fixed effect is ideal, it is equivalent to including the average GDP share of sector j across all prefectures (Klemm and Van Parys,2012). If the regression equation includes both a year fixed effect (i.e., simple mean
GDP share) and a spatial autoregressive term (i.e., weighted mean GDP share) simultaneously, they will be highly correlated. Therefore, it would be difficult to identify thetrue impact of each variable.28 To address this, we follow Olney (2013) and use a 5-year
fixed effect to control for trends in the data while avoiding the issues associated withincluding a year fixed effect. Also note that for each observation, the sum of the dependent variables (the value-added shares) over all equations always equal one. Together
with the parameter restrictions, if there are N sector equations, only N − 1 are linearly
independent. In other words, the coefficients of the N -th sector can be computed fromthe coefficients of the other N − 1 sectors. We thus estimate the system of equations
26
For example, Nickell, Redding, and Swaffield (2008) utilized variables such as the share of government expenditure, the share of imported intermediate inputs, and tariffs as instruments. However, these
are available at the country level but not at the prefecture level.
27
Section 3.4 re-estimates the model with alternative fixed effects to evaluate the robustness of the results.
28
For details, see Elhorst (2010).

14

after dropping one sector (Other services) from the estimation.29
Let the spatial weighting matrix be W , that is, a Z × Z positive symmetric andnonstochastic matrix with element wzz 0 :30

w

zz 0

=




1

if regions z and z 0 are contiguous;0

if regions z and z 0 are not contiguous.

(4)

Because the analysis is based on five sectors (N = 5) and two factors (M = 2: capital KPP
and labor L), with parameter restrictions (i.e., j βjk = 0 and i γij = 0), we estimate
the following system of equations:s1zt = β01 +s2zt = β02 +s3zt = β03 +s4zt = β04 +

4
X
k=1
4
X
k=1
4
X
k=1
4
X
k=1

!

Kzt
ϕkzt pkzt
β1k ln+ γ1 ln+ λ1
ϕ5zt p5zt
Lzt

X

ϕkzt pkzt
Kzt
β2k ln+ γ2 ln+ λ2
ϕ5zt p5zt
Lzt

X

Kzt
ϕkzt pkzt+ γ3 ln+ λ3
β3k lnϕ5zt p5zt
Lzt

X

ϕkzt pkzt
Kzt
β4k ln+ γ4 ln+ λ4
ϕ5zt p5zt
Lzt

X+ α1z + α1τ + u1zt

wzm sjmtm!
wzm sjmt+ α2z + α2τ + u2ztm!
wzm sjmt+ α3z + α3τ + u3ztm!
wzm sjmt+ α4z + α4τ + u4zt ,m(5)where βjk = βkj ;Pm wzm sjmt is the spatial autoregressive term and αjz is the prefecture–

sector fixed effect. In matrix form, equation (5) is written as:31

sjt = βj Xjt + λj Wsjt + ujt

and ujt = ρj Wujt + jt .

(6)

The signs of λj and ρj are undetermined a priori because they depend upon the structure of spatial interdependence.
For each sector j, the variables are obtained at the prefecture-year level (z and t) andthus these subscripts are suppressed in matrix form. Note that the SUR considers thecorrelation of error terms between industries for a given prefecture, whereas the spatial
29

Strictly speaking, the spatial terms do not face parameter restrictions. We also re-estimate the systemof equations by dropping Other production instead of Other services as a robustness check and find thatthe signs and levels of significance of the coefficients are generally the same as those of the main results.
30
By convention, wzz = 0 for the diagonal elements.
31
In matrix form, the model with a spatial autoregressive term is written as sjt = βj Xjt + λj Wsjt + jt ;and the model with spatial errors is written as: sjt = βj Xjt + ujt and ujt = ρj Wujt + jt .

15

interdependence accounts for the correlation of the dependent variable and error term
between prefectures for a given industry. The SUR and spatial interdependence thus
focus on correlation across different dimensions.
Also note that theoretically, it is also possible to include spatial lags for the regressors (i.e., WXjt ). However, it would be technically difficult to estimate this model
because of the fixed effects (i.e., number of year and region dummies). We thus focus
on the spatial autoregressive term and spatial errors.32

2.3.2

Spatial weighting matrix

The spatial weighting matrix is constructed on whether prefectures have a common
border or are connected by bridges or by tunnels if there are seas between them.33 The
spatial weighting matrix is assumed to be the same across equations and time periods.
As is common, we use a row-standardized weighting matrix where it is normalized sothat each row sums to unity.
As an alternative, the weighting matrix could be constructed using information on
distance rather than contiguity. However, because the capital of the prefecture is notnecessarily the center of economic activity in the prefecture, it remains controversial
how to measure the distance between prefectures. To check the robustness of the results, Section 4 utilizes an alternative weighting matrix using information on highways
and railways.

2.3.3

Notes on factor mobility and factor prices

A concern is whether the neoclassical trade model is applicable to regional analysis
because factor mobility is higher within a country than between countries. However,
the model does not make any assumptions about factor mobility. Indeed, equation (2)and thus equation (5) hold irrespective of factor mobility (Redding and Vera-Martin,
2006). Nevertheless, factor mobility changes the interpretation of these relationships.
On the one hand, when factors are geographically immobile, exogenous changes in factor endowments lead to endogenous changes in production structure. Therefore, the32This in turn implies that the analysis addresses the spatial correlation of deindustrialization itself. The
spatial interdependence through regressors (e.g., productivity spillovers between prefectures) is beyond
the scope of the analysis.
33
We use data for bridges or tunnels from 2000 and most were constructed before 1990. The number ofneighboring prefectures is presented in Figure B1.

16general equilibrium relationship between production structure and factor endowments
should be interpreted in supply-side terms. On the other hand, when factors are geographically mobile, an exogenous change in demand and therefore production causes
factors to move endogenously across regions, which is a demand-side interpretation.
The equation could then reflect both demand- and supply-side effects.
In Japan at least, labor mobility is low. Fujita, Mori, Henderson, and Kanemoto(2004) pointed out that the three largest metropolitan areas (i.e., Tokyo, Osaka, andNagoya) experienced a high rate of net migration until 1970 with a peak early in the
1960s. Kiyota (2012) also showed that annual migration across prefectures was about
one percent between 1995 and 2000, which is mostly the same as the migration rates ofsome OECD countries, such as Switzerland.34 The demand-side effect does not seemto be so serious in the case of Japan.35 Note also that factor endowment is measured by
the ratio rather than the absolute value. The effect of capital and labor movement will
be mitigated if both capital and labor move from one prefecture to another prefecture
simultaneously.
In addition, the use of regional data allows us to mitigate some problems from useof cross-country data. For example, both measurement error and policy differences arelikely to be much smaller across prefectures within a country than across countries. A
similar argument can be applied to institutional differences in the labor market. Indeed,
several empirical tests of the trade model, such as Kiyota (2012), utilized prefectural
data within a country, as does this analysis.
In contrast, the disparities in factor prices across prefectures are much smaller withina country than between countries. Even so, Kiyota (2012) confirmed large wage disparities, even among prefectures, in Japan. For example, the wage rate in Kanagawa is
twice as high as the wage rate in Aomori. It is also important to note that in the neoclassical trade model, any differences in wages across prefectures should be reflectedin differences in relative factor abundance if the skill composition is the same acrossprefectures.36
34
As a result, average manufacturing wages vary across prefectures. The average manufacturing wage
rate in Kanagawa prefecture was twice as much as that in Aomori prefecture.
35
Section 3.4 employs an alternative period in the sample when labor mobility was low.
36
Section 3.4 employs alternative measure of labor input to control for the differences in skill composition across prefectures.

