Discussion Paper No. 88
Spatial Dependence and Social Networks
in Regional Labor Migration
Koji Murayamay
Jun Nagayasu

October, 2018

Data Science and Service Research
Discussion Paper

Center for Data Science and Service Research
Graduate School of Economic and Management
Tohoku University27-1 Kawauchi, Aobaku
Sendai 980-8576, JAPANSpatial Dependence and Social Networks in Regional
Labor Migration∗
Koji Murayama†,

Jun Nagayasu‡

Abstract

This study empirically analyzes the determinants of regional labor migration in
Japan. Using spatial models of origin-destination flows and considering the network effects of labor, we obtain results more consistent with standard migration
theory than previous studies. First, unlike prior research, we find that migration
decisions are made by economic motivations consistent with economic theories. In
particular, the unemployment rate in the destination region and income in the origin
are found to be driving forces of labor migration. Second, we report that network
effects, which help reduce migration costs, have encouraged the relocation of labor.
Third, by using several definitions of spatial weights, we show that spatial dependence in regional migration is more complex than what previous studies assumed.
Keywords: labor migration, spatial models, origin-destination flows, regional economy, network effects
JEL classification: C32, O47∗

An earlier version of this paper was presented at the International Conference of Economics Forumat National Chengchi University. We would like to thank Akira Hibiki and Hao-Chung Li for their usefulcomments. Murayama acknowledges the financial support of the Japan Investment Advisors Association
for travel expenses.
†
Tohoku University, Graduate School of Economics and Management, Address: 27-1 Kawauchi, Aobaku, Sendai, Miyagi 980-8576 JAPAN. Email: hakuryu.888@outlook.jp.
‡
Tohoku University, Graduate School of Economics and Management, Address: 27-1 Kawauchi, Aobaku, Sendai, Miyagi 980-8576 JAPAN. Email: jun.nagayasu.d8@tohoku.ac.jp, Tel: +81 22 795 6265, Fax:
+81 22 795 6270.

1

Introduction

Migration has been an important research topic globally. Massive immigration from
the Middle East has resulted in socioeconomic conflicts in Europe. As a result, many
European countries have imposed a cap on immigration; the United Kingdom has evendecided to leave the European Union (Brexit) to control its own immigration policy.
Blanchard and Katz (1992), Debelle and Vickery (1999), and Choy et al. (2002) discussed
migration as a factor in reducing income disparities; however, the recent political trend
is to prevent the free movement of people and economic convergence among countries.
While cross-border migration may have been the main political focus recently, interregional migration has also drawn the interest of researchers and policymakers. In Japan,
which has experienced rapid demographic changes, the unidirectional movement of laborhas widened regional heterogeneity and become a serious socioeconomic problem in recent
decades. People tend to move to urban areas where there are more job opportunities andeasier access to medical facilities, shops, and public transportation. As a result, manyrural regions known as Genkai-shuraku face depopulation and risk disappearing in thenear future. Moreover, policymakers need to consider the different impacts of monetary
policies designed to fit all regions on regional economies.
Against this background, we attempt to identify the socioeconomic factors affecting
regional labor migration in Japan by using spatial models of origin-destination flows.
The distinguishing points in this study are threefold. First, although many studies of
migration exist, this is one of the few focusing on labor migration (see the next section
for previous studies). Labor is an ingredient of production and economic activities, andtherefore, is closely related to household income and utility. Furthermore, as discussed,labor mobility is an important factor for economic and regional convergence.
Second, unlike most previous studies that have focused on net migration, we distinguish between migration inflows and outflows; moreover, because migration flows are
known to be spatially correlated, we model regional dependence by using spatial statistics.1 The consideration of the origin and destination in spatial models enriches ourunderstanding of labor movement, and we use spatial statistics, which has become a pop1

The study by Paelinck and Klaassen (1979) was the first comprehensive attempt to outline a field of
spatial analyses and its distinct methodology. Spatial correlation is sometimes called spatial interaction.

2

ular investigation approach to obtain consistent parameters in various research fields, tomodel regional dependence.2 Third, we introduce several definitions of spatial weightmatrixes to capture the different types of regional dependence in the data. This departs
from previous migration analyses that have used only a single spatial weight matrix basedon the geographical distance between regions. Finally, we control for the network effectsof migrants, which have often been omitted in previous studies. Our results suggest thatthe last two contributions particularly help reduce the bias in many of the parametersand make our estimates more consistent with standard economic theory.

2

Related studies of migration

Previous studies of labor migration tend to focus on the relationship between migrationand determinants such as regional labor market conditions; therefore, labor decisions on
relocation are driven largely by economic motivations. Such research also has some shortcomings; for example, even when spatial models are used, net migration across regions
is often analyzed by assuming one particular type of spatial dependence. Furthermore,
the social networks of labor have not been considered in previous studies of Japanese
relocation decisions.
Unemployment rates: Labor market conditions are probably the most popular
explanation of labor migration in previous studies. According to migration theory (Karemera et al., 2000; Pedersen et al., 2008), expected income is closely associated with the
unemployment rate; labor moves to low-unemployment-rate regions in which the economic conditions are better than those in the origin (Hunt, 2006). Moreover, job security
is considered to be high in these regions (Romer, 2012) because a low unemployment rate
reduces the risks of dismissal for an individual and increases the chances of reemployment
after being fired. Among Japanese migration studies, Kondo and Okubo (2015) analyzed
2
For instance, in epidemiology, Grillet et al. (2010) studied the spatial pattern of malaria incidence
and persistence in Venezuela using spatial statistics and geographically weighted regression. In veterinaryscience, Joly et al. (2006) analyzed the spatial distribution and correlation of epidemics in deer. In ecology,
Getzin et al. (2008) analyzed the effect of environmental heterogeneity in the spatial dynamics of plantcommunities and confirmed that biological processes interact with spatial heterogeneity. Furthermore, inpolitical sciences, Chen and Rodden (2010) confirmed that partisan bias arises from geographical factors,
and in criminology, Vilalta (2010) analyzed the spatial distribution and correlation of drug possession in
Mexico. In education, Gu (2012) confirmed that the admission score chosen by universities in China isspatially autocorrelated with their neighboring competitors.

