Does immigration cause Japan prefectures’ economy to diverge?
Evidence from Geographically Weighted Panel Regression
Dung Anh Luong
Yoichi Matsubayashi
June 2023
Discussion Paper No. 2310

GRADUATE SCHOOL OF ECONOMICS
KOBE UNIVERSITYROKKO, KOBE, JAPANDoes immigration cause Japan prefectures’ economy todiverge? Evidence from Geographically Weighted Panel
Regression
By Dung Anh LUONG *, Yoichi MATSUBAYASHI †Abstract
This paper analyzes the impact of immigration on different macroeconomic
indicators, using the production function. We use data on the immigrant stock andprefectures’ accounts from 2009 to 2018. Geographically Weighted Panel
Regression (GWPR) indicates that immigrants’ positive impacts on employment,
and negative impacts on capital-to-GDP ratio are significant in selective prefectures,
which are resulted from an increase in GDP but not capital. Regressing thecoefficients generated by GWPR on immigrant population grouped by education orindustry reveal interesting patterns of economic impacts by immigrant workers.
Keywords: immigrant, GWPR, production function, labor, Japan
Highlight:-

Immigration does not crowd out local native workers.

-

GWPR reveals the heterogenous economic impact of immigrants between
prefectures.

-

Immigration leads to a lower capital-GDP ratio in some selected prefecturesdue to a positive impact on GDP and labor force, but not capital stock.

-

The economic impacts of immigrants are different between education andindustry groups.

JEL Classification: C32, J15, J61*†

Corresponding author at: Graduate School of Economics, Kobe University, Japan.
Email: dluong.econ@gmail.com (D. LUONG)
Graduate School of Economics, Kobe University, Japan1

1. Introduction
The economic impacts of immigration have been studied extensively andproduced mixed results. Additionally, most researches have been using Westerncountries, which are relatively open towards immigration, as their subjects. On theother hand, Japan provides a much more unique case of immigration. While its
native population has been aging fast and has experienced negative growth rates inrecent years, the immigrant population has been growing steadily, despite therestrictive immigration policy. A closer look at the data provided by the Ministryof Health, Labour and Welfare (MHLW) shows that of the 125% increase in foreign
workers between 2010 and 2018, “Technical Intern” and “International Student”
contributed 36.7% and 25.6%, respectively. Additionally, most papers have been
trying to identify the average effects of immigrants across local economies.
However, immigrants may have varying economic impacts, depending on thecharacteristics of the local economy.
In this paper, we try to analyze the heterogeneous impacts of immigrants acrosslocal economies. Specifically, gross domestic production (GDP) is decomposed
into several input components using the production function. Then, we estimate
immigrants’ effects on each component using Geographically Weighted Panel
Regression (GWPR). The method generates different estimates for each local
economy, reflecting the heterogeneous effects of immigrants.
Data on production inputs such as capital stock, immigrants, and total
employment of 47 Japan prefectures from 2009 to 2018 are extracted fromgovernment data. Furthermore, average wage, worked hours, and the number offoreign workers can be extracted from MHLW.
Applying the GWPR method produces interesting results on the distinct impactsof immigrants between prefectures. Specifically, immigration negatively affects the2capital-to-GDP ratio in some selected prefectures. Capital-to-GDP ratio is further
separated into the difference between the growth of capital and the growth of output.
We find that immigration is positively correlated with capital stock and GDP in
selected prefectures. However, focusing on prefectures that have their capital-toGDP ratio negatively affected by immigration, the negative correlations can be
explained by the positive link between immigration with GDP growth but not withcapital growth. Furthermore, immigrants positively impact total employment andGDP but not capital stock in some selected prefectures. These results suggest that,in Japan, immigration increases GDP by raising the labor input, not capital input.
The results also suggest that the marginal productivity of labor is higher in theseselected prefectures.
While many of the coefficients generated by the GWPR method are insignificant,the spread of coefficients carries valuable information on the heterogeneous effects
of immigration across prefectures. Using these coefficients as independent
variables and regressing them on the number of immigrants from different
education and industry groups reveal interesting results. Specifically, highly
educated immigrants enhance the positive impacts on total employment, while theirless educated counterparts lessen the magnitude. These results suggest that, to somedegree, the highly educated group expresses a complementary relationship with thenative workers, while the less educated group shows a substitute relationship.
Another possibility is that native workers are more likely to improve their education
to avoid competing with less educated immigrant workers. Nonetheless, the overall
effect on total employment remains positive. On the other hand, highly educatedimmigrants lower the positive effects’ magnitude on capital stock, while the lesseducated ones enhance them. Since the data on capital only records physical capitalstock, it is possible that highly educated immigrants improve human capital rather
than physical capital.

3

Grouping immigrant workers into primary, secondary, and tertiary industries
shows that prefectures with more immigrant workers working in the secondary
industry have higher capital stock’s coefficients, while a higher number of
immigrants in the primary and tertiary industries lower them. Since the secondary
industry is usually capital intensive (e.g., machinery, manufacturing plants), higher
immigrants in this industry provide the prefectures with an opportunity to expand
the industry further, thus raising the demand for capital.
The positive effects immigrant workers have on total employment are enhanced
by a higher count of immigrants in the primary industry but are lessened by a higher
count of immigrants in the secondary industry. These results are consistent with theindustrial structure of Japan’s prefecture. Maps generated by GWPR show that
immigrants have positive and significant effects on the capital stock of prefecturesthat are relatively more focused on the secondary industry. In comparison,prefectures that lean more toward the primary industry experience positive andsignificant effects on total employment.
Our study has two significant contributions. First, we contribute to thedevelopment of the GWPR method. Second, we identify the pattern of economic
impacts of immigrants on the local economy.
The rest of this paper is organized as follows. Section II reviews previous studies
on the link between immigration and economic growth, and the GWPR method.
Section III describes the production function approach, measure of immigration,
GWPR method, and data used. Sections IV and V present and discuss the results.
Section VI provides concluding remarks.