17

3

Results

3.1

Descriptive analysis

Before proceeding to the regression results, this subsection examines the changes in
the independent variables. Panel A in Figure 3 presents the log of average prefecture
prices by sector from 1972 to 2012, which suggest an inverse U-shape for all sectors after
peaking in the mid-1990s. However, the Manufacturing price declines more rapidly
than that for the other sectors. As a result, the Manufacturing price in 2012 was smaller
than that in 1972. Panel B in Figure 3 presents the log of TFP from 1972 to 2012 bysector. As shown, productivity increased over the period in all sectors. However, theproductivity of Manufacturing grew more rapidly than the other sectors. Because thepositive effects of productivity growth offset the negative effects of prices, the changes
in the price–productivity term (∆ ln(ϕ2 p2 )) is greater in the Manufacturing sector thanthe other sectors except for Other services, as presented in Table 1.
Panel A in Figure 4 plots the average prefecture capital–labor ratio and the average labor input between 1972 and 2012. We highlight three main observations. First,
the capital–labor ratio grew steadily over the period. Second, labor inputs declined
after the early 1990s. Finally, despite this decline in labor inputs, the growth of thecapital–labor ratio slowed from 2000. The dashed line in this figure indicates the linear
trend of the capital–labor ratio using the data from 1972 to 2000. After 2000, the actual
capital–labor ratio is below the trend line. Moreover, the gap between the actual andtrend lines increased from 2000 to 2012. This slowdown of capital accumulation may
be attributable to the expansion of FDI and/or declining opportunities for investment
given the aging and declining population in Japan.37 While these are important issues,
more detailed analyses are needed to explain them, which is beyond the scope of thispaper.
Panel B in Figure 4 presents a scatterplot of the changes in the share of value-added
and those for the Manufacturing price, Manufacturing TFP, and prefecture capital–
labor ratio from 1972 to 2012. The sectoral share of value-added is computed by eachprefecture. The results suggest a negative relationship with the changes in the Manu37

Japan’s outward FDI stock rapidly increased after 2000. In 2015, it was 1,167 billion dollars, which ismore than five times greater than in 2000 (251 billion dollars). For more details, see Greaney and Kiyota(2020, Table A2).

18

Figure 3: Changes in Sectoral Prices and Productivity, 1972–2014
Panel A: Changes in sectoral prices (value-added deflator)
0.400
0.200

-0.200-0.400-0.600-0.800-1.000Agriculture
Manufacturing-1.200

Other production
Business services-1.400

2012

2011

2010

2009

2008

2007

2006

2004

2003

2002

2001

2000

1999

1998

1997

1996

1995

1994

1993

1992

1991

1990

1989

1988

1987

1986

1985

1984

1983

1982

1981

1980

1979

1978

1977

1976

1975

1974

1973

1972

-1.600

Other services
2005

Log of price indices (2000 = 0)

0.000

Panel B: Changes in TFP
1.000

Log of total factor productivity (TFP)

0.500

0.000

-0.500Agriculture
Manufacturing-1.000

Other production
Business services

2012

2011

2010

2009

2008

2007

2006

2005

2004

2003

2002

2001

2000

1999

1998

1997

1996

1995

1994

1993

1992

1991

1990

1989

1988

1987

1986

1985

1984

1983

1982

1981

1980

1979

1978

1977

1976

1975

1974

1973

1972

Other services-1.500Notes: For Panel A, the figure presents the log of sectoral price deflators, and the price is measured relative
to the price in 2000 (ln P = 0 for 2000). For Panel B, TFP is measured relative to the geometric mean forthe prefecture in 2000.
Source: Author’s estimation using RIETI (2017) R-JIP Database.

19

Table 2: Lagrange Multiplier Test for the Existence of a Spatial Effect
Null hypothesis
No spatial effects(sjt = βj Xjt + jt )Alternative hypothesis
Spatial autoregressive term
(sjt = βj Xjt + λj Wsjt + jt )Spatial errors(sjt = βj Xjt + ujt & ujt = ρj Wujt + jt )Spatial autoregressive term & spatial errors(sjt = βj Xjt + λj Wsjt + ujt & ujt = ρj Wujt + jt )97.5(0.000)113.3(0.000)189.2(0.000)Notes: Figure in parentheses is the p-value.
Source: Author’s estimation based on the RIETI (2017) R-JIP Database.

facturing price but a positive relationship with the growth of Manufacturing TFP and
the prefecture capital–labor ratio. While only indicative, these suggest that these variables might play an important role in explaining the spatial unevenness of deindustrialization. The following subsection investigates this point further using the spatial
econometric analysis.

3.2

Model selection

Before proceeding to the spatial regressions, it is important to check whether there is
any spatial correlation. Note that there are several spatial models available. To address
this issue, we employ the Lagrange multiplier test, as mentioned in Section 2.3. The
choice of model depends on the following two steps. First, we compare the spatialmodels with an autoregressive term and/or spatial errors with that without the spatial
effect.38 Table 2 presents the results of the Lagrange multiplier test. The null hypothesisis that the model without spatial effect is valid. The alternative hypothesis is that one
or more of 1) the model with an autoregressive term, 2) the model with spatial error,and 3) the model with both autoregressive term and spatial error are valid. Table 2
indicates that the model without spatial error is rejected at the 1 percent level in all thealternatives. This result suggests the existence of a statistically significant spatial effect.
Next, we examine which spatial model is more appropriate. To inform this, we conduct a Lagrange multiplier test where the null hypothesis is that each model (either the38

The tests and estimations in this paper use the R-package spsur (version 1.0.0.4) developed by Ana
Angulo, Fernando A. López, Roman Minguez, and Jesus Mur.

20

Figure 4: Changes in the Share of Value-Added and the Capital–Labor Ratio, 1972–2012

3.500

14.55

3.000

14.50

2.500

14.45

2.000

14.40

1.500

14.35

1.000

Worker hours (million)

Average region capital-labor ratio (log value)

Panel A: Changes in prefecture capital–labor ratio

14.30

Average capital-labor ratio
Linear trend from 1972-2000 data

0.500

14.25

0.000

1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012

ln L
14.20

Panel B: Changes in the share of manufacturing value-added and key independent
variables, 1972–2012

Notes: The sectoral share of value-added is computed for each prefecture. The solid line denotes the fitted
value from ordinary least squares estimation. Gray areas denote 95 percent confidence intervals.
Source: Author’s estimation based on the RIETI (2017) R-JIP Database.

21

Table 3: Lagrange Multiplier Test for Model Selection
Null hypothesis
No spatial
Spatialautoregressive term autoregressive term&&
spatial errors
no spatial errors
Alternative hypothesis
Spatial autoregressive term
& spatial errors

98.4(0.000)123.9(0.000)Notes: Figure in parentheses is the p-value.
Source: Author’s estimation based on the RIETI (2017) R-JIP Database.

model with spatial errors but without spatial autoregressive term or the model withspatial autoregressive term but without spatial errors) is valid while the alternative hypothesis is that the model with both the spatial autoregressive term and spatial errors
is valid. Table 3 presents the results. Table 3 shows that both models reject the null
hypothesis. This supports the model with both a spatial autoregressive term and spatial errors. Based on these test results, a model with a spatial autoregressive term andspatial errors becomes the baseline model.

3.3

Main results

Table 4 presents the estimation results of the SUR model with spatial effects. We highlight four main findings. First, the Breusch–Pagan test statistic indicates that the null
hypothesis that the error terms across equations are contemporaneously uncorrelated isrejected. This suggests that a system of equations should be estimated that accounts forthe correlation of the error terms across equations. Second, the coefficients on the spatial autoregressive term are significant in Agriculture and Business services while thespatial error is significant in Agriculture, Manufacturing, and Business services. Thesesignificantly positive spatial errors suggest that the unobserved sector-year shocks arecorrelated locally rather than uniformly across prefectures in Japan.39 This confirms theimportance of spatial interdependence in explaining deindustrialization, which is hitherto unknown in the existing literature such as Redding (2002) and Nickell, Redding,and Swaffield (2008).
39

This are known as “correlated effects” (Elhorst, 2010). In the context of our analysis, correlated effects
imply that the neighboring prefectures face similar environments and thus common unobserved shocks.

22

Table 4: Regression Results: SUR With Spatial Effects
Agriculture
Relative productivity & price
Agriculture(ln(ϕ1 p1 /ϕ5 p5 ))Manufacturing(ln(ϕ2 p2 /ϕ5 p5 ))Other production(ln(ϕ3 p3 /ϕ5 p5 ))Business services(ln(ϕ4 p4 /ϕ5 p5 ))Relative endowment(ln(K/L))
Spatial autoregressive term
(Ws)
Spatial errors(Wu)
Number of observations
R-squared
Log-likelihood
Breusch-Pagan statistic

0.012***(0.002)-0.019***(0.001)0.006***(0.001)-0.003***(0.001)-0.078***(0.002)-0.266***(0.025)0.315***(0.031)
0.943

Manufacturing

Other
production

Business
services

0.172***(0.003)-0.028***0.089***(0.001)(0.001)-0.013***-0.009***(0.001)(0.001)
0.067***
0.013***(0.004)(0.002)-0.0170.022(0.018)(0.024)0.321***
0.042(0.027)(0.037)
1972
0.976
0.950
27431.9
837.4***

0.056***(0.001)0.007***(0.001)-0.235***(0.022)0.404***(0.028)0.966

Notes: Figures in parentheses are standard errors. ***, **, and * denote the significance level at 1, 5, and 10
percent, respectively.
Source: Author’s estimation based on the RIETI (2017) R-JIP Database.