3

labor inflows and outflows without distinguishing between origin and destination regions.
They found that the unemployment rate increases outflows in some periods (1985–1990
and 1995–2000), but not in another (2005–2010). Tamesue and Tsutsumi (2012) and
Tsutsumi and Tamesue (2012) studied inter-prefectural migration using a spatial autoregression model. They analyzed the effects of the unemployment rate in the origin anddestination separately but concluded that, unlike the theoretical predictions, a higher
unemployment rate in both regions increases migration flows.
Income: Income is another important labor market indicator. Sjaastad (1962) advocated the human capital investment theory of migration, and most modern migration
studies use this analytical framework (Bodvarsson et al., 2015). According to this theory,
people migrate if the benefits from migration exceed the costs. After subtracting the
migration costs, people compare the real income that will be gained in the destination
with that in the origin. Then, they relocate if they can maximize the present value of
their lifetime income in the destination. Using Japanese regional data, Kondo and Okubo(2015) confirmed that consistent with migration theory, net labor inflows increase whenregional income is high, without considering the spatial correlation in migration flows.
Amenities: Amenities are rarely included in the utility function of migrants; however, unlike the human capital investment theory of migration, the consumer theory of
migration includes in the utility function non-tradable goods such as amenities (Bodvarsson et al., 2015). When there are disparities in amenities, even if income differs among
regions, utility may not improve through migration. Therefore, in the presence of differences in amenities, regional economic disparities do not disappear but rather persist.
Greenwood (1997) discussed that temperature is a typical amenity for migrants, findingthat amenities increase when temperature is higher.
Age: In theory, migration decisions are influenced by the life-cycle of households; forexample, younger people are more likely to migrate than older people. According to Becker(1965), the present value of benefits from migration declines by age because older people
spend less time in a destination and thus stand to gain fewer benefits. Consequently,
regions with younger households are expected to experience more emigration.
Distance: In many migration analyses, the geographical distance between regions isused as a proxy for migration costs, such as transportation costs and the costs of obtaining

4

information on labor markets in the destination. Migration costs are assumed to increaseby distance.
Network effects: Bodvarsson et al. (2015) found that psychological and information
costs decline if there is close contact among migrants from the same origin. In sociological migration theory, communities of families and friends and those of migrants inthe destination who come from the same origin are called kinship and migrant networks,
respectively. Yap (1977) and Hugo (1981) reported that when the historical number of
migrants from a specific origin to a destination is high, people tend to relocate to that
destination because the costs of finding out market information in the destination are low.
Carrington et al. (1996) found that these networks decrease psychological and information costs, and migration costs can be proxied by the size of past migration. Here, wename such community-level social networks without distinguishing between kinship andmigrant networks.

3

Migration theory

Our analysis is based on a gravity model, which is a popular economic approach applied
to a number of research areas such as international and regional economics. The nameof the gravity model originates from the law of universal gravitation. We use this model
because it can be extended to include the socioeconomic variables identified in Section 2.
The gravity model in migration studies points to a negative relationship between distance(dod ) and migration flows (Yod ) from the origin (o) to the destination (d):Yod = K

Xoβ1 Xdβ2
dβod3

(1)

where Xo and Xd represent the regional characteristics of o and d, respectively. K is aconstant, and β1 , β2 , and β3 are the parameters to be estimated. This allows us to model
migration inflows and outflows separately. In empirical studies, researchers have often
used the natural logarithm of Eq. (1):ln Yod = ln(K) + β1 ln Xo + β2 ln Xd − β3 ln dod

5(2)

While the gravity model is popular in economic analyses because of its simplicity, it issometimes criticized for lacking theoretical foundations. Therefore, to add the microfoundation to the standard gravity model, we use the random utility maximization modelin line with McFadden (1974), Andersson and Ubøe (2012), and Beine et al. (2016). First,
using the notation ln Y = y, the migration equation can be defined as
yodt = podt sot(3)

where yodt is the number of migrants who move from o to d at time t, sot is the population
stock in o at t, and podt ∈ [0, 1] is the proportion of people who move from o to d at t.
Next, we define the utility function of individual a associated with migration as
Uaodt = wodt − codt + aodt

d = 1, ..., n(4)

where Uaodt is the utility of a arising from migration from o to d at time t, wodt is thenon-stochastic effect on utility, codt is the cost of migration from o to d, and aodt is thestochastic and individual-specific effect on utility. Then, we can express the probabilityof individuals also migrating from o to d as podt :podt = P (Uaolt ≤ Uaodt , ∀l 6= d)= P (wo1t − co1t + ao1t ≤ wodt − codt + aodt , ..., wont − cont + aont ≤ wodt − codt + aodt )= P (ao1t ≤ wodt − codt − (wo1t − co1t ) + aodt , ..., aont ≤ wodt − codt − (wont − cont ) + aodt )Z ∞Yn=P (aolt ≤ (wodt − codt ) − (wolt − colt ) + x)f (x)dx−∞ l=1l6=dFurthermore, assuming that aodt follows the i.i.d. Gumbel distribution (type-I extreme
value distribution), the cumulative distribution function of  is−xF (x) = P (aodt ≤ x) = ee

6Hence, we can express podt as
podt =

=

=

Z ∞Y
n
−∞ l=1l6=d
Z ∞Yn−∞ l=1
l6=d
Z ∞Y
n
0

P (aolt ≤ (wodt − codt ) − (wolt − colt ) + x)fε (x)dx(w

ee olt(w−colt )−(wodt −codt )+x e−x e−e−x

e−e olt−colt )−(wodt −codt ) udx

e−u dul=1
l6=d

Z ∞ −(1+Pn e(wolt −colt )−(wodt −codt ) )u
l=1
l6=d
=
e
du
0

=

ewodt −codtP=n(w −c )−(wodt −codt )wolt −coltl=1 e olt olt
l=1 e

(5)

ewodt −codt
E(yodt ) = Pn w −c sot
olt
olt
l=1 e

(6)

1

1+

Pn

l6=d

From Eqs. (3) and (5),Rewriting Eq. (6), E(yodt ) can be expressed asE(yodt ) = φodt
where xdt = ewodt , φodt = e−codt , and Ωot =

xdt
sot
Ωot

(7)

Pn

l=1 φolt xlt .

Similarly, E(yoot ) can be expressed asE(yoot ) = φoot

xot
sot
Ωot

(8)

Now, assuming no living costs in o and φoot = 1, the ratio of E(yodt ) to E(yoot ) can be
written asE(yodt )xdt= φodtE(yoot )xot(9)where Ωot is canceled out. This equation is the same as the gravity model because theleft-hand side of Eq. (9) is decided by the migration costs associated with the move fromo to d (φodt ), non-stochastic factors in utility by migrating to d (xdt ), and non-stochastic
factors influencing utility by not migrating from o (xot ). By taking the natural logarithmic

7

form, we can obtain a specification consistent with Eq. (2):ln

E(yodt )E(yoot )= ln xdt − ln xot + ln φodt

(10)

where ln xdt , ln xot , and ln φodt correspond to ln Xd , ln Xo , and ln dod in Eq. (2), respectively. As discussed in Section 2, xdt and xot comprise regional data on the unemployment
rate, income, temperature, and average age of labor. In addition, we consider the network
effects between specific regions, which are expected to reduce overall migration costs andincrease current migration. In an application of Eq. (10) to migration studies, Tamesue
and Tsutsumi (2012), for example, focused on migration flows yodt and used only yodt asa dependent variable in Eq. (10).

