The Economic Dynamics of City Structure:
Evidence from Hiroshima’s Recovery∗
Kohei Takeda
NUS

Atsushi Yamagishi
Princeton

June 22, 2023
Preliminary Draft

Abstract
This paper studies the evolution of the spatial distribution of population and employment withina city. We exploit an unusually large shock to city structure: the atomic bombing of Hiroshima,
which completely destroyed its city center but not its periphery. Newly digitizing spatially granular data, we first document that the city center strongly recovered just about five years after
being destroyed. Furthermore, we show that this rebuilding is not well explained by the fundamental locational characteristics of the city center. We then develop and calibrate a novel
dynamic urban economics model to further investigate the mechanisms underlying the recovery. Our findings suggest that strong agglomeration economies, together with individuals’ expectations in the recovery, created a strong incentive to reconstruct the city center despite its
catastrophic shock.

Keywords: agglomeration, history, expectations, quantitative spatial model, atomic bombing
JEL classification: C73, N45, O18, R12, R23∗ We are grateful to Steve Redding for his continued guidance and support. We particularly thank Leah Boustan andNobuhiro Kiyotaki for their numerous helpful comments, and also Gabriel Ahlfeldt, Ellora Derenoncourt, Mayara Felix,Gene Grossman, Richard Hornbeck, Guy Michaels, Tomoya Mori, David Nagy, Kentaro Nakajima, Ezra Oberfield,
Gianmarco Ottaviano, Pablo Ottonello, Luigi Pascali, Esteban Rossi-Hansberg, Yasuhiro Sato, Daniel Sturm, David
Weinstein, Xuanli Zhu, and seminar and conference participants for their feedback. We thank the Chugoku Region
Development Bureau, the Ministry of Land, Infrastructure, Transport and Tourism, for providing the access to theperson-trip survey data. We acknowledge the financial support from the International Economics Section, Princeton
University, the Institute of Economic Research, Hitotsubashi University, and the Funai Foundation for Information
Technology. Hiroki Chiba provided excellent research assistance. An earlier version of this paper was circulated under
the title “History versus Expectations in the Spatial Economy: Lessons from Hiroshima.” We take sole responsibility
for errors in this paper. Takeda: Department of Economics, National University of Singapore, AS2, 1 Arts Link,
Singapore, 117570 (Email: k.takeda@nus.edu.sg); Yamagishi: Department of Economics, Princeton University, Julis
Romo Rabinowitz Building, Princeton NJ, USA, 08544 (Email: ayamagishi@princeton.edu).

1 Introduction
City structure, the spatial distribution of population and employment within a city, evolves differently in various contexts. For example, Los Angeles and Houston experienced significant suburbanization in the 20th century and their city centers became less dense, whereas the historicalcity centers of New York, Paris, and Tokyo remained relatively dense. What factors determine theevolution of city structure? Studies have highlighted the importance of two key factors (Lin and
Rauch 2022). The first consists of fundamentals such as transportation costs and natural amenities.
The second factor is history, which influences the path of the city structure through the durability of investments and lock-in effects arising from spillover effects. In addition, although muchless studied empirically, expectations regarding future city structure may also influence the paththrough forward-looking location decisions (Krugman 1991; Matsuyama 1991). Understanding theevolution of city structure and its underlying mechanisms is essential for evaluating the short- andlong-term effects of spatial policies, such as infrastructure investment and urban renewal. These
policies change the dynamics of city structure, which in turn affects important outcomes, such as
productivity, amenities, commuting time, and environmental pollution, that have repercussions on
welfare.
This paper examines the dynamics of city structure through the experience of Hiroshima. Since
the atomic bombing drastically changed the city structure, the evolution of Hiroshima after thebombing is an interesting laboratory for studying the mechanisms underlying the dynamics of urban configuration. To this end, we newly collect granular data on population, employment, andfundamental characteristics at the block level within Hiroshima. Using these data, we find thestrong path-independence in Hiroshima: the completely destroyed city center recovered just five
years after the atomic bombing. In particular, our reduced-form analysis reveals that the fundamental location advantages of the city center do not plausibly explain the rebuilding. Therefore, the city
center achieved the rapid recovery, the key characteristic of the dynamics of the city structure ofHiroshima, thanks to something other than its fundamental locational advantages.
To further investigate the mechanism underlying the recovery of central Hiroshima, we develop
and calibrate a novel dynamic quantitative urban model. In the model, finitely-lived individuals can
switch their residence and workplace while anticipating future productivity and amenities, subject
to migration frictions and idiosyncratic taste shocks; and both productivity and amenities at eachlocation depend on current and historical employment and population density, as well as fundamental characteristics. The calibration of the model shows that it adequately explains the resurgenceof population and employment in the city center after the bombing, and agglomeration economies
are the key to making central Hiroshima again an attractive place to live and work. Furthermore,by contrasting with an alternative version of our model in which people do not foresee the recoveryof the city center, we demonstrate that expectations in the recovery are essential for agglomeration in the city center to be realized. Taken together, our quantitative findings highlight the role of1

agglomeration economies and expectations in shaping the dynamics of city structure.
Section 2 describes historical background and newly collected data on the distribution of economic activities within Hiroshima. Due to the unprecedentedly large shock to its city structurecaused by the atomic bombing, Hiroshima provides a unique case study for understanding the dynamics of city structure. The majority of the administrative region of Hiroshima city lies within
6 kilometers of the city center, and on August 6, 1945, almost all structures within 2 kilometersof the city center were destroyed by the atomic bomb. However, many buildings on the outskirts
were not entirely destroyed. Some areas on the outskirts even experienced an increase in population
due to the inflow of survivors from the city center. Consequently, the atomic bombing reversed
the monocentric city structure, leaving the city center with the lowest population and employment
density.
In Section 3, our reduced-form analysis reveals the strong path-independence in Hiroshima despite the unprecedented magnitude of the historical shock. Our key findings are twofold. First,
the completely destroyed city center recovered within five years of the atomic bombing. Although
history has been identified as a major determinant of city structure, the influence of the atomic
bombing on Hiroshima’s city structure quickly disappeared in the post-war period. This recovery
result is consistent with historical-shock independence in the across-city distribution after bombing(e.g., Davis and Weinstein 2002). Notably, however, our recovery result is obtained for the withincity population distribution that tends to exhibit path dependence in other empirical settings (Linand Rauch 2022). Second, our novel result is that the recovery of central Hiroshima is not plausibly
explained by fundamental locational advantages of the city center. To this end, we control explicitly
for observable location characteristics and restrict our sample of study to a small, relatively homogeneous area of the city. We also analyze Nagasaki, in which the periphery was completely destroyedin contrast to Hiroshima, and find that the destroyed areas recovered also in Nagasaki. In sum, ourempirical analysis suggests that history or fundamentals alone could not predict the fast and strong
rebuilding of central Hiroshima.
We investigate the underlying mechanisms of the recovery by developing a novel dynamic quantitative urban model in Section 4. In particular, our model is the first quantitative spatial model that
accommodates commuting, forward-looking location choice, and path-dependence in location decisions and fundamentals. A city has heterogeneous location-specific amenities and productivity,and people commute within a city. In our model, (i) agents correctly anticipate the future path ofthe economy when making location decisions, and (ii) neighborhood amenities and productivity
depend on population and employment density. Therefore, the location decisions of individuals
hinge on the future changes in population and employment distribution in the city, which define
the option value associated with each neighborhood. Our model also incorporates a perspectiveof backward-looking location decisions, which may result in history-dependence in our model. In
particular, amenities and productivity depend on past population and employment density (Allenand Donaldson 2022), and migration is subject to frictions (Caliendo, Dvorkin and Parro 2019).

2

In Section 5, we calibrate our model and assess how well our model explains the recovery ofcentral Hiroshima. For calibration, we use the data on population, employment and other observed
characteristics during the post-recovery period in Hiroshima from 1950 to 1975. We leverage thestructure of the model to estimate model parameters and recover unobserved location characteristics. Our key parameters are spillovers in amenities and productivity that determine the value of
future returns from location choices. We find strong net agglomeration economies in both amenities and productivity: a high population and employment density today improves current amenities
and productivity, respectively. In addition, a higher population density five years ago increases thecurrent value of amenities, while a high employment density five years ago is negatively associatedwith the current level of productivity. Our spillover estimates are broadly in line with Allen and
Donaldson (2022) in the across-county setting of the US, except that the net amenity spillovers are
positive in our setting due to the positive contemporaneous spillovers. We then assess the ability of
our calibrated model to explain the data from 1945 to 1950 when people returned to the completely
destroyed city center. We demonstrate that our model can well explain the resurgence. Moreover,
we highlight that agglomeration economies are the key for driving the recovery. In particular, by
shutting down agglomeration forces, the model fails to predict the recovery of the central Hiroshima.
In contrast, the recovery is not attributed to location specific amenities and productivity of the city
center because they are not superior to those of the periphery, which is consistent with our reducedform findings. Overall, the recovery of population and employment in the city center enhances its
attractiveness through agglomeration economies, providing an incentive for people to live and work
there.
In Section 6, we analyze an implicit prerequisite for agglomeration economies to rationalize therecovery: people expect the recovery of central Hiroshima when choosing their residence and workplace. Specifically, if people expected that the center would not recover, they would not choose tolive and work in the city center because the attractiveness of the city center due to agglomeration
economies was not expected to realize. We formalize this intuition by considering an alternative
version of our model in which workers take their best responses not by expecting the recovery of
population and employment in the city center but by anticipating that population and employment
distributions right after the bombing would continue. This model with expectations in no recovery
fails to predict the observed resurgence but predicts that the old periphery of the city achieves highlevels of population and employment, a prediction of path-dependence in contrast to the observed
data. As discussed in Krugman (1991) and Matsuyama (1991), this result suggests that, in the presence of strong agglomeration economies, expectations in the recovery may become self-fulfilling.
Finally, although we remain agnostic about the origin of the expectations in the recovery and focus on showing their importance for accounting for the recovery given their emergence, we briefly
discuss the possible causes of the expectations in recovery. In particular, we highlight the presenceof governmental recovery plans, the anchoring effect of the transportation network, property rights,
and the popular narrative of rebuilding that may have induced “memory-based” expectations.