42. Literature Review
2.1 Immigrant
Immigrants’ impact on domestic market performance has been a hot research
topic, especially on labor market outcomes. The answer to how native workers react
to immigrant workers has been mixed. In his book, Borjas (2014) summarizes many
related researches to provide a foundation on how to analyze the impact ofimmigration on the native labor market. However, Card and Peri (2016) describe
the overall tone of the book toward immigration as “uniformly dismal”, saying that
it is only “half the story”. In many of his works, Peri (2011, 2012) shows that thenegative impacts of immigrants on wage or employment level of their native
counterparts are nonsignificant. The author provides evidence that immigrant
workers and native workers are imperfect substitutes for each other, since bothpossess different skill sets. Thus, native workers will move to other occupations
where they have a comparative advantage over immigrant workers (Peri & Sparber,2009).
The correlation between immigration and capital input has not been a focus inthis field. Theoretically, neoclassical growth model predicts that capital-to-GDP
ratio will stay constant in the long term. Hence, a net positive inflow of immigration,
which increases the destination countries’ population, should not affect the capitalto-GDP ratio. Empirically, Peri (2012) confirms this long-term pattern by analyzing
data between 1960 and 2006. In short-term trend, Lewis (2011) uses data between
1988 and 1993 to show that least-skilled immigrant workers and automation
machinery are substitutes.
Overall, immigrants are found to have a positive correlation with productivity.
Using the production function approach, Peri (2012) finds that immigrants improve
total factor productivity of the receiving U.S. states. Using Canadian firm-level data,5Gu et al. (2020) find a positive correlation between immigrant workers and laborproductivity, defined as the ratio between value-added output and labor input. The
authors find the relationship is stronger for less-skilled immigrants. One channel
through which immigrants can improve productivity is by inducing technologicalprogress, which in turn depends on innovative activities. Using data on the H-1B
visa program, Kerr and Lincoln (2010) find that cities with higher H-1 B admission
rates lead to higher patent counts from Chinese and Indians.
On the other hand, empirical research on immigration in Japan is minimal. Mitani(1993), using the Japanese Census, studied the impacts of immigrant workers on
Japanese women part-time laborers. The study finds a negative relationshipbetween the number of immigrant workers and the number of Japanese women
workers only in manufacturing industries, but nonsignificant overall. The author
also finds a positive impact of immigrant workers on wages across industries,
except for manufacturing industry. Another paper by Ohtake and Ohkusa (1993)
find that while immigrant workers are substitutes for capital and non-regular
workers, they are complements of regular workers. Korekawa (2015) studies theassimilation 1 of Chinese and Brazilian immigrant workers in Japan using the 2010
Census. The study finds that when compared with Japanese men, the economic
achievements of Chinese men are similar, but lower for Brazilian men. Additionally,high economic achievements among Chinese men are further enhanced for thosewith higher education, while the adverse effects among Brazilian men are alleviated
if they are less educated and are married to a Japanese national.

1

Assimilation is defined as the probability of working as Administrative and Managerial workers, or as Profession andengineering workers.

6

2.2 Geographically Weighted Panel Regression
GWPR is an extension of GWR by allowing data to vary over time. GWR iswritten in detail by Fotheringham et al. (2002). The method allows regression
coefficients to vary spatially by running different regressions for each region. In
each regression, regions are weighted by their proximity to other regions using
distance decay function. Applications of GWR include Benson et al. (2005) andFarrow et al. (2005), in which the determinants of poverty are spatial non-stationary,suggesting that policy aiming at reducing poverty should be designed to target
specific areas. Huang and Leung (2002) study the regional industrialization in
Jiangsu province and find that the determinants can vary differently in signs andsignificant levels between northern, southern, and central regions. In regional
growth, Partridge et al. (2009) find that the determinant factors of employment
growth vary between U.S. nonmetropolitan. Similarly, Lewandowska-Gwarda(2018) reaches a similar conclusion when analyzing Poland’s regional
unemployment data.
GWPR is first proposed by Yu (2010) and developed further by Yu et al. (2021).
The latter finds that the development of high-speed rail system benefits rural
regions or areas with lower access to the rail system. The paper concludes that thebenefits of the rail system diminish for regions with better accessibility. Other
application of GWPR includes the study of weather conditions on agricultural yield(Cai et al., 2014). Specifically, the authors find weather’s effect on corn yields in
different U.S. states can be either positive or negative. The average effect estimatedby traditional OLS fails to capture this pattern.
To the authors’ knowledge, neither GWR nor GWPR has been used to study theheterogeneous effects of immigrants on macroeconomic indicators.

7

3. Data and Methodology
3.1 Production function method
The production function method in this study is similar to that of Peri (2012).
Assume each prefecture 𝑝𝑝 at year 𝑡𝑡 has the following production function
(1)

1−𝛼𝛼

𝛼𝛼
𝑌𝑌𝑝𝑝𝑝𝑝 = 𝐴𝐴𝑝𝑝𝑝𝑝 𝐾𝐾𝑝𝑝𝑝𝑝
�ℎ𝑝𝑝𝑝𝑝 𝑁𝑁𝑝𝑝𝑝𝑝 𝜙𝜙𝑝𝑝𝑝𝑝 �

where 𝑌𝑌𝑝𝑝𝑝𝑝 is the total production, 𝐾𝐾𝑝𝑝𝑝𝑝 captures aggregate private physical capital,ℎ𝑝𝑝𝑝𝑝 indicates average worked hours per person, 𝐴𝐴𝑝𝑝𝑝𝑝 measures total factor
productivity, 𝛼𝛼 is the elasticity of substitution between capital and labor, 𝐿𝐿𝑝𝑝𝑝𝑝

represents the total number of workers, and 𝜙𝜙𝑝𝑝𝑝𝑝 is a wage index. Next, output per
worker is defined as 𝑦𝑦𝑝𝑝𝑝𝑝 = 𝑌𝑌𝑝𝑝𝑝𝑝 /𝐿𝐿𝑝𝑝𝑝𝑝 , and equation (1) is rewritten as follows(2)

𝑌𝑌𝑝𝑝𝑝𝑝11−𝛼𝛼ypt = 𝐿𝐿 = 𝐴𝐴𝑝𝑝𝑝𝑝 � 𝑌𝑌 �
𝑝𝑝𝑝𝑝

𝛼𝛼

𝐾𝐾𝑝𝑝𝑝𝑝 1−𝛼𝛼𝑝𝑝𝑝𝑝

ℎ𝑝𝑝𝑝𝑝 𝜙𝜙𝑝𝑝𝑝𝑝

Finally, we rewrite equation (2) in terms of growth rate by taking the logarithm
derivate with respect to time to obtain(3)

�

𝐾𝐾𝑝𝑝𝑝𝑝1
𝛼𝛼𝑌𝑌�𝑝𝑝𝑝𝑝 = 𝐿𝐿�𝑝𝑝𝑝𝑝 + 𝑦𝑦�𝑝𝑝𝑝𝑝 = 𝐿𝐿�𝑝𝑝𝑝𝑝 + �1−𝛼𝛼� 𝐴𝐴̂𝑝𝑝𝑝𝑝 + �1−𝛼𝛼�+ ℎ�𝑝𝑝𝑝𝑝 + 𝜙𝜙�𝑝𝑝𝑝𝑝
𝑌𝑌𝑝𝑝𝑝𝑝According to equation (3), total production value for each prefecture increases
due to an increase in total employment 𝐿𝐿�𝑝𝑝𝑝𝑝 or of an increase in output per worker

𝑦𝑦�𝑝𝑝𝑝𝑝 . The last equality states that an increase in 𝑦𝑦�𝑝𝑝𝑝𝑝 can be further broken down into
four parts: total factor productivity 𝐴𝐴̂𝑝𝑝𝑝𝑝 , capital-to-GDP ratio
worked ℎ�𝑝𝑝𝑝𝑝 , and wage index 𝜙𝜙�𝑝𝑝𝑝𝑝 .

𝐾𝐾�
𝑝𝑝𝑝𝑝
𝑌𝑌𝑝𝑝𝑝𝑝, average hours

Following Peri (2012), equation (4) below is estimated to analyze how

immigration affects each term on the right-hand side of equation (3)8δ�𝑝𝑝𝑝𝑝 = 𝜂𝜂𝑡𝑡 + 𝜂𝜂𝑝𝑝 + 𝛽𝛽𝜃𝜃�𝑝𝑝𝑝𝑝 + 𝜀𝜀𝑝𝑝𝑡𝑡(4)� 𝑝𝑝𝑝𝑝 ,where δ�𝑝𝑝𝑝𝑝 will be replaced with total employment 𝐿𝐿�𝑝𝑝𝑝𝑝 , total factor productivity A
capital-to-GDP ratio

𝐾𝐾�
𝑝𝑝𝑝𝑝
𝑌𝑌𝑝𝑝𝑝𝑝, average hours worked ℎ�𝑝𝑝𝑝𝑝 , and wage index 𝜙𝜙�𝑝𝑝𝑝𝑝 . 𝜂𝜂𝑡𝑡 , 𝜂𝜂,and 𝜀𝜀𝑝𝑝𝑝𝑝 are time-fixed effects, individual-fixed effects, and random error,

respectively. Finally, 𝜃𝜃�𝑝𝑝𝑝𝑝 is a measure of change in immigrant workers between two
periods.