4Spatial models of origin-destination flows

There are many types of spatial models; however, unlike most previous studies on migration, we examine spatial dependence while distinguishing between origin and destination
regions as well as between inter-prefectural and intra-prefectural migration. The separate
treatment of origin and destination flows is important because a large flow in one particular direction (say, from the origin to the destination) will be ignored in net migration
analyses when it is offset by a large flow in the opposite direction (i.e., from the destination to the origin). As it becomes clear in this study, such a distinction in migration
flows helps us better understand labor movement.
Following LeSage and Pace (2008), the spatial model of origin-destination flows fromthe origin (o) to the destination (d) is expressed as follows:
yod = ρo Wo yod + ρd Wd yod + ρw Ww yod + ιN α + Xo βo + Xd βd + distod γ(11)+ ιi αi + Xi βi + ε
where yod is an N × 1 matrix representing inter-prefectural labor migration (N = n2 ) andn is the number of prefectures. ιN is N × 1 and consists of unity, and α is an intercept. Xo
is an N × k matrix of o’s characteristics, whose elements are zero when the corresponding
dependent variables represent intra-prefectural migration. ιi is an N × 1 vector whose8elements are equal to one, but zero when the corresponding dependent variables represent
intra-prefectural migration. Xi is an N × l matrix where the elements are zero if thecorresponding dependent variables capture inter-prefectural migration. distod is an N1 × 1
matrix that measures the distance between o and d if the corresponding dependent variable
is inter-prefectural migration, but takes zero otherwise. ε is an N × 1 disturbance. ρd ,ρo , and ρw represent the strength of spatial dependence, and βo , βd , αi , and γ are theparameters.
Wo , Wd , and Ww are the spatial weight matrixes that are the origin-based dependence,
destination-based dependence, and origin-to-destination dependence, respectively. The
origin-based spatial dependence (Wo ) measures the strength between migration from an
origin to a particular destination and migration from the origin’s neighbors to the same
destination (Fig. 1). The destination-based dependence (Wd ) measures the relationshipbetween migration from o to d and migration from o to the destination’s neighbor (Fig. 2).
Ww is the origin-to-destination dependence, capturing migration flows from the origin’s
neighbors to the destination’s neighbors (Fig. 3).
For illustrative purposes, let us consider three regions, a, b, and c, to explain W . In
this example, the vector of the dependent variables becomes yod = [yaa , yab , yac , yba , ybb , ybc ,yca , ycb , ycc ]0 , where yaa is intra-regional migration within a and yab shows inter-regionalmigration from a to b. In the context of these three regions, W can be expressed as

0 wab wacW = wba 0 wbc 
wca wcb 0
The elements in W indicate the strength of the contiguity between regions, and the sum of
the rows of W is normalized. Then, the origin-based spatial weight Wo can be expressed
as Wo = W ⊗ In :








0 wab wac0
wab In wac In








Wo = wba 0 wbc  ⊗ In = wba In
0
wbc In 
wca In wcb In
0wca wcb 0

9Therefore, Wo yod can be shown as


0

0

0

wab

0

0

wac

0

0



yaa





wab yba + wac yca     0000 wab 00 wac 0   yab   wab ybb + wac ycb     


 0
0
0
0
0 wab 00 wac   yac   wab ybc + wac ycc     
wba 00
0
0
0 wbc 00   yba  wba yaa + wbc yca   
  

Wo yod =  0 wba 000
0
0 wbc 0   ybb  =  wba yab + wbc ycb     
 00 wba 00
0
0
0 wbc   ybc   wba yac + wbc ycc   
  wca 0
0 wcb 00000yw y + wcb yba   ca   ca aa  
 0 wca 0
0 wcb 0000   ycb   wca yab + wcb ybb   
00 wca 00 wcb 000ycc
wca yac + wcb ybc
where, for example, wab yba + wac yca corresponds to yaa and wab ybb + wac ycb to yab . The
origin-based dependence of yab is captured by Wo yab . Wo represents the fact that migration
flows from o to d are affected (i) strongly by migration from “regions near o” to d and(ii) weakly by migration from “regions distant from o” to d. Fig. 1 illustrates theirrelationship, where region c is subdivided into a close neighbor (A) and a distant neighbor(B). For example, migration from “regions near o” to d is shown as a thick gray arrowfrom A to d and migration from “regions distant from o” to d is shown as a thin grayarrow from B to d. The thickness of the gray arrows expresses the strength of the effectof the gray arrows on the black arrow (i.e., migration from o to d). The capital of thecountry, Tokyo, may be a typical destination to which labor tends to move from all otherregions in Japan.
[Figure 1]
Similarly, the destination-based spatial weight matrix (Wd ) can be defined as Wd =In ⊗ W , that is,





1 0 0
W 0 0








Wd = 0 1 0 ⊗ W =  0 W o 




0 0 1
0 0 W

10

Therefore, Wd yod becomes0

wab wac

0

0

0

0

0

0



yaa





wab yab + wac yac    
wba 0 wbc 000000   yab  wba yaa + wbc yac     
wca wcb 0
0
0
0
0
0
0   yac  wca yaa + wcb yab      0000 wab wac 000   yba   wab ybb + wac ybc   
  

Wd yod =  0
00 wba 0 wbc 000   ybb  =  wba yba + wbc ybc      0
00 wca wcb 0000   ybc   wca yba + wcb ybb   
  



 0



0
0
0
0
0
0 wab wacyw y + wac ycc   ca   ab cb  


 0
0
0
0
0
0 wba 0 wbc   ycb   wba yca + wbc ycc   


0
0
0
0
0
0 wca wcb 0
ycc
wca yca + wcb ycb
Hence, wab yab +wac yac corresponds to yaa and wba yaa +wac yac to yab . The destination-based
dependence of yab captured by Wd yab is depicted in Fig. 2, and Wd indicates that yab isaffected (i) strongly by migration from o to “regions near d” and (ii) weakly by migrationfrom o to “regions distant from d.” In Fig. 2, migration from o to “regions near d”
is shown as a thick gray arrow from o to C and migration from o to “regions distantfrom d” is shown as the thin gray arrow from o to D. The thickness of the gray arrows
expresses the strength of regional dependence. The Kanto region, consisting of, among
others, Chiba, Saitama, and Yokohama, which are located adjacent to Tokyo, may be atypical migration destination of this spatial weight, where more attractive employment
opportunities tend to exist than in the origin.
[Figure 2]
Finally, the origin-to-destination spatial weight is defined as Ww = W ⊗ W :








0 wab wac0
wab W wac W








Ww = wba 0 wbc  ⊗ W = wba W
0
wbc W 
wca wcb 0
wca W wcb W
011

Hence, Ww yod becomes


0

0

0

0

wab wabwab wac



 0
0
0
wab wba0
wab wbc 000
wab wca wab wcb
0


 0
wba wab wba wac
0
0
0


Ww yod = wba wba
0
wba wbc000
wba wca wba wcb
0
0
0
0


 0
wca wab wca wac
0
wcb wab wcb wacwca wba
0
wca wbc wcb wba
0
wcb wbcwca wca wca wcb
0
wcb wca wcb wcb
0

w w y + wab wac ybc + wac wab ycb + wac wac ycc
 ab ab bbwab wba yba + wab wbc ybc + wac wba yca + wac wbc ycc wab wca yba + wab wcb ybb + wac wca yca + wac wcb ycb wba wab yab + wba wac yac + wbc wab ycb + wbc wac ycc = wba wba yaa + wba wbc yac + wbc wba yca + wbc wbc ycc wba wca yaa + wba wcb yab + wbc wca yca + wbc wcb ycb wca wab yab + wca wac yac + wcb wab ybb + wcb wac ybc wca wba yaa + wca wbc yac + wcb wba yba + wcb wbc ybc 
wca wca yaa + wca wcb yab + wcb wca yba + wcb wcb ybb