3Overall, our analysis of the experience of Hiroshima highlights that agglomeration economies,
combined with the expectations in the recovery, may play the key role in shaping the evolution of city
structure. Therefore, although fundamental locational characteristics and path-dependence may also
crucially affect the evolution of city structure in other contexts, taking into account agglomeration
economies and expectations may be important for understanding how city structure evolves and therelevant policy effects.
Related literature. This paper contributes to the extensive literature on the determinants of thespatial distribution of economic activities. The first strand of research examines whether a historical event has a persistent impact on the spatial distribution of economic activities. Previous
studies exploiting war-time destruction as a shock often discovered path independence (Davis andWeinstein 2002, 2008; Brakman, Garretsen and Schramm 2004; Bosker, Brakman, Garretsen andSchramm 2007; Miguel and Roland 2011; Feigenbaum, Lee and Mezzanotti 2022). In particular,
the seminal work by Davis and Weinstein (2002) finds that across-city population distribution ofJapan after World War II converged to the pre-war trend, including Hiroshima and Nagasaki. Yet,path dependence may arise depending on the historical event and the outcome variables of interest(Arthur 1994; Redding, Sturm and Wolf 2011; Bleakley and Lin 2012; Schumann 2014; Siodla
2015; Hornbeck and Keniston 2017; Michaels and Rauch 2018; Brooks and Lutz 2019; Ambrus,
Field and Gonzalez 2020; Kocornik-Mina, McDermott, Michaels and Rauch 2020; Heblich, Trew
and Zylberberg 2021; Allen and Donaldson 2022; Brooks, Rose and Veuger 2022; Yamasaki, Nakajima and Teshima 2022; Yamagishi and Sato 2023; See Glaeser 2022; Lin and Rauch 2022 for recent
review). Our paper is distinctive from these studies in three important ways. First, we use the new
spatially granular data to analyze the intra-city spatial distribution of economic activities.¹ Second,
we use the atomic bombing of Hiroshima as an exogenous and unprecedentedly large shock to theinternal structure of the city. Finally and most importantly, we apply a novel dynamic quantitative
urban model to this historical shock to investigate why we observe path independence in Hiroshima,highlighting the role of agglomeration economies and expectations in overcoming the catastrophic
history.
Our paper also relates to the literature emphasizing the fundamental locational characteristics
as a determinant of city structure. This is a spirit of the theories of urban economics dating at least
back to the Alonso-Muth-Mills model (Fujita 1989), and the importance of fundamental locational
characteristics, such as transportation costs and natural conditions, has been empirically investigated(e.g., Anas, Arnott and Small 1998; Glaeser and Kahn 2004; Saiz 2010; Lee and Lin 2018; Harari2020). Our paper does not at all deny the importance of fundamental locational characteristics indetermining city structure. Nevertheless, by showing that the rebuilding after the atomic bombing¹As reviewed by Lin and Rauch (2022), the focus on the within-city setting is recent but growing (e.g., Ahlfeldt,
Redding, Sturm and Wolf 2015; Hornbeck and Keniston 2017; Brooks and Lutz 2019; Ambrus et al. 2020; Heblich
et al. 2021). We investigate the atomic bombing, which is also analyzed by Davis and Weinstein (2002, 2008) in theacross-city setting, by focusing on its effect on the city structure.

4

in Hiroshima is unlikely to be explained by locational fundamental characteristics alone, our paper
suggests that factors other than locational fundamental characteristics, especially agglomeration
economies and expectations, can also be important determinants of the city structure.
This paper also contributes to the discussion about the role of expectations in shaping the evolution of the spatial economy. Krugman (1991) and Matsuyama (1991) show that self-fulfilling
expectations can induce a transition from one steady state to another when multiple equilibria exist,
implying that the initial condition determined by history can be overcome by expectations.² A spatial
economy with strong agglomeration economies is a primary example in which multiple equilibria
and equilibrium selection matter because the positive spillovers can lead to multiple equilibria (Fujita, Krugman and Venables 1999; Redding and Rossi-Hansberg 2017).³ Combining our model anddata, we empirically demonstrate that the dynamics of the city structure would be totally different if
there were not expectations in the recovery. In this sense, we provide new evidence of the potential
importance of self-fulfilling expectations in the spatial economy based on a large historical shock
and a structural model, which has been scarce as pointed out by Lin and Rauch (2022). Investigating
the role of self-fulfilling expectations is policy-relevant because, if they matter, then even a smallscale policy can have a large welfare impact by affecting people’s expectations (Kline and Moretti2014).
Our structural analysis also relates to recent advancement of quantitative spatial models (Redding and Rossi-Hansberg 2017). Our model is the first quantitative urban model to incorporate thefollowing three key components. First, we incorporate commuting to account for differences in location as a residential place and a workplace within a city (Ahlfeldt et al. 2015; Dingel and Tintelnot
2020; Tsivanidis 2022). Second, individuals make forward-looking migration decisions with perfectforesight (Desmet, Nagy and Rossi-Hansberg 2018; Caliendo et al. 2019; Balboni 2021; Heblich etal. 2021; Allen and Donaldson 2022; Kleinman, Liu and Redding 2023) in order to account for expectations. Third, we include history-dependent amenities and productivity and migration frictions
to account for the influence of history (Allen and Donaldson 2022).⁴ Importantly, we integrate theseelements into a single framework while keeping it parsimonious in other aspects since the availability of historical data is relatively limited. This parsimony may be particularly useful in applying ourmodel to data-scarce environments.
Lastly, this paper is related to studies on the recovery of Hiroshima from the atomic bombing²Fukao and Bénabou (1993) corrects a mathematical problem in Krugman (1991). See, among others, Rauch (1993),
Baldwin (2001), Ottaviano (2001), Oyama (2009), and Barreda-Tarrazona, Kundu and Østbye (2021) for further developments on the idea of Krugman (1991) and Matsuyama (1991) in economic geography.
³The self-fulfilling expectations also matter in other important economic contexts with multiple equilibria, suchas bank runs (Diamond and Dybvig 1983); structural transformation in economic development (Murphy, Shleifer and
Vishny 1989); and health insurances (Foley-Fisher, Narajabad and Verani 2020).
⁴In particular, our model extends Allen and Donaldson (2022) by introducing commuting to analyze the internal
structure of a city. Furthermore, we set a much lower discount factor for future values compared to Allen and Donaldson(2022) so that expectations play a more important role. This reflects the difference in time horizon. We consider shortperiods (every 5 years), while Allen and Donaldson (2022) suppose 50 years for one period since their primary focus
is on the long-run impact of history (i.e., the initial conditions).

5

(Hiroshima City Government, 1971; 1983a). However, there is little econometric analysis on the
distribution of economic activities within the city and what can account for the resurgence of the city
center. We newly digitize historical resources on population and employment at a spatially granularlevel to analyze the impact of the atomic bombing at a high spatial resolution. In addition, wedevelop and calibrate a novel quantitative economic model to understand the economic mechanisms
behind the recovery of central Hiroshima.
This paper is structured as follows. Section 2 provides historical context and data. Section 3
introduces the reduced-form analysis and shows the fast and strong resurgence of central Hiroshima
after the bombing. Section 4 presents our baseline model. Section 5 calibrates the model and demonstrates that our model explains the recovery of central Hiroshima and agglomeration economies are
the key driving force. In Section 6 we highlight that expectations in the recovery are essential for
agglomeration economies to induce the recovery by using an alternative model in which people do
not anticipate the recovery of central Hiroshima. Section 7 concludes.

2 Historical Background and Data
In this section, we briefly describe the historical background of Hiroshima City and the data of ourstudy. In Subsection 2.1, we summarize the history of the city from the period before the bombing
and how the atomic bombing had an impact on the city. In Subsection 2.2, we describe how weconstruct new spatially-granular data on population, employment and other location characteristics
of Hiroshima city. Section A of the online appendix provides further details including summary
statistics of the data.
2.1 Historical backgroundThe development of Hiroshima city started in the late 16th century when Terumoto Mōri, a local
samurai lord, built the Hiroshima castle. Hiroshima city has been a major city in the Chugoku region since then. The early 20th century saw rapid growth of the city: Hiroshima had 310,118 people
living there in 1935, making it the seventh-largest city in Japan by population. The growth slowed
down and finally reversed as Japan gradually transitioned to a total-war system following the Second
Sino-Japanese War (1937-) and the Pacific War (1941-). Prior to the atomic bombing, the city had
approximately a population level of 350,000. As the U.S. overwhelmed Japan during World War II(WWII), most Japanese cities endured extensive non-atomic air raids (Davis and Weinstein 2002).
However, since the U.S. desired to preserve Hiroshima as the “best laboratory” to demonstrate theeffects of the atomic bomb, the U.S. intentionally refrained from bombing on Hiroshima.⁵ Consequently, the atomic bombing was essentially the only direct destruction the city experienced in
WWII.
⁵See “Minutes of the second meeting of the Target Committee Los Alamos, May 10-11, 1945” (http://www.dannen.
com/decision/targets.html Last accessed on May 14, 2022).

6

Figure 1: Destruction of the Atomic Bombing in Hiroshima(a) Total destruction near the epicenter(b) Block-level destruction rate of buildings

Note: Panel (a) is a photograph from the United States Strategic Bombing Survey made available by the U.S. National
Archives and Records Administration. Panel (b) shows the map of Hiroshima city at the time of the bombing, alongwith block-level data (197 blocks in total) on the fraction of totally destroyed buildings and the epicenter (Hiroshima
City Government 1971; Takezaki and Soda 2001). We overlay the area of our study on an aerial photograph. Since theold photographs right after the bombing are not of high image quality, we use the contemporary image for illustration.

The U.S. Air Force dropped the atomic bomb (Little Boy) near the city center of Hiroshima on
August 6, 1945. This was the first time in human history that the atomic bomb was used to kill people. The damage to people and buildings was unprecedentedly catastrophic.⁶ The city governmentof Hiroshima estimates that 140,000 people perished by the end of 1945 as a result of the atomic
bombing, although it is difficult to determine the exact number.⁷ Because many of the victims diedafter 1945 as the atomic bombing caused severe injuries and diseases due to radiation, the actual
death toll is anticipated to be even higher than this. The death rate was exceptionally high and near
100 percent for those within 1 kilometer from the epicenter. The bomb also destroyed a large number of buildings: 70,147 out of 76,237 buildings in Hiroshima city were destroyed in excess of fifty
percent. The majority of buildings within two kilometers of the city center were completely destroyed. The situation in which almost all buildings were destroyed can be seen in the photo Figure
1a, which was taken near the epicenter of the bombing. Consequently, the population of Hiroshimacity dropped to 136,518 in November 1945, which is about one-third of the pre-war population.
In contrast to the total destruction in central Hiroshima, the outskirts of the city more than 2kilometers away from the city center experienced relatively moderate destruction. Figure 1b shows
⁶This damage was even much more severer than other cities that endured extensive air raids. For example, the population of Tokyo was approximately 7 million in 1940. During the war, the U.S. air raids on Tokyo killed over 100,000
civilians and damaged approximately 700,000 housing units. Source: https://tokyo-sensai.net/about/tokyoraids/ (InJapanese, last accessed on May 13, 2022). While the absolute number is large in Tokyo, the destruction ratio in Hiroshima is substantially greater than in Tokyo due to its smaller population size.
⁷Source: https://www.city.hiroshima.lg.jp/site/english/9803.html (last accessed on November 4, 2022).