23

Third, the effects of own-sector price-productivity are significantly positive in all
sectors. This suggests that increases in the own-sector price relative to the other sector
or the growth of productivity lead to the increases in the sector’s value-added share.
This is consistent with the economic priors: that is, own-sector prices and productivity have typically significantly positive effects on the share of sectoral GDP. Fourth,although the effect of factor endowment varies across sectors, there are some similarities. For instance, even though the prefecture capital–labor ratio has positive effects
in Manufacturing, Other production, and Business services, it has negative effects inAgriculture. These suggest that both Manufacturing and Business services are capitalintensive sectors whereas Agriculture and Other production are labor-intensive sectors.
Because both the own-sector price and endowment display significant coefficientsthat conform to their expected signs, the neoclassical model well explains the unevenpace of deindustrialization across prefectures within Japan. While the analysis could
identify the possible factors in explaining the regional unevenness of deindustrialization, it does not identify the relative importance of each factor. The following section
addresses this along with some other specification issues.
Note that the analysis in this paper is positive rather than normative. It thus is unable to evaluate whether deindustrialization itself is desirable or not. Nevertheless, if
rapid deindustrialization involves large adjustment costs, the welfare gains from deindustrialization will decline. In that case, the results suggest that policies to mitigate
rapid price changes or to facilitate factor movements across sectors may be helpful toaccommodate the deindustrialization process.

3.4

Alternative models

In addition to the baseline model, we estimate the following alternative models to address various concerns:
1. A model without spatial effects
2. A model with alternative fixed effects
3. A model without fixed effects
4. A model with an alternative weighting matrix

24

5. A model with an alternative measure of labor input
6. A model with an alternative sample period
This subsection briefly summarizes the concerns and results. More detailed results arepresented in Appendix D.
The first concern is how the results change if the analysis ignores the spatial effect.
To respond to this question, we estimate the system of equations assuming no spatial
effects. The results indicate that all the estimated coefficients, except for the coefficientson the spatial terms that are excluded from the regression, provide the same signs andsignificance levels (Table D1).
However, the magnitudes are slightly different. For example, for Manufacturing,the coefficient for the prefecture capital–labor ratio declines from the baseline model tothe model without spatial effects. This suggests that the coefficients on these variables
will be underestimated if spatial effects are not considered.
The second concern is that the use of a sector–5-year fixed effect may not be sufficient to control for the movement of labor or unobserved demand and/or supply
shocks more generally. However, it is difficult to include both a year fixed effect anda spatial autoregressive term simultaneously (see Section 2.3). To check the sensitivityof the results while avoiding multicollinearity, we specify a 2-year fixed effect insteadof 5-year fixed effect, which allows us to account for short-term unobserved economic
shocks. The results indicate that the sign and significance level of the coefficients show
little difference from those for the baseline results (Table D2). This reassures us about
the robustness of our results when the analysis considers short-term demand and/or
supply shocks.
The third concern is whether the results change when the analysis excludes prefecture–
sector and sector–5-year fixed effects. To address this concern, we re-estimate the system of equations after removing these fixed effects. The estimation results indicate thatsome of the coefficients have different signs from those of the baseline model (Table
D3). These suggest the importance of controlling for unobserved prefecture–sector andsector–period fixed effects.
The fourth concern is whether the weighting matrix employed in the baseline analysis is appropriate. In the baseline analysis, the spatial weighting matrix is constructed,

25

based on whether the prefectures are contiguous. In Japan, all prefectures are connected by roads if they have common borders. Nevertheless, the existence of a roadconnection does not necessarily infer large transactions between these prefectures because some prefectures are connected by only minor roads.
For example, Nagano prefecture, which is surrounded by mountains, is contiguouswith eight other prefectures, the most of any prefecture. However, three of these prefectures are connected by neither highways nor railways, just ordinary roads. It may
thus be difficult to imagine that Nagano prefecture is equally interdependent with its
eight neighboring prefectures. To address issue, we use an alternative weighting matrix, defining contiguity only when prefectures are directly connected by highways or
railways.
The results indicate that while the spatial effects become insignificant for Businessservices, the sign and significance levels are the same for all sectors (Table D4). Moreover, the estimated coefficients are almost the same as those of the baseline results for
Manufacturing, except for the coefficients of spatial terms. The results are thus robust
even when contiguity is defined as highway and railway connections.
The fifth concern lies in the measurement of the labor input in the baseline analysis.
Although the baseline analysis does not consider differences in skill composition between prefectures, deindustrialization may also be affected by skill abundance. As discussed, labor is not disaggregated by skills in the 2017 R-JIP Database. To crudely consider the differences in skill composition across prefectures, we use total wages rather
than work hours at the prefecture level as the measure of labor endowment. Hsieh andKlenow (2009) also employ this approach to consider the differences in hours worked
and human capital. The data on total wages by prefecture are also available in the 2017
R-JIP Database.
The estimation results using the alternative measure of labor input indicate thatthe estimated coefficients are again mostly the same as those of the baseline resultsfor Manufacturing (Table D5). One notable difference is that the coefficient for the
spatial autoregressive term becomes significantly positive. This suggests that the effectof spatial interdependence is more evident given skill difference in the labor input.
Otherwise, the baseline results are mostly robust.
The final issue is the effect of labor mobility. Although the size of migration de26

clined after 1970, Fujita, Mori, Henderson, and Kanemoto (2004) found that the Tokyo
metropolitan area experienced a high rate of net migration around the mid-1980s. The
estimation results thus may be affected by labor mobility. Unfortunately, it is difficult
to control for the effect of factor mobility in this framework. As a compromise, we estimate the model, focusing only on the latter half of the sample period (i.e., between
1992 and 2012) when labor mobility was lower than the first half of the sample period.
From the estimation results (Table D6), we can see that the estimated coefficients arealmost the same as those of the baseline results for Manufacturing. A notable differenceis that the coefficient for the spatial autoregressive term is now significant. The effectof spatial interdependence is thus more evident in the more recent period.
In this regard, the data may not reflect current fast-changing realities because thesample period in the 2017 R-JIP Database ends in 2012. The latest version of the 2021
R-JIP Database was released in March 2022 (RIETI, 2022).40 The 2021 R-JIP Database
was substantially revised from the previous version (i.e., 2017 R-JIP Database). For
example, the sample period of 2021 R-JIP Database is 1994–2018, which is significantly
shorter than the sample period of the previous version (i.e., 1972–2012 in the 2017 R-JIP
Database). The changes in the share of manufacturing value-added were also small
after 2012 in Japan (on average, 21.6 percent in 2012 to 23.0 percent in 2018).
Because the 2021 R-JIP Database is not directly comparable to the 2017 R-JIP Databasegiven the changes in the data compilation, the data cannot be extended from 1972–2012
to 1972–2018. Accordingly, given our focus is the long-run (over four decades) changes
in manufacturing, we present the results using the 2021 R-JIP Database as a further
robustness check.
The estimation results (Table D7) indicate that the estimated coefficients are generally the same as those of the baseline results for Manufacturing. However, there are
two notable differences. First, the coefficient for the capital–labor ratio is insignificant
for manufacturing. As confirmed in Panel A in Figure 4, capital accumulation in Japanslowed after 2000. This may suggest that with the growth of other countries like China,
Japan is losing its earlier comparative advantage in capital-intensive sectors. Second,
like the results using the alternative measure of labor input, the coefficient of the spa40

Unlike the country-level JIP Database, the regional-level JIP Database is not updated as frequently.
For details, see https://www.rieti.go.jp/en/database/r-jip.html

27

tial autoregressive term become significantly negative. This implies that the effect of
spatial interdependence becomes more important recently. However, the main findingof the analysis is unchanged, even when we focus on a more recent period.

