How did Disaster Victims Migrate after the Great East
Japan Earthquake?: Long-Term Recursive Migration
Model after Super Disasters
INU021003

Rena Koseki
koseki@bin.t.u-tokyo.ac.jp
Eiji Hato
hato@bin.t.u-tokyo.ac.jp

Abstract
This study focuses on long-term recursive migration after a super disaster and describes the dynamic
migration process based on the ever-changing situation and future utility after a disaster. As natural
disasters become more severe due to climate change, it is urgent to establish aid schemes for disasterinduced migration. Although various case studies have clariﬁed the relationship between disasters andmigration, few studies have focused on the long-term migration process after disasters. We aim to model
the long-term migration with a discounted recursive logit model where victims choose their location andrelocation timing considering the future utility. As a case study, we adapted the model to the 10-year
residential history of the Great East Japan Earthquake victims and conﬁrmed the usability of the model.
The time discount rate is estimated to be smaller for the victims in Fukushima Prefecture, who wereforced to evacuate from their hometowns due to the nuclear power plant accident and continued to be in
an uncertain situation for a long period. The result indicates that it was diﬃcult for them to choose aplace to live with an eye on the future due to extreme uncertainty. In addition, it shows that the level ofincome and life cycle would be essential factors for victims to choose their location and timing of housing
recovery. This model helps consider not only the scale of reconstruction projects but also their optimal
timing because it can incorporate the progress of projects and environmental changes over time.

Koseki and Hato

1

INTRODUCTION
In discussing the movement after disasters, it is needed to manage two movements: evacuation andmigration. The former is related to studies on dynamic traffic management to maximize evacuation
flow per unit time by controlling traffic capacity and information (1)(2)(3), while the latter isthe problem of managing migration and resettlement of migrants after disasters. Although thesemigration choices taken by disaster-affected people until they settle on can be defined as a dynamic
decision-making problem (4)(5), it is difficult to say that there is an established methodology todescribe it.
Evacuation is a decision made in a short period, and therefore easy to obtain data to understand the phenomena, leading to a large amount of research accumulated in traffic management.
On the other hand, disaster-induced migration could be a long-term movement that takes placeover a while, so many things are not understood from a phenomenological point of view. Aggregate analyses of the relationship between disasters and migration are often conducted over decades(6)(7). However, because of the limited availability of residential trajectory data on individual migration, many works, especially micro-level models, are forced to focus on the initial residential
choice or the one at one particular point in time (8). Urata et al. (9) uses mobile phone traffic data
to reveal changes in the Spatio-temporal characteristics of population distribution before and aftera disaster for one month. However, such big data might not be suitable for analyzing long-term
residential choices over decades. Such partial observations and modeling make it challenging toanalyze the behavior of disaster victims who are displaced over the long term and design disastercompensation schemes that respond to differences in disaster conditions.
As for the dynamic effect of migration on transportation demand, in the framework of panel
analysis, it has been shown that migrants have different transportation behavioral characteristics
from natives, and it takes several years or more to assimilate. Therefore, it is essential to understandthe migration trends and their influences on the transport demand in the destination city to improveurban transit demand modeling and long-term investment decisions (10)(11).
On the other hand, the residential choice itself has often been taken as a static problem,
like the model of McFadden (12), pioneering work in discrete choice modeling. In recent researchon urban traffic demand forecasting, microsimulation, which can simulate the decision-makingof each traveler individually and dynamically, is getting more critical compared to the traditional
four-step (13)(14). These models need population synthesis methods for constructing a list of the
population as an input, which is put together with comprehensive demographic and socioeconomic
attributes (15). In this way, to acquire the population as an essential input for the transportation
demand forecast, extensive studies are trying to reproduce underlying distribution and statisticalproperties of the actual population as accurately as possible, using available micro samples andmarginals from census data (16)(17). While these models produce each individual’s activity pattern in a typical day as output, when we consider the disaster-induced discontinuous population
flows resulting from dynamic migration choices, it is important to explicitly model the dynamic
and recursive decision-making. Recursive decision-making here means thinking about the future
utility, including the life cycle changes or environmental and policy variables.
When extreme events such as disasters and wars occur, people who lose their original lives
begin to travel to new cities, as depicted in Exodus. After a disaster, people temporarily leave thecity, and the affected area’s population rapidly decreases. While some people may return to thecity after reconstruction, others may not because of the time it takes or because gentrification has
progressed. In considering the post-disaster population movement, the control of the insuranceKoseki and Hato

2

fitting to the life stage, residential rent support systems, and the timing of infrastructure reconstruction will be significant policy variables (18)(19)(20). It is difficult to say that a methodology
has been established to examine policies to maintain the population in disaster-affected areas or
optimize the scale of reconstruction projects in light of a declining population. As the first step,
it is necessary to understand how the affected people ultimately reached their final decision undervarious constraints to protect their families and keep the community.
From these perspectives, this study tries to model the long-term recursive migration choices
after super disasters theoretically. First, we summarize the existing studies on migration and dynamic decision-making models. Next, the recursive migration model framework is presented andformulated, and then the results of a case study of the Great East Japan Earthquake are presented.
Finally, the last chapter concludes and summarizes directions for future development.
LITERATURE REVIEWDisaster and Migration
The increasing number of disasters caused by climate change and extreme weather events worldwide lead to significant loss of life and property and forced displacement. Since migration could
be the only adaptation response in developing countries with high disaster risk and low adaptive
capacity, it is necessary to prepare a humanitarian aid framework for the migration of vulnerable
people affected by disasters or long-term environmental change (21)(22). Case studies have revealed various factors in the destination choices for disaster migrants, such as proximity, income,level of education, location of social capital. Based on these factors, it is essential to establish
the adaptive capacity of host communities to receive disaster migrants (23). In this context, it isnecessary to understand the decision-making mechanism of disaster migration to build a support
system for reactive post-disaster migration.
Although disaster-induced migration has become an increasingly important issue due tofrequent and devastating disasters, few studies have adopted quantitative micro-level models of
the relationship between disasters and migration. In order to forecast disaster-induced migration
as a household decision-making process, a micro-level approach is necessary (24). Do Yun andWaldorf (24) indicates whether households migrate or not is affected by the severity of the damage
and their resilience, and disaster-affected people are classified into three types, voluntary movers,
stayers, and forced movers, based on their income changes after the disaster. Endogenous Switching Regression Results and treatment analysis point out that forced movers suffer from the double
burden of damage caused by the disaster and lower income in the destination city. In order tounderstand the determinants of migration in disaster-prone areas of Mexico, a regression analysis
of aggregate data from 1990 to 2000 was conducted, and it is found that lower-income, frequency
of disasters, and education level were significant factors determining migration (7). In this way,
many case studies have been carried out to reveal determinants of disaster migration and its effects, but they often focus on one particular point in time. So the decision-making process of eachhousehold/individual over time until reconstruction projects are complete is not well understood.
The reasons why many location choice models are forced to focus on one particular choiceover time are lack of residence trajectory data (8), and lack of the modeling approaches for representing life course dynamics (5). Despite this difficulty, some researches on migration focusing on
the time axis have been conducted. Åslund (8) tries to challenge this problem by comparing theresults of destination choice logit models using two data collected in different periods and finds thedifference in factors affecting destination choice between the first and second migration. However,Koseki and Hato3