7

the fraction of completely destroyed buildings at the block level (Hiroshima City Government 1971;
Takezaki and Soda 2001). While nearly all buildings in the dark-colored areas close to the epicenter
were destroyed, the majority of buildings in the light-colored areas away from the epicenter avoided
complete destruction. As a result, the outskirts of Hiroshima experienced a significant increase inpopulation as survivors from the city center escaped to them. Most notably, on November 1, 1945,
areas beyond 3 kilometers from the epicenter had 142 percent of their pre-bombing population.
The war ended on August 15, 1945, when Japan accepted the Potsdam Declaration. People
initially doubted whether Hiroshima could recover. In particular, radioactive contamination was amajor concern immediately after the bombing: rumors circulated that “nothing will grow here for
75 years.”⁸ However, the serious radioactive contamination caused by the bombing decayed rapidly
with time.⁹ Furthermore, a large typhoon hit Hiroshima on September 17, 1945 (i.e., about six
weeks after the bombing) and it presumably washed away contaminated substances according to
the Atomic Bomb Casualty Commission established by the US, leading to a safe level of radioactivity (Takahashi 2008). Given such evidence, we do not take into account the potential radioactive
contamination in analyzing the recovery of Hiroshima because living in Hiroshima was unlikely tocause diseases after this typhoon.¹⁰
The city government of Hiroshima attempted some early public efforts to promote the recovery,
but a shortage of resources prevented a large-scale action. There was no special aid from the central
government for Hiroshima until 1949 despite the exceptionally severe damage. Notwithstanding
the lack of strong public actions, the Hiroshima city, including its city center, had started to recoverstrongly due to the private efforts. In 1955, Hiroshima city had a population level of 357,287,
which was already larger than the 1935 population. Hiroshima continued to grow and the city area
expanded along the way. Today, Hiroshima city has a population of approximately 1.2 million in
2022, ranking it 10th among all Japanese municipalities and the largest in the Chugoku region ofJapan.
2.2 Data
We have collected and, when necessary, digitized various information on the economic activity in
Hiroshima before and after the war. Here, we provide a brief overview of the essential data used inthis paper. See Section A of the online appendix for more details.
Spatial units. The spatial unit of our analysis is mainly a city block (cho-cho-moku) in Hiroshimacity. As our primary definition of city blocks, we use the GIS data of block boundaries as of the
⁸Source: https://www.bbc.com/news/world-asia-53660059 (last accessed on March 13 2022).
⁹According to the Hiroshima city government (https://www.city.hiroshima.lg.jp/site/english/9809.html, last accessed on November 4, 2022), the radiation level at the epicenter became 1/1,000th a day after the bombing and
1/1,000,000th a week later.
¹⁰Note that considering the potential radioactive contamination would, if any, reinforce the main finding of our
reduced-form analysis (Section 3) that the city center recovered. Since radioactive contamination is a disamenity thatmakes the city center less attractive, failing to control for it would underestimate the strength of the recovery.

8

bombing constructed by Takezaki and Soda (2001). To make the comparison between the pre-war
and the post-war period, we focus on areas that already belonged to Hiroshima city as of the bombing.¹¹ We additionally digitize the block boundaries as of 1966 and 1976 to account for revisions of
the block boundaries by the government. Throughout the paper, the number of blocks is 174 andthe average size of blocks is 0.32 square kilometers. This implies that our spatial unit of analysis
is generally small, although there is some heterogeneity in the size of blocks. The block tends tobe small near the city center. The average area size for blocks is 0.04 square kilometers within 1
kilometer of the CBD and 0.13 square kilometers within 3 kilometers from the CBD. In contrast,
the average block area is 2.19 square kilometers among blocks more than 3 kilometers away fromthe CBD.
The destruction level by the atomic bombing. Similar to Davis and Weinstein (2002) and Brakman et al. (2004), we primarily use the fraction of totally destroyed buildings as a severity measureof destruction. The block-level destruction rate is reported in Hiroshima City Government (1971).
Building on the digitization by Takezaki and Soda (2001), we augment it by consulting Hiroshima
City Government (1971) to correct typos in their data and obtain additional information on missing
values. Figure 1b in the previous section illustrates the share of completely-destroyed buildings ineach block on a map.
Population. We collect and digitize the population data at the block level. For the period 19331936, we refer to the Statistical Handbook of Hiroshima city (Hiroshima-shi toukei sho). For 19451953, we refer to the Statistical Abstract of Hiroshima city (Hiroshima shisei youran). From 1955,
we exploit data from the Population Census. We address changes in the block boundaries by theareal weighting interpolation. For 1945–1950, population is reported in less geographically granular
units than blocks, which we address by utilizing the best available block-level information to approximate the block-level population distribution. Figure 2a provides a visualization of the populationin Hiroshima over time. The total population in Hiroshima increased prior to the atomic bombing
and significantly dropped after the bombing. After WWII, the total population again increased overtime. We also observe that the central area of Hiroshima showed a declining share of the population
over time. This is suggestive of suburbanization and the development of the outer suburbs of thecity that absorbed the population growth of the city, which was a general trend in cities during thepost-WWII period. Note that the declining trend was already observed in the pre-WWII period,
suggesting that a lower population share of the center after the WWII does not necessarily meanthat the recovery was incomplete.
¹¹The city boundaries gradually expanded since 1955 through municipal mergers as Hiroshima metropolitan area
grew. The administrative Hiroshima city as of 1945 roughly corresponds to the central four wards (Naka-ku, Nishi-ku,
Minami-ku, Higashi-ku) of Hiroshima city today. With the expansion of the administrative boundaries and commuting
zones of Hiroshima city, it implies that our data concentrate more and more on the central locations as time elapses.

9

Employment. We collect and digitize employment data at the block level.¹² For the year 1938,
we refer to the Survey of Commerce and Industry in Hiroshima city (Hiroshima-shi shoukou-gyou
keiei chousa) that records the number of establishments at the block level. The number of commercial buildings right after the bombing is available in the Statistical Abstract of Hiroshima city
(Hiroshima shisei youran). For 1953, we exploit the Survey on the Daytime Population of Hiroshima(Hiroshima-shi chukan jinko chosa). From 1957 to 1975, we use the Business Establishment Statistical Survey (Jigyousho toukei chousa). We address changes in the block boundaries by the areal
weighting interpolation. For 1953–1963, employment is reported in less geographically granular
units than blocks, which we address by combining the best available block-level information to approximate the block-level employment distribution. Finally, when employment data is unavailable
but establishment data is available, we follow Ahlfeldt et al. (2015) to assume that the number of
establishments is proportional to the number of employment. Based on the data described above,
we then approximate the block level employment every five years from 1950 to 1975 to match theyears in which the population data is available. Figure 2b shows the change in employment in Hiroshima city. The total employment dropped significantly in 1945 after the bombing, but it increased
again post-war, and the number of employment in the central area recovered to a similar level to thepre-war period. The share of employment in the central area had been increasing throughout the
post-war period, implying the concentration of employment over time.

.15

400
.1
300

200
.05
100

0

0
33343536

454950515253 55

Year

60

Total Number

65

70

75

Number within 1km from CBD

250

.25

200

.2

150

.15

100
.1
50
.05
0
38

45

53

57

Year

Total Number

Share within 1km from CBD (right axis)

Share in 1km from CBD

Employment in Hiroshima city (thousands)

500

Share in 1km from CBD

Population in Hiroshima city (thousands)

Figure 2: Change in Population and Employment in Hiroshima city

63

66

75

Numbers within 1km from CBD

Share within 1km from CBD (right axis)(a) Population(b) Employment

Note: The total number of population and employment of the entire city and within one kilometer from the CBD (leftaxis), as well as the share of the population and employment within one kilometer from the CBD (right axis). See
Section A of the online appendix for data construction.

¹²Throughout this paper, we focus on employment in manufacturing or service sectors and abstract from agricultural
employment. This is a relatively moderate restriction because we focus on an urban area and the agricultural employment
is small. Even in 1950, in which agricultural employment was large in the entire Japanese economy, the Population
Census suggests that less than 10 percent of workers are in the agricultural sector in Hiroshima city.

10Commuting and transportation networks. We use the trip-level microdata from the 1987 Hiroshima City Person Trip Survey to analyze the commuting pattern, which collects the workplace,residence, and the representative travel mode for the commuting trip. We also collect and digitize
road networks, bus networks, and train networks in Hiroshima city, and compute the bilateral travel
time between blocks for each mode: walk, bike, car, bus, and train. Although the public transportation networks were generally stable during our sample period, there were some changes, notably thediscontinuation of the Ujina line in 1966. To address this, we use the public transportation networks
of 1950 for years prior to 1966 and those of 1987 for later years.
Locational characteristics. We collect various information on the locational characteristics ofeach block. In particular, we exploit data on altitude, ruggedness, soil condition, distance to train
stations, distance to water and cultural assets for each block.

3 Reduced-form Evidence
In this section we analyze population density to illustrate the pattern of destruction and recovery in
Hiroshima. Subsection 3.1 describes how the atomic bombing destroyed central Hiroshima and how
the city recovered in its subsequent periods. In Subsection 3.2, we conduct a regression analysisof the changes in population distribution and argue that the fundamental advantages of central Hiroshima are unlikely to explain its recovery. Subsection 3.3 examines the case of Nagasaki, which
is another city hit by atomic bomb to discuss the external validity. Subsection 3.4 investigates therecovery as measured by the employment distribution and land prices, an alternative regression
specification that explicitly considers the characteristics of neighboring blocks, and the effects ofpublic recovery policies.
3.1 Descriptive evidence of the destruction and recovery within Hiroshima
In Figure 3 we non-parametrically plot the population density in the city of Hiroshima by the distanceto the central business district (CBD), where we normalize the total population of the city to 100,000
for all years to facilitate comparisons of the inner-city structure across years. The figure showsthat the city structure of Hiroshima completely changed due to the atomic bombing but it quickly
recovered to the pre-WWII city structure. In 1936, the city had a typical monocentric city structure.
The city center had the highest population density and it decreased as one moved away from thecenter. This monocentric pattern had been completely reversed because the atomic bomb hit themost densely populated city center. Figure 3 shows that, after bombing, the city center became
totally destroyed and consequently had the lowest population density in the city. In contrast, areasthat are about 2 kilometers away from the city center, which avoided the total destruction of buildings(see Figure 1b), became the most crowded places in the city. Areas further away from the city center
also experienced a significant increase in population density. Indeed, the outskirts experienced an

11increase in population density as many survivors in the city center escaped to the outskirts.

Log population density (per square km)

Figure 3: Population Density by the Distance to the City Center
9

8

7

6

5
0

1

2

1936

1945

3

4

Distance to CBD (km)
1950

5

6

1950(counterfactual)

Note: The figure shows the local polynomial regression of the log population density on the distance to the central
business district (CBD) using the block-level data for different years. To eliminate the effect of changes in the total
population, we normalize the total population each year to 100,000. Distances are calculated using the centroid ofeach block shape and CBD is defined as the mid-point of Kamiya-cho block and Hacchobori block, which are the two
prominent areas in CBD of Hiroshima city both in the pre and post-WWII. The counterfactual population distributionof 1951 is generated from the 1936 population distribution, assuming that each block has the annual population growthrate during 1933–1936.

Despite the “reversal” of the monocentric city pattern after the bombing, the monocentric city
structure had already re-emerged in 1950, just five years after the bombing. This is quite surprising
given that the city center, which was nearly completely destroyed, quickly became the most prosperous place again. While the recovery from the total destruction appears to be robust, the recovery
may not be perfect, as the concentration of the population around the CBD appears to be less dense
in 1950 than in 1936. However, this does not necessarily imply that the recovery was incomplete
because the city center already had a slow rate of population growth prior to the war. This can beillustrated by the similarity between the actual population distribution in 1950 and the counterfactual one, which was constructed by assuming that there was no atomic bombing and the pre-war
population growth rate continued from 1936 until 1950.
If the initial population distribution immediately after the end of the war determined by theatomic bombing had a persistent impact, then we would expect a lower population density in thecenter and a higher population density in the outskirts. The recovery result is analogous to the pathindependence result of Davis and Weinstein (2002) for inter-city population distribution of Japanafter WWII. However, we obtain the recovery in a within-city setting of Hiroshima that experienced

12

an extremely larger shock: the complete destruction of the city center.¹³ The next section formalizes
this point by a regression analysis.
3.2 Regression analysis of the recovery of central Hiroshima
We now look at the magnitude of the resurgence at a spatially granular level of blocks. We estimate
the following regression model analogous to Davis and Weinstein (2002):
ln

Popdensi,tPopdensi,1945!