0

wac wabwac wba0

wac wcawac wcb0

wbc wabwbc wba0

wbc wca

wbc wcb

0

0

0

0

0

0

 
y
  aa  
wac wbc   yab 
 
 
0   yac 
 
 
wbc wac   yba 
 
 
wbc wbc   ybb 
 
 
0   ybc 
 
 
0   yca 
 
 
0   ycb 
 
ycc
0

wac wacTherefore, yaa = wab wab ybb + wab wac ybc + wac wab ycb + wac wac ycc and yab = wab wba yba +wab wbc ybc +wac wba yca +wac wbc ycc . Ww indicates that yod is affected (i) strongly by migrationfrom “regions near o” to “regions near d” and (ii) weakly by migration from “regions
distant from o” to “regions distant from d.” In Fig. (3), migration from “regions near o”
to “regions near d” is shown as the thickest gray arrow from A to C and migration from“regions distant from o” to “regions distant from d” is shown as the thinnest gray arrowfrom B to D. Because Ww yod involves multiple origins and destinations, the interpretationof this weight is complicated. Hence, we do not have any particular expected relationshipwith migration from o to d unlike the other two spatial weights.3[Figure 3]
3

See LeSage and Pace (2008) on the difficulties of interpreting this spatial weight matrix in an economically meaningful way.

12

5

Data

Our dataset covers the 47 regions (i.e., prefectures) of Japan. Regional labor migration
data are obtained from Japan’s National Census (Kokusei Chosa) in 2010,4 and therefore
unusual labor movement due to the 2011 earthquakes and tsunami are not covered here.
The Census is the most comprehensive dataset that collects details of residents in Japanand is conducted every five years. Migrant labor refers to workers who have relocatedresidences from one prefecture to another in the past five years.5 The labor force consistsof employed and unemployed people; employed workers are those older than 15 years
earning income, and the unemployed are those who do not have earnings but are seeking
work. In 2010, about 65 million people were in the labor force, of which 63 million people
were employed. Given Japan’s population of 128 million in 2010, half the population
can thus be regarded as in the labor force. This proportion is very low by international
standards because Japan is one of the most aged countries.
Other data are collected from various sources. Real GDP per capita, which is a proxyfor income, is obtained from the Japanese Cabinet Office and is equal to nominal GDP
per capita (1000 yen) in 2005 divided by a GDP deflator in 2005. Unemployment rates(%) are calculated from the National Census in 2010. Regional temperatures (◦ C) are
the average temperatures between 2005 and 2010, and are obtained from the Statistics
Bureau, Ministry of Internal Affairs and Communications (MIAC). The average age ofprefectural labor is calculated based on information in the National Census in 2010,6 andthe geographical distance between prefectures is from Japan’s Geospatial Information
Authority. Social networks are from the MIAC, and are proxied by cumulative migration
between prefectures from October 2000 to September 2005. Finally, regional goods flows
in 2005, which are used to construct the spatial weight, are collected from the Logistics
Census of the Ministry of Land, Infrastructure and Transport.
Table 1 presents the descriptive statistics of the data, showing regional disparities inmany statistics. For example, Fig. 4 shows the unemployment rate of each prefecture.
The highest unemployment rate (11.9%) is recorded for Okinawa and the lowest (4.24%)
for Fukui. The gap in these regional unemployment rates is about 8 percentage points,
4This is the most recent data disseminated to the public.
The National Census was conducted in October.
6
In this dataset, workers older than 85 years are treated as 85 years old.
513

implying that significant regional disparities exist in the labor market conditions. In
addition, Fig. 5 reports the income of each prefecture. The highest real GDP per capita
of 5.17 million yen is recorded for Tokyo and the lowest (2.04 million yen) for Okinawa.
The regional difference is about 3.13 million yen.
[Table 1 & Figs. 4 and 5]
The importance of spatial dependence in migration studies has been underlined, butwhat are elements of W (i.e., w) that determines the definition of neighbors? Here, we use
three definitions of a spatial weight matrix based on 1) the distance between prefectural
capitals, 2) past migration, and 3) goods flows. The majority of previous studies have usedgeographical distance, assuming that the proximity of regions indicates a tight economic
relationship with each other. Further, we use additional definitions to check the robustnessof our findings because there are three metropolitan areas in Japan (i.e., Tokyo, Osaka,
and Aichi) to which many people and goods flow—even from distant rural regions.
Thus, the first definition of a spatial weight is based on the geographical distance
between regions: Wo , Wd , and Ww . This definition is the most popular in previous spatial
analyses and assumes that spatial dependence is related to the physical proximity between
regions. Let us define a 47 × 47 spatial weight matrix W consisting of wod :dist−p P47 od −p , if o 6= d
d=1 distod
wod =


0,
otherwise
where distod is the distance between prefectural capitals and p can take any realpositive value (p=1, 2, or 3 in this study). Then, we can construct spatial weight matrixes
by using the Kronecker product as Wo = W ⊗ I, Wd = I ⊗ W , and Ww = W ⊗ W , where
I is a 47 × 47 identity matrix.
The second spatial weight utilizes the size of cumulative migration (W o , W d , andW w ). According to this spatial weight, when many migrants have relocated to particular
destinations in the past, labor migration to these regions is also expected to be high today.
Assuming a 47 × 47 spatial weight matrix W , it consists of wod where the elements of the14

rows are normalized.
(z od,t−1 + z do,t−1 )


 P47
, if o 6= d+z)(zod,t−1do,t−1
d=1
wod =



0,
otherwise
where z do,t−1 is past migration from o to d. As before, we can define three spatial weightmatrixes by using the Kronecker product as W o = W ⊗ I, W d = I ⊗ W , and W w =W ⊗ W.
The final definition of spatial weight matrixes utilizes the size of goods flows between
prefectures (W̃o , W̃d , and W̃w ), which are constructed using a 47×47 spatial weight matrixW̃ that consists of w̃od , where the sum of the rows is normalized:(god,t−1 + gdo,t−1 )


 P47
, if o 6= d(g+g)
od,t−1do,t−1d=1w̃od =0,otherwise
where god,t−1 is the past goods flow between o and d. We assume that the higher the past
goods flow between regions, the greater is the importance of their relationship. Therefore,
this spatial matrix is closely related to regional relationships through trading economic
goods. These three spatial weight matrixes are again obtained by using the Kronecker
product as W̃o = W̃ ⊗ I, W̃d = I ⊗ W̃ , and W̃w = W̃ ⊗ W̃ .