3.2 Measure of immigrant workers’ change
To capture the change in the immigrant labor force between two periods, one canfollow Borjas (2003, 2006, 2014) and use the ratio of immigrant workers to total
employment 𝑟𝑟𝑝𝑝𝑝𝑝 , defined as

𝐹𝐹𝑝𝑝𝑝𝑝(5)

𝑟𝑟𝑝𝑝𝑝𝑝 = 𝑁𝑁 +𝐹𝐹
𝑝𝑝𝑝𝑝

𝑝𝑝𝑝𝑝

� is the number of native
where 𝐹𝐹 is the number the immigrant workers, and 𝑁𝑁
workers. Then, the change of immigrant workers between periods 𝜃𝜃� in equation (4)can be measured as the ratio of immigrant workers between two periods
θ�𝑝𝑝𝑝𝑝 = 𝑟𝑟𝑝𝑝𝑝𝑝 − 𝑟𝑟𝑝𝑝𝑝𝑝−1(6)

However, Card and Peri (2016) point out that such specification cannot correctly
capture the effect of immigrant flow. Applying the first order Taylor expansion onθ�𝑝𝑝𝑝𝑝 shows that 2(7)2

Δ𝐹𝐹𝑝𝑝𝑝𝑝
Δ𝑁𝑁𝑝𝑝𝑝𝑝θ�𝑝𝑝𝑝𝑝 ≈ �1 − 𝑟𝑟𝑝𝑝𝑝𝑝−1 � 𝐿𝐿
− 𝑟𝑟𝑝𝑝𝑝𝑝−1 𝐿𝐿
𝑖𝑖𝑖𝑖−1See Appendix A for the full Taylor expansion.

9𝑖𝑖𝑖𝑖−1

where 𝐿𝐿𝑖𝑖𝑖𝑖 = 𝐹𝐹𝑖𝑖𝑖𝑖 + 𝑁𝑁𝑖𝑖𝑖𝑖 is the sum of immigrant workers and native workers, Δ𝐹𝐹𝑝𝑝𝑝𝑝 =𝐹𝐹𝑝𝑝𝑝𝑝 − 𝐹𝐹𝑝𝑝𝑝𝑝−1 is the change in immigrant workers’ number, and Δ𝑁𝑁𝑝𝑝𝑝𝑝 = 𝑁𝑁𝑝𝑝𝑝𝑝 − 𝑁𝑁𝑝𝑝𝑝𝑝−1

is the change in native workers’ number. Equation (7) shows that θ�𝑝𝑝𝑝𝑝 is theweighted average of the change in immigrant workers and of the change in native

workers. Thus, θ�𝑝𝑝𝑝𝑝 depends not only on the change of immigrant labor but also on

the change of native labor. The negative sign of the second term in equation (7)highlights another problem. If, for instance, a demand shock leads to a positive
correlation between economic indicators and the native labor force in a prefecture.
Then, equations (5) and (7) indicate a negative bias in coefficient 𝛽𝛽.

To construct a variable that can correctly account for the change in the immigrantlabor force, we first define the growth rate of total employment of prefecture 𝑝𝑝
Lpt −𝐿𝐿𝑝𝑝𝑝𝑝−1

(8)

Lpt−1

where the numerator can be written in terms of immigrant and domestic workers
�𝐹𝐹𝑝𝑝𝑝𝑝 +𝑁𝑁𝑝𝑝𝑝𝑝 �−(𝐹𝐹𝑝𝑝𝑝𝑝−1 +𝑁𝑁𝑝𝑝𝑝𝑝−1 )Lpt−1

By grouping immigrant workers and domestic workers variables,(9)�𝐹𝐹𝑝𝑝𝑝𝑝 −𝐹𝐹𝑝𝑝𝑝𝑝−1 �−(𝑁𝑁𝑝𝑝𝑝𝑝 −𝑁𝑁𝑝𝑝𝑝𝑝−1 )
Lpt−1

=

Δ𝐹𝐹𝑝𝑝𝑝𝑝 +Δ𝑁𝑁𝑝𝑝𝑝𝑝
𝐿𝐿𝑝𝑝𝑝𝑝−1

the growth rate of labor market size consists of the growth rate of immigrant and
Δ𝐹𝐹𝑝𝑝𝑝𝑝domestic workers. Thus, 𝐿𝐿

𝑝𝑝𝑝𝑝−1can be used to capture only the impact of theimmigrant labor force. This is also the first term on the RHS of equation (7) without
multiplying the weights. Constructing our explanatory variable this way is also
consistent with Peri (2012) and Card and Peri (2016).

10

3.3 Geographically Weighted Panel Regression
Geographically Weighted Regression (GWR) is used to estimate the spatiallyvarying coefficients using cross-section data (Fotheringham et al., 2002). GWPR
extends this method by utilizing panel data. Thus, both methods are similar in theestimation procedures. First, we will present the basics of GWR.
(10)

𝑦𝑦𝑗𝑗 = 𝑥𝑥𝑗𝑗 𝛽𝛽𝑖𝑖 + 𝜀𝜀𝑗𝑗

where 𝑖𝑖, 𝑗𝑗 = 1, 2, 3, … , 𝑛𝑛 index the geographic location, 𝑦𝑦𝑗𝑗 is the dependent

variable, 𝑥𝑥𝑗𝑗 is the independent variable, and 𝜀𝜀𝑗𝑗 is the error. Different from linear
regression, where we have only one unique coefficient for each independent

variable, GWR produces different coefficients for each at each geographic location.
In other words, if our sample size is 𝑛𝑛, GWR will produce 𝑛𝑛 coefficients. In matrix

form, coefficients of GWR can be estimated as follow(11)

𝛽𝛽̂𝑖𝑖 = [𝑋𝑋 ′ 𝑊𝑊(𝑖𝑖)𝑋𝑋]−1 [𝑋𝑋′𝑊𝑊(𝑖𝑖)𝑌𝑌]

where 𝑊𝑊(𝑖𝑖) is an 𝑛𝑛 by 𝑛𝑛 diagonal weighting matrix of the form
(12)0
𝑤𝑤1 (𝑖𝑖)0
𝑤𝑤2 (𝑖𝑖)
𝑊𝑊(𝑖𝑖) = �
⋮
⋮
0
0

⋯
0
…
0
�
⋱
⋮
⋮ 𝑤𝑤𝑛𝑛 (𝑖𝑖)where 𝑤𝑤𝑛𝑛 (𝑖𝑖) is the weight assigned to data point 𝑛𝑛 while estimating the model atlocation 𝑖𝑖.