4

Discussion

4.1

Economic magnitude

The estimation results confirm the statistically significant effects of spatial interdependence. Another important question is how large the spatial effects are because statistically significant results do not necessarily infer economically significant results. Notethat based on the estimated coefficients, the regression equation is written as:sjzt = β̂0j +

X

+λ̂j

X

β̂jk lnkKzt
ϕkzt pkt+ γ̂j ln
ϕ5zt p5zt
Lzt!

wzm sjmt(7)+ α̂jz + α̂jτ + ρ̂ujzt + εjzt .

m

The second term can be decomposed into the price and productivity terms. Taking thedifference between t = 0 and t = T , it is possible to decompose the changes into theshare of manufacturing GDP to the effects of prices, productivity, and endowments aswell as the spatial effect:41

∆sjzT

=

X

β̂jk ∆ ln|k{z

ϕkzT XpkzT
β̂jk ∆ ln
+
ϕ5zT
p5zT
} |k
{z
}

Productivity effect+ γ̂j ∆ ln(KzT /LzT ) +{z}|
Endowment effectPrice effect∆α̂jτ| {z }

Period effect+ λ̂∆W sjzT + ρ̂∆ujzT + ∆εjzt ,|{z} | {z }Spatial effect

(8)

Error

where ∆ is the difference between t = 0 and t = T . In this exercise, we focus on
the changes between 1972 and 2012. The estimated coefficients are based on the main
results in Table 4. Note that as mentioned in footnote 10, any effects of preferences
including nonhomothetic preferences will appear through relative prices because themodel does not make any assumptions on consumer preferences.
Figure 5 presents the decomposition results of equation (8) for manufacturing in
41

Other studies employ a similar decomposition exercise. For example, see, Harrison and McMillan(2011) and Kambayashi and Kiyota (2015).

28

Japan as a whole and by prefecture. For ease of explanation, we suppress the changes
in the error term. The major findings are threefold. First, in Japan as a whole (i.e.,
JAPAN in Figure 5), the negative price and period effects outweigh the positive effects
of productivity and endowment. In particular, the negative contribution of price islarge. As a result, the share of Manufacturing GDP declined. The large negative period
effect suggests the importance of unobserved period-specific factors, such as demand
and/or supply shocks.
Second, at the prefecture level, the price and productivity effects exhibit larger variations than the endowment and period effects. This suggests that the contribution ofthese effects varies across prefectures. This in turn implies that the large variation indeindustrialization within a country is attributable to differences in productivity andprice changes across prefectures. In contrast, the effect of the slowdown in capital
accumulation (Panel A in Figure 4), at least partly from the expansion of FDI or offshoring, appears not in specific prefectures but is common to all prefectures. Note thatthe variation in the changes in productivity and price across prefectures arises fromthe differences in the composition of industry within manufacturing. Prefectures withindustries that face sharp price declines and/or exhibit slow productivity growth are
more likely to deindustrialize. The following subsection discusses this in more detail.

29

30
endowment

Source: Author’s estimation based on the RIETI (2017) R-JIP Database.

period30

JAPANproductivity
price

Notes: JAPAN is the prefecture average for Japan. Manufacturing value-added is based on current prices.

-0.600-0.400-0.200

0.000

0.200

0.400

0.600
spatialtotal

Figure 5: Changes in the Share of Manufacturing Value-Added by Prefecture: Decomposition by Contribution

Decomposition of the changes in the share of manufacturing value added(% point)

Kanagawa
Tokyo
Saitama
Osaka
Chiba
Wakayama
Hyogo
Kyoto
Tottori
Ishikawa
Nara
Mie
Okayama
Okinawa
Niigata
Aichi
Hiroshima
Ehime
Gifu
Fukuoka
Fukui
Ibaraki
Hokkaido
JAPANToyamaNagasaki
Kochi
Iwate
Tochigi
Yamaguchi
MiyagiShizuoka
Gumma
KagawaNaganoShimaneFukushima
Tokushima
Miyazaki
Shiga
Kagoshima
Akita
Yamagata
Kumamoto
Yamanashi
Saga
AomoriOita

Finally, the effect of spatial interdependence also matters. At first sight, the average
spatial effect looks small in Japan as a whole. However, this is because the prefecturelevel positive and negative effects offset each other. Indeed, the spatial effect has bothlarge positive and negative effects in some prefectures. This suggests that the deindustrialization of a particular prefecture could also affect neighboring prefectures. It is
important to note that the spatial effect here is measured at the prefecture level. Therefore, even though our analysis captures the spatial interdependence across prefectures,
it cannot capture the spatial interdependence within a prefecture across cities or towns.
The spatial effect may then be more important in a detailed geographic classification.

4.2

Do the changes in industry composition within Manufacturing matter?

In this paper, we focus on the changes in the share of manufacturing value-added as awhole. A concern may then be that the changes in productivity and prices reflect thechanges in the composition of industries within the Manufacturing sector rather thanchanges in the productivity and prices themselves because the Manufacturing sector
includes 13 industries in the R-JIP Database.
Figure 6 presents the changes in the share of manufacturing value-added by prefecture. The solid line is the total changes in the Manufacturing sector, which equals
the vertical difference between 1972 and 2012 in Figure 2 for each prefecture. The prefectures are sorted from left to right, based on the changes in the total share of the
Manufacturing sector from 1972 to 2012.

31

32

Changes in the share of manufacturing value-added (% point)

Nara

Ishikawa

Tottori

Hyogo
Kyoto

Wakayama

Osaka

Chiba

Saitama

Kanagawa

Tokyo

Food and beverages
Petroleum and coal products
General machinery
Other manufacturing

IbarakiFukuoka
Fukui

Ehime
Gifu

Hiroshima

Niigata

Aichi

Okayama

Okinawa

Textile mill products
Ceramics, stone and clay
Electrical machinery
All manufacturing

Mie

Source: Author’s estimation based on the RIETI (2017) R-JIP Database.

JAPAN

32

Shizuoka

Miyagi
Tochigi

Iwate
Kochi
ToyamaPulp and paper
Basic metal
Transport equipment

Yamaguchi

Hokkaido

Notes: JAPAN is the prefecture average for Japan. Manufacturing value-added is based on current prices.

-0.350-0.300-0.250-0.200-0.150-0.100-0.050

0.000

0.050

0.100

JAPAN

Nagasaki

0.150

Yamanashi

Kumamoto

Yamagata

Kagoshima

Akita
Miyazaki

Shiga
Tokushima

Fukushima

Chemicals
Processed metals
Precision instruments

Oita

Saga
ShimaneKagawaNaganoGumma

Figure 6: Changes in the Share of Manufacturing Value-Added by Prefecture: Decomposition by Industry

Aomori

There are two notable findings in Figure 6. First, for Japan as a whole (i.e., JAPANin Figure 6), the value-added share declined in all manufacturing industries except formachinery industries (i.e., General machinery, Electrical machinery, Transport equipment, and Precision instruments). This suggests that the declining share of valueadded is a trend common to almost all manufacturing industries in Japan. Second,although it is not easy to identify a common pattern across prefectures, changes in industry structure suggest that the changes in aggregate productivity and prices are fromthe changes in the composition of industries rather than the changes in productivity
and prices themselves.
To address this further, we apply the alternative decomposition exercise developed
by Foster, Haltiwanger, and Krizan (2001). Let Z be the Manufacturing productivity or
price aggregated from more detailed manufacturing industries. Denote each detailed
manufacturing industry as f . Define the productivity or price at the aggregate manufacturing level as:
ln Zt ≡

X(9)

vf t ln zf t ,fwhere vf t is the share of value-added industry f at year t and zf t is either productivity
or price of industry f at year t. Following Foster, Haltiwanger, and Krizan (2001),
decompose the aggregate growth of the Manufacturing variable from t − 1 to t, ln Zt −ln Zt−1 , as follows:ln Zt − ln Zt−1 'Xvf,t−1 ∆ ln zf t

f

{z

|
+

}

Within effectX X∆vf t ln zf,t−1 − ln zt−1 +∆vit ∆ ln zf t ,

f

|

(10)

f

{z

Between effect

}

|

{z

Covariance effect}where ∆ is the difference between year t − 1 and year t. An upper bar denotes thearithmetic average.
This decomposition consists of three parts. The first term is a within-industry component based on changes in each industry, weighted by the value-added share in yeart − 1. Because this reflects the change within each industry, it is called the “within effect.” The second term represents a between-industry component that reflects changing
value-added shares, weighted by the deviation of each industry in year t − 1 from the33average. An increase in the value-added share contributes positively to the betweenindustry component only when the industry has higher productivity or price than average in year t − 1. This is a “between effect” because it reflects the reallocation of
resources between industries. The final term represents a covariance term and is the“covariance effect.” This term makes a positive contribution if industries that increased
productivity or price were more likely to do so by generating additional value-added.
If the changes in aggregate manufacturing are driven by changes in the composition ofindustries, a large contribution of the between effect is expected.
Table 5 presents the decomposition results. We highlight two main findings. First,
productivity growth is primarily from the within effect. This implies that the changes
in industry composition do not have a significant effect on the growth of aggregate
manufacturing productivity. Second, in contrast, the changes in the price of aggregate
manufacturing are mainly from the covariance effect, not the between effect. This suggests that the changes in industry composition within manufacturing alone cannot be
the main source of changes in the aggregate manufacturing price. In other words, notonly the changes in industry composition but also those in prices affect the changes in
the aggregate manufacturing price.
Table 5: Decomposition of the Effects for Manufacturing: Industry Composition
Total
Within Between Covariancechange effecteffecteffect
TFP
1.779
1.648
-0.1150.247
Price -0.065
0.012
0.070
-0.147
Source: Author’s estimation based on the RIETI (2017) R-JIP Database.