6

Empirical results

6.1

Results from the non-spatial models

Initially, we estimate a cross-sectional migration model without considering spatial dependence. Maintaining the notations of the variables used in the previous section and inline with LeSage and Pace (2008, 2009), this basic model can be written as Eq. (12) but
includes past cumulative migration (z od,t−1 ) as a proxy for social networks:

yod = ιN α + Xo βo + Xd βd + distod γ + z od,t−1 δ + ε(12)

The OLS results in Table 2 show that the treatment of social networks influences15the empirical outcomes. In Column (1-1), which does not control for social networks, theunemployment rate in both o and d has a positive and significant effect on labor migration.
By contrast, in Column (1-2), which controls for social networks, the unemployment rate ino is insignificant, but this rate in d has a negative and significant effect on labor migration.
This negative sign is consistent with the theoretical predictions and suggests that labor
moves to low-unemployment-rate regions. Because the parameter of the network effects isfairly large (0.962) and the Akaike information criterion (AIC) in Column (1-2) is smaller
than that in Column (1-1), controlling for social networks improves the model performance
significantly, suggesting a large omitted bias in the estimates reported in Column (1-1).
From the fact that labor does not react to the origin’s unemployment rate but to thedestination’s unemployment rate, it is conceivable that labor migrates if the labor market
conditions of the destination are seen to be good—regardless of the origin’s unemployment
rate. Such a phenomenon, which can be represented as “the grass is always greener on theother side,” is confirmed by Dinger et al. (2012) and can be used to explain our results.
A similar outcome is obtained from the other variables. For example, in Column (11), income in both o and d has a positive and significant effect on labor migration. This
result, that labor migration increases with high income in o, is inconsistent with migration
theory. By contrast, in Column (1-2), both the income parameters are correctly signed,
although they no longer have statistical significance. Together with these results and thepositive and significant parameter for the social network effects, we conclude that social
networks are important factors in relocation decisions and act to increase labor migration.
Next, we consider the spatial dependence absent from our analyses so far.
[Table 2]

6.2

Results from the spatial models

6.2.1

A spatial weight matrix based on geographical distanceHere, the level of regional ties is determined by their physical location; labor is expected
to move to destinations near the origin in terms of the distance between regions. Because
migration flows may influence the explanatory variables such as income and unemployment
rates, we estimate such spatial migration models by using the spatial two-stage leastsquares (S2SLS) method to deal with the potential endogeneity problem (see the Appendix
16

for more details on the S2SLS). Tables 3, 4, and 5 show the empirical results of Eq. (13)that uses the spatial weights based on the distance between prefectures. More specifically,
the spatial weights considered here are based on the inverse distance (Table 3), the squareof the inverse distance (Table 4), and the cubic form of the inverse distance (Table 5):

yod =ρo Wo yod + ρd Wd yod + ρw Ww yod + ιN α + Xo βo + Xd βd + distod γ + z od,t−1 δ(13)+ ι i α i + Xi βi + ε
In these tables, all ρo , ρd , and ρw are reported to be statistically significant, suggesting that migration flows have complex spatial dependence. In particular, the first two
parameters are positive and confirm that labor migration from o to d is highly associatedwith migration from o to prefectures close to d as well as with migration from prefecturesnear o to d. The negative ρw implies that regional heterogeneity is prominent in Japan.
Among the different forms of spatial matrixes, the spatial model with the square of theinverse distance (p = 2) fits the data best because the AIC is the smallest; furthermore,this spatial model explains labor migration better than the non-spatial model (Table 2)
based on their AICs.
Let us look more closely at the results in Table 4 (p = 2) with the smallest AIC.
We again confirm the importance of social networks in migration decisions and large
omitted bias in Column (3-1) that does not consider this effect. There, the unemployment
rate in both o and d does not affect labor migration significantly. In Column (3-2), theunemployment rate in o does not have a significant effect on labor migration, but the rate
in d has a negative and significant effect. Therefore, it is important to distinguish between
immigrants and emigrants; otherwise, we could not conclude that only the unemployment
rate of the destination has a significant and negative effect on labor migration. Ourfinding concurs more closely to migration theory than those of Kondo and Okubo (2015),
who reported that the unemployment rate has no significant effect on migration between
2005 and 2010, and Tamesue and Tsutsumi (2012) and Tsutsumi and Tamesue (2012)
who reported that the unemployment rate in both the origin and the destination increases
migration.
Similarly, omitted bias is reported for the other variables in Column (3-1). Income in17both o and d has a significant effect on labor migration in Column (3-1), but in Column (32) income in o has a negative and significant effect on labor migration. Since lower incomein the origin should motivate workers there to consider relocation, it is important to control
for both spatial dependence and the social network effects in migration studies. The resultthat only income in the destination has a significant negative effect is more consistent withthe theoretical predictions than previous studies (e.g., Tamesue and Tsutsumi, 2016)that have found that high income in both the origin and the destination regions reduces
migration. Our results from the spatial models are also in contrast to those obtained
from the non-spatial models and thus confirm the importance of regional dependence inmigration studies.
[Tables 3, 4, and 5]
6.2.2

A spatial weight matrix based on past migration

Column (5) in Table 6 shows the S2SLS results of the model (Eq. (14)) that uses theweight matrixes based on past migration. Thus, neighboring regions are defined by thehistorical number of migrants between regions:yod =ρo W o yod + ρd W d yod + ρw W w yod + ιN α + Xo βo + Xd βd + distod γ + z od,t−1 δ(14)+ ιi αi + Xi βi + ε
In general, the empirical results are similar to those obtained by using the distancebased spatial weight matrixes. Again, ρo , ρd , and ρw are all statistically significant with thesame parameter signs obtained from the distance-based matrixes. This outcome indicatesthat current labor migration flows are influenced by historical movement. On the effectsof the unemployment rate in Table 6, this rate of o does not have a significant effecton labor migration, whereas the unemployment rate of d has a negative and significant
effect on labor migration to d. Moreover, the income of o has a negative effect on labor
migration from o, whereas the income of d does not have a significant effect on labor
migration. These results are the same as those in Column (3-2), which used the squareof the inverse distance-based weight matrix; however, the model performance is not as
good as that when using the distance-based spatial weight matrix. Indeed, the AIC of18this model is larger than that for the model using the distance-based weight matrix with
p = 2.
[Table 6]
6.2.3