it does not treat the residential trajectories of the same household. On the other hand, Maslova
and King (25) attempts to clarify the characteristics of domestic housing trajectories of Italians
and Russians in London through semi-structured qualitative interviews. Bhat et al. (11) shows thatit takes a long time for immigrants to be assimilated with the residential preferences and travel
behavior of natives by a joint choice model of residence and auto ownership of immigrants in the
U.S., which takes into account immigration status and length of stay as an explanatory variable.
Loebach (26) shows that households with migration experience are more likely to migrate after adisaster to improve their livelihood by discrete-time event history analysis using migration history
data from 1996 to 2001, including the year 1998 when Hurricane Mitch happened. A study ofrural-urban migration in developing countries shows it is meaningful to take into account not only
the income growth expectation but also the discount factor based on the time required to obtain a
job and the risk of unemployment in urban areas (27).
In this way, some studies consider migration as behavior that occurs over a while witha certain length, while most of the quantitative analyses are static. So the effects of dynamic
environmental changes over time and a life plan of each decision-maker on households’ residential
decision-making are not apparent. From a long-term perspective, the understanding of long-term
migration trajectories would be necessary for reconstruction projects to be planed on an appropriate
scale, especially in small towns under depopulation trends.
Some studies share this research objective of describing the dynamics in the residential
choices. Yu et al. (5) develops a dynamic residential choice model over the life course by explicitly expressing the time-constant and time-varying preference influenced by the past life eventsand the future expectations. In addition, by introducing discount factors to the past, present, andfuture utility, each contribution to the location choice at the time can be understood. While thismodel is sophisticated in accommodating inter-temporal dependencies to describe the very longterm decision-making process over the life course, it cannot describe when to move or the decision
to stay at the same place. Our model could be another modeling approach to capture the dynamics
in the residential location choices because it can describe when to and where to relocate simultaneously as a sequential residential history after disasters, incorporating the future utility (Figure
1).
From these perspectives, we focus on the sequence of residential location choices over time,
accounting for the discount factor, which indicates how the disaster-affected households anticipate
the future utilities defined by the speed of reconstruction, housing recovery support, or their life
events.
Dynamic decision making model
Based on these insights about disaster-induced migration and difficulties in studying residential
trajectories, this study proposes a long-term recursive migration choice model for disaster-affectedhouseholds. In this section, we review some of the dynamic decision-making models that havebeen developed in the transportation field.
In this study, we apply the Recursive Logit Model (RL model) as a sequential route choicemodel proposed by Fosgerau et al. (28) to model a dynamic and recursive migration choice underpost-disaster uncertainty. The RL model by Fosgerau et al. (28) corresponds to dynamic discrete
choice models (29) and describes the route choice problem as the result of a series of link choices.
Here, sequential path choice is performed at each node to maximize the sum of instantaneous
utility and expected downstream utility to the destination. Then the Discounted Recursive Logit

Koseki and Hato

4(a) Existing Residential Location Choice Model(b) Long-term Recursive Migration Choice Modelt: time2011 2012 2013

...

2017

...

2020

T: Reconstruction Period(politically decided)(Basic decision-making Models)Household characteristics
Environmental attributes(Sophisticated Models)

Past experiences

l: location...

location

Disaster

City4
City3
City2
City1
: Residence in the time of disaster

Future Anticipation

Housing Recovery
at the original city

FIGURE 1 Residential choices on the time-space network after large-scale disasters

Model (DRL model) was proposed (30), where the expected future maximum utility is discounted
by the discount factor β , considering that uncertainty exists in the future for the decision-maker.
Moreover, the nested recursive logit model (31) and the recursive cross-nested model (32) havebeen proposed to relax the independence from irrelevant alternatives (IIA). In addition, a mixed RL
model has been applied to the activity-travel scheduling decisions model in a time-space network
where activity, location, time, and traffic mode are defined as state nodes (33).
In this study, we try to model the decision-making process of disaster victims who have tochoose their residence under the ever-changing post-disaster uncertainty. We suppose they anticipate the future utility to some extent and capture it using the DRL model with discount factor. This
study is characterized by applying a dynamic decision-making model to analyzing the long-term
migration after a super disaster.
MODELING FRAMEWORKIn this chapter, we formulate the long-term recursive migration choice model for post-disastervictims, based on the DRL model proposed by Oyama and Hato (30).
Time-Space Network
First, the residential trajectories of disaster victims are represented on a time-space network with atime axis after a disaster and a spatial axis representing a vast urban area, as shown in Figure 1 (b).
Consider the time-space network G = (S, A). S is a state node representing the residential
place at time t, and A is a set of links representing the Spatio-temporal transition behavior of theresidence. In order to describe a city that changes in the process of post-disaster reconstruction, S
has different residential nodes s = (t, l), (t ∈ T, l ∈ L) for each time point t. T is the reconstruction
period, and L is the set of cities considered alternatives in residential location choice.
The dynamic migration history of the disaster victims from the onset of the disaster to theperiod T is represented as a series of links where they chose their housing location s at each time