4.3

Where does this price change come from?

The previous subsections showed that the negative contribution of price is large andthat the changes in industry composition within manufacturing alone cannot be themain source of changes in the aggregate manufacturing price. One may then ask why
the price effect is so large. While identifying the source of the declining price itself
is a major concern in Japan, for which more detailed analysis is required, this subsection briefly discusses several reasons implied by both the findings of this study andprevious studies.

34

There are at least five possibilities. The first is transportation costs because they
have continuously declined over time (Anderson and van Wincoop, 2004). What is
puzzling, however, is that the sectoral prices changed nonmonotonically over the period. The changes in the sectoral prices indicated an inverse U-shape (Figure 3), which
does not correspond to the continuous decline in transportation costs. Accordingly, although the change in transportation costs could be one of the factors, there seems to be
more important ones.
The second is the effect of technology growth, which enables firms to reduce their
marginal costs. If technology growth is more rapid in manufacturing than other sectors,
this may result in the decline of relative manufacturing prices. However, our analysis
has already considered the effect of technology growth by introducing TFP into theregression analysis. Therefore, the effect of technology growth on relative price seems
to be, if anything, marginal.
The third possible reason is the effect of deflation. Following the second half of the
1990s, Japan suffered a period of prolonged deflation, in which the consumer price index has declined in general (Watanabe and Watanabe, 2018). Thus, one may argue thatthe declining manufacturing price is attributable to deflation. However, the analysis
covers the period between 1972 and 2012, which includes not only a deflation period
but also an inflation period. Indeed, among five sectors in the analysis, only the Manufacturing sector experienced a decline in price over the period between 1972 and 2012
(Table B3). More importantly, the manufacturing price is measured as the price relative
to that in Other services. In that sense, the key question may be why the price of manufacturing declines more rapidly than in Other services. Although deflation can explain
the decline in absolute price of manufacturing (i.e., p2zt ), it does not necessary explain
the decline in the relative price of manufacturing (i.e., p2zt /p5zt ).
The fourth reason is the effect of imports from low-wage countries that produce
less-expensive goods than high-wage countries.42 The domestic manufacturing price
may also decline as imports from low-wage countries expand. Noting that imports
affect tradable goods only, it is plausible that the decline in the relative price of manu42

In this sense, one may be concerned about the effects of the decline in export prices because Japaneseterms of trade (i.e., the ratio of export to import prices) declined over the period. However, this is attributable to the increases in import prices rather than a decline in export prices, where the increases inimport prices are attributable to a rise in the price of the natural resources (e.g., oil). Therefore, the effectsof the decline in export prices do not seem to be a strong reason.

35

facturing can be attributed to increasing imports from low-wage countries. Besides, thedecline in the aggregate manufacturing price started in the mid-1990s (Figure 3), whichcoincides with the establishment of the World Trade Organization. Indeed, Zeng andZhao (2010) developed a theoretical model showing that globalization causes deindustrialization.43 Dauth and Suedekum (2016) found that deindustrialization was driven
by increases in international trade. Our results are also consistent with their findings. However, Broda and Weinstein (2010) found that the effect of Chinese exports
on Japanese prices was small between 1992 and 2005. Their analysis can be improved
because they address a shorter period than in this analysis and focus only on imports
from China. In sum, the effects of imports on domestic price remain ambiguous. Moredetailed analysis is needed.
The fifth reason is the declining markup. Several studies have pointed out the declining markup of Japanese firms. For example, Kiyota, Nakajima, and Nishimura(2009) concluded that the average markup of Japanese firms declined from the 1970s
and 1980s to the 1990s. Similarly, Kiyota (2018) showed that the markup of Japanesemanufacturing firms declined between 1995 and 2012 based on study by Dobbelaere
and Kiyota (2018). A more recent study by Nakamura and Ohashi (2019) also indicateda slight decline in the markup of Japanese manufacturing firms from 2001 to 2016.
Because the analysis in this paper relies on neoclassical trade theory, price does not include markup. However, the actual data may include markup. The declining relative
price of manufacturing may thus be attributable to the declining markup of Japanesefirms due to, for example, increasing competition among firms.
In sum, the decline in markup of Japanese manufacturing firms is one of the possible reasons explaining the large negative price effect on deindustrialization. Increasing
imports from low-wage countries is another possible reason. In contrast, other factors
such as technology growth, deflation, and the changes in transportation costs do notseem to be strong reasons. However, more detailed analysis is needed to explain why
the relative price of manufacturing has declined so rapidly.
43
Their model is based on a new economic geography model while our empirical framework is basedon a neoclassical trade model. Although the results are consistent with the implications of their model,
we do not necessarily test the empirical validity of their model.

365Concluding Remarks

The declining share of manufacturing value-added, often called “deindustrialization,”is becoming a major concern for policymakers as well as academic researchers, especially in high-income countries. Compared with country-level analysis, however, theregional-level analysis of deindustrialization within a country remains limited. Against
this background, this paper empirically examines how and why deindustrialization
patterns vary across regions within a country. Our theoretical and empirical approachis based on a series of studies by Redding and colleagues (Redding, 2002; Redding
and Vera-Martin, 2006; Nickel, Redding, and Swaffield, 2008), which analyzed crosscountry specialization patterns, building upon neoclassical trade theory. The contribution of this study is to: 1) consider the spatial interdependence of deindustrialization
across regions using spatial econometric techniques and 2) quantify the contribution of
those factors that could affect deindustrialization.
Focusing on regions in Japan over the last four decades, we found that the large
variation of deindustrialization within a country is attributable to differences in productivity and price changes across prefectures. This implies that prefectures with manufacturing industries that face sharp price declines and/or exhibit slow productivity
growth are more likely to deindustrialize. In contrast, it appears that the effect of
the slowdown of capital accumulation, partly caused by the expansion of FDI or offshoring, is common to all prefectures rather than to specific prefectures. The effect of
spatial interdependence is not only statistically significant but also nonnegligible interms of its magnitude. This confirms the importance of the spatial interdependence
in explaining deindustrialization, which is unknown in the existing literature such as
Redding (2002) and Nickell, Redding, and Swaffield (2008). Another important finding is that the changes in aggregate manufacturing productivity and price cannot be
attributable to the change in industry composition within manufacturing alone. Such
price changes in manufacturing may come from several factors such as increasing competition from low-wage countries and declining markups. However, more detailed
analysis is needed to explain why the relative price of manufacturing has declined
rapidly.
These findings also have an important policy implication in that the decline in the37manufacturing share can be mitigated by productivity growth, as the largest variationin deindustrialization is attributable to differences in productivity and price changes.
It is important to note that productivity is measured at the sector level rather than at
the firm level. This is important as sectoral productivity growth is not only achievable through the productivity growth of firms, but also through the entry of more productive firms and the exit of less productive firms (Nishimura, Nakajima, and Kiyota,
2005). Even though deindustrialization itself is inevitable for advanced countries, it isimportant for policymakers to recognize that its shock can be accommodated by theturnover of firms along with the productivity growth of existing firms.
This study also has some limitations. First, the main contributions of this study are
empirical, and we acknowledge that the paper lacks theoretical innovation. Second, theanalysis does not address potential endogeneity because of technical difficulty in developing a SUR including a spatial effect. Nonetheless, this paper contributes majorly
to the literature by introducing a new technique and presenting new findings.
Before closing, we point out several remaining research challenges. First, addressing the potential endogeneity in the SUR with the spatial effect is an important issue.
To do so, more advanced econometric techniques are required. Second, another interesting research avenue would be to investigate the sources of the price effects ingreater detail. Identifying the sources of these price changes will have useful implications for policymakers as well as academic researchers. Finally, it is important to investigate adjustment mechanisms in more detail at the micro level using, for example,
establishment-level data.44 The construction of establishment-level panel data covering both manufacturing and nonmanufacturing industries would enable us to address
this and other concerns in future research.