Equation (11) states that, at each location 𝑖𝑖 , 𝛽𝛽̂𝑖𝑖 can be estimated using the

Weighted Least Square method, and the weighting matrix follows equation (12).
However, instead of having a constant weight matrix, it will vary according to eachlocation 𝑖𝑖. The weighting scheme is based on the proximity between 𝑖𝑖 and otherdata points. Specifically, higher weight is assigned to data points geographically11

closer to 𝑖𝑖. Many kernel functions can be used to achieve this result. For this paper,
we use the bi-square decay function defined as follows(13)

𝑑𝑑 (𝑖𝑖) 2

2

𝑛𝑛
𝑤𝑤𝑛𝑛 (𝑖𝑖) = ��1 − � 𝑏𝑏 � �
0where 𝑏𝑏 is the bandwidth.

𝑖𝑖𝑖𝑖 |𝑑𝑑𝑛𝑛 (𝑖𝑖)| < 𝑏𝑏𝑜𝑜𝑜𝑜ℎ𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒

Equation (13) assigns weight at a decaying rate depending on how far 𝑛𝑛 is from𝑖𝑖, and assigns weight equal to zero for any points further than a threshold dictatedby bandwidth 𝑏𝑏.

There are two types of bandwidths: fixed bandwidth and adaptive bandwidth. The

former will result in similar bandwidth for every location. However, irregularly

spaced geographical units exist since some prefectures can be smaller than others.
This problem can lead to the extreme case where only one data point is used, thus
leading to a perfect fit. To remedy this problem, adaptive bandwidth is preferable.
Instead of producing a similar optimal bandwidth for all locations, adaptive
bandwidth determines the dataset size be used at each location. Next, to calculate
the appropriate bandwidth, golden-section search optimization method is used tosearch for the optimal bandwidth 𝑏𝑏 that minimizes the following cross-validation

score (CV-score)(14)∑𝑛𝑛𝑖𝑖[𝑦𝑦𝑖𝑖 − 𝑦𝑦�≠𝑖𝑖 (𝑏𝑏)]2

Finally, we extend to GWPR by simply stacking cross-section data over 𝑇𝑇

periods. Specifically, assuming there are 𝑡𝑡 periods, then (10) becomes(15)

𝑦𝑦𝑗𝑗𝑗𝑗 = 𝑥𝑥𝑗𝑗𝑗𝑗 𝛽𝛽𝑖𝑖 + 𝜀𝜀𝑗𝑗𝑗𝑗

The coefficient 𝛽𝛽̂𝑖𝑖 can still be estimated using equation (11), where the matrix 𝑋𝑋

and 𝑌𝑌 will have (𝑛𝑛 ∗ 𝑡𝑡)-by-1 dimension, and the weight matrix 𝑊𝑊(𝑖𝑖) will have12(𝑛𝑛 ∗ 𝑡𝑡)-by-(𝑛𝑛 ∗ 𝑡𝑡) dimension as follow

𝑋𝑋11
⎡ ⋮ ⎤
⎢ 𝑋𝑋 ⎥𝑋𝑋 = ⎢ 1𝑡𝑡 ⎥⎢𝑋𝑋21 ⎥⎢ ⋮ ⎥⎣𝑋𝑋𝑛𝑛𝑛𝑛 ⎦

(16)

𝑌𝑌11
⎡ ⋮ ⎤
⎢ ⎥
𝑌𝑌
𝑌𝑌 = ⎢ 1𝑡𝑡 ⎥⎢𝑌𝑌21 ⎥⎢ ⋮ ⎥⎣𝑌𝑌𝑛𝑛𝑛𝑛 ⎦

(17)

(18)

⎡
⎢
𝑊𝑊(𝑖𝑖) = ⎢⎢⎢⎣𝑤𝑤11 (𝑖𝑖)
⋮
0
0
⋮
0

…
0
⋱
⋮
… 𝑤𝑤1𝑡𝑡 (𝑖𝑖)
…
0
⋱
⋮
…
0

0
⋮
0
𝑤𝑤21 (𝑖𝑖)
⋮
0

…
0
⋱
⋮ ⎤
⎥
…
0 ⎥
…
0 ⎥
⋱
⋮ ⎥
… 𝑤𝑤𝑛𝑛𝑛𝑛 (𝑖𝑖)⎦

Since geographical distances between regions do not change over time, the kernel
function (13) can be used to get the weight matrix 3. CV-score can be estimated byextending equation (14) to(19)∑𝑡𝑡𝑘𝑘 ∑𝑛𝑛𝑖𝑖�𝑦𝑦𝑖𝑖,𝑡𝑡 − 𝑦𝑦�≠𝑖𝑖,𝑡𝑡 (𝑏𝑏)�

2

Time- and individual-fixed effects are also included to control for time-variant
and time-invariant unobservable. All the above estimations are done using R (RCore Team, 2022). The codes are based on the package gwpr (Gaboriault et al.,3This also implies that 𝑤𝑤11 (𝑖𝑖) = 𝑤𝑤12 (𝑖𝑖) = ⋯ = 𝑤𝑤1𝑡𝑡 (𝑖𝑖). In other words, at location 𝑖𝑖, the weights of location indexed as
1 are constant over time.

13

2020), and modified using lfe (Gaure, 2022), plm (Croissant & Millo, 2018), andGWmodel (Gollini et al., 2015) packages.
3.4 Data
We consider the data from 47 prefectures in Japan between 2009 and 2018. Data
on GDP, the number of workers, and private capital stock can be taken from theGross Prefectural Account of the Cabinet Office. Capital utilization rate is takenfrom the Ministry of Economy, Trade and Industry. Data on the number of foreign
workers and average hours worked per person (from the Monthly Labor Survey)
and wage data (from the Basic Survey on Wage Structure) can be extracted from
the MHLW.
To construct capital stock for each prefecture, two problems need to be addressed:(a) the most recent data for capital stock and capital utilization rate is only available
until 2017, and (b) the capital utilization rate is only available on the national level.
We solve the first problem by interpolating the capital stock in 2018 by using thecapital stock in 2017 and the coefficient obtained from the following linear
regression(20)

𝑘𝑘𝑡𝑡 = 𝛿𝛿𝑘𝑘𝑡𝑡−1 + 𝜖𝜖𝑡𝑡

The procedure is done separately for each prefecture.
Next, to construct the capital utilization rate for each prefecture, monthly capitalutilization rates of the manufacturing and service industries are averaged to get theannual rate for both industries separately. Then, the weighted average of both rates
is calculated, where the weight of the manufacturing (service) industry is the ratio
between the GDP value of the manufacturing (service) industry and the sum of bothindustries’ GDP. Following these steps, each prefecture’s capital utilization rate
differs depending on its manufacturing and service industry size. Then, the capital

14

utilization rate for 2018 is interpolated similarly to capital stock. Finally, capitalstock is multiplied by the capital utilization rate to obtain 𝐾𝐾𝑝𝑝𝑝𝑝 .

Total factor productivity 𝐴𝐴𝑝𝑝𝑝𝑝 is not observable. However, it can be calculated byrewriting (1) to(21)

𝐴𝐴𝑝𝑝𝑝𝑝 =𝑌𝑌𝑝𝑝𝑝𝑝1−𝛼𝛼𝛼𝛼𝐾𝐾𝑝𝑝𝑝𝑝 �ℎ𝑝𝑝𝑝𝑝 𝑁𝑁𝑝𝑝𝑝𝑝 �Thus, 𝐴𝐴𝑝𝑝𝑝𝑝 is obtainable after we decide on the value of parameter 𝛼𝛼. Following(Takizawa, n.d.), the elasticity of output to capital 𝛼𝛼 is calculated on the national

level as follows(22)𝛼𝛼 = 1 −(𝑤𝑤+𝑇𝑇)
𝑌𝑌

where 𝑤𝑤 is the compensation of employees, 𝑇𝑇 is the taxes on production andimports. Both 𝑤𝑤 and 𝑇𝑇 are available from the Gross Prefecture Product of the
Cabinet Office.