Popdensi,1945= γ lnPopdensi,1936!

+ ηXi + vi ,(1)

where i is the block and t is the year, Xi is the vector of control variables and vi is the error term. In
this specification we regress the post-war log population density change rate on the log population
change rate induced by the atomic bombing from 1936 to 1945. If γ = 0, the log post-war population density is proportional to the log population density right after the bombing, irrespective of
the pre-war population density. This is consistent with path dependence: the historical shock by
the atomic bombing is crucial in determining the population distribution. In contrast, if γ = −1,
the population change due to the atomic bombing is completely negated. This is consistent withpath independence: the historical shock of the bombing no longer matters. Therefore, the estimatedcoefficient of γ informs whether the data is better characterized by path dependence or path independence. Throughout Section 3, we keep the analysis descriptive and do not claim causality. The
causal interpretation of γ is inessential as a descriptive summary measure of the strength of theobserved recovery.
We start with a simple case of no control variable. Figure 4 illustrates the relationship between
the post-war population density growth rate and that during the bombing period for each block,along with the regression line of (1). The first panel in Figure 4 shows that in 1950. The fitted line
is somewhat less steep but already close to the slope of −1, implying that the strong resurgence of thedestroyed areas had already occurred just five years after the bombing. The second panel of Figure
4 demonstrates that a similar result is obtained when examining the population distribution in 1960,
suggesting that the recovery was essentially completed by 1950. Columns 1 and 4 of Table 1 provide
detailed regression results depicted in Figure 4. The coefficient is −0.712 in 1950 and −0.688 in
1960, both of which are statistically distinguishable from zero, thus the complete path dependence
is rejected. Although we can also statistically reject γ = −1 (i.e., perfect path independence) inthese regressions, the results suggest a strong recovery just within five years.
The regression specification (1) has been estimated in other contexts and our result is comparable to those estimates. The coefficient around −0.7 in our simple regression is larger in absolute¹³Moreover, our results may differ from Davis and Weinstein (2002) in terms of the rate of recovery. In Davis andWeinstein (2002), it took approximately 20 years for the total population of Hiroshima to return to the level predictedby the pre-war trend. In our within-city case, it took just about five years conditional on the location characteristics (seeColumns 2 and 3 of Table 1).

13value than Brakman et al. (2004) in their across-city analysis of Germany, suggesting that the recovery was stronger in our context. On the other hand, the coefficient is somewhat smaller in absolutevalue than some specifications of Davis and Weinstein (2002, Columns 1 and 3 of Table 3), suggesting that weak path dependence might be observed for the within-city population distribution ofHiroshima.¹⁴ That said, we show in the next subsection that, conditional on control variables, we
also obtain a coefficient of around −1. The high R-squared despite the fact that we only include
the population change from 1936 to 1945 as the explanatory variable implies a close relationshipwith the postwar population change.¹⁵ Overall, our results indicate the fast and strong resurgence ofcentral Hiroshima.

5

Change in log population density, 1945-60

Change in log population density, 1945-50

Figure 4: Population Change due to the Atomic Bombing and the Subsequent Population Change

4
3
2
1
0
-1
-4

-3

-2

-1

0

4
3
2
1
0
-1
-4

Change in log population density, 1936-45 (after bombed)
Fitted line

5

Slope of -1-3-2

Fitted line(a) Population change in 1945-50-10Change in log population density, 1936-45 (after bombed)
Slope of -1(b) Population change in 1945-60

Note: The figures plot change in log of population density from 1945 to 1950 or 1960 to those from 1936 to 1945,
which is largely driven by the atomic bombing. Each circle represents a block (i.e., an observation), where the sizeof the circle is proportional to the population density in 1936. We plot the (unweighted) linear fit between these twovariables (solid line) as well as the slope of −1 (dashed line), which would be obtained if the population change during
the bombing period is completely reversed in the post-war period.

Locational advantages of the central Hiroshima. Precedent studies (e.g., Bleakley and Lin
2012; Schumann 2014; Lin and Rauch 2022) have argued that the spatial heterogeneity of geography in terms of climate and topography may be crucial in explaining the path-independence resultof Davis and Weinstein (2002) for the across-city population distribution in post-WWII Japan. If
the damaged locations were innately attractive, people would rebuild there. Although this may be aplausible explanation for the across-city population distribution in Davis and Weinstein (2002), we
argue below that locational advantages do not appear to play a significant role in the resurgence ofcentral Hiroshima within the Hiroshima city.
¹⁴Column 2 of Table 3 in Davis and Weinstein (2002) reports the coefficient of −0.759, which is close to −0.7.
¹⁵The high R-squared also suggests that the effect of measurement error is relatively limited in our data.

14

Table 1: Changes in Population Density and the War-Time Damage
(1)
(2)
(3)
(4)
(5)
(6)
Change in log population density Change in log population density
1945 - 1950
1945 - 1960
Change in log population density 1936-1945 -0.712 -0.931-0.979-0.688 -0.929-1.007(0.026) (0.100)(0.097)(0.030) (0.101)(0.117)p-value from testing γ = −1
0.000
0.499
0.835
0.000
0.492
0.949
Control variables✓✓✓✓
Within 3 km from the city center✓✓
Number of blocks
174
174
158
174
174
158
R-squared
0.809
0.862
0.880
0.772
0.854
0.862
Note: We report the OLS estimation result of the equation (1). Fundamentals consist of the quadratics of the distanceto the nearest station, the distance to the nearest cultural asset, the distance to the nearest water area, the altitude, andthe slope. We also include a dummy for a bad soil condition. We also control for the quadratic of the pre-war (19331936) population growth rate, the fractions of the half-destroyed, moderately-destroyed, and intact buildings, and thegeographical coordinates (the latitude, the longitude, and their interaction). In columns 3 and 6, we confine the sample
to blocks within 3 kilometers from the city center, in which fundamental conditions are more homogeneous. We report
the p-value from testing the null γ = −1, meaning that the 1936 population distribution matters for the population in1950 and 1960 but not the 1945 population distribution. Robust standard errors in parentheses.

Before proceeding with the regression analyses, we discuss heuristically why the locational advantage of central Hiroshima does not appear to account for its resurgence. First, natural conditions
within Hiroshima are homogeneous. This is intuitive because our geographic scope is limited andmost of the city area lies within up to 6 kilometers of the city center. The majority of Hiroshima city
is located in the delta area of Ota river, which provides the flat terrain with loose soil. Moreover,the distance to the nearest water area is homogeneous within the city, reflecting the fact that the city
is cut through by many branches of Ota river and faces the sea to the south.
Second, the key manmade advantages of central Hiroshima prior to WWII were substantiallydamaged by the bombing. The city center of Hiroshima, areas around Hacchobori and Kamiya-cho,
is located next to the Hiroshima castle, which had been a symbol of the city since the samurai period
and may be a historical amenity. It was also adjacent to the area called Nakajima-cho, which developed during the samurai period due to its convenient access to the castle and water transportation.
The city center also had convenient access to the tram network. These advantages were lost by thebombing. Hiroshima castle was totally destroyed and Nakajima-cho was also completely obliterated by the atomic bomb. Although the city center might retain some advantage in the transportation
access, the access to workers and jobs would have been substantially worsened as their neighborhoods were completely destroyed and other areas of the city may have had better conditions after
the bombing.¹⁶
We now use our regression model (1) to formally assess the role of locational advantages. Specif¹⁶For instance, areas around Hiroshima station also provide convenient access to transportation but experienced muchless destruction by the bombing, which may make Hiroshima station as the potential new center of Hiroshima city. In adifferent Japanese city (Yokohama), Takano (2022) documents that the city center moved to an area with transportation
advantages after the requisition of the former city center by the US army for nearly ten years.

15

ically, we control for the observable characteristics of each block. If the resurgence is not driven
by fundamental advantages of central Hiroshima, the severity of destruction would retain its explanatory power and vice versa. We consider the following control variables: the quadratic form the
distance to the nearest train station as of 1950, the distance to the nearest cultural asset, the distanceto the nearest water area, the altitude and the the ruggedness, an indicator for a bad soil condition andgeographic coordinates. These variables capture the fundamental locational advantages of the citythat can be considered as given after the WWII period.¹⁷ Additionally, we control for the population
growth from 1933 to 1936.¹⁸ The pre-war growth trend is expected to capture unobserved attractiveness of each location. We also control for the fractions of half-destroyed, moderately-destroyed,
and intact buildings, which we expect to serve as proxies for the initial conditions of each location
immediately after the bombing such as the quality of the housing stock and infrastructure after thedestruction.
Column 2 and 5 of Table 1 present the regression results of equation (1) for 1950 and 1960 withthe rich set of control variables described above. Compared with columns 1 and 4, coefficient γ
is now statistically indistinguishable from -1 even for 1950, suggesting the complete path independence. This result implies that if any, locations that grew more due to the attractive fundamental
conditions might have experienced milder destruction from the atomic bombing, which is in contrast to the center having location advantages and experiencing rapid resurgence. Columns 2 and5 thus imply that, conditional on observed fundamentals, the damage due to the atomic bombing
no longer matters. This result suggests that the observed fundamental locational advantages of thecentral Hiroshima do not explain its resurgence.
To further address the concern that the unobserved attractiveness of each location could drive
the result, we restrict our sample to blocks within 3 kilometers from the city center. Since the edgeof this circle was less damaged and had better access to the undamaged areas, it would be in abetter position right after the bombing (see Figure 3). At the same time, these areas have morehomogeneous natural conditions and transportation access as we have focused on a smaller area,leading to a smaller omitted variable bias.¹⁹ Columns 3 and 6 of Table 1, however, show that,coefficient γ is statistically distinguishable from zero but not from −1. This result further suggeststhat fundamental locational advantages of the city center are unlikely to explain its resurgence.
3.3 When the bomb hit the outskirts of the city: the case of Nagasaki
Our findings regarding Hiroshima suggest that the recovery of central Hiroshima is attributed to thelevel of destruction caused by the atomic bomb; however, the fundamental location advantages do
not appear to account for the recovery. To provide further support for this argument, we document¹⁷While most of the pre-war stations were restored by 1950, no new rails were constructed between 1945 and 1950.
¹⁸To avoid extreme values due to idiosyncratic reasons or measurement errors, we cap the annualized growth rate at
10 percent in absolute value.
¹⁹Table A.1 suggests that the standard errors of locational characteristics are smaller in this subsample. A similar
idea has been invoked in Schumann (2014) in a different context.