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In this context, Fort, Pierce, and Schott (2018) decomposed the decline in US manufacturing employment into decline caused by the exit of plants and decline caused by the contraction of continuing plants.

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43

A

Derivation of equation (2)This appendix explains the derivation of equation(2) from equation (1). To simplifyP
the notation, denote revenue function as r = j pj yj . We drop the subscript z and t forease of exposition. Taking the log of revenue and differentiating it with respect to thelog of price i, we have:
pj dr
pj
pj yj
d ln rdr pj=== yj == sj ,
d ln pj
r dpj
r dpj
r
r

(A1)

where sj is the revenue share of industry j, which corresponds to the left-hand-side ofequation (2).
To further simplify the notation, drop productivity term ϕ for the moment, andrewrite the revenue function as:
X
1 XX
r = β00 +β0j xj +βjk xj xk
2
j
j
k
XX
X
1 XX
δih zi zh +γji xj zi ,(A2)+
δ0i zi +
2
i

i

j

h

i

where xj = ln pj and zh = ln vi . Differentiating the revenue function with respect to xj(= the log of pj ), the intercept β00 and the first and the second terms in the second line
in equation (A2) disappear because these terms do not have xj . Also note that
• Second term:X

β0j xj = β01 x1 + β02 x2 + ... + β0j xj .

(A3)

j

From d ln r/d ln xj , the second term = β0j .
• Third term:
1 XX
1
βjk xj xk = (β1j x1 xj + β2j x2 xj + ... + βj1 xj x1 + ... + βjk xj xk + ...) .
2
2
j

k

Because βjk = βkj , from d ln r/d ln xj , the third term becomes:X1(2βj1 x1 + 2βj2 x2 + ... + 2βjk xk + ...) =βjk xk .
2

(A4)

k

• Last term:XXγji xj zi = γ11 x1 z1 + ... + γ1i x1 zi + ... + γj1 xj z1 + ... + γji xj zi + ... (A5)jiFrom d ln r/d ln xj , the last term becomes:
γj1 z1 + ... + γji zi + ... =X

γji zi .

(A6)

iFrom equation (A1) and these three terms, we have:XX
sj = β0j +βjk xk +γji zi .
i

k

44

(A7)

Return the productivity term and subscripts z and t into this equation. Add an error
term. Then equation (2) can be derived from equation (1).

B

Data Appendix
Figure B1: Number of Prefectures With Common Borders

Notes: If two regions have a common border or are connected by bridges or tunnels, they are counted.
Colors are based on the number of neighboring regions. A darker color indicates a region with a larger
number of common borders. The Japanese map data are from https://gadm.org/.
Source: RIETI (2017) R-JIP Database.

45

Figure B2: Number of Prefectures With Common Borders: Alternative Definition

Notes: Prefectures are regarded as having common borders only when they are connected by highways
or railways. For other notes and sources, see Table B2.

46

Table B1: Industry Classification
Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23

Industry
Agriculture, forestry, and fisheries
MiningFood and beverages
Textile mill products
Pulp and paper
ChemicalsPetroleum and coal products
Ceramics, stone and clay
Basic metal
Processed metals
General machinery
Electrical machineryTransport equipment
Precision instruments
Other manufacturing
Construction
Electricity, gas and water utilities
Wholesale and retail trade
Finance and insurance
Real estateTransport and communications
Non-government other services
Government other services

Source: RIETI (2017) R-JIP Database.

47

SectorAgriculture
Other production
Manufacturing
Manufacturing
Manufacturing
Manufacturing
Manufacturing
Manufacturing
Manufacturing
Manufacturing
Manufacturing
Manufacturing
Manufacturing
Manufacturing
Manufacturing
Other production
Other production
Other services
Business services
Business services
Other services
Other services
Other services

Table B2: Prefecture Classification
Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24

Prefecture nameHokkaido
Aomori
Iwate
Miyagi
Akita
Yamagata
Fukushima
IbarakiTochigi
Gunma
Saitama
Chiba
Tokyo
Kanagawa
NiigataToyamaIshikawa
Fukui
Yamanashi
NaganoGifu
Shizuoka
Aichi
Mie

Number
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47

Source: RIETI (2017) R-JIP Database.

48

Prefecture name
Shiga
Kyoto
Osaka
Hyogo
Nara
Wakayama
Tottori
Shimane
Okayama
Hiroshima
Yamaguchi
Tokushima
KagawaEhime
Kochi
Fukuoka
Saga
Nagasaki
Kumamoto
Oita
MiyazakiKagoshima
OkinawaTable B3: Summary Statistics: Average of Levels Across Prefectures by Year
Agriculture
Value-added share
Log of priceLog of productivity
Manufacturing
Value-added share
Log of priceLog of productivity
Other production
Value-added share
Log of priceLog of productivity
Business services
Value-added share
Log of priceLog of productivity
Other services
Value-added share
Log of priceLog of productivity
Region level endowment
Log of capital stock
Log of laborLog of capital–labor ratio

s
ln P
ln ϕ
s
ln P
ln ϕ
s
ln P
ln ϕ
s
ln P
ln ϕ
s
ln P
ln ϕ
ln K
ln L
ln K/L

1972
0.092-0.628-0.0521972
0.305-0.569-0.0601972
0.139-1.379-0.0521972
0.065-0.726-0.0601972
0.400-1.060-0.0521972
15.21814.451
0.767

1982
0.056
0.024
-0.0541982
0.268-0.019-0.0571982
0.146-0.390-0.052
1982
0.069-0.031-0.0511982
0.461-0.281-0.0471982
15.89714.488
1.409

1992
0.038
0.148
-0.055
1992
0.274
0.106
-0.0531992
0.146-0.026-0.051
1992
0.068
0.033
-0.0551992
0.473-0.008-0.0481992
16.40814.508
1.900

2002
0.028
-0.092-0.057
2002
0.234-0.039-0.0512002
0.123-0.033-0.0482002
0.070-0.015-0.051
2002
0.545-0.035-0.047
2002
16.69214.383
2.308

2012
0.025
-0.167-0.0572012
0.222-0.619-0.0502012
0.099-0.078-0.0472012
0.058-0.152-0.052
2012
0.596-0.112-0.0472012
16.69714.3252.371∆ 1972-2012-0.0670.461-0.005∆ 1972-2012-0.083-0.0490.010∆ 1972-2012-0.0401.301
0.005∆ 1972-2012-0.0060.574
0.008∆ 1972-2012
0.197
0.947
0.004
∆ 1972-2012
1.478-0.1261.604

Note: ∆ 1972–2012 indicates the difference in each variable from 1972 to 2012.
Source: Simple average across regions for price and productivity. Author’s calculation, based on the RIETI(2017) R-JIP Database.

C

Measurement of TFPApproximating constant returns to scale production technology with a translog functional form, this superlative index number evaluates productivity in each prefecture
and year relative to a hypothetical average prefecture in the sector. Let Y, L, K denote
the real value-added, labor input (hours worked), and real capital stock, respectively.
Denoting the geometric mean of the variables as an upper bar, this relative TFP is written as follows:
Yzjt
Lzjt
Kzjt
− σzjt ln− (1 − σzjt ) ln
Ȳjt
L̄jt
K̄jt
Ȳjt
L̄jt
K̄jt
+ ln
− σ̄jt ln− (1 − σ̄jt ) ln
,
Ȳj0
L̄j0
K̄j0

ln ϕzjt = ln

(C1)

where σzjt = 1/2 · (czjt + c̄jt ) is the average of labor share in total cost in prefecture z(czjt ) and the arithmetic mean labor share (c̄jt ); σ̄jt = 1/2 · (c̄jt + c̄j0 ). Note that, fora given year t, the productivity of sector j in prefecture z is measured relative to the(geometric) average productivity of sector j in all prefectures in Japan in year 0. Thus,49

if the estimated productivity of sector j in prefecture z is greater (smaller) than zero, its
productivity is greater (smaller) than the average productivity of sector j in Japan in thebenchmark year. We set 2000 as the benchmark year (i.e., ln ϕzjt = 0 if t = 2000). Thismeans that TFP is measured relative to the hypothetical average prefecture in 2000. We
set 2000 as the benchmark year (i.e., ln ϕzjt = 0 if t = 2000). This means that TFP is
measured relative to the hypothetical average prefecture in 2000.