Wage index in each prefecture is constructed by first combining the data on

ordinary and part-time workers to get the wage indexes for all industries. Then, we
combine these indexes to obtain the wage index for each prefecture. Specifically,for ordinary workers, scheduled hours worked and overtime worked hours are
summed up and multiplied by 12 to get the total worked hours annually in eachindustry. Similarly, for part-time workers, the total worked hours annually in eachindustry is calculated by multiplying the average worked days per month by theaverage worked hours per day and by 12. Annual earning (including bonus) is thendivided by the total worked hours to get the average earning per hour. Afterward,
the average earning per hour of ordinary and part-time workers are combined using
weighted average, where the weights are the ratio between total worked hours ofordinary workers (part-time workers) to total worked hours of both types of workers.
Finally, the average earning per hour for each prefecture is again obtained using

15

weighted average, where the weights are now the ratio between the total worked
hours of each industry and the total worked hours of all industries.
Following the above procedure, the wage index 𝜙𝜙𝑝𝑝𝑝𝑝 can be thought of as theaverage earnings per hour in each prefecture. However, one drawback of using the

Basic Survey on Wage Structure is that the data does not include workers from
“Agriculture and Forestry” and “Fisheries” since earnings in these sectors fluctuatesignificantly due to seasons or weather conditions. Nevertheless, the survey still
includes valuable information on wages because it covers most parts of theeconomy.
4. Empirical Result
Before looking at the estimates of GWPR, we present a simple spatial
autocorrelation test using Moran’s I. The calculation steps of Moran’s I in panel
data are written in detail by Beenstock and Felsenstein (2019). The weight matrix
is defined simply as the inverse of distance between prefectures. Table 1 indicatesthat we can reject the null hypothesis of no spatial autocorrelation in two out of six
models: output per worker and capital-to-GDP ratio. For this paper, we decide touse GWPR instead of any other spatial models since it can generate different
coefficients for each prefecture, which allows a better understanding of the impactof immigration on the local economy.

16

Table 1. Moran’s I for panel regression

Moran's I p-value
0.380

0.352

1.537

0.062

� 2.487
𝛼𝛼/1 − 𝛼𝛼 ∗ 𝐾𝐾/𝑌𝑌
1/1 − 𝛼𝛼 ∗ 𝐴𝐴̂
0.722
ℎ�
0.859

0.006

𝐿𝐿�

𝑦𝑦�

𝜙𝜙�

1.137

0.235
0.195
0.128

The weight matrix can be calculated using different kernel functions. In order toselect the appropriate function, we compare the corrected Akaike Information
Criterion (AICc) in Table 2 for bi-square, tri-square, and gaussian kernel functions.
Overall, the bi-square kernel function produces the lowest AICc value. However,the differences seem negligible. For this paper, GWPR will be estimated using thebi-square kernel function.
Next, the AICc value of the baseline OLS model is calculated and compared withGWPR in Table 3. The results indicate that GWPR yields lower AICc values in all
five models. In other words, GWPR is better at fitting the data than OLS.

Table 2. Corrected Akaike Information Criterion value of different GWPR models using
different kernel functions

17

Table 3. AICc of baseline OLS model and GWPR

Finally, GWPR results are presented in the following structure: the left-side map
indicates the coefficient 𝛽𝛽, while the right-side map indicates the t-value. The
𝐾𝐾�
impact of immigrant workers on 𝐿𝐿�, 𝑦𝑦�, 𝑌𝑌 , 𝐴𝐴̂, ℎ�, 𝜙𝜙� are shown in Figures 1, 2, 3, 4, 5,

and 6, respectively.

According to Figure 1, immigrants positively affect total employment in all
prefectures but are only significant in some prefectures. Prefectures from regions
other than the Chubu and Kansai regions enjoy the benefits of additional immigrant
workers. In Figure 2, while indicating positive effects on output per worker, theeffects are insignificant. Coefficients for the capital-to-GDP ratio, as shown in
Figure 3, are spread from negative to positive. The significant coefficients areconcentrated on prefectures of the Tohoku region and Hokkaido prefecture. In
Figure 4, the impacts on total factor productivity are negative and insignificant
across prefectures. Finally, Figures 5 and 6 show that immigrants positively affectthe average worked hours and wage index. However, both are insignificant acrossprefectures.
GWPR indicates that immigrants’ impact on the capital-to-GDP ratio can besignificant in some regions. To better understand the relationship, we separate the18ratio into the growth rate of capital, and the growth rate of GDP, as below
(23)

𝛼𝛼

�1−𝛼𝛼�

𝐾𝐾�
𝑝𝑝𝑝𝑝
𝑌𝑌𝑝𝑝𝑝𝑝𝛼𝛼
�𝑝𝑝𝑝𝑝 − � 𝛼𝛼 � 𝑌𝑌�𝑝𝑝𝑝𝑝
= �1−𝛼𝛼� 𝐾𝐾
1−𝛼𝛼The decomposition is important in understanding how immigrants influence capital
input. According to (23), three patterns can lead to a negative capital-to-GDP ratio:(a) the growth rate of capital is negative, while that of GDP remains constant; (2)the growth rate of GDP is positive, while that of capital remains constant; and (3)both growth rates are positive, but GDP grows at a faster rate. The results of reestimating GWPR separately on the growth rates of capital and GDP are shown in
Figure 7 and Figure 8, respectively. Immigrants can positively and significantly
affect the capital stock of most prefectures in Chubu and Kansai regions.
Furthermore, immigrants have a positive effect on GDP in the northern part ofJapan.

19

Figure 2. GWPR results of immigrants' effects on total employment

Figure 1. GWPR results of immigrants' effects on output per worker

20

Figure 4. GWPR results of immigrants' effects on capital-to-GDP ratio

Figure 3. GWPR results of immigrants' effects on total factor productivity

21

Figure 6. GWPR results of immigrants' effects on average worked hours

Figure 5. GWPR results of immigrants' effects on wage index

22Figure 8. GWPR results of immigrants' effects on capital

Figure 7. GWPR results of immigrants' effects on GDP

23

The coefficients generated by the GWPR method imply that immigrants affecteach prefecture differently. We take one step further from previous literature andregress these coefficients on different groups of immigrants. Specifically, using
publicly available statistics from the 2010 Census, the immigrant working
population (15-64 years old) is categorized into three groups: highly educated(those who finish vocational school, have a college degree or higher), and lesseducated (those with highs school education or less, or are attending school).
International students are included since they are also vital to the labor force 4. They
are categorized as less educated because they are only allowed to work 28 hours
per week and cannot work as regular employees. The findings are presented inTable 4. For brevity, we focus on the coefficients that demonstrate theheterogeneous impacts of immigrants on the local economy, which are the total
employment, capital stock, and GDP. Columns (1), (3), and (5) of the top panel use
the 2010 Census to construct the three immigrant variables, while columns (2), (4),and (6) use the 2020 Census 5. The bottom panel categorizes immigrants into threeindustry groups: primary industry, secondary industry, and tertiary industry6. The
dependent variables are the coefficients of total employment, capital, and GDP
generated by the GWPR method above.
The results indicate that highly educated immigrants are correlated with higher
total employment’s coefficients, but lower capital stock’s coefficients. On thecontrary, the less educated group is correlated with lower total employment’s
coefficients, but higher capital stock’s coefficients. On the other hand, grouping

4 According to MHLW, in 54.95% of foreign workers in Accommodation, and Food Services are international students.
5 While Japan Census is conducted every 5 years, education retainment is asked every 10 years (e.g., 2000, 2010, 2020).