Koseki and Hato

5

point t, σ = [s1 , .....sT ](sT = d = (T, l)). In the following, the residential state node at time t isdenoted as st to express the state node’s time step explicitly.
Since the state node is defined by time and space, the residential choice path does notinclude a cyclic path. Therefore, we can depict various residential trajectories such as a path wherea person moves out of the region and then returns, a path where a person stays in the same city
continuously, and paths where households stay in the same city for different periods.
Formulation
In the time-space network mentioned above, the residence in the next time step is chosen sequentially. A disaster victim in the residential state sτ at a certain point in time τ chooses the residential
state sτ+1 (whether to stay in the same city or migrate and if migration chosen, to which city) at
the next time step from the set of possible residential states S(sτ ) at the next point in time. Here,the victim n chooses the residence state sτ+1 at the next time point τ + 1 so as to maximize the sumof the instantaneous utility u(sτ+1 | sτ ) obtained from the residential state sτ+1 and the expected
maximum utility V d (sτ+1 ) from the residential state sτ+1 to the residence state sT = d = (T, l).
The instantaneous utility u(sτ+1 | sτ ) is expressed in Equation (1). For the sake of simplification,
the subscript n indicating the affected household is omitted in the following.
u(sτ+1 | sτ ) = v(sτ+1 | sτ ; θ ) + µε(sτ+1 )(1)v(sτ+1 | sτ ; θ ) = v(xsτ+1 |sτ ; θ ) is the deterministic utility component of instantaneous utility,xsτ+1 |sτ is a vector of observed characteristics of the connected states (sτ , sτ+1 ), and θ is an unknown
parameter vector to be estimated. ε(sτ+1 ) is a random term of the instantaneous utility and follows
an i.i.d extreme value I with scale parameter µ. The expected maximum utility V d (sτ ) to theresidence state d at T is formulated by the Bellman equation (34), described recursively as Equation(2). In the notation below, the unknown parameter θ is omitted for simplification.
V d (sτ )
"
=

max E

sτ+1 ∈S(sτ )#T∑ β t−τ u(sτ+1 | sτ )

(2)

t=τ




d
= E max {v(sτ + 1 | sτ ) + βV (sτ + 1 ) + µε(sτ + 1 )}sτ+1 ∈ S(sτ )S(sτ ) is a set of residential states available after the state sτ . β is a discount factor satisfying
0 ≤ β ≤ 1. The closer to one the value of β is, the more highly valued the future expected utility
in the decision-making. In contrast, the closer to 0 the value of β is, the more myopic decisionmaking takes place, which highly values the instantaneous utility. The discount factor makes it
possible to consider the uncertainty after disasters in our model.
Then, since the random term is assumed to be an i.i.d extreme value I, the probability ofchoosing the residential state sτ+1 after the state sτ is formulated as follows (Equation(3)):
1d

P (sτ + 1 | sτ ) =de µ {v(sτ+1 |sτ )+βV (sτ+1 )}
1

∑

0

d

0

e µ {v(sτ+1 |sτ )+βV (sτ+1 )}(3)

s0τ+1 ∈ S(sτ )We assume a Markov process in which the affected household n makes sequential choicesof residential status in each period, taking into account future residential status, and arrives at final

Koseki and Hato

6

residential status. By introducing a discount factor, we describe the recursive choice of residencewith a view to the future and the short-sighted decision-making that must be made in response touncertain situations.
The choice probability of such a dynamic residential choice path σ = [s1 , ..., sT ](sT = d =(T, l)) is expressed as the product of the residential state choice probabilities at each time point τ(Equation (3)) as Equation (4)T −1

Pn (σn ) = ∏ Pd (sτ+1 | sτ )

(4)

τ=1

Then, since ε is assumed to be Gumbel distribution, Equation (2) is transformed into theform of log-sum (Equation (5)).
1sτ+1{v(sτ+1 |sτ )+βV d (sτ+1 )} µ ln ∑ δsτ · e µs∈ S(s )
d(sτ 6= d)(5)
V (sτ ) =0(sτ = d)sτ+1where δsτ is an indicator that equals one if the state sτ + 1 is connected to the state sτ , and 0
otherwise. There is no node following the node d at the last time step, V d (d) is always equals zero.
Since the cyclic structure of the residential path is eliminated in the time-space network,
the expected utility V d (sτ ) can be calculated by a simple backward induction method by repeatedlyusing Equation (5).
τ+1

τ

Estimation
We estimate the parameters of the recursive migration choice model formulated in the previous
section by the maximum likelihood method. When the instantaneous utility u(sτ+1 | sτ ) is expressed as a linear sum of the parameters and explanatory variables, the log-likelihood function LL
is defined as follows according to Equation (4).
N

N T −11(6)(vn (sτ + 1 | sτ ) + βVnd (sτ + 1 )−Vnd (sτ ))n=1
n=1 t=1 µ
N is the total number of affected households observed (the total number of path data), andT is the number of time steps (i.e., the number of states included in a residential choice path σ ).

LL(θ , β ) = ln ∏ Pn (σn ) = ∑ ∑Sampling Alternatives
In this section, we explain the sampling method of alternatives for residential locations. In thedecision-making process to choose a place to live in, it is not practical to assume that a person
identifies all possible cities and selects a single place, so we sample a set of alternative places. In
this model, the sampling procedure is based on the Markov Chain Monte Carlo (MCMC) method.
The sampling procedure is as follows.
1. Randomly draw one city ri from the set of all possible alternatives and set it as the initialstate.
2. Randomly select another city r j .
PD(r )

3. Calculate the ratio of the choice probabilities of the two extracted cities, γ = PD(rij) .
4. Generate ε, a uniform random number in (0, 1). If γ > ε, replace ri with r j and return

Koseki and Hato7

to 2. If γ < ε, return to 2 without replacement.
These steps 2-4 are first repeated many times to relax the initial conditions and then sampled
at sufficiently large intervals while repeating many times.
EMPIRICAL ANALYSIS
In this chapter, we estimate the parameters of the long-term recursive migration choice model
presented above using actual data on the 10-year residential histories of the victims of the Great
East Japan Earthquake, and discuss the results.
The massive earthquake occurred in 2011 and affected vast areas of Japan. The earthquake caused the tsunami, and many people in that area lost their houses. In addition, the tsunami
triggered the nuclear accident in Fukushima prefecture. In order to protect residents in areas surrounding the power station, the Government established the Areas of Evacuation Order, forcing
about 110,000 people to evacuate from their hometowns. Because of this complex disaster, many
people experienced intra-regional or inter-regional migration. Although the evacuation orders havebeen gradually lifted, more than 40,000 Fukushima citizens, including the voluntary evacuees who
are not officially ordered to evacuate, are displaced even ten years after the disaster.
Web Survey and Data
We conducted a web survey to collect longitudinal data on the post-disaster residence after theGreat East Japan Earthquake. The survey was conducted in January in 2021, using a major Web
survey company in Japan, and 1,700 samples currently living in six Tohoku prefectures or seven
Kanto prefectures were obtained. Screening condition is that people who lived in the coastal
area severely damaged by the tsunami (eight cities in Iwate prefecture and ten cities in Miyagi
prefecture, 500 samples, respectively), or people who lived in Fukushima prefecture then and haveexperienced evacuation from the nuclear power plant accident (700 samples). A summary of thesurvey items is as follows.
1. Current family information (family members, residence location, residence type, income, and properties)
2. Family information at the time of the disaster (family members, residence location,
residence type, income, properties, and damage of the disaster)
3. Residential biography from 2011 to 2020 (residence location, residence type, family
structure, and subsidies and compensation)
We estimate parameters for 285 samples who properly answered the questions about theirresidence and relocation timing in their 10-year residential biography.
Figure 2 shows examples of residential trajectories from the web survey. For example,
sample 2 was affected by the disaster in Kesennuma City and was forced to evacuate. After living
in a post-disaster public-funded rental accommodation in Itabashi Ward in Tokyo for about five
years, she returned to Kesennuma City in 2018 and rebuilt her house through the group relocation
project. In the case of sample 3, he lived in his own house in Namie Town at the time of theearthquake. After the nuclear accident, he had to move out and spent five years in a post-disasterpublic-funded rental accommodation in Fukushima City, changing his job to work there. After
that, in 2016, he rebuilt his house in Iwaki City, which is within commuting distance from Namie
town, and is now working in Namie Town. He might anticipate the partial lifting of the evacuation
order of Namie Town in March 2017. On the other hand, sample 4, affected by the disaster inNamie Town, lived in public housing in Kashiwazaki City in Saitama Prefecture for eight years