16

the recovery from the bombing in Nagasaki, the second and last city in human history to be destroyedby an atomic bomb. In Section B of the online appendix we examine the population data in Nagasaki.
In Nagasaki, the atomic bomb hit the outskirts of the city (see Figure B.1a). This is in contrast
to Hiroshima, where the atomic bomb hit the city center. Consequently, the comparison with Hiroshima helps distinguish the fundamental advantages of the pre-war city center, some of which
are potentially unobserved, from the level of destruction in explaining post-war population growth.
Figure B.1b illustrates with a fitted line from the regression of equation (1) for Nagasaki that heavily
destroyed areas on the outskirts of Nagasaki recovered strongly. The coefficient of our interest isaround -0.88 and statistically indistinguishable from -1, suggesting path independence in population distribution within Nagasaki. Therefore, the recovery of the destroyed outskirts of Nagasaki
suggests that they did not play a major role in the strong recovery of the destroyed area.
3.4 Further discussions on the recovery of central Hiroshima
Employment distribution. We have looked at the evolution of the population distribution. However, due to commuting, the population distribution and employment distribution in a city may
differ. As the city center is also the center of employment, the atomic bombing would also alter theemployment distribution. In Section C of the online appendix we analyze the impact of the atomic
bombing on the distribution of jobs using establishment location data for 1938, 1945, and 1966.
We find that the number of jobs in central Hiroshima recovered, and the regression results are very
similar to those for the population.
Land prices. We also examine land prices. A challenge of this approach is that we do not havecomprehensive land price data during our sample period. Alternatively, we could investigate thelocation with the highest land price in the city, which could be interpreted as a central location of
the city. Both in 1931 and 1959, the highest land price was observed in the block of Hacchobori
area, the city center both before and after the war.²⁰ Thus, the resurgence of central Hiroshima isalso observed in land prices.
Characteristics of neighboring blocks. In Section C of the online appendix, we consider the
possibility that the post-war population growth rate of a block may depend not only on its own
characteristics, but also on the characteristics of its neighboring blocks. To consider the characteristics of neighbors, we adopt the so-called “SLX model” in spatial econometrics literature(Halleck Vega and Elhorst 2015) and add the spatial lags of the following three neighborhood
characteristics to our main regression model (1): (i) the population change rate by the bombingln(Popdensi,1945 /Popdensi,1936 ), (ii) the locational characteristics Xi , and (iii) the population²⁰The block containing the plot with the highest land price is the Horikawa-cho block adjacent to the Hacchobori
block. Other available evidence on pre-war land prices suggests a similar conclusion (Nozawa 1934; Hayakawa andNakaouji 1965).

17

distribution right after the war, which is meant to capture market access after the bombing.²¹ Table
C.2 shows that the addition of these spatial lag variables does not change our path-independence result. Note that while this is a reduced-form approach to account for spatial interdependence acrossblocks, our theoretical model in Section 4 structurally incorporates it through transportation networks.
Timing of the recovery and public recovery policies. As demonstrated in this section, our population data at the block level suggests that the recovery was complete by 1950. To shed additional
light on when the recovery began, we use the population data for 1946, 1947, and 1948 from theStatistical Abstract of Hiroshima as reported by distance from the epicenter of the bombing. The
recovery process began in 1946, as depicted in Figure A.4 in the online appendix. This finding may
suggest that the direct impact of public recovery policies on the recovery was limited. In particular,
the Hiroshima city government faced severe budget constraints when implementing a recovery plan.
It was not until the enactment of the Hiroshima Peace Memorial City Construction Law in 1949 that
Hiroshima could receive special recovery grants from the central government. Consequently, Hiroshima city was only able to spend approximately 1.8 percent of the total rebuilding budget plan byAugust 1949 and 3.2 percent by May 1950 (Ohshima 1950). Such a serious budget shortage makes
it difficult to attribute the early-stage rebuilding to the recovery plan. In addition, even the small
budget spending did not seem to be a main factor in explaining the recovery. While the primary
goal of the Hiroshima city government was to provide housing, the public sector provided less than
3,000 housing units by 1950.²² This is a small fraction of the over 70,000 buildings that were at least
partially destroyed by the atomic bombing. Consistently, we find that controlling for public housing
has little effect on our regression results (see Section C of the online appendix ). These suggest thatthe reconstruction policies had a limited direct impact on the recovery of central Hiroshima. Yet,
we do not rule out the possibility of indirect effects of reconstruction policies to coordinate recovery
expectations. We return to this discussion in Section 6.3.
In summary, our reduced-form analysis has revealed that the resurgence of central Hiroshimaoccurred within five years after the bombing. We have also demonstrated that it is difficult to explain
the recovery through its fundamental location advantages. This raises the following question: why
could central Hiroshima recover despite the destruction? We answer this question in the remainderof this paper by taking a structural approach, and highlight the role of agglomeration economies andexpectations in recovery.
²¹In particular, it addresses the possibility that the city center could recover as the “donut hole of the city:” it might still
have relatively good market access thanks to its central location despite that the city center itself was totally destroyed.
²²Another primary expenditure was to rebuild damaged infrastructure, such as the water system and trains. While
the rebuilding of the infrastructure is important, it did not appear to provide central Hiroshima with any particularadvantages over the outskirts, as the outskirts already had comparable infrastructure.

18

4 Theoretical Model
This section presents a novel dynamic quantitative spatial model with three key elements. First,
individuals in a city choose their residence and workplace that are potentially different, which define
the equilibrium commuting patterns within a city as in Ahlfeldt et al. (2015). Second, finitely lived
workers determine future residential places and workplaces in a forward-looking way, taking into
account migration costs and future option values associated with the locations. Third, the model
incorporates amenities and productivity spillovers that are dependent on population and employment
density in the current period and in the past. With such externalities, there may exist the selffulfilling prophecy and a multiplicity of transitions that hinge on both expectations and the past.²³
These three elements are essential to matching the model to the observed spatial distribution of
economic activities: the separation of workplace and residential place of workers in a city, different
patterns of population and employment changes across locations over time, and concentration ofjobs in the city center. Our model is the first tractable dynamic quantitative model for the internal
structure of the city that possesses these elements in a unified framework. Section D of the online
appendix provides the details of derivations.
4.1 Model setup
Time is discrete and indexed by t. We consider a single city C embedded in the large economy E :C ⊂ E . The set of locations in a complementary set O = E \C is the outside of the city. The city C
consists of discrete number of locations indexed by i, j, n, ℓ. These locations correspond to blocks
and they are differentiated by fundamental productivity, amenities, land endowment, and geography.
The fundamental productivity and amenities can change over time, while land endowment remains
the same.
Individuals in the economy live for a finite time, T. The mass of the population in the economy(E ) is M and it is exogenous. We suppose that there is a potentially large number of people in thewhole economy throughout time and M is constant. Instead, the total population of the city, which isembedded in the whole economy, changes over time through migration flows. This allows us to focus
on the distribution of individuals within the city. Individuals are endowed with one unit of labor thatis supplied inelastically and they are geographically mobile across locations in a city. They commute
from their residential block to their workplace block subject to commuting costs. Individuals outsideof the city are prohibited from commuting so individuals living outside of the city (O ) work there.
Production occurs in every location in the economy and firms produce homogeneous tradable goods
that can be freely traded across locations. In every period, an individual may have an opportunity tochange their residential and workplace block in the economy (E ). In particular, individuals obtain
their chance to change their locations with exogenous probabilities in every period and they decide²³Allen and Donaldson (2022) introduces this type of local externalities to characterize path dependence in the spatial
distribution of economic activities in the U.S. Kleinman et al. (2023) analyzes the properties of the spatial equilibrium
when workers determine the future path of mobility in a forward-looking way, taking account of future shocks.

19their locations in a forward-looking way, correctly anticipating future economic conditions. Theirlocation choice is based on their current real income but also an option value associated with thatlocation. The forward-looking location choices allow us to characterize the transitions of populationand employment distribution in the city that hinges on their expectations.
Production. Firms in the economy are competitive and produce homogeneous tradable goods.
Firms are myopic, therefore we do not formulate a dynamic problem for firms.²⁴ Production technology of a representative firm in location i ∈ C is:
Yit = Ait Lit ,(2)

where Yit is production in location i, Ait is productivity and Lit is employment in location i at time
t.²⁵ Following Allen and Donaldson (2022), the productivity (Ait ) depends on the current and theprevious employment density in the location:  α1 
Lit−1 α2Lit,
(3)
Ait = aitSi
Si
where ait represents the exogenous component in productivity and Si is the area size of locationi that is time-invariant. The parameter α1 controls the contemporaneous productivity spillovers
with respect to employment density, and the parameter α2 controls the effect of lagged employment
density on productivity such as durable investments. A positive value of α1 implies a local agglomeration force that increases productivity, while α2 captures the history dependence in productivity
spillovers.
In Section D.5 of the online appendix, we provide two different microfoundations of the spillovers
in productivity. The first microfoundation introduces local capital in production that augments labor productivity. The local capital is produced by using local public goods (e.g., roads and water
facilities), final goods, and land. The current employment density is positively associated with theprovision of local capital (α1 > 0). The supply of local public goods and land for local capitalalso depends on lagged employment density. In particular, when high employment density in thepast induces the depreciation of local public goods and additional transaction costs in land supply,
current local capital is negatively associated with lagged employment density (α2 < 0). The second
microfoundation is the creation of ideas in production. Suppose incumbent workers with no opportunity to change their workplace between period t − 1 to t engage in innovation to improve firms’
productivity in period t. In period t, interactions with another worker with a novel idea allow incumbent workers to update their ideas, while ideas of the incumbent workers become obsolete without
such interaction. Then, we show that a large number of current workers induce more successful²⁴Given the linear technology and perfect competition, producers always earn zero profit. Thus considering dynamic
incentives does not change our arguments as long as firms correctly expect that future profits are always zero.
²⁵While the production technology in (2) uses labor only, this production function is isomorphic to a model withdurable investments in local productivity (Allen and Donaldson 2022).

20

knowledge spillovers (α1 > 0), and more incumbent workers make it difficult to find a worker tointeract with for updating their ideas (α2 < 0). Note that, as exemplified by these microfoundations,(α1 , α2 ) captures not only pure externalities but also other channels through which current or past
employment density affects productivity.
Homogeneous goods are freely tradable in the economy and therefore we normalize their prices
to one. The zero profit condition implies that the wage rate at location i in period t is wit = Ait .
Therefore, the wage rate in any particular location is a function of exogenous productivity, contemporaneous employment density, and previous employment density in that location.
Preference. Individuals live for finite periods and have a discount factor, ρ ∈ (0, 1). Individuals
consume only homogeneous tradable goods and inelastically supply one unit of labor. Their period
utility of living in location n and working in location i at period t isln uint = ln Bnt + ln wit − ln κint ,(4)

where Bnt is the common utility benefit from residential amenities at residential place n in periodt, κint is the utility cost due to commuting from n to i, and wit is labor earnings in workplace i.²⁶
The value of amenities in residential place (Bnt ) depends on current and past population density:
Bnt = bnt

RntSn

 β1 

Rnt−1
Sn

 β2
,

(5)

where bnt is an exogenous component in the value of amenities for each location, Rnt is populationof location n in period t and Rnt−1 is that in period t − 1.
In this specification two parameters (β 1 , β 2 ) capture the strength of the net agglomeration effectin the residential place from the current and previous population density. The former parameter (β 1 )captures various externalities in the residential place from the current population including housing
prices and consumption amenities. The latter parameter (β 2 ) captures externalities from the past
population including the effect of the stock of housing and amenities. In particular, we provide
one microfoundation for both the current and lagged effects of spillovers in amenities in Section
D.6 of the online appendix, which introduces developers of floor spaces with adjustment costs intheir investment. This microfoundation also highlights that similarly as the productivity parameters(α1 , α2 ), (β 1 , β 2 ) captures not only pure externalities but also other channels through which current
or past population density affects amenities.
In any location outside of the city (o ∈ O ), individuals receive common utility uot in period t,which is exogenous in every period.
Forward-looking location choice. Workers are forward-looking in making migration decisions
subject to the exogenous migration frictions. At the end of period t, the share θt ∈ (0, 1] among²⁶In Section 5.1, we compute ln κint as the expected commuting cost in a travel mode choice model.