As a result, while this study does not cover the 2020 period, 2020 Census is used instead of 2015 Census as a robustness
check.
6

Different from education retainment, categorizing using industry groups use only immigrants who are actually working.

24

Table 4. Regression of immigrant groups on coefficients generated by GWPR
Dependent variable
Total employment

OutputCapital

2010

2020

2010

2020

2010

2020

(1)

(2)

(3)

(4)

(5)

(6)

2.553***

2.481***

0.415*

0.516**

2.892***

3.084***(0.234)(0.245)(0.220)(0.241)(0.792)(0.773)-0.0001*** -0.00005***

0.00001

0.00002

Panel (a):Education
Constant
Highly educatedLess educated0.0001*** 0.00003***(0.0000)(0.0000)(0.0000)(0.0000)(0.0001)(0.0000)-0.0001*** -0.00005***

0.0001***0.0001***-0.00005-0.0001(0.0000)(0.0000)(0.0000)(0.0000)(0.0001)(0.0000)

2.290***

2.000***

0.773***

0.907***

2.716***

2.628***(0.243)(0.253)(0.257)(0.280)(0.848)(0.872)0.0005**0.0004***-0.0005**-0.0003*

0.001

0.001

(0.0002)(0.0001)(0.0002)(0.0001)(0.0010)(0.0004)-0.0001*** -0.00005***

0.0001***Panel (b): Industry
Constant
Primary indsutry
Secondary industry
Tertiary industry
Observations(0.0000)

0.00005*** -0.0001*-0.0001**(0.0000)(0.0000)(0.0000)(0.0001)(0.0000)

0.00001

0.00001 -0.00003*** -0.00002***-0.00001-0.00001(0.0000)

0.0000(0.0000)(0.0000)(0.0000)(0.0000)

47

47

47

47

47

47

Note: The dependent variables are the coefficients generated by GWPR method for total
employment in (1) and (2), capital in (3) and (4), output in (5) and (6). The independent
variables in panel (a) are the number of highly educated immigrants and less educatedimmigrants. The independent variables in panel (b) is the number of immigrants working inprimary industry, secondary indsutry, and tertiary indsutry. Weighted OLS is used, where
weights for 2010 and 2020 are total employment from Census 2010 and Census 2020,
seperately. Standard errors are in parenthesis. *p<0.1; **p<0.05; ***p<0.01

immigrants into industry groups reveal another interesting trend. An increase inimmigrant workers in the primary industry is correlated with higher total
employment’s coefficients, but lower capital stock’s coefficients. An increase inimmigrant workers in the secondary industry, however, is correlated with lower
coefficients’ magnitude of total employment and GDP, but higher coefficients’25

magnitude of capital stock. Finally, immigrant workers in tertiary industry lower
the magnitude of capital stock’s coefficients but have insignificant effects on thecoefficients of total employment and GDP.
5. Discussion
GWPR method reveals the differentiated effects of immigrants on capital-toGDP across prefectures. Separately estimating the effects on capital and GDP
shows the negative and significant coefficients in selected prefectures are because
immigration increases GDP but not capital. Furthermore, the distribution of thecapital coefficients indicates that an increase in immigration raises the capital stockof the Kansai and part of the Chubu region. One possible explanation is that these
prefectures focus more on the manufacturing industry (Table B.1 in Appendix B).
As a result, an increase in immigration may lead to an increase in investment inphysical capital (e.g., factories, machinery, etc.).
Interestingly, immigration does not bring the same benefit to Tokyo. The reason
might be that Tokyo is concentrated with technology-based firms, where humancapital and non-physical capital are much more important. Nonetheless, most of thecapital stock’s coefficients are positive, suggesting that immigration and physicalcapital are not substitutes for each other.
Combining the results of Figures 1, 7, and 8 show two notable trends. First,
prefectures that experience higher physical capital stock from immigration do notsee higher GDP due to immigration. Second, Hokkaido prefecture and prefecturesfrom the Tohoku, Shikoku, and Kyushu regions benefit from a larger labor force
due to higher immigration. However, only Hokkaido prefecture and part of the
Tohoku region see increased GDP due to higher immigration. Using the production
function, GDP can be increased through two channels: an increase in capital input
or labor input. The above results indicate that, in Japan, while immigration can lead26

to a higher physical capital stock and a larger labor force, only the labor channel issignificant enough to increase GDP. Furthermore, the second trend also implies
higher marginal productivity of labor in Hokkaido prefecture and part of the
Tohoku region. The magnitude of the significant coefficients suggests that the
expansion of the local labor force is not only because of immigration but also
because of a positive net migration by natives. Specifically, if a local labor market
has an additional new immigrant worker, the total number of workers in the region
should increase by one, assuming that the number of native workers remains
constant. Coefficients greater than one indicate that an additional immigrant attracts
more than one worker. Therefore, the magnitude of these coefficients suggests that
immigration has a crowd-in effect in some prefectures.
The coefficients mapped out in Figure 5 do not vary much, suggesting that theimmigrants’ impacts on average worked hours are similar across prefectures.
Moran’s I tests fail to reject the null hypothesis further confirm the results. Whileimmigrant workers positively affect the wage index, they are neglectable. The
insignificant might be the results of the combined effects of immigrants on different
types of workers. However, due to data limitations, we cannot further disentangle
the wage effect of immigrants. Equivalently, Figure 4 also shows that immigrants
exert negative but insignificant effects on TFP. The magnitude is also similar acrossprefectures.
The coefficients computed using GWPR, while insignificant in many cases, carryvaluable information on how immigrants are heterogeneously affecting the local
economies. Utilizing Census data in 2010 and 2020, we try to dig deeper into thisphenomenon. Grouping immigrants by education suggests that, to some degree,
highly educated immigrant workers have a complementary relationship with native
workers, while their less educated counterparts may have a substitute relationship.
However, the aggregate effect on total employment is positive. One possible