D

Alternative Models

D.1

Alternative specifications

The baseline results in Section 3.3 indicate the statistically significant effect of spatial
interdependence. However, one may be interested in how the results change if theanalysis ignores the spatial effects. To respond, we estimate the system of equations
assuming no spatial effects. Table D1 provides the results. The results are like those of
the baseline model. The Breusch–Pagan test statistic indicates that the null hypothesisthat error terms across equations are contemporaneously uncorrelated is rejected. All
the estimated coefficients, except for the coefficients on spatial terms that are excluded
from the regression, yield the same signs and significance levels.
Table D1: Regression Results: SUR With No Spatial Effects

Relative productivity & price
Agriculture(ln(ϕ1 p1 /ϕ5 p5 ))Manufacturing(ln(ϕ2 p2 /ϕ5 p5 ))Other production(ln(ϕ3 p3 /ϕ5 p5 ))Business services(ln(ϕ4 p4 /ϕ5 p5 ))Relative endowment(ln(K/L))
Spatial autoregressive term
(Ws)
Spatial errors(Wu)
Number of observations
R-squared
Log-likelihood
Breusch-Pagan statistic

Agriculture

Manufacturing

Other
production

Business
services

0.012***(0.002)-0.021***(0.002)0.006***(0.001)-0.003***(0.001)-0.073***(0.002)n.a.

0.179***(0.003)-0.029***(0.001)-0.015***(0.001)
0.046***(0.003)n.a.

0.089***(0.001)-0.008***(0.001)0.014***(0.002)n.a.

0.055***(0.001)0.007***(0.001)
n.a.

n.a.

n.a.

n.a.

n.a.

0.950

0.961

1972
0.973
27281.7
910.2***

0.936

Notes: Figures in parentheses are standard errors. ***, **, and * denote the significance level at 1, 5, and 10
percent, respectively.
Source: Author’s estimation based on the RIETI (2017) R-JIP Database.

However, the magnitudes are slightly different. For example, for Manufacturing,the coefficient on the prefecture capital–labor ratio (i.e., ln(K/L)) declines from 0.067
in the baseline model to 0.046 in the model without spatial effects. Given that these50coefficients have small standard errors, these results suggest that the coefficients onthese variables will be underestimated if spatial effects are not considered.
One may then argue that the use of the sector–5-year fixed effect may not be sufficient to control for the movement of labor or for unobserved demand and/or supply
shocks more generally. However, it is difficult to include both a year fixed effect and a
spatial autoregressive term simultaneously (see Section 2.3). To check the sensitivity of
the results while avoiding multicollinearity, we use a sector–2-year fixed effect insteadof sector–5-year fixed effect, which allows us to account for short-term unobserved
economic shocks. Table D2 presents the results. The results indicate that the sign andsignificance level of the coefficients present little difference from those in the baseline
results. This reassures the robustness of the results even when the analysis considers
the short-term demand and/or supply shocks.
Table D2: Regression Results: SUR With Sector–2-Year Fixed EffectAgriculture
Relative productivity & price
Agriculture(ln(ϕ1 p1 /ϕ5 p5 ))Manufacturing(ln(ϕ2 p2 /ϕ5 p5 ))Other production(ln(ϕ3 p3 /ϕ5 p5 ))Business services(ln(ϕ4 p4 /ϕ5 p5 ))Relative endowment(ln(K/L))
Spatial autoregressive term
(Ws)
Spatial errors(Wu)
Number of observations
R-squared
Log-likelihood
Breusch-Pagan statistic

0.015***(0.002)-0.026***(0.002)0.006***(0.001)-0.003***(0.001)-0.072***(0.003)-0.277***(0.032)0.217***(0.037)
0.935

Manufacturing

Other
production

Business
services

0.176***(0.003)-0.027***0.088***(0.001)(0.001)-0.012***-0.010***(0.001)(0.001)0.080***
0.005**(0.004)(0.002)0.018-0.013(0.017)(0.023)0.071**-0.088**(0.030)(0.037)
7708
0.977
0.954
27533.3
851.6***

0.054***(0.001)0.004***(0.001)-0.238***(0.024)0.362***(0.030)0.966

Notes: Figures in parentheses are standard errors. ***, **, and * denote the significance level at 1, 5, and 10
percent, respectively.
Source: Author’s estimation based on the RIETI (2017) R-JIP Database.

In this context, one may also ask how the results change when the analysis excludes
prefecture–sector and sector–5-year fixed effects. To address this, we estimate the system of equations after dropping these fixed effects (i.e., αzj , αjτ ). Table D3 indicatesthe estimation results, which are different from the baseline results. For example, for
Manufacturing, the coefficient on the prefecture capital–labor ratio (i.e., ln(K/L)) turns
negative. This implies that the Japanese manufacturing sector is labor-intensive, which
is not easy to explain. Moreover, the coefficient on the own-sector price-productivity
term (i.e., ln(ϕ2 p2 /ϕ5 p5 )) increases from 0.172 to 0.221. The results suggest the importance of controlling for the unobserved prefecture–sector and sector–period fixed
effects.

51

Table D3: Regression Results: SUR With Spatial Effects/No Fixed Effects
Agriculture
Relative productivity & price
Agriculture(ln(ϕ1 p1 /ϕ5 p5 ))Manufacturing(ln(ϕ2 p2 /ϕ5 p5 ))Other production(ln(ϕ3 p3 /ϕ5 p5 ))Business services(ln(ϕ4 p4 /ϕ5 p5 ))Relative endowment(ln(K/L))
Spatial autoregressive term
(Ws)
Spatial errors(Wu)
Number of observations
R-squared
Log-likelihood
Breusch-Pagan statistic

0.032***(0.001)-0.021***(0.001)0.009***(0.001)-0.013***(0.000)-0.026***(0.001)-0.043***(0.016)
0.108***(0.030)0.827

Manufacturing

Other
production

Business
services

0.221***(0.002)-0.040***0.105***(0.001)(0.001)-0.020***-0.010***(0.000)(0.001)-0.032***0.012***(0.002)(0.001)
0.043***
0.016(0.011)(0.010)0.079***
0.345***(0.027)(0.025)
1972
0.847
0.872
22305.9
678.7***

0.073***(0.001)0.007***(0.001)-0.183***(0.009)0.621***(0.017)0.876

Notes: Figures in parentheses are standard errors. ***, **, and * denote the significance level at 1, 5, and 10
percent, respectively.
Source: Author’s estimation based on the RIETI (2017) R-JIP Database.

52

D.2

Alternative weighting matrix

In the baseline analysis, the spatial weighting matrix is constructed based on whether
prefectures are contiguous or not. In Japan, all prefectures are connected by roads toeach other if the prefectures have common borders. Nevertheless, the existence of aroad connection does not necessarily imply large transactions between these prefectures because some prefectures are connected only by minor roads.
For example, Nagano prefecture, which is surrounded by mountains, is contiguouswith eight other prefectures, the most of any prefecture. However, among these eight
prefectures, three are connected by neither highways nor railways, just ordinary roads.
It thus may be difficult to imagine that the Nagano prefecture is equally interdependent with its prefectures. To address this, we employ an alternative weighting matrix,
defining contiguity only when the prefectures are directly connected by highways or
railways.
Table D4 presents the estimation results. Although the spatial effects are insignificant for Business services, the sign and significance levels for other variables are thesame for all sectors. Moreover, the estimated coefficients are the same as those of thebaseline results for Manufacturing. The results are thus robust even when contiguity isdefined as highway and railway connections.
Table D4: Regression Results: SUR With Alternative Weighting Matrix
Agriculture
Relative productivity & price
Agriculture(ln(ϕ1 p1 /ϕ5 p5 ))Manufacturing(ln(ϕ2 p2 /ϕ5 p5 ))Other production(ln(ϕ3 p3 /ϕ5 p5 ))Business services(ln(ϕ4 p4 /ϕ5 p5 ))Relative endowment(ln(K/L))
Spatial autoregressive term
(Ws)
Spatial errors(Wu)
Number of observations
R-squared
Log-likelihood
Breusch-Pagan statistic

0.012***(0.002)-0.019***(0.001)0.006***(0.001)-0.003***(0.001)-0.077***(0.002)-0.227***(0.025)0.253***(0.032)
0.942

Manufacturing

Other
production

Business
services

0.172***(0.003)-0.028***0.089***(0.001)(0.001)-0.013***-0.009***(0.001)(0.001)
0.066***
0.013***(0.004)(0.002)-0.0210.016(0.018)(0.023)0.275***
0.041(0.027)(0.035)
1972
0.975
0.950
27406.3
838.0***

0.056***(0.001)0.007***(0.001)-0.228***(0.021)0.378***(0.028)0.966

Notes: Figures in parentheses are standard errors. ***, **, and * denote the significance level at 1, 5, and 10
percent, respectively.
Source: Author’s estimation based on the RIETI (2017) R-JIP Database.