Koseki and Hato

8
t: timedisaster 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020
Kashiwazaki Cityl: location

Itabashi WardSouka City
Fukushima City?
Iwaki City
Iwaki City

Namie Town
Preparing for going backto Namie in the near future

Kesennuma
City
Miyako Ciy

sample1

sample2

Kesennuma City
Morioka City

sample3

sample4

owned house
house to rent

private rental housing-turned-temporary housing

relocated house(owned)

public housing
for reconstruction? others

FIGURE 2 Examples of residential trajectories after large-scale disasters

and moved to public housing in Iwaki City in 2019. This household is currently constructing theirhouse on their property in Namie. They seem to have moved to Iwate City close to Namie Town toreturn to Namie Town shortly.
As shown in these examples, disaster victims dynamically choose their residential locations
following the changes over time in factors such as life cycles, reconstruction projects, and thelifting of evacuation orders while thinking about their final housing recovery in the future.
Figure 3 shows the results of basic analysis of the web survey. Figure 3-A shows those whopurchased, received, or inherited land in 2011 or later in the Sanriku area (N=340) and Fukushima
prefecture (N=260). In Sanriku, the largest number of respondents acquired land in 2011, immediately after the disaster, followed by 2012 and 2015. On the other hand, more people in Fukushima
Prefecture acquired land in 2012 and 2015 than in 2011. It means their housing reconstruction was
more delayed than those in Sanriku. In both Sanriku and Fukushima Prefectures, land acquisition
was active immediately after the disaster and again in 2015, four years later.
Figure 3-B shows income groups as of 2011 and whether the households currently residein the same municipality as at the time of the earthquake. A higher percentage of households
in the income group of 5 million yen or more (4.5.6) moved out of the home municipality thanhouseholds in the income group of 5 million yen or less (1.2.3). Households with lower incomesare more likely to stay in their former places of residence, maybe because they own land andbuildings there and temporary housing or low-cost reconstruction public housing are available.
Next, we look at people who were affected by the disaster to the extent that they had tomove into temporary housing or were ordered to evacuate, or who acquired their own house after
the earthquake. The percentage of households that moved out of their original residence was 34.2%
for households that owned their own house in 2011 (N=379) and 47.5% for households that lived
in rented housing (N=653). The out-migration rate was higher in the latter group.
Figure 3-C plots the rents of households living in rented housing in both 2011 and 2021,

Koseki and Hato

9

FIGURE 3 Results of basic analysis of the web survey

showing that many plots are above the straight line where the rents in 2011 and 2021 are the same.
It indicates that many households have higher rents now than before the earthquake. It suggeststhat non-homeowning households tend to move out of the home municipality to cities with higher
rents.
Table D in Figure 3 shows the change in household type with the number of times thehousehold moved after the earthquake (0-4 times). It shows that many cases of migration areaccompanied by a change in family structure. Therefore, it is essential to consider the change infamily structure when predicting the number of people and households after the earthquake, whichis the planning unit for reconstruction projects. Capturing the changes in family structure in ourmodel is a future challenge.

Koseki and Hato

10

Affected Coastal Area
andTokyo Metropolitan Area

Morioka City
Miyako City

Out-migration rate to population in 2010

Iwate
Kamaishi City

Yamamoto Town(0.112)

Rikuzentakata City

Minamisanriku Town(0.097)

Ishimomaki City

Onagawa Town(0.091)

Sendai City
50km

Fukushima City

Fukushima

Human Casualties
Deceased: 19,729
Missing:

2,559

Injured:

6,233

20km

Fukushima nuclear
power plant

Iwaki City

Out-migration rate

Miyagi

Kesennuma City

Inundated area

Damaged Buildings

year

Completely destroyed: 121,996
Half destroyed: 282,941
Partially Destroyed: 748,461

Tokyo(a)Miyagi

50km

Evacuation Order Lifted
TomiokaMinamisoma

Out-migration rate

Out-migration rate

Rikuzentakata City(0.072)

NarahaOtsuchi Town(0.105)

NarahaMinamisoma
Tomioka

year
year(b) Iwate(c) Fukushima

FIGURE 4 Affected area and out-migration rate to population in 2010 (a)(b)(c)

Basic analysis based on statistical data
In this section, we present the outcome of the basic statistical analysis conducted as a basis forsetting up the model to estimate the parameters. For the analysis of population movement, weused the National Census and data on migration provided by the Ministry of Internal Affairs andCommunications.
Figures 4(a), (b), and (c) show the ratio of out-migration to the 2010 population in Miyagi,
Iwate, and Fukushima prefectures, respectively. The percentage of out-migration in 2011 is extremely high (about 10%) in Yamamoto Town, Minamisanriku Town, Onagawa Town in Miyagi
Prefecture, and Otsuchi Town in Iwate Prefecture. In all the municipalities, the out-migration raterose sharply in 2011, but in most of them, the out-migration rate settled down to the pre-earthquake
level in 2012. On the other hand, in Onagawa, Minamisanriku, and Yamamoto, the out-migration
rate remained high for three years.