21

workers in the economy can change their location pairs and the share of 1 − θt among workers will
stay in the current location choices in the next period t + 1.²⁷ If θt = 1, all workers are able tochange their location pairs and a low value of θt leads to the stickiness of workers’ mobility in theeconomy.²⁸ When a worker obtains the opportunity to change their locations at the end of period t,they draw idiosyncratic shocks related to location choice in period t + 1. For an individual worker,
the idiosyncratic shock is independently drawn from the time-invariant independent Type-I extreme
distribution F (ε) = exp(− exp(−(ε + Γ))) where Γ is Euler-Mascheroni constant. At the end of
period t, workers decide their residential place and workplace for the next period taking into accountthe option value of their location choice {Vint+1 } associated with each workplace and residence pair.
Consider a worker ω living in n and working in i at period t. When the worker can move todifferent location pairs in the next period, they solve the following problem of location choices:
vint (ω ) = ln uint + max ρVjℓt+1 + σε jℓt+1 ; ρVot+1 + σε ot+1

(6)where Vjℓt+1 refers to the value function of choosing different pair of residential place ℓ and workplace j in period t + 1 and Vot+1 is the option value of choosing to live in the outside of the city.
ρ is the discount factor governing the importance of the future values and σ is a positive constantgoverning the variance of the idiosyncratic shocks. Note that this is a forward-looking migration
decision in the sense that at time t, a worker chooses their residence and workplace at t + 1 expecting the path of the exogenous and endogenous variables. In particular, an individual correctly
expects the path of the population distribution { Rnt } and employment distribution { Lit } that areendogenously determined in equilibrium.
With the idiosyncratic shocks following the extreme distribution and migration frictions, we can
express the option value of living in n and working in i assessed in period t by
Vint = ln uint + (1 − θt+1 )ρVint+1 + θt+1 σ ln∑d∈{C×C , o }exp(Vdt+1 )ρ/σ .

(7)

The first term is the current utility from the location choice of residential place n and workplace i.
The second term is the expected value of staying in the same location choices in the next period with
non-migration opportunity 1 − θt+1 . The third term is the expected utility for future value when aworker is able to change the location pairs with probability θt+1 . For workers who live outside of
the city, we can express their option value by
Vot = ln uot + (1 − θt+1 )ρVot+1 + θt+1 σ ln∑d∈{C×C , o }exp(Vdt+1 )ρ/σ .

(8)When workers have an opportunity of migration, they can choose any location pairs in the economy
and therefore the last term of the expected utility for future value is the same as in (7).
²⁷We allow people to choose the same pair of residence and workplace when they can choose other options.
²⁸This Calvo-style migration friction is also adopted in other recent quantitative spatial models to capture the persistence of migration decisions (e.g., Caliendo et al. 2019 Section 5.3; Heblich et al. 2021).

22Given the idiosyncratic shocks {ε jℓ , ε o } are independent and follow the type-I extreme distribution F (ε), we derive the share of workers that live in n and work in i in the city in the next periodt + 1 when they have migration opportunity:λint+1 =exp(Vint+1 )ρ/σ,∑d∈{C×C , o} exp(Vdt+1 )ρ/σi, n ∈ C .

(9)

The probability λint+1 characterizes the location dynamics of workers in the city for period t + 1.
Workers choose the pair of residential place and workplace with taking into account future changes
in commuting costs, wages, and residential amenities. Since there is no location-workplace specificmigration cost, equation (9) applies to all workers with the migration opportunity in period t. As wefocus on migration within a city, bilateral mobility costs in a city are likely sufficiently small andhomogeneous relative to inter-city migration costs. Therefore bilateral mobility costs are assumed
away in our model. Further, the share of workers that live outside of the city in the period t + 1 conditional on they can change their locations is given by probability λot+1 = 1 − ∑( j,ℓ)∈C×C λ jℓt+1 .
Using these choice probabilities of workers, we can express the mass of workers in the city wholive in n and work in i in period t + 1:
Lint+1 = (1 − θt+1 ) Lint + θt+1 λint+1 M.

(10)This is the number of commuters within the city. On the right-hand side, the first term is equal to
the number of commuters who continue the same workplace and residence, and the second term isthe total of workers who move from outside of the city and those who change their locations within
the city. The commuting market clears in the city. Therefore, the mass of workers in workplace i
becomes:
Lit = (1 − θt ) Lit−1 + θt M ∑ λint ,
(11)
n∈C

where a mass of workers in workplace i is the sum of workers who have no opportunity of changing
locations and those who sort into the workplace in period t. Analogously, the mass of workers inresidence n becomes:
Rnt = (1 − θt ) Rnt−1 + θt M ∑ λint .
(12)
i ∈C

Lastly, the total population in the city in period t + 1 is given by Lt+1 = ∑(i,n)∈C×C Lint+1 .
Note that conditional on wage variation and exogenous location characteristics, the mobility ofworkers in our model is controlled by the parameter of Calvo-style stickiness (θt ) and the parameterof taste shocks (σ). Both a low degree of stickiness and more dispersion in idiosyncratic taste shocks
in location choices increase workers’ mobility in a city. However, we emphasize the difference ininterpretations. The parameter of Calvo-style migration friction captures the immobility of workers
even if they would like to change their locations. Intuitively, this reflects any physical constraint thatprevents workers from relocating. In contrast, the dispersion of taste shocks captures the individual valuation attached to the location pair and controls the degree of sorting in response to utility23differences. In the present model, we introduce both migration frictions and idiosyncratic shocks
since we can take account of both mobility constraints and the sorting of workers in their residence
and workplace choices.
4.2 Equilibrium
Having the assumptions in our model above, we now define a forward-looking competitive equilibrium in the economy. The economy starts with the initial distribution of the population (Ri0 ) andemployment (Li0 ). The exogenous variables of the model are fundamental productivity (ait ) andamenities (bnt ) of blocks, the area size of blocks (Sn ), bilateral commuting costs in a city (κint ),the path of stickiness in reallocation of workers (θt ) and path of the utility outside of a city (uot ).
The economy-wide parameters in the model are spillovers in productivity (α1 , α2 ), spillovers inamenities (β 1 , β 2 ), a discount factor of workers (ρ), the variance of idiosyncratic shocks in location
choices (σ) and a mass of workers in the economy (M). Then, a forward-looking equilibrium isdefined as follows:
Definition 1. Given the exogenous variables of the model and economy-wide parameters, a forwardlooking equilibrium is characterized by the sequence of wages {wit }, population { Rnt }, employment { Lit }, and value functions associated with location choices {Vint } such that (i) value functions of workers for their location choices {Vint , Vot } satisfy (7) and (8) with VinT = ln uinT and
VoT = ln uoT for the last period T, (ii) commuting market clears in the city and the masses of workers in workplaces and residential places are given by (11) and (12), and (iii) firms maximize theirprofits and the zero profit condition leads to a wage rate equal to (3).
Since productivity and amenities evolve with employment density and population density, we
can summarize the transition equilibrium by population, employment, and value function adjusted
by the value of outside of the city. Equations (3), (7), (8), (11), and (12) constitute N 2 + 3N
equations for each t, and that can be solved for N 2 + 3N endogenous variables for each t. The
location choices of people are based on their current real income but also option values associatedwith the pair of locations, and they determine the future path of location choices taking into accountfuture shocks. In the present model, there are externalities in real income through productivity andamenities, as well as mobility frictions. With small mobility frictions and strong externalities, there
may exist the self-fulfilling prophecy and multiplicity of transitions that hinges on the expectationsof people. In particular, large values of the spillovers in productivity (α1 ) and amenities (β 1 ) andlarge mobility (θt ) may lead to multiple equilibria.
We call an economy is in a steady-state equilibrium if population and employment distributions
are constant given the exogenous time-varying factors being constant. The steady state equilibriumin this economy exists, and it is unique when the net externalities are small in both productivity andamenities. We summarize these results in the following proposition:

24

Proposition 1. (i) Given the initial state and exogenous factors, the forward-looking competitive
equilibrium such that, for all periods t = 1, 2, · · · , T, Rnt ≥ (1 − θt ) Rnt−1 and Lit ≥ (1 −θt ) Lit−1 , exists. (ii) The steady-state equilibrium exists when α1 + α2 ̸= σ/ρ and β 1 + β 2 ̸= σ/ρ.
(iii) Suﬀicient conditions for the unique steady state are negative net spillovers: α1 + α2 ≤ 0 and
β 1 + β 2 ≤ 0.
Section D.3 of the online appendix provides proof. While Proposition 1 (i) and (ii) show theexistence of an equilibrium and a steady state, there may be multiple steady states and multiple
equilibrium paths. Proposition 1 (iii) shows that the steady state is unique if net spillovers arenegative: α1 + α2 ≤ 0 and β 1 + β 2 ≤ 0. In this case, the economy will converge to the uniquesteady state in the long run, although there could be multiple paths toward the steady state. Second,
there can be multiple steady states, which can happen when net spillovers are positive according to
Proposition 1 (iii). In this case, after a shock in the economy that affects the initial condition, either
the initial condition or expectations about the future distribution of population and employment
matters in determining which steady state or path realizes (Krugman 1991; Matsuyama 1991).
In our calibration, we solve the model backward for the observed changes in population andemployment. We do not require that the economy is exactly in the steady state in the last period T,
but we assume that it is sufficiently close to the steady state so that the commuting gravity equation
approximately holds, which we estimate in our calibration in Subsection 5.1. Our calibration does
not require the uniqueness of the steady state nor the unique path to the steady state because it
relies only on the observed equilibrium path and the steady state. This feature allows us to calibrate
the model when there are multiple steady states so that different expectations may lead to different
steady states. That said, the multiplicity of equilibrium, by its nature, may pose a challenge in somecounterfactual analyses as we need to select one equilibrium out of multiple possible counterfactual
equilibria (Redding and Rossi-Hansberg 2017).