A spatial weight matrix based on goods flows

Column (6) in Table 6 shows the S2SLS results of the model, Eq. (15), which uses thespatial weight matrixes based on goods flows. This is an alternative way to define neighbors; here, neighboring regions are determined by the volume of trade between regions.
This definition of neighbors is expected to be relevant in Japan where metropolitan areas
are scattered across a country and regions physically close to each other may not have a
direct economic relationship:
yod =ρ˜o W̃o yod + ρ̃d W̃d yod + ρ̃w W̃w yod + ιN α + Xo βo + Xd βd + distod γ + z od,t−1 δ(15)+ ι i α i + Xi βi + ε
The general conclusion remains the same as before. Social networks play a positive andsignificant role in labor migration, and similarly ρ̃o , ρ̃d , and ρ̃w are statistically significant
and maintain the same parameter signs; therefore, migration flows are closely related tothe size of trade not only between two regions but also among their neighbors. Furthermore, the unemployment rate in o does not have a significant effect on labor migration,
whereas this rate in d has a negative and significant effect on labor migration flows to d.
These results are the same as those in Column (3-2) based on the square of the inverse
distance-based weight matrix and Column (5) based on the past migration weight matrix.
Moreover, the income of o has negative effects on labor migration from o, whereas theincome of d does not. However, the performance of this model is not as good as thatof the other spatial models using weight matrixes based on distance and past migrationaccording to the AICs.
6.2.4

A combination of the spatial weight matrixes

So far, we have assumed only one type of spatial weight matrix in a spatial model following
the conventional approach. Here, we consider different combinations and definitions of
the spatial weights used in this section (i.e., Eqs. (16)–(19)) because spatial dependence19may be more complicated than previous studies have assumed. While maintaining thesame notations as before, Eq. (16) contains the spatial weight matrixes based on distanceand past migration (W and W̄ ), Eq. (17) on distance and goods flows (W and W̃ ), andEq. (18) on past migration and goods flows (W̄ and W̃ ). Eq. (19) contains all types ofspatial weights:

yod =ρo Wo yod + ρd Wd yod + ρw Ww yod + ρo W o yod + ρd W d yod + ρw W w yod(16)+ ιN α + Xo βo + Xd βd + distod γ + z od,t−1 δ + ιi αi + Xi βi + ε

yod =ρo Wo yod + ρd Wd yod + ρw Ww yod + ρ˜o W̃o yod + ρ̃d W̃d yod + ρ̃w W̃w yod(17)+ ιN α + Xo βo + Xd βd + distod γ + z od,t−1 δ + ιi αi + Xi βi + ε

yod =ρo W o yod + ρd W d yod + ρw W w yod + ρ˜o W̃o yod + ρ̃d W̃d yod + ρ̃w W̃w yod(18)+ ιN α + Xo βo + Xd βd + distod γ + z od,t−1 δ + ιi αi + Xi βi + ε

yod =ρo Wo yod + ρd Wd yod + ρw Ww yod + ρo W o yod + ρd W d yod + ρw W w yod+ ρ˜o W̃o yod + ρ̃d W̃d yod + ρ̃w W̃w yod + ιN α + Xo βo + Xd βd + distod γ + z od,t−1 δ (19)+ ι i α i + Xi βi + ε
Table 7 summarizes the S2SLS results of these models. Column (7) uses the spatial
matrixes based on distance and past migration, Column (8) uses those on distance andgoods flows, Column (9) uses those on past migration and goods flows, and Column (10)uses all three types of the weight matrixes. The AICs of these models in Table 7 except
Column (9) are smaller than those of the models with one weight matrix reported inTables 3–6, indicating that the goodness of fit has improved by using several types ofweight matrixes.
[Table 7]
The common results from Columns (7)–(9) are that the unemployment rate of d has a20negative effect on labor migration to d and that income in o has a negative and significant
effect on labor migration from o. Furthermore, the social network effects are reported
to increase labor migration, consistent with the theoretical predictions. Moreover, inColumns (7) and (8), whose AICs are smaller than that of Column (9), two types ofweight matrixes are statistically significant, suggesting that using only one spatial weightmatrix is inadequate to fully capture the spatial dependence in migration flows.
In Column (10), which uses all three types of weights, all three distance-based spatial
weight matrixes and all three past migration-based spatial weight matrixes are statisticallysignificant. Furthermore, we find that the unemployment rate of d has a negative andsignificant effect on labor migration to d and that the income of o has a negative andsignificant effect on migration from o. Because the AIC is the smallest, the results ofColumn (10) are considered to be the most reliable.
In short, we find that not only the distance between regions, but also past migrationand goods flows are important factors for capturing the spatial correlation, which is an
original contribution of this study. For example, LeSage and Pace (2008, 2009), Tamesue
and Tsutsumi (2012, 2016), and Tsutsumi and Tamesue (2012) used a spatial weightmatrix based on inverse distance only and often reported statistical evidence inconsistent
with migration theory. Therefore, regional dependence is more complex than researchers
have thought, and it is important to consider several types of spatial correlations whenmodeling labor migration.
We have explained the empirical results by focusing on the relationship between labor
migration and economic motivations; however, other control variables are also often foundto be statistically significant. For example, in Columns (7)–(10), we report that the higher
the temperature in o, the lower is the migration from o and that the higher the temperaturein d, the higher is the migration to d, as expected from the theory. Because amenitiesof labor are expected to increase in warmer regions in Japan, we confirm that relocation
decisions are sensitive to temperature.
With respect to the age of labor, Columns (7)-(10) show that the younger the averageage in o, the higher is the migration from o. As explained in Section 2, when the proportionof young labor is high in a region, migrants tend to move from there. Similarly, the younger
the average age in d, the higher is the migration to d. This finding reflects the fact that21

many young people live in urban areas that are typical destination regions for migrants.
The distance between o and d is also reported to be significant in Columns (7)–(10),suggesting that the longer distance between prefectures has resulted in less migration fromo to d. This finding implies that migration to a distant region is considered to incur higher
costs and uncertainty. Similarly, we find that regions with high intra-regional migration
often experienced high inter-regional migration during our sample period. Thus, there
seems to be regional differences in attitudes toward the relocation of residence.

7

Conclusion

This study empirically analyzes the effects of regional characteristics on inter-prefecturallabor migration by using spatial models of origin-destination flows. The considerationof network effects and different types of spatial dependence leads us to empirical results
more consistent with the theoretical predications than previous studies. More specifically,
we find that labor is more likely to react to the destination’s unemployment rate andorigin’s income. Second, social networks of migrants, which help reduce the costs ofgathering information and uncertainty about the destination, are important factors when
making migration decisions. Third, many spatial migration analyses have used only adistance-based spatial weight matrix, whereas we find that spatial dependence is more
complicated than conventionally thought; regions are also closely linked to, for example,
economic goods flows.
In short, based on a comprehensive migration model, we show that regional labormobility can be explained by socioeconomic factors in Japan, and thus the recent wideningof the gap between urban and rural regions is a natural outcome of migration decisions.
In this regard, this decoupling process cannot be slowed or prevented by market forces;
the intervention of the public sector seems to be indispensable to make rural regions
sufficiently attractive to be considered to be destination regions by workers.