Koseki and Hato

11
Percentage to total number of residents moving out

Largest Cities
in the Prefectureinternal migrationinter-prefectural
7%~
20%~
30%~

Destination Prefectures
outside the Prefecture

Miyagi(Number): percentage of internal migrationfrom the city

Fukushima

Iwate●Kesennuma ●(52.8)

Miyagi

31.6

32.1
20

.8

(64.6)

8
25.

12.6

●Higasimatsushima

14.0
2
24 .

●Natori

19.9

1

9
0.

11.6

(70.7)●Rikuzentakata(53.7)

13.0(38.9)(50.4)

20.8●Shichigahama●Tagajo ●(59.8)

Miyagi

1

Tokyo

12.2

14
.
53

9.7

.1

●Naraha●(40.3)

24.2
Iwaki

8.7
Kanagawa

27.0●Iwanuma(32.7)

Saitama

9.4●Ofunato●

11.4(53.7)●Okuma●●Tomioka●●Shiogama ●

.5

.5

15.3

29

15

8.1

●Kamaishi (58.3)●Futaba●(28.4)

9.1.2(64.9)

30.1(29.5)

8.5

9.5
Chiba

26.9

.6

13

Sendai●Otsuchi (70.0)

11.1●Namie●

7.1

16.6

19

9.5
8.5

●Yamada (65.4)

14.3

20.0

(32.6)

23.4

17.7

Morioka●Ishinomaki

18.1●Minamisoma●●Miyako (57.2)

27.5

53.8
1

8.
2

(48.4)

16.2●Onagawa (86.3)

4
8.

Fukushima●Kuji●Minamisanriku (76.0)(62.0)FIGURE 5 Destination cities of out-migration
Largest Cities
in Fukushima Prefecture
Destination Prefectures
outside Fukushima Prefecture

Percentage to total number of residents moving out
internal migrationinter-prefectural
7%~
10%~

2011

2015

●

Miyagi

Miyagi
Fukushima
City

Fukushima
City

Fukushima
City

●

●

Minamisoma

Koriyama
City

●

●

Minamisoma City

●

Namie

Chiba

2020

Soma City

Miyagi

Koriyama
City

Futaba ●Chiba

Namie ●

Futaba ●

●

●

Okuma

Minamisoma ●●Namie ●

●

●

●

●

Futaba ●Chiba●

Okuma ●●

Okuma ●

Saitama●Tomioka ●●●Tomioka ●SaitamaNaraha●Ibaraki

●

●

●

●

IbarakiTomioka

SaitamaNarahaNaraha
●

●

Tokyo
Iwaki
City

Tokyo
Kanagawa

Tokyo
Iwaki
City

Iwaki
City

FIGURE 6 Changes in trends of migration over 10 years in Fukushima
On the other hand, Fukushima Prefecture, where the population has moved significantly
due to the evacuation from nuclear power plants, shows a different picture from the other two
prefectures. In municipalities where evacuation orders were issued, the evacuation orders havebeen lifted sequentially since 2014. Interestingly, the number of people moving out rose again in
the period after the lifting of the evacuation orders, such as in Naraha Town (lifted in September2015), Minamisoma City (lifted in July 2016), and Tomioka Town (partially lifted in 2017). Notethat many households among the nuclear disaster evacuees lived in other cities without transferring
their residence records, so caution is required in interpreting the results.
As shown above, there are differences in the population movements in the disaster-affectedareas. It can be inferred that factors such as the disaster situation, the content and progress ofKoseki and Hato

12

reconstruction projects, and the lifting of evacuation orders affect the decisions of individuals andhouseholds. In order to explain the post-disaster population flow, it is necessary to incorporate
these factors into the model.
Figure 5 shows major destination cities to which people migrate from coastal cities in thethree prefectures in 2012, which shows a marked difference among the three prefectures. In Miyagi
Prefecture, where intra-prefectural out-migration was remarkable after the earthquake, we can seethat in addition to the tendency to concentrate in Sendai City, the largest city in the Tohoku region,
there is also a high tendency to move to the central city in each region. In Iwate and Fukushima
Prefectures, the same tendency is observed, but the percentage of out-migration to other prefectureswith large cities is higher, especially in Fukushima. We can see a trend of out-migration to Miyagi
Prefecture from southern Iwate and northern Fukushima Prefectures and migration to the Tokyo
metropolitan area from southern Fukushima Prefecture. From the above analysis, it can be assumed
that the residential location choice set of the disaster victims differs greatly depending on the placeof residence as of 2011, and we will attempt to reflect this point in the choice sampling.
Figure 6 shows the dynamic change in the destination cities from Fukushima prefecture
within ten years after the disaster. Overall, there is no strong trend to which they move; in otherwords, people move out to various cities. In 2011, people seldom moved within Fukushima prefecture and chose the inter-prefectural migration, especially to the Tokyo metropolitan area. Overtime, there has been an increasing migration trend to larger cities within the prefecture, especiallyto Iwaki City, which is the largest city in Fukushima prefecture and the closest to the area affectedby the nuclear accident.
These analyses suggest that the city size and distance have a significant impact on the population movement. In addition, we could confirm the dynamics of out-migration trends with timeafter disasters. Therefore, in the next section, we propose a model that takes them into account.
Settings of the Case Study
The data acquired by the web survey is used for parameterization and we treat the household as
the subject of migration choice.
Time-Space Network
Since the reconstruction period from the Great East Japan Earthquake was politically set at ten
years, the target period is ten years from 2011 to 2020. As shown in the results of the basic
analysis, there is a significant movement in 2011. Therefore, here, the time of the disaster is set at
t = 1 and the last period at T = 14, assuming the time-space network with four steps/year only in2011 and one step/year after 2012.
In this model, the value function is discounted by a discount factor β for each step, so
it is reasonable to make all the time steps the same length. In reality, the timing of residential
decision-making during the reconstruction period and ordinary life is related to the fiscal year due
to the renewal of temporary housing, job transfer, advancement to higher education. Moreover, theheterogeneity between the immediate post-disaster period with great uncertainty and the normal
period should be considered. In addition, it is difficult to obtain explanatory variables that fluctuate
in short time unit such as one month. For these reasons, this paper uses the time-space network
described above for estimation. The length of a time unit is to be further studied.