53

D.3

Alternative measure of labor input

The baseline analysis does not consider the differences in skill composition between
prefectures. However, deindustrialization may also be affected by skill abundance.
As mentioned, however, labor is not disaggregated by skills in the R-JIP Database.
To crudely reflect the differences in skill composition across prefectures, we use total
wages rather than work hours at the prefecture-level as the measure of labor endowment. Hsieh and Klenow (2009) also employ this approach to consider the differencesin hours worked and human capital. The data on total wages by prefecture are alsoavailable in the R-JIP Database.
Table D5 provides the estimation results using the alternative measure of labor input. The estimated coefficients are mostly the same as those of the baseline resultsfor Manufacturing. One notable difference is that the coefficient of the spatial autoregressive term is now significantly positive. This suggests that the effect of spatial interdependence is more evident if skill differences in the labor input are considered.
Otherwise, the baseline results are mostly robust.
Table D5: Regression Results: SUR With Alternative Measure of Labor Input
Agriculture
Relative productivity & price
Agriculture(ln(ϕ1 p1 /ϕ5 p5 ))Manufacturing(ln(ϕ2 p2 /ϕ5 p5 ))Other production(ln(ϕ3 p3 /ϕ5 p5 ))Business services(ln(ϕ4 p4 /ϕ5 p5 ))Relative endowment(ln(K/L))
Spatial autoregressive term
(Ws)
Spatial errors(Wu)
Number of observations
R-squared
Log-likelihood
Breusch-Pagan statistic

0.019***(0.002)-0.024***(0.001)0.003***(0.001)-0.003***(0.001)-0.052***(0.003)-0.506***(0.026)
0.584***(0.022)
0.936

Manufacturing

Other
production

Business
services

0.176***(0.003)-0.027***0.088***(0.001)(0.002)-0.012***-0.009***(0.001)(0.001)
0.067***-0.002(0.004)(0.002)-0.036**0.038(0.017)(0.024)0.277***
0.027(0.027)(0.037)
1972
0.975
0.948
27124.9
790.8***

0.053***(0.001)0.002**(0.001)-0.274***(0.023)0.451***(0.027)
0.966

Notes: Figures in parentheses are standard errors. ***, **, and * denote the significance level at 1, 5, and 10
percent, respectively.
Source: Author’s estimation based on the RIETI (2017) R-JIP Database.

D.4

Alternative sample period

Fujita, Mori, Henderson, and Kanemoto (2004) pointed out that the three largest metropolitan areas (i.e., Tokyo, Osaka, and Nagoya) experienced a high rate of net migration until 1970 with the peak early in the 1960s.45 Although our baseline analysis covers the45

Nagoya is located in Aichi prefecture.

54

period from 1972, Fujita, Mori, Henderson, and Kanemoto (2004) also indicated that
the Tokyo metropolitan area experienced a high rate of net migration around the mid1980s. The estimation results may thus be affected by labor mobility. Unfortunately,
however, it is difficult to control for the effect of factor mobility in our framework. As
a compromise, we re-estimate the model focusing only on the latter half of the sample
period (i.e., between 1992 and 2012) when labor mobility was lower.
The estimation results are presented in Table D6. From the estimation results, theestimated coefficients are mostly the same as those of the baseline results for Manufacturing. A notable difference is that the coefficient of the spatial autoregressive term is
now significant. Accordingly, the effect of spatial interdependence is more evident in
the recent period.
Table D6: Regression Results: SUR With Alternative Sample Period, 1992–2012
Agriculture
Relative productivity & price
Agriculture(ln(ϕ1 p1 /ϕ5 p5 ))Manufacturing(ln(ϕ2 p2 /ϕ5 p5 ))Other production(ln(ϕ3 p3 /ϕ5 p5 ))Business services(ln(ϕ4 p4 /ϕ5 p5 ))Relative endowment(ln(K/L))
Spatial autoregressive term
(Ws)
Spatial errors(Wu)
Number of observations
R-squared
Log-likelihood
Breusch-Pagan statistic

0.025***(0.001)-0.010***(0.001)-0.001(0.001)-0.003***(0.001)-0.016***(0.001)-0.070**(0.035)0.228***(0.048)0.986

Manufacturing

Other
production

Business
services

0.136***(0.003)-0.024***0.087***(0.002)(0.002)-0.010***-0.007***(0.001)(0.001)0.035***-0.012***(0.005)(0.003)0.074**-0.007(0.033)(0.031)0.391***
0.201***(0.041)(0.047)
987
0.991
0.969
16459.5
138.6***

0.049***(0.001)0.010***(0.001)-0.098***(0.032)0.171***(0.048)0.986

Notes: Figures in parentheses are standard errors. ***, **, and * denote the significance level at 1, 5, and 10
percent, respectively.
Source: Author’s estimation based on the RIETI (2017) R-JIP Database.

In this context, one may be further concerned that the data do not reflect current
fast-changing realities because the data used in this paper, the 2017 R-JIP Database,ended in 2012. The latest version of the 2021 R-JIP Database was released in March
2022.46 The 2021 R-JIP Database was substantially revised from the previous version(i.e., 2017 R-JIP Database). For example, the sample period of 2021 R-JIP Database is
1994–2018, which is significantly shorter than the sample period of the previous version(i.e., 1972–2012 in the 2017 R-JIP Database). The changes in the share of manufacturing
value-added were small after 2012 in Japan: on average, from 21.6 percent in 2012 to
23.0 percent in 2018.
46

Unlike the country-level JIP Database, regional-level JIP Database is not frequently updated. For moredetail, see https://www.rieti.go.jp/en/database/r-jip.html

55

Because the 2021 R-JIP Database is not directly comparable to the 2017 R-JIP Databasegiven the changes in the data compilation method, the data cannot be extended from
1972–2012 to 1972–2018. As our focus is the long-run (over four decade) changes inmanufacturing, we present the results of the 2021 R-JIP Database as another robustness
check.
Table D7 provide the estimation results. As shown, the estimated coefficients are
the same as those of the baseline results for Manufacturing. However, there are two
notable differences. First, the coefficient for the capital–labor ratio is insignificant for
manufacturing. As confirmed in Panel A in Figure 4, capital accumulation in Japanslowed after 2000. This result may suggest that with the growth of other countries
like China, Japan is moving from a capital-abundant to a capital-scarce country in the
global economy. Second, like the results of alternative measure of labor input, thecoefficient for the spatial autoregressive term turns significantly negative. This implies
that the effect of spatial interdependence becomes more important in the recent period.
However, the main message of the analysis is mostly unchanged even when we focus
on the more recent period.
Table D7: Regression Results: SUR With Alternative Sample Period, 1994–2018
Agriculture
Relative productivity & price
Manufacturing(ln(ϕ2 p2 /ϕ1 p1 ))Other production(ln(ϕ3 p3 /ϕ1 p1 ))Business services(ln(ϕ4 p4 /ϕ1 p1 ))Other services(ln(ϕ5 p5 /ϕ1 p1 ))Relative endowment(ln(K/L))
Spatial autoregressive term
(Ws)
Spatial errors(Wu)
Number of observations
R-squared
Log-likelihood
Breusch-Pagan statistic

0.016***(0.001)-0.005***(0.001)-0.002***(0.001)-0.002***(0.001)-0.004***(0.001)-0.346***(0.040)0.658***(0.028)0.981

Manufacturing

Other
production

Business
services

0.150***(0.003)-0.022***0.076***(0.002)(0.002)-0.016***-0.025***(0.001)(0.003)0.009-0.016***(0.006)(0.004)-0.078**-0.037(0.032)(0.035)0.246***
0.153***(0.042)(0.047)
1175
0.987
0.935
18577.2
308.4***

0.048***(0.001)0.001(0.001)-0.086***(0.032)0.360***(0.039)0.973

Notes: Figures in parentheses are standard errors. ***, **, and * denote the significance level at 1, 5, and 10
percent, respectively.
Source: Author’s estimation based on the RIETI (2022) R-JIP Database.

56