27

explanation is that since immigrants are more likely to work in low-paying jobs,
they may have a substitute relationship with the native workers, especially the nonregular workers (similar to the results of Mitani (1993) and Ohtake and Ohkusa(1993)). Another possibility is the return to school effect, where natives areencouraged to complete high school (Hunt, 2017) or attain higher education to
avoid competing with immigrants (Brunello et al., 2020).
The less educated group leads to higher capital stock’s coefficients. The results
confirm the possible link between highly educated immigrants and human capital.
Since the data does not include human capital, if highly educated immigrants are
better at utilizing their professional knowledge to improve human capital, an
increase in highly educated immigrants has less impact on the physical capital stock.
On the other hand, prefectures with a higher number of less educated immigrants
see a greater positive impact on capital stock.
This point is further explored in the bottom panel of Table 4. The results suggestthat an increase in immigrants working in the manufacturing industry (secondary
industry) leads to greater magnitude of capital stock’s coefficients. Since the
manufacturing industry requires more physical capital stock, an increase inimmigrants working in the industry raises the physical capital stock. Figure 7 also
confirms this point, as immigration positively and significantly impacts the capitalstock of prefectures focusing on the manufacturing industry. For example, Aichi
prefecture is one of the prefectures that experiences higher capital stock due to ahigher number of immigrants. The prefecture has the most prominent secondary
industry in terms of GDP value (Table B.1 in Appendix B). It also has the second
largest immigrant worker population, next to Tokyo, but the largest immigrant
worker population in the manufacturing industry (Table B.2 in Appendix B).
A higher number of immigrants working in the primary industry is linked tohigher total employment’s coefficients, but lower capital stock’s coefficients. Since28

the primary industry is relatively more labor-intensive, prefectures looking for
more immigrants to work in the primary industry may not be incentivized to invest
in capital stock. This point is further confirmed in Figures 1, 7, and 8: higher
immigrant counts in the primary industry lead to higher GDP due to an increase intotal employment, not physical capital stock. According to the Prefectural Accountpublished by Cabinet Office (Table B.1), seven prefectures fitting into this trend
put greater focus on the primary industry than other prefectures.
6. Conclusion
This paper uses the production function approach and GWPR method to study
the relationship between immigrant workers and the economic inputs of Japanese
prefectures. The method allows one to explore the possible distinct effects acrossprefectures.
Immigrants are shown to negatively affect the capital-to-GDP ratio in northern
Japan. Further analysis shows the negative effects are due to the positive
relationship between immigration and GDP. In other words, immigration drives
GDP growth but not capital growth, thus lowering the capital-to-GDP ratio.
Additionally, an increase in immigrants is correlated with higher GDP and total
employment, but not capital also shows that marginal productivity of labor is higher
in northern Japan.
We also find evidence that highly educated immigrants dampen the positiveeffects on total employment but enhance the positive effects on capital stock.
Immigrant workers in the labor-intensive primary industry exert greater impacts on
total employment but lessen the magnitude of the impacts on capital stock. On thecontrary, immigrants in the capital-intensive manufacturing industry are linked tohigher capital stock’s coefficients, but lower total employment’s coefficients.
Combining these results with the maps generated by GWPR shows that the29economic impacts of immigrants depend on the industrial structure of theprefectures.

30

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35

APPENDIX A
� 𝒑𝒑𝒑𝒑 = 𝒓𝒓𝒑𝒑𝒑𝒑 − 𝒓𝒓𝒑𝒑𝒑𝒑−𝟏𝟏
First order Taylor expansion of 𝜽𝜽

From
(A.1)

𝐹𝐹𝑝𝑝𝑝𝑝θ�𝑝𝑝𝑝𝑝 = rpt − 𝑟𝑟𝑝𝑝𝑝𝑝−1 = 𝐹𝐹 +𝑁𝑁
𝑝𝑝𝑝𝑝

𝑡𝑡𝑡𝑡𝑡𝑡

The first-order derivative of θ�𝑝𝑝𝑝𝑝 is− 𝐹𝐹

𝐹𝐹𝑝𝑝𝑝𝑝−1

𝑝𝑝𝑝𝑝−1 +𝑁𝑁𝑝𝑝𝑝𝑝−1

𝐹𝐹𝑝𝑝𝑝𝑝∂θ�𝑝𝑝𝑝𝑝 (𝐹𝐹𝑝𝑝𝑝𝑝 , 𝑁𝑁𝑝𝑝𝑝𝑝 )
1
=
−
∂Fpt
𝐹𝐹𝑝𝑝𝑝𝑝 + 𝑁𝑁𝑝𝑝𝑝𝑝 �𝐹𝐹 + 𝑁𝑁 �2
𝑝𝑝𝑝𝑝
𝑝𝑝𝑝𝑝
∂θ�𝑝𝑝𝑝𝑝 (𝐹𝐹𝑝𝑝𝑝𝑝 , 𝑁𝑁𝑝𝑝𝑝𝑝 )𝐹𝐹𝑝𝑝𝑝𝑝=−2∂𝑁𝑁𝑝𝑝𝑝𝑝�𝐹𝐹𝑝𝑝𝑝𝑝 + 𝑁𝑁𝑝𝑝𝑝𝑝 �Thus, the Taylor series of θ�𝑝𝑝𝑝𝑝 (Fpt , Npt ) around (𝐹𝐹𝑝𝑝𝑝𝑝−1 , 𝑁𝑁𝑝𝑝𝑝𝑝−1 ) is(A.2)

θ�𝑝𝑝𝑝𝑝 ≈ �𝐹𝐹

𝐹𝐹𝑝𝑝𝑝𝑝−1

𝑝𝑝𝑝𝑝−1 +𝑁𝑁𝑝𝑝𝑝𝑝−1

+ �F

1

pt−1 +𝑁𝑁𝑝𝑝𝑝𝑝−1

−

Fpt−1

− 𝐹𝐹

𝐹𝐹𝑝𝑝𝑝𝑝−1

𝑝𝑝𝑝𝑝−1 +𝑁𝑁𝑝𝑝𝑝𝑝−1−

�Fpt−1 +Npt−1 �

2

Fpt−1

�

�Fpt−1 +Npt−1 �2

� (𝐹𝐹𝑝𝑝𝑝𝑝 − 𝐹𝐹𝑝𝑝𝑝𝑝−1 )(Npt − Npt−1 )Hence, (A.2) can be further rewritten as(A.3)

θ�𝑝𝑝𝑝𝑝 ≈ 0+ �1 − F

Fpt−1

pt−1 +Npt−1

� �F

𝐹𝐹𝑝𝑝𝑝𝑝 −𝐹𝐹𝑝𝑝𝑝𝑝−1

pt−1 +Npt−1

36

�

−F

Fpt−1

�

Npt −Npt−1

pt−1 +Npt−1 Fpt−1 +Npt−1

�
𝐹𝐹𝑝𝑝𝑝𝑝

Let ΔF = Fpt − 𝐹𝐹𝑝𝑝𝑝𝑝−1 , and ΔN = Npt − 𝑁𝑁𝑝𝑝𝑝𝑝−1 . Also, recall that rpt = 𝐹𝐹 +𝑁𝑁
𝑝𝑝𝑝𝑝

and Lpt = 𝐹𝐹𝑝𝑝𝑝𝑝 + 𝑁𝑁𝑃𝑃𝑃𝑃 , then
(A.4)

Δ𝐹𝐹
ΔN
θ�𝑝𝑝𝑝𝑝 = �1 − rpt−1 � �L � − 𝑟𝑟𝑝𝑝𝑝𝑝−1 �L �
pt−1

37

pt−1

𝑝𝑝𝑡𝑡

APPENDIX B
Table B. 1 Output value of primary, secondary, tertiary industries in 2018
(JPY millions)
PrefecturePrimary Secondary
industry industry

Hokkaido

807,709

Aomori
Iwate
Miyagi
Akita
Yamagata
Fukushima
IbarakiTochigi
Gunma
Saitama
Chiba
Tokyo
Kanagawa
NiigataToyamaIshikawa
Fukui
Yamanashi
NaganoGifu
Shizuoka
Aichi
Mie
Shiga
Kyoto
Osaka
Hyogo
Nara
Wakayama
Tottori
Shimane
Okayama
Hiroshima
Yamaguchi
Tokushima
KagawaTertiary
industry