Koseki and Hato

13
TABLE 1 Explanatory Variables

Population density(10−4 /km2 )Distance (10−3 /km)
Progress rates
High income (dummy)
Low income (dummy)
House owner (dummy)
Renter (dummy)
Damaged (dummy)
Education (dummy)
Destination city (dummy)
Destination_early (dummy)
Home_early (dummy)

Population density, divided by 10000 for scale adjustment
Distance between cities, divided by 1000 for scale adjustment
Progress rates of housing reconstruction (cumulative progress rates of public andprivate housing lots) If not a disaster affected city, nodes in all time steps are set as 1.
Annual income of 5 million yen or more as of 2011
Annual income of less than 5 million yen as of 2011
House owner as of 2011
Renter as of 2011
Dummy for disaster victims (those who were affected to the extent that they had tomove into temporary housing or were ordered to evacuate)
Dummy for the timing of moving up to elementary school, junior high school,or high school during the targeted period
Dummy for the location at the last time-step (place of residence 10 years after the disaster)Nodes from the origin up to the year 2013 among the destination city dummies
Node from the origin up to 2013 among the dummies for the location in 2011

Sampling choice set
The sampling of alternative residential locations for each household is carried out using the method
described in the previous chapter. The sampling is based on the residence of each household at thetime of the earthquake (2011) (O). The choice probability for each city (D), required in sampling
procedure 3 is set as the percentage of out-migration to that city (D) to the total number of outmigration from O. The data on out-migration from each municipality is provided by the Ministryof Internal Affairs and Communications. In this data, the OD of the out-migration is available
for each municipality only for 2012 and later, so we used 2012. The scale of cities in the choice
set is defined as municipalities for in-prefecture migration and as prefectures for out-of-prefecture
migration.
The sampling process 2-4 was repeated 10,000 times to mitigate the effects of the initialconditions, and then three cities were selected at intervals of 1,000 times of this procedure. Eachhousehold eventually has a choice set of four cities, including the city chosen in the actual residence
history (from one to four cities). The choice set is the same for the entire period.
This sampling method allows us to consider the heterogeneity of choice set according to theresidential locations at the time of the earthquake, but further study is needed to take into accountthe changes in the choice set over time.
Utility function
Explanatory variables of instantaneous utility xsτ+1 |sτ presented in Equation (1) is constructed byexamining the variables shown in Table 1.
Estimation Result
In this paper, the following four patterns are estimated and compared; 1. all samples (285), 2. Iwate
Prefecture (65), 3. Miyagi Prefecture (108), 4. Fukushima Prefecture (112). In the following, thescale parameter is fixed at µ = 1. Chosen variables and estimated parameters are shown in Table
exp(β )
2. To estimate time discount factor β with 0 to 1 constraints, γ is estimated as γ = 1+exp(β).
First of all, the discount factor, an essential factor in this model, is estimated to be 0.725
in Miyagi Prefecture, which is statistically significant, and 0.215 in Fukushima Prefecture, thestatistical significance level lower. It indicates that the discount rate in Fukushima is relatively
low, which could mean that a myopic residential choice was taking place. In Fukushima Prefec-

Koseki and Hato

14
TABLE 2 Estimation Result

All
Iwate
Miyagi
Fukushima
parameter t-value
parameter t-value parameter t-value parameter t-value1)Population density (10−4 /km2 )
3.028
13.74
28.256
16.01
3.234
11.34
1.811
5.36
2)Progress rates * Damaged * House owner
0.162
1.46
0.034
0.10
0.196
0.98
0.040
0.21
3)Destination_early * High income *Damaged
1.236
9.01
1.709
4.80
1.347
5.67
1.456
5.96
4)Destination city * Education
1.575
8.66
0.828
1.99
1.402
4.84
2.019
5.90
5)Distance (10−3 /km)
-27.567 -32.43-42.510 -19.89-35.824 -19.36-20.977 -22.66
0.542
0.000
0.725
0.215
Discount factor
0.78
-0.13
4.18
-1.41
(γ=0.168)(γ=-11.657)(γ=0.970)(γ=-1.297)
No. of samples
285
65
108
112
Initial likelihood-5136.22-1171.42-1946.36-2018.44
Final likelihood-2492.02-436.89-959.84-974.65
Likelihood ratio
0.51
0.62
0.50
0.51

TABLE 3 Comparison of Parameter Ratios
all iwate miyagi fukushima5)Distance / 1)Population-9.10 -1.50 -11.08-11.585)Distance / 3)High income-22.29 -24.87 -26.60-14.415)Distance / 4)Education-17.51 -51.34 -25.55-10.393)High income / 1)Population
0.41
0.06
0.42
0.80
4)Education / 1)Population
0.52
0.03
0.43
1.12
3)High income / 4)Education
0.96
0.72
0.79
2.06

ture, those who suffered from the triple disasters and had to evacuate from nuclear plants due toevacuation orders, and those who evacuated for fear of the risks of contamination from radioactive
releases, were forced to focus on the instantaneous utility because of the long period of uncertainty
about whether they would be able to return.
The variable 3) in Table 2 is a dummy variable that is set to 1 if the affected high-income
household had reached their final residence by 2013. This parameter is statistically significant
for all estimation patterns, with a value of 1.347 for Fukushima Prefecture. Looking at the parameter ratios in Table 3 for this variable, it can be said that there is a higher tendency for highincome individuals affected by the disaster to reach their final place of residence at an early stagein Fukushima Prefecture, in comparison to other prefectures. This result is consistent with thefact that high-income people can rebuild their houses on their own regardless of the subsidies andcompensation they receive. Actually, low-income people in Iwate and Miyagi prefectures tended
to stay in the affected areas, living in temporary housing and waiting for disaster recovery public
housing completed. However, victims in the Fukushima nuclear power plant-affected areas wereordered to evacuate, so they had no choice to stay in their original places of residence. Therefore, it
is likely that lower-income victims temporarily moved to a municipality where they could receive
support and continued their temporary residence while waiting to hear about the situation in theaffected hometowns. A more detailed description about the facts above using our model could help
examine disaster relief policies that consider diversity in damage and income.
Next, the population density parameter was positively significant, and the distance parameter was negatively significant for all estimation patterns. Looking at the parameter ratios, the ratioof population density to distance in Iwate is very large. This can be attributed to the fact that thetarget cities of Iwate Prefecture (cities that are always included in the choice set as the origin in his-