22

Appendix
S2SLS model
Following LeSage and Pace (2008), we construct a spatial regime model and estimate it
by using S2SLS. The spatial lagged variables Wo yod , Wd yod , Ww yod , W o yod , W d yod , W w yod ,W̃o yod , W̃d yod , and W̃w yod in this study may be endogenous variables in a migration
function, and therefore we use S2SLS in accordance with Badinger and Egger (2011).
Defining Z that consists of all the exogenous explanatory variables in the model, theinstrumental variables of the endogenous variables of Wo y, Wd y, and Ww y are H =(Z, Wo Z, Wd Z, Ww Z, Wo2 Z, Wd2 Z, Ww2 Z, Wo Ww Z, Wd Ww Z) in model (14). Similarly, theinstrumental variables of W o yod , W d yod , and W w yod are222

H = (Z, W o Z, W d Z, W w Z, W o Z, W d Z, W w Z, W o W w Z, W d W w Z), and the instrumental
variables of W̃o yod , W̃d yod , and W̃w yod areH̃ = (Z, W̃o Z, W̃d Z, W̃w Z, W̃o2 Z, W̃d2 Z, W̃w2 Z, W̃o W̃w Z, W̃d W̃w Z).

23

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26

Table 1: Descriptive Statistics
Mean
Log of inter-prefectural migration
6.16
Unemployment rate
5.94
Log of real GDP per capita
7.93
Average annual temperature
15.5
Log of average age of labor
3.80
Log of distance
5.98
Log of past inter-prefectural migration
7.32
Log of inter- and intra-prefectural migration 6.28
Log of past intra-prefectural migration
12.2
Note: Standard deviation (SD).

27

SD
1.62
1.34
0.16
2.38
0.02
0.80
1.60
1.81
0.92

Min Max
2.48 11.8
4.24 11.9
7.62 8.55
9.26 23.4
3.73 3.84
2.35 7.72
2.64 12.9
2.48 13.9
10.8 14.5

Table 2: OLS results
Dependent variable: log of inter-prefectural labor migration
Explanatory variable
(1-1)
(1-2)
Intercept
177.979∗∗∗
16.689∗∗∗(8.614)(1.597)0.140∗∗∗
0.006
Unemployment rate o(0.022)(0.004)
Unemployment rate d
0.058∗∗−0.066∗∗∗(0.022)(0.004)
1.615∗∗∗−0.057Log of real GDP per capita o(0.209)(0.032)2.003∗∗∗
0.029
Log of real GDP per capita d(0.190)(0.035)−0.057∗∗∗−0.015∗∗∗
Average annual temperature o(0.010)(0.002)Average annual temperature d−0.023∗0.007∗∗∗(0.010)(0.002)−24.001∗∗∗−1.377∗∗∗Log of average age of labor o(1.276)(0.233)−27.169∗∗∗−2.973∗∗∗Log of average age of labor d(1.268)(0.227)Log of distance between prefectures−0.992∗∗∗−0.062∗∗∗(0.031)(0.006)
Log of past human migration
0.962∗∗∗(0.004)
Sample size
2162
2162
2
Adjusted R
0.657
0.987
AIC
5914.839−1184.446
Note: ***p<0.001, **p<0.01, *p<0.05
Heteroscedasticity robust standard errors are shown in ()28

Table 3: S2SLS results (Inverse-distance based weight matrix)
Dependent variable: log of inter-prefectural labor migration
Explanatory variable
(2-1)
(2-2)
Intercept
5.499
15.529∗∗∗(3.741)(1.633)
Unemployment rate o
0.010
0.003
(0.009)(0.004)
Unemployment rate d
0.014−0.062∗∗∗(0.009)(0.004)−0.419∗∗∗−0.132∗∗∗Log of real GDP per capita o(0.074)(0.035)Log of real GDP per capita d−0.457∗∗∗0.031(0.074)(0.037)−0.010∗∗−0.015∗∗∗
Average annual temperature o(0.004)(0.002)−0.013∗∗∗0.006∗∗∗
Average annual temperature d(0.003)(0.002)0.300−0.875∗∗∗Log of average age of labor o(0.553)(0.247)Log of average age of labor d
0.297−2.950∗∗∗(0.571)(0.266)
Log of distance between prefectures−0.121∗∗∗−0.066∗∗∗(0.021)(0.006)
Log of past human migration
0.903∗∗∗(0.013)
ιi
17.080∗∗∗−14.983∗∗∗(4.473)(1.766)−1.2790.424∗∗∗
Log of the number of labor i(0.703)(0.094)Log of past migration i−0.0120.433∗∗∗(0.628)(0.075)ρo1.098∗∗∗
0.096∗∗∗(0.014)(0.016)ρd1.092∗∗∗
0.062∗∗∗(0.014)(0.016)ρw−1.181∗∗∗−0.124∗∗∗(0.032)(0.021)
Sample number
2209
2209
AIC
1880.203−1342.174
Note: ***p<0.001, **p<0.01, *p<0.05
Heteroscedasticity robust standard errors are shown in ()29

Table 4: Result of S2SLS (Square of inverse-distance based weight matrix)
dependent variable: log of inter-prefectural labor migration
explanatory variable
(3-1)
(3-2)
Intercept
17.387∗∗∗15.242∗∗∗(3.864)(1.565)
Unemployment rate o
0.009
0.001
(0.008)(0.004)
Unemployment rate d−0.004−0.062∗∗∗(0.008)(0.004)
0.335∗∗∗−0.079∗Log of real GDP per capita o(0.079)(0.032)Log of real GDP per capita d
0.364∗∗∗
0.056(0.081)(0.034)−0.004−0.013∗∗∗
Average annual temperature o(0.003)(0.002)−0.0000.007∗∗∗
Average annual temperature d(0.003)(0.002)−2.629∗∗∗−1.060∗∗∗Log of average age of labor o(0.575)(0.224)Log of average age of labor d−3.302∗∗∗−2.913∗∗∗(0.609)(0.236)
Log of distance between prefectures
0.043∗−0.048∗∗∗(0.022)(0.007)Log of past human migration
0.886∗∗∗(0.017)ιi−2.063−14.899∗∗∗(4.547)(1.675)−1.067
0.396∗∗∗
Log of the number of labor i(0.600)(0.097)Log of past migration i
0.384
0.462∗∗∗(0.521)(0.076)ρo0.886∗∗∗
0.103∗∗∗(0.023)(0.017)ρd0.880∗∗∗
0.074∗∗∗(0.023)(0.018)ρw−0.877∗∗∗−0.108∗∗∗(0.031)(0.018)Sample size
2209
2209
AIC
1628.63−1411.023
Note: ***p<0.001, **p<0.01, *p<0.05
Heteroscedasticity robust standard errors are shown in ()30