3,568,708

15,942,170

206,594

915,3453,399,709

146,332

1,398,785

3,342,965

139,496

2,532,873

7,359,968

110,177

806,520

2,665,312

121,077

1,362,292

2,827,141

120,506

2,671,817

5,266,273

283,151

5,633,366

8,384,131

165,796

4,251,072

4,972,858

111,272

3,783,491

5,357,842

98,1196,107,900

17,370,424

204,5025,207,103

16,022,623

52,54913,515,327

101,970,849

42,322

8,575,381

26,686,075

163,397

2,780,404

6,360,734

46,4101,840,566

3,034,380

43,403

1,469,861

3,381,758

31,236

1,178,561

2,462,886

55,7791,348,539

2,189,999

153,4112,986,227

5,449,688

61,4162,754,231

5,164,096

132,793

7,746,819

10,169,480

167,145

17,246,486

24,752,379

80,544

3,869,690

4,613,732

37,8133,339,314

3,527,959

37,195

3,414,128

7,264,726

20,3308,569,385

32,336,642

100,602

6,835,141

15,062,048

21,385910,3902,980,067

74,6701,272,666

2,361,467

49,855400,914

1,455,378

48,022651,733

1,936,609

73,9922,710,348

5,120,166

69,5783,810,989

8,337,469

36,7602,658,355

3,766,620

58,584

1,091,997

2,063,987

56,5391,062,841

2,818,636

38(%)

Primary
industry
4.0
4.6
3.0
1.4
3.1
2.8
1.5
2.0
1.8
1.2
0.4
1.0
0.0
0.1
1.8
0.9
0.9
0.9
1.6
1.8
0.8
0.7
0.4
0.9
0.5
0.3
0.0
0.5
0.5
2.0
2.6
1.8
0.9
0.6
0.6
1.8
1.4

Secondary Tertiaryindustry industry
17.6
20.2
28.6
25.2
22.5
31.6
33.2
39.4
45.3
40.9
25.9
24.3
11.7
24.3
29.9
37.4
30.0
32.1
37.5
34.8
34.5
42.9
40.9
45.2
48.4
31.9
20.9
31.1
23.3
34.3
21.0
24.7
34.3
31.2
41.1
34.0
27.0

78.5
75.2
68.4
73.4
74.4
65.6
65.3
58.6
53.0
57.9
73.7
74.8
88.3
75.6
68.4
61.7
69.1
67.1
60.9
63.4
64.7
56.3
58.7
53.9
51.1
67.8
79.0
68.5
76.2
63.7
76.4
73.5
64.8
68.2
58.3
64.2
71.6

Ehime
2.0
29.2
68.7
104,552
1,497,876
3,518,690
Kochi
3.8
16.6
79.6
94,421
407,334
1,953,978Fukuoka
0.8
20.3
78.9
161,143
4,046,671
15,722,748
Saga
2.5
29.5
67.9
81,466951,274
2,187,478
Nagasaki
2.6
24.1
73.3
123,663
1,153,586
3,514,007
Kumamoto
3.0
26.3
70.6
190,416
1,644,903
4,416,771
Oita
2.0
30.9
67.2
90,332
1,421,658
3,093,606
Miyazaki
4.5
24.5
70.9
170,312921,367
2,665,235
Kagoshima
4.6
21.4
74.1
261,060
1,223,094
4,243,853
Okinawa
1.3
17.4
81.3
60,060798,6393,737,329
5,567,886 154,345,967
423,232,941
Total
Note: Output value of primary, secondary, and tertiary industries are shown in JPY million in thesecond to fourth columns. The last three columns show the ratio of output value of each industry
to the total output value in each prefecture.
Source: “Prefectural Account” published by Cabinet Office

Table B. 2 Number of immigrant workers in all industries and in the manufacturingindustry in 2009 and 2018

All industries

Manufacturing industry

Prefecture

2009

2018

Growth
rate

2009

2018

Growthrate

Hokkaido

6,125

21,026

243%

2,395

5,781

141%

Aomori

1,126

3,137

179%

673

1,569

133%

Iwate

1,948

4,509

131%

1,443

2,687

86%

Miyagi

3,689

11,001

198%

1,501

4,155

177%

Akita

1,550

1,953

26%

1,139

987

-13%

Yamagata

1,856

3,754

102%

1,346

2,143

59%

Fukushima

3,448

8,130

136%

2,076

3,382

63%

Ibaraki

14,16135,062

148%

7,092

15,215115%

Tochigi

10,34224,016

132%

3,996

10,579

165%

Gunma

12,34934,526

180%

6,384

14,432

126%

Saitama

23,29865,290180%

11,85525,827

118%

Chiba

18,20154,492

199%

6,437

14,320

122%

Tokyo

138,907438,775

216%

11,162

26,302

136%

Kanagawa

31,70079,223150%

12,891

24,60091%

39

Niigata

3,936

8,918

127%

2,213

4,080

84%

Toyama

4,842

10,334

113%

2,681

5,217

95%

Ishikawa

4,224

9,795

132%

2,561

5,214

104%

Fukui

4,057

8,651

113%

3,056

3,873

27%

Yamanashi

4,266

6,910

62%

2,860

2,780

-3%

Nagano10,226

17,923

75%

6,329

9,215

46%

Gifu

18,621

31,27968%

10,83618,09967%

Shizuoka

34,61857,35366%

18,82324,93632%

Aichi

67,728

151,669

124%

34,831

68,77697%

Mie

15,19527,464

81%

9,571

14,228

49%

Shiga

9,235

17,23887%

5,665

10,164

79%

Kyoto

6,624

17,436

163%

1,978

5,075

157%

Osaka

29,54590,072

205%

9,281

23,395

152%

Hyogo

12,98534,516

166%

5,824

14,804

154%

Nara

2,233

4,116

84%

1,266

1,950

54%

Wakayama

973

2,395

146%

551

1,002

82%

Tottori

1,352

2,755

104%

897

1,495

67%

Shimane

1,864

4,297

131%

1,047

1,742

66%

Okayama

7,154

16,297

128%

3,772

7,702

104%

Hiroshima

14,49331,851

120%

7,828

16,887

116%

Yamaguchi

2,727

7,723

183%

1,275

3,285

158%

Tokushima

2,511

4,389

75%

1,606

2,056

28%

Kagawa

2,823

8,703

208%

2,062

4,860

136%

Ehime

4,156

8,376

102%

2,991

5,649

89%

Kochi

982

2,592

164%

248

730

194%

Fukuoka

11,74546,273

294%

2,668

9,779

267%

Saga

1,624

5,258

224%

1,020

2,565

151%

Nagasaki

2,513

5,433

116%

1,170

1,933

65%

Kumamoto

3,038

10,155

234%

1,150

2,878

150%

Oita

3,017

6,254

107%

874

2,169

148%

40

Miyazaki

1,273

4,144

226%

562

1,882

235%

Kagoshima

1,839

6,862

273%

859

3,040

254%

Okinawa

1,699

8,138

379%

155

903

483%

Total

562,818 1,460,463

159%

218,900 434,342

Source: “Foreigner Employment Status” published by MHLW

41

98%