Koseki and Hato

15tory) have a minimal city size. The population density of targeted cities in Iwate is 66.6 people per
km2 on average, while that in Miyagi is 959.3 people per km2 on average, and that in Fukushima(where all municipalities are included) is 156.8 people per km2 on average. As for Fukushima
Prefecture, the actual average is larger because many of the people in the sample are from cities
with relatively large urban areas. On the other hand, the population density of Tokyo, the largest
city in the metropolitan area, is 6305.7 persons per km2 , which is extremely large. Therefore, it
is assumed that the population density parameter in Iwate is larger than in other prefectures to
explain the migration from Iwate to the Tokyo metropolitan area, which has a massive differencein population density.
As for the estimation of the discount factor, we obtained significant values in Miyagi Prefecture and informative values in Fukushima Prefecture, but we failed to estimate it reasonably in
Iwate Prefecture. The reason for this could be that due to the large population density parameterin Iwate Prefecture, the utility of staying in the Tokyo metropolitan area becomes very large whencities in the metropolitan area are included in the choice set. Note that the utility of moving to thearea is not as large as the utility of staying in the affected area because of the distance. Therefore, it
is likely that the degree of the consideration of future utility, i.e., the discount rate β , varied greatly
depending on whether the households with the metropolitan cities in their choice set chose themor not. In other words, there are varieties between those who chose to stay in the disaster-affectedarea because it is costly to move to a large city (myopic choice), and those who decided to moveto a large city, considering future utility (high utility of staying in a city).
In reality, however, future utility is not only determined by distance and city size. In orderto estimate and improve the accuracy of the discount rate for all patterns, firstly, it is necessary toconstruct a utility function that is not too dependent on one particular variable. It should reflect
diverse values of future utility, such as life cycle, attachment to hometown, and properties. In
addition, it is necessary to study the estimation structure assuming latent classes, the sampling
method for alternatives, and the number of cities in the choice set.
Unfortunately, the parameter of variable 2) in the Table 2, which represents the progress rateof reconstruction, was not significant. This model uses the cumulative progress rate of the preparednumber of public or private housing units. However, it does not capture essential factors related todamage and reconstruction, such as evacuation orders and land-use changes between the affected
and upland areas. It is necessary to consider other valuable variables to evaluate reconstruction
projects.
CONCLUSION
In recent years, disasters have become more frequent and severe worldwide due to climate change,
forcing disaster victims to make involuntary or unavoidable choices to migrate. Understanding
disaster-induced migration and establishing appropriate assistance schemes are urgently needed.
Although individual case studies have revealed the factors that lead to post-disaster migration,
previous residential choice models have not described the long-term recursive residential decisionmaking process. This study developed a long-term recursive migration choice model that considers
the decision-making process over decades after a disaster. In this model, victims simultaneously
select a location and relocation timing at each time-step, considering the future utility. By introducing a discount factor, future utility is discounted, which enables to describe the choices thatmust be made under uncertain conditions after a super disaster.
We confirmed the usability of our model by conducting a case study of residential histories

Koseki and Hato

16

for the ten years after the Great East Japan Earthquake and confirmed the possibility of estimating
the discount factor. The discount factor was estimated to be lower in Fukushima Prefecture than inothers. Disaster victims in Fukushima prefecture could not see any prospect of returning to theirhometowns due to the complex disaster including nuclear accident. In addition, it is indicated that
there is a higher tendency for high-income people to reach their final place of residence at the earlystage in Fukushima than in other prefectures, which suggests that the speed of residential recovery
differs depending on income. In the future, we will add an analysis of the amount and timingof housing recovery monetary assistance and compensation payments to nuclear disaster victims,
which may be applied to the investigation of a fair distribution of monetary assistance.
In addition, the impact of the time related to education on the timing of residential reconstruction is suggested, so the development of the model that considers the life cycle of households
could be meaningful. Although the reconstruction progress rate was not significant in this casestudy, the model can incorporate variables that differ by location and time, such as the damage
situation, the progress rate of reconstruction projects, and the distribution and timing of subsidies.
This study helps determine not only the appropriate scale of reconstruction projects but also theeffective timing. Moreover, the disaster-affected residents drastically move into large cities after adisaster, and it results in friction, which also happened in Fukushima. By using the model proposed
here, it will be possible to perform dynamic control to allow temporary urban functions to serveas buffers and evaluate the next best measures to support residents without relying on excessive
reconstruction.
Finally, we summarize the challenges that remained. First, the discount factor introducedin this model is assumed to be constant across time. However, the discount factor in the periodof uncertainty immediately after a disaster and that in the reconstruction period several years later
are considered different. Hence, developing a framework that considers the time variability of the
discount rate is necessary. In addition, the method of describing uncertainty in the post-disasterperiod needs to be further studied. In this model, uncertainty is expressed only by the discountfactor. However, the myopic choice here means "knowing the future utility but valuing the immediate utility," which does not directly reflect the reality of the post-disaster situation where thefuture situation is completely unforeseeable. One possible countermeasure is to limit the number of alternatives in the immediate aftermath of a disaster, but further study is needed. In thecase study, we estimated parameters for each disaster-affected municipality with different types ofdamage and different geographical environments. However, there is heterogeneity in the characteristics of disaster victims even within the same municipality. In order to estimate the discountfactor stably, it could be effective to take into account the latent class. In fact, after the Great East
Japan Earthquake, the separation of households co-occurred as the separation of communities due
to migration. In order to understand this phenomenon, it will be essential to extend the framework
to include the household’s life-cycle and describe the choice of household structure that may havecoincided with the location choice.