5 Quantifying the Model
Our goal in this section is to show how the present model can be matched to the observations in
Hiroshima. The quantification proceeds in three steps and we discuss it step by step. Section E of
the online appendix presents further details on calibration.
In Subsection 5.1 we first estimate the commuting costs by estimating a travel mode choicemodel. Our model accommodates two aspects of migration frictions, the dispersion of idiosyncratic
taste shocks (σ) and the stickiness of migration decisions (θt ), and we calibrate them using different
information. The dispersion of idiosyncratic taste shocks (σ) is calibrated from the commuting
elasticity ρ/σ that we estimate by a commuting gravity equation and from the calibrated discountfactor (ρ). We infer the stickiness (θt ) from additional data on the mobility of people during theperiod of study, which informs the share of people who stayed in their residential places so that we
can infer how migration decisions were persistent. The outside utility (uot ) is chosen to match the25observed total population of the city.
Given the parameters, in Subsection 5.2, we leverage the structure of the model to back out
the composite of amenities and productivity that rationalize the observed population and employment changes over time. Intuitively, changes in population and employment by block allow us to
invert option values associated with each location. The option values reflect the attractiveness ofeach location as a residential place or workplace, which is a function of location fundamentals andagglomeration.
In Subsection 5.3, we estimate the key parameters that govern the strength of spillovers in productivity (α1 , α2 ) and amenities (β 1 , β 2 ). Given the recovered option values and variation of population density and employment density at different periods, we can recover the unobserved fundamentals in productivity and amenities. For those fundamentals, we define the moment conditions
and estimate the parameters. In the estimation, we use the data from 1950 to 1975.
Having fully quantified our model, in Subsection 5.4, we assess how the model can rationalize
the recovery of population and employment in the city after the bombing during 1945-50. To thisend, we first use the data on population and employment in 1945 and 1950 to back out the location advantages. We then decompose the advantages into two parts: (i) advantages in productivity
and amenities explained by the model including spillovers, and (ii) structural residuals. We showthat our model performs well in explaining the recovery of central Hiroshima in the sense that themodel can predict the recovery only with model-based mechanisms (i). Furthermore, by analyzing the counterfactual prediction in the absence of agglomeration economies, we demonstrate that
agglomeration economies are the key to making central Hiroshima attractive and inducing recovery.
5.1 Step #1: Parameter calibration (ρ, σ, κint , θt , uot )Travel mode choice and commuting costs (κint ) To estimate commuting costs, we extend themodel by incorporating the choice of travel modes following Tsivanidis (2022). In particular, we
suppose that workers minimize their commuting costs by deciding their travel mode for commuting
after choosing their workplace and residence. We solve the problem backward: first, we consider themode choice of an individual given their workplace and residence. Second, we calculate expected
commuting costs before workers choose their locations. We briefly describe the procedure here andmore details are found in Section E.1 of the online appendix.
There are five modes of transportation: walk, bicycle, car, bus, and train. In each period, aworker chooses the mode of transportation that minimizes the realization of observed and idiosyncratic travel costs. It is assumed that the idiosyncratic travel cost follows a Gumbel distribution
with two nests: (i) public modes consist of walking, bus and train; and (ii) private modes consistof bicycle and car. We estimate this nested discrete choice model of travel mode by exploiting the1987 Hiroshima City Person Trip Survey and compute the expected commuting cost for two types ofworkers who may or may not use cars, given their workplace and residence.²⁹ Then, we estimate the²⁹When a car is unavailable for a worker, the nest of private modes is reduced to a single choice, bicycle.

26

overall expected travel cost (c̄int ) for residence n and workplace i using the information on the carownership rate in Japan in different years. We denote the exponential transformation of the bilateralm ≡ exp( cm ), where cm is realized travel cost of mode m. Then, we can express
travel cost by κintint
intm ) = c̄ . Replacing the commuting costthe expectation of the logarithm of travel cost as E (ln κint
int
ln κint in equation (4) with the expected travel cost (c̄int ) keeps our extension of travel mode choiceconsistent with the characterization of location choices in Section 4.
Gravity of commuting (ρ/σ) A feature of our model is that the commuting pattern in the steadystate is consistent with the gravity equation. We posit that the economy is approximated by a steadystate in the last period and estimate the commuting elasticity of workers using the 1987 Hiroshima
City Person Trip Survey. Plugging the average commuting time in 1987 that we computed above
into the equilibrium commuting pattern in the steady state yields the gravity equation:
ρln Lin = − c̄in + Wi + H n + M,σ(13)where Wi and H n are workplace and residence indicators and M is a constant. We replace workplace and residence indicators with fixed effects and estimate (13) using the Pseudo Poisson Maximum Likelihood (PPML). The main estimation shows that ρ/σ = 8.019, which is comparable tothe estimates of Dingel and Tintelnot (2020) and Ahlfeldt et al. (2015). In the following, we set ρ/σto be 8. See Section E.1 of the online appendix for detailed derivations and estimation results.
Discount factor (ρ) We assume that the annual discount rate of around 8.5 percent, which isconsistent with the discount rate widely used in the context of developing countries (e.g., GarciaCicco, Pancrazi and Uribe 2010). Note that Japan’s GDP per capita in 1950 was less than one-fifthof that of the U.S. Since one period in our calibration corresponds to five years, we set ρ = 0.66 ≃(1/1.085)5 .
Migration frictions (θt ) Individuals can change their residence and workplace for the period twith probability θt . In our calibration, we consider 174 blocks in a city and idiosyncratic taste
shocks. Therefore, we suppose that people would change their residence conditional on obtaining
the migration opportunity and match the parameter of migration friction to the probability thatpeople change their residence during five years, the length of one period in calibration. The 1960
Population Census shows that around 86 percent of people stayed in the same residence one year
before. Then, we set the parameter θt = 1 − (0.86)5 ≃ 0.53 for t = 1955, 1960, · · · , 1975.³⁰
Utility outside the city (uot ) We set the outside utility (uot ) for each period to match the total
population of Hiroshima City. Formally, we choose the outside value to match the observed total
population (Popt ) and the model-predicted population of the city (1 − λot )M = Popt , where λot³⁰Although in a different context, this value is very close to 0.52 used in the model of Heblich et al. (2021).

27

is the probability to choose outside of the city computed in the model. Since the relative location
choice probability in a city does not depend on the outside utility conditional on living in the city,
the choice of the outside utility only affects the total population in our model.
5.2 Step #2: Inversion of the option values
When individuals are forward-looking, their location choices depend on current real income and theoption value associated with the location. In this step we back out the option values by leveraging
the population and employment dynamics of the model. Specifically, the option value of location n
as a residential place can be summarized by the continuation value of amenities in the location:Ξnt = bnt

RntSn

 β1 

Rnt−1
Sn

 β2



T

∏

bnτ

τ = t +1RnτSn β1 

Rnτ −1Sn β2 !ρτ−t ∏τs=t+1 (1−θs ).

(14)

Analogously, the option value of location i as a workplace can be written by:Ωit = ait

LitSi

 α1 

Lit−1
Si

 α2



T

∏


aiτ

τ = t +1LiτSi α1 

Liτ −1Siα2 ρτ−t ∏τs=t+1 (1−θs ).

(15)

The option values (Ξnt , Ωit ) express the attractiveness of each location as residence and workplace
and are a composite of amenities and productivity that include both fundamental amenities andproductivity (ait , bnt ) and the spillovers from past and future population and employment density.³¹
When θt = 1 for all periods, these option values are reduced to values of amenities (Bnt ) andproductivity (Ait ). Intuitively, all workers can change locations every period, and therefore, thefuture values of their choice are not attached to the current location choices. In contrast, a smallvalue of the migration opportunity (θt ) leads to more weight for the future evolution of amenities
and productivity in the location since workers are less likely to change their locations. In sum, these
option values reflect the value of amenities and productivity by locations when workers choose
locations in a forward-looking way.
In equilibrium (11) and (12) imply that (Ξnt , Ωit ) satisfy the following equations:Rnt − (1 − θt ) Rnt−1 = ∑i

Lit − (1 − θt ) Lit−1 = ∑
n

ρ/σ


L
−
(
1
−
θ
)
L
,
t
it
it
−
1
ρ/σ

Kint Ξnt∑ j Kijt Ξ jt
ρ/σKint Ωitρ/σ∑ j K jnt Ω jt



(16)

Rnt − (1 − θt ) Rnt−1 ,where Kint is the continuation value of commuting costs. Intuitively, equations (16) state that the
number of residents that actively choose to live in block n for period t, Rnt − (1 − θt ) Rnt−1 , is³¹ Equations (14) and (15) imply that our definition of the option values (Ξnt , Ωit ) of each location does not incorporate the convenience of commuting access to other locations. The importance of the commuting access in migration
decisions enters in equations (16), which we use to back out (Ξnt , Ωit ).

28

written as the sum of the products of the number of workers that actively choose to work in block ifor the period t (Lit − (1 − θt ) Lit−1 ) and their conditional choice probability of location n as theirρ/σρ/σresidence ( Kint Ξnt /(∑ j Kijt Ξ jt )). We solve the system of equations (16) for option values (Ξnt ,Ωit ) conditional on observed population (Rnt ), employment (Lit ), commuting costs (Kint ), and migration frictions (θt ), and obtain the unique option values.³² Therefore, we can recover (Ξnt , Ωit )that rationalize the observed changes in the mass of workers without using any information on theunobserved characteristics. In addition, this step does not require the parameter values of spillovers(α1 , α2 , β 1 , β 2 ) despite that strong spillovers may induce unobserved alternative equilibria. Therefore, the possibility of multiple equilibria does not invalidate this step.
5.3 Step #3: Estimation of spillover parameters (α1 , α2 , β 1 , β 2 )In the second step, we obtain option values such that observed changes in population and employment in the city are consistent with equilibrium. We can back out fundamental productivity (ait )and amenities (bnt ) by using observed employment and population density, according to the definition of option values (Ξnt , Ωit ). In particular, for each period t = 1955, 1960, · · · , 1975, we
derive unique values of fundamentals by location, and these fundamentals are structural residuals
in our calibration for the observation to be equilibrium. We assume that the fundamentals consistof location-fixed components, time-trend components, and time-varying errors:ln ait = ln aiF + ln a∗t + ln aVarit ,Varln bnt = ln bnF + ln bt∗ + ln bnt
,

(17)



where { aiF }, {bnF } are location fixed productivity and amenities, { a∗t }, {bt∗ } are trend of proVar
ductivity and amenities, and { aVarit }, { bnt } are stochastic parts of fundamental productivity andamenities. The location-fixed productivity and amenities capture the fundamental advantages oflocations and the trend of productivity and amenities reflects the change in their levels over time inVar
the city. { aVarit }, { bnt } are the structural residuals in our model in the sense that they allow us
to perfectly match the observed population and employment distribution in the city. As such, they
incorporate any factors affecting the attractiveness of each location but not in the model (see also
Section 6.3 for more discussion).
Averaging out the trend terms and taking differences between two periods, we suppose the following moment conditions:E [∆ ln e
ait × 1i (k )] = 0,
E [∆ ln e
bnt × 1 n (k )] = 0,

(18)³²The solution is up to scale because equations (16) exploit only the information on the relative migration probabilities
across blocks within the city. Since we take the total population of Hiroshima city from data and assume that the outside
utility ln uot adjusts to rationalize it (see subsection 5.1), we do not need to determine the absolute levels of {Ξnt } and{Ωit } governing the migration condition between Hiroshima city and the outside world. We normalize the geometricmean of {Ξnt } and {Ωit } to one.