Table 5: Result of S2SLS (Cubic form of inverse-distance based weight matrix)
Dependent variable: log of inter-prefectural labor migration
Explanatory variable
(4-1)
(4-2)
Intercept
57.240∗∗∗16.710∗∗∗(6.883)(1.576)
Unemployment rate o
0.042∗∗∗
0.001(0.012)(0.004)0.012−0.064∗∗∗
Unemployment rate d(0.011)(0.004)0.759∗∗∗−0.079∗Log of real GDP per capita o(0.117)(0.033)0.901∗∗∗
0.050
Log of real GDP per capita d(0.124)(0.034)
Average annual temperature o−0.016∗∗−0.013∗∗∗(0.005)(0.002)−0.0050.007∗∗∗
Average annual temperature d(0.005)(0.002)Log of average age of labor o−8.113∗∗∗−1.277∗∗∗(0.988)(0.224)−9.596∗∗∗−3.059∗∗∗Log of average age of labor d(1.090)(0.229)Log of distance between prefectures−0.173∗∗∗−0.059∗∗∗(0.033)(0.007)Log of past human migration
0.924∗∗∗(0.012)ιi−47.774∗∗∗−17.271∗∗∗(7.516)(1.633)Log of the number of labor i−0.6600.471∗∗∗(0.411)(0.073)0.552
0.476∗∗∗
Log of past migration i(0.351)(0.055)ρo0.634∗∗∗
0.058∗∗∗(0.040)(0.011)ρd0.621∗∗∗
0.033∗∗(0.042)(0.011)
ρw−0.597∗∗∗−0.061∗∗∗(0.046)(0.011)
Sample size
2209
2209
AIC
2909.507−1354.176
Note: ***p<0.001, **p<0.01, *p<0.05
Heteroscedasticity robust standard errors are shown in ()31

Table 6: S2SLS results (Past migration based and goods flow based weight matrixes)
Dependent variable: log of inter-prefectural labor migration
Explanatory variable(5)Intercept
15.115∗∗∗(1.571)
Unemployment rate o
0.002(0.004)−0.060∗∗∗
Unemployment rate d(0.004)−0.172∗∗∗Log of real GDP per capita o(0.035)0.034
Log of real GDP per capita d(0.039)Average annual temperature o−0.014∗∗∗(0.002)0.006∗∗
Average annual temperature d(0.002)Log of average age of labor o−0.639∗∗(0.241)
Log of average age of labor d−3.015∗∗∗(0.267)Log of distance between prefectures−0.072∗∗∗(0.006)
Log of past human migration
0.865∗∗∗(0.022)ιi−14.230∗∗∗(1.740)0.356∗∗
Log of the number of labor i(0.120)0.448∗∗∗
Log of past migration i(0.098)ρo0.127∗∗∗(0.021)
ρd0.084∗∗∗(0.023)ρw−0.116∗∗∗(0.023)ρ̃oρ̃dρ̃w
Sample size
2209
AIC
−1378.606
Note: ***p<0.001, **p<0.01, *p<0.05
Heteroscedasticity robust standard errors are shown in ()32(6)
15.411∗∗∗(1.574)0.003(0.004)−0.061∗∗∗(0.004)−0.179∗∗∗(0.036)0.036(0.041)−0.013∗∗∗(0.002)0.006∗∗∗(0.002)−0.670∗∗(0.245)−3.072∗∗∗(0.261)−0.071∗∗∗(0.006)0.895∗∗∗(0.015)−14.967∗∗∗(1.679)0.385∗∗∗(0.104)0.469∗∗∗(0.082)

0.098∗∗∗(0.016)
0.055∗∗∗(0.017)−0.086∗∗∗(0.018)2209−1341.942

Table 7: S2SLS results (Combination of weight matrixes)
Dependent variable: log of inter-prefectural labor migration
Explanatory variable(7)Intercept
13.799∗∗∗(1.551)
Unemployment rate o
0.000(0.004)−0.059∗∗∗
Unemployment rate d(0.004)Log of real GDP per capita o−0.141∗∗∗(0.034)0.059
Log of real GDP per capita d(0.038)Average annual temperature o−0.011∗∗∗(0.002)Average annual temperature d
0.007∗∗∗(0.002)−0.627∗∗Log of average age of labor o(0.242)−2.858∗∗∗Log of average age of labor d(0.269)Log of distance between prefectures−0.063∗∗∗(0.008)Log of past human migration
0.810∗∗∗(0.022)
ι−12.277∗∗∗(1.737)0.284∗
Log of the number of labor i(0.124)Log of past human migration i
0.429∗∗∗(0.102)ρo0.077∗∗∗(0.018)ρd0.083∗∗∗(0.018)ρw−0.117∗∗∗(0.017)ρo0.111∗∗∗(0.023)ρd
0.066∗∗(0.024)ρw−0.053∗(0.023)ρ̃oρ̃dρ̃w
Sample size
2209
AIC
−1480.389
Note: ***p<0.001, **p<0.01, *p<0.05
Heteroscedasticity robust standard errors are shown in ()33(8)
13.351∗∗∗(1.560)0.001(0.004)−0.058∗∗∗(0.004)−0.138∗∗∗(0.035)0.061(0.040)−0.012∗∗∗(0.002)0.006∗∗∗(0.002)−0.599∗(0.247)−2.805∗∗∗(0.268)−0.056∗∗∗(0.007)0.828∗∗∗(0.019)−12.114∗∗∗(1.732)0.3148∗∗(0.120)0.426∗∗∗(0.098)0.094∗∗∗(0.018)0.096∗∗∗(0.018)−0.130∗∗∗(0.018)(9)14.299∗∗∗(1.568)0.002(0.004)−0.058∗∗∗(0.004)−0.180∗∗∗(0.035)0.007(0.040)−0.014∗∗∗(0.002)0.005∗∗(0.002)−0.552∗(0.242)−2.804∗∗∗(0.266)−0.075∗∗∗(0.006)0.830∗∗∗(0.022)−12.738∗∗∗(1.748)0.303∗(0.141)0.429∗∗∗(0.119)(10)12.836∗∗∗(1.554)0.001(0.004)−0.056∗∗∗(0.004)−0.135∗∗∗(0.035)0.049(0.039)−0.012∗∗∗(0.002)0.006∗∗∗(0.002)−0.553∗(0.246)−2.682∗∗∗(0.269)−0.064∗∗∗(0.008)0.782∗∗∗(0.022)−10.971∗∗∗(1.746)0.266(0.138)0.397∗∗∗(0.118)0.090∗∗∗(0.019)0.095∗∗∗(0.019)−0.138∗∗∗(0.018)0.172∗∗∗
0.135∗∗∗(0.038)(0.036)0.115∗∗∗
0.085∗(0.035)(0.034)−0.162∗∗∗−0.105∗∗(0.039)(0.038)0.081∗∗∗−0.009−0.005(0.016)(0.028)(0.027)0.041∗
0.009
0.004(0.018)(0.025)(0.026)−0.0260.009
0.044(0.020)(0.031)(0.031)
2209
2209
2209
−1468.255−1391.960−1489.003

Figure 1: Origin-based dependence of yab

Figure 2: Destination-based dependence of yab

Figure 3: Origin to destination dependence of yab

34

Figure 4: Unemployment rate (%) in October, 2005 from national census of 22th year of
the Heisei period

Figure 5: Real GDP per capita (ten thousand yen) in 2005 from GDP created by theJapanese cabinet office35