Koseki and Hato

17

REFERENCES
1.
Abdelgawad, H., B. Abdulhai, and M. Wahba, Multiobjective optimization for multimodal
evacuation. Transportation Research Record, , No. 2196, 2010, pp. 21–33.
2.
Wang, F., L. Bu, C. Li, J. Rong, and R. Guo, Simulation study of evacuation routes andtraffic management strategies in short-notice emergency evacuation. Transportation Research Record, Vol. 2459, 2014, pp. 63–71.
3.
Hess, D., B. Conley, and C. Farrell, Improving transportation resource coordination for
multimodal evacuation planning. Transportation Research Record, , No. 2376, 2013, pp.
11–19.
4.
Fatmi, M. R., S. Chowdhury, and M. A. Habib, Life history-oriented residential location
choice model: A stress-based two-tier panel modeling approach. Transportation ResearchPart A: Policy and Practice, Vol. 104, 2017, pp. 293–307.
5.
Yu, B., J. Zhang, and X. Li, Dynamic life course analysis on residential location choice.
Transportation Research Part A: Policy and Practice, Vol. 104, 2017, pp. 281–292.
6.
Boustan, L. P., M. E. Kahn, and P. W. Rhode, Moving to Higher Ground: Migration Response to Natural Disasters in the Early Twentieth Century. American Economic Review,Vol. 102, No. 3, 2012, pp. 238–244.
7.
Saldaña-Zorrilla, S. O. and K. Sandberg, Spatial econometric model of natural disaster
impacts on human migration in vulnerable regions of Mexico. Disasters, Vol. 33, No. 4,
2009, pp. 591–607.
8.
Åslund, O., Now and forever? Initial and subsequent location choices of immigrants.
Regional Science and Urban Economics, Vol. 35, No. 2, 2005, pp. 141–165.
9.
Urata, J., Y. Sasaki, and T. Iryo, Spatio-Temporal Analysis for Understanding the Traffic
Demand After the 2016 Kumamoto Earthquake Using Mobile Usage Data. In 2018 21stInternational Conference on Intelligent Transportation Systems (ITSC), 2018, pp. 2496–
2503.
10.
Chakrabarti, S. and G. Painter, Geographic mobility of recent immigrants and urban transit
demand in the U.S.: New evidence and planning implications. Transportation ResearchPart A: Policy and Practice, Vol. 120, No. December 2018, 2019, pp. 71–82.
11.
Bhat, C., R. Paleti, R. Pendyala, K. Lorenzini, and K. Konduri, Accommodating immigration status and self-selection effects in a joint model of household auto ownership andresidential location choice. Transportation Research Record, , No. 2382, 2013, pp. 142–
150.
12.
McFadden, D., Modelling the Choice of Residential Location, 1977.
13.
Bhat, C. R., J. Y. Guo, S. Srinivasan, and A. Sivakumar, Comprehensive econometricmicrosimulator for daily activity-travel patterns. Transportation Research Record, , No.
1894, 2004, pp. 57–66.
14.
Balmer, M., K. Axhausen, and K. Nagel, Agent-Based Demand-Modeling Frameworkfor Large-Scale Microsimulations. Transportation Research Record, Vol. 1985, 2006, pp.
125–134.
15.
Beckman, R. J., K. A. Baggerly, and M. D. McKay, Creating synthetic baseline populations. Transportation Research Part A: Policy and Practice, Vol. 30, No. 6 PART A, 1996,
pp. 415–429.
16.
Ye, X., K. C. Konduri, R. M. Pendyala, B. Sana, and P. Waddell, Methodology to Match
Distributions of Both Household and Person Attributes in Generation of Synthetic Popu-Koseki and Hato

17.
18.

19.

20.

21.
22.
23.

24.

25.

26.

27.
28.

29.

30.

31.

18

lations. Transportation Research Board Annual Meeting 2009, Vol. 9601, No. 206, 2009,
pp. 1–24.
Sun, L., A. Erath, and M. Cai, A hierarchical mixture modeling framework for population
synthesis. Transportation Research Part B: Methodological, Vol. 114, 2018, pp. 199–212.
Mannella, A., M. D. Ludovico, A. Sabino, A. Prota, M. Dolce, and G. Manfredi, Analysisof the population assistance and returning home in the reconstruction process of the 2009
L’aquila earthquake. Sustainability (Switzerland), Vol. 9, No. 8, 2017.
Contreras, D., G. Forino, and T. Blaschke, Measuring the progress of a recovery process
after an earthquake: The case of L’aquila, Italy. International Journal of Disaster Risk
Reduction, Vol. 28, No. October 2017, 2018, pp. 450–464.
Bleemer, Z. and W. van der Klaauw, Long-run net distributionary effects of federal disasterinsurance: The case of Hurricane Katrina. Journal of Urban Economics, Vol. 110, No.
December 2017, 2019, pp. 70–88.
Matias, D. M. S., Climate humanitarian visa: international migration opportunities as postdisaster humanitarian intervention. Climatic Change, Vol. 160, No. 1, 2020, pp. 143–156.
McAdam, J., The emerging New Zealand jurisprudence on climate change, disasters anddisplacement. Migration Studies, Vol. 3, No. 1, 2015, pp. 131–142.
Erdiaw-Kwasie, M. O., M. Abunyewah, and O. Yamoah, ‘After the disaster comes destination thoughts’: A review and conceptualization of consolidative disaster adaptive capacity
model. International Journal of Disaster Risk Reduction, Vol. 35, No. February, 2019, p.
101098.
Do Yun, S. and B. S. Waldorf, THE DAY AFTER THE DISASTER: FORCED MIGRATION AND INCOME LOSS AFTER HURRICANES KATRINA AND RITA. Journal of
Regional Science, Vol. 56, No. 3, 2016, pp. 420–441.
Maslova, S. and R. King, Residential trajectories of high-skilled transnational migrants
in a global city: Exploring the housing choices of Russian and Italian professionals in
London. Cities, Vol. 96, No. August 2019, 2020, p. 102421.
Loebach, P., Household migration as a livelihood adaptation in response to a natural disaster: Nicaragua and Hurricane Mitch. Population and Environment, Vol. 38, No. 2, 2016,
pp. 185–206.
Todaro, M. P., A Model of Labor Migration and Urban Unemployment in Less Developed
Countries. The American Economic Review, Vol. 59, No. No. 1, 1969, pp. 138–148.
Fosgerau, M., E. Frejinger, and A. Karlstrom, A link based network route choice modelwith unrestricted choice set. Transportation Research Part B: Methodological, Vol. 56,
2013, pp. 70–80.
Rust, J. B. Y., Optimal Replacement of GMC Bus Engines : An Empirical Model of Harold
Zurcher Author ( s ): John Rust Published by : The Econometric Society OF GMC BUS
ENGINES :. Econometrica, Vol. 55, No. 5, 1987, pp. 999–1033.
Oyama, Y. and E. Hato, A discounted recursive logit model for dynamic gridlock network
analysis. Transportation Research Part C: Emerging Technologies, Vol. 85, No. September, 2017, pp. 509–527.
Mai, T., M. Fosgerau, and E. Frejinger, A nested recursive logit model for route choiceanalysis. Transportation Research Part B: Methodological, Vol. 75, 2015, pp. 100–112.

Koseki and Hato
32.

33.

34.

19

Mai, T., A method of integrating correlation structures for a generalized recursive route
choice model. Transportation Research Part B: Methodological, Vol. 93, 2016, pp. 146–
161.
Zimmermann, M., O. Blom Västberg, E. Frejinger, and A. Karlström, Capturing correlation with a mixed recursive logit model for activity-travel scheduling. Transportation
Research Part C: Emerging Technologies, Vol. 93, 2018, pp. 273–291.
Bellman, R., Dynamic Programming. Science, Vol. 153, No. 3731, 1966, pp. 34–37.