29

e
eVar
where ∆ ln e
ait = ∆ ln eaVar
it and ∆ ln bnt = ∆ ln bnt are changes in the idiosyncratic shocks in
productivity and amenities adjusted with their geometric means. 1 n (k) is an indicator such thatlocation n is in the grid k. The grid is defined based on the distance from the CBD. Our identification
assumption for using the moment condition is that any improvements or declines in the stochastic
terms of fundamental productivity and amenities during any five-year period are not systematicallycorrelated to the distance from the city center. While this moment condition accommodates arbitrary
location-fixed amenities and productivity, it requires that the systematic change in the gradient of
economic activity relative to the distance from the CBD is explained by the mechanisms of themodel rather than by systematic changes in the pattern of structural residuals. This identification
assumption seems plausible in post-recovery Hiroshima because the spatial extent of our study issmall and all blocks in data would face similar changes in the economic and political environment.³³
Indeed, all blocks in our sample are located just within 6 kilometers from the CBD. To check its
robustness, we also estimate the set of parameters using blocks in 3 kilometers to CBD, which
are expected to face even more homogeneous conditions and so more likely to satisfy the moment
conditions. We use the moment conditions (18) to estimate the set of parameters of agglomeration
economies.³⁴
Table 2: Generalized Method of Moments Estimates for Agglomeration Parameters(1)
Productivity
Elasticity of employment density (α1 )0.237(0.0010)
Elasticity of past employment density (α2 )-0.065(0.0008)
Elasticity of population density (β 1 )Elasticity of past population density (β 2 )LocationsMigration frictions (θt ) after 1955
Value of commuting elasticity (ρ/σ)(2)
Amenities

0.198(0.0014)0.023(0.0009)
All blocks
0.53
0.53
8
8

(3)
(4)
Productivity Amenities
0.239(0.0001)-0.066(0.0001)
0.222(0.0046)
0.006(0.0043)
Blocks in 3 km to CBD
0.53
0.53
8
8

Note: This table reports estimates of the generalized method of moments (GMM) using data for five periods (1955, 60,
65, 70 and 75) and 174 blocks (all blocks) or 158 blocks (blocks in 3 kilometers to CBD). In constructing the moment
conditions (18), we divide the blocks into five grids according to the distance from the CBD. We use the two-step GMM
estimation and the standard errors are in parentheses. In Column 1 and 2, we use all blocks and in Columns 3 and 4, we
use blocks in 3 kilometers to CBD. We also report parameter values of migration frictions and commuting elasticity.

Table 2 reports the efficient GMM estimation results. Columns 1 and 2 report our baseline esti³³We also emphasize that the effect of radioactivity faded away quickly from 1945 (see Section 2.1), and it would be
irrelevant for changes in amenities and productivity as our estimation data run from 1950.
³⁴Figure E.2 graphically illustrates that under our GMM estimates, the moment conditions appear plausible regardlessof the distance from the city center.

30

mates of spillover parameters in productivity (α1 , α2 ) and amenities (β 1 , β 2 ) respectively. Overall
productivity (Ait ) in the workplace rises by 0.24 percent when current employment density increases
by one percent, but falls by 0.07 percent when employment density increases by one percent in theprevious period. The negative spillovers from the past employment density may capture the congestion effects, such as depreciation in public goods, reduced land supply, and fewer successful
matching to achieve innovation (see our microfoundations in Section D.5), implying the possibilityof creative destruction (Hornbeck and Keniston 2017). Its magnitude is smaller than the positive
spillovers from the contemporaneous employment density. Turning to amenities, a one percent
increase in current population density is associated with a 0.20 percent increase in the value ofamenities, while a one percent increase in past population density is associated with a 0.02 percent
increase in the value of amenities. Other columns 3 and 4 in Table 2 show estimates when we restrict locations within 3 kilometers in our estimation, and we find similar results. These estimates
imply that strong contemporaneous externalities in both amenities and productivity may create aself-fulfilling prophecy, which leads to multiple equilibria. In addition, we also find some effectsof past economic activities in both productivity and amenities, implying that a historical event may
matter in determining the transition path of the economy.³⁵
5.4 Accounting for the 1945–1950 recovery and agglomeration economies
We are now at the position to assess how well our calibrated model explains population and employment changes during the recovery period (1945–1950), which are not used for calibration. To thisend, we evaluate how the endogenous part of location advantages and time-invariant unobserved
characteristics can account for population and employment changes during the recovery of the cityfrom the atomic bombing. Intuitively, we evaluate how much of the incentive to work or live in agiven location during the recovery period can be explained by our model.
Our calibrated model predicts the recovery of central Hiroshima. We first calculate the predicted population and employment distribution using our calibrated model. We use equations (14)fand (15) to construct the predicted option values of each location as residence {Ξn,1950 } and workf

place {Ωi,1950 } and substitute them into equation (16) to solve for the predicted population andemployment of each block in 1950. By construction, the option values in our model are a composite of (i) location-fixed advantages, (ii) endogenous terms of spillovers, (iii) future option values
associated with the location, and (iv) idiosyncratic shocks. Among them, factors (i) through (iii)³⁵Our estimates of spillovers in productivity are broadly similar to those in Allen and Donaldson (2022) that uses
long-run county-level data of the U.S. However, they find negative contemporaneous spillovers in amenities. Thisdifference may arise from the difference in spatial extent. As we discussed in the microfoundation (see Section D.6 ofthe online appendix), the negative externalities in amenities capture congestion in a local housing market. Our estimate
implies that such congestion externalities are dominated by positive externalities, including consumption externalities orneighborhood network effects. In a spatially-granular setting such as ours, those positive externalities are likely strong(see, for example Tsivanidis 2022).

31

capture the location advantages that can our model and calibration can explain. In contrast, theidiosyncratic terms (iv) are structural residuals in the location advantages and absorb any othercharacteristics unrelated to the model specification. In order to evaluate how well our model can
explain the recovery, we exclude the structural errors when constructing the model-predicted optionffvalues for residence {Ξn,1950 } and workplace {Ωi,1950 }, respectively.³⁶
In obtaining the predicted location decisions for the recovery period (1945-1950), we use thesame parameter values as our main calibration with data from 1950-1975, with the exception of alower discount rate and a higher migration probability for 1945-1950. We assume that individuals
in 1945 discount the option values in 1955 by the discount rate ρ = 0.33, which is half of our baseline discount rate because many individuals faced extreme poverty and are likely to be relatively
impatient or even live hand-to-mouth.³⁷ We set a higher migration opportunity θ1950 = 0.9 because
available evidence suggests the mobility rate was substantially higher, possibly for war-related reasons such as the loss of jobs or homes and the end of temporal reallocation during the war.³⁸
Figures 5a and 5b demonstrate the population and employment distribution predicted by ourmodel for 1950. In Figure 5a, the predicted population density is plotted against the distance to the
CBD. The city center’s recovery is predicted to have the highest population density, indicating therecovery. Figure 5b shows that this recovery result holds true for the employment distribution as
well. Overall, our calibrated model successfully predicts the recovery of the city center, which we
indeed observe in the data.
The role of agglomeration economies in accounting for the recovery. The recovery of the city
center is achieved because workers regard the city center as an attractive residence and workplace.
We now argue that strong agglomeration economies are the primary source of attractiveness and thatregaining population and employment density enhances attractiveness through positive spilloversof density. To formally investigate the importance of agglomeration economies, we obtain the predicted population and employment distribution of the model using the same procedure as Figures
5a and 5b, except that we shut down agglomeration forces by setting α1 = α2 = β 1 = β 2 = 0.³⁹
Workers still make forward-looking migration decisions taking into account fundamental productivity (ai ), amenities (bi ), and transportation access (κint ). If the recovery of the city center is driven³⁶Specifically, we substitute the average amenities and productivity during 1955-1975, our estimate of the block-fixedamenities and productivity, into ( ai1950 , bn1950 ).
³⁷The hand-to-mouth behavior is anticipated based on a survey conducted in December 1945: Approximately 86
percent of Hiroshima city residents answered that they face a very serious risk of starvation (https://hiroshimaforpeace.
com/en/fukkoheiwakenkyu/vol1/1-47/, last accessed on April 20, 2023). In addition, empirical studies (e.g., Carvalho,
Meier and Wang 2016) suggest that the poor generally tend to have higher discount rates.
³⁸According to the 1949 city population registry in the Statistical Abstract of Hiroshima City, roughly 20 percent of
the population moved out of the city in one year. When we assume that the ratio of the migration between municipalities
to the migration within the city is comparable to that in the 1960 census, the probability of staying in the same residence
is approximately 64 percent. This suggests θt ≃ 0.9 for t = 1950.
³⁹Since parameters (α1 , α2 , β 1 , β 2 ) capture not only pure externalities of density but also other channels throughwhich population or employment density affects productivity and amenities (see Section 4.1), setting them equal tozero implies turning off all of these density effects simultaneously.

32

Figure 5: Population and Employment Distribution Under Different Model Assumptions(b) Employment (main model)
Log employment density (per square km)

Log population density (per square km)(a) Population (main model)
12
10
8
6
4
2

0

2
4
Distance to CBD (km)19451950 (prediction)1950 (prediction)

6

12
10
8
6
4
2

0

1950 (data)
1950 (data)

1945

12
10
8
6
4

0

2
4
Distance to CBD (km)19451950 (prediction)1950 (prediction)1950 (prediction)1950 (prediction)

6
1950 (data)
1950 (data)(d) Employment (no agglomeration)
Log employment density (per square km)

Log population density (per square km)(c) Population (no agglomeration)

2

2
4
Distance to CBD (km)61950 (data)
1950 (data)

12
10
8
6
4
2

0

2
4
Distance to CBD (km)19451950 (prediction)1950 (prediction)

6
1950 (data)
1950 (data)

Note: Each figure plots the results of local polynomial regressions of the log population density (panels a and c) or
employment density (panels b and d) on the distance from the city center. We conduct three regressions separately
for the 1945 population density in data, the 1950 population density in data, and the 1950 population or employment
density under the counterfactual scenario. “Main model” shows the counterfactual population or employment density
predicted by our main model. “No agglomeration” shows the counterfactual population or employment density by ourmodel that shuts down agglomeration spillovers.

33

by fundamental location advantages, solving the model without agglomeration forces would still
result in the recovery. Alternatively, if agglomeration economies are the key to making the city
center an attractive place, then this exercise would not be able to predict the recovery.⁴⁰
The predicted population and employment density in the absence of agglomeration economies is
depicted in Figures 5c and 5d, respectively. The model now does not predict the recovery of central
Hiroshima in terms of both population and employment, which is in stark contrast to the predictionof our main calibrated model in Figure 5a and 5b. This contrast indicates that the presence of
agglomerations is essential for accounting for the recovery of central Hiroshima, given that the
only deviation from our main calibrated model is the shutdown of agglomeration economies. The
result that the recovery cannot be explained by a model without agglomeration economies suggeststhat the recovery is not primarily driven by the fundamental locational characteristics of the city
center. In Figure E.1 we demonstrate that, in our calibrated model, location-fixed amenities andproductivity are generally flat in the distance to the city center. This implies that the fundamental
advantages of the city center are unlikely to explain the recovery of central Hiroshima, consistent
with our findings in Figure 5 and our reduced-form results. Rather, strong agglomeration economies
enhance the attractiveness of the city center.

6 The Role of Expectations in the Recovery
Having demonstrated that our calibrated model can account for the resurgence of central Hiroshima
because of agglomeration economies, we now evaluate the importance of expectations in explaining
the resurgence. In particular, if individuals expected that the city center would never recover, theywould not choose to live and work there since the attractiveness of the city center was not anticipatedto be realized. In Subsection 6.1 we formalize this intuition by introducing an alternative version of
our model in which individuals take their best responses not by expecting the recovery of populationand employment in the city center, but rather by anticipating that population and employment distributions immediately after the bombing would continue. Subsection 6.2 conducts the comparison
between this version of the model to the observation and demonstrates that, without expectationsof recovery, the model fails to explain workers’ incentive to live and work in the city center despite
including agglomeration economies. Throughout the analysis, note that we remain agnostic about
why the expectations in the recovery emerged, and we show their importance in accounting for therecovery by taking as given the emergence of expectations in the recovery. In Subsection 6.3 webriefly explore the potential factors contributing to the formation of expectations.
⁴⁰To focus on the population and employment distribution within the city, we assume that the total population matches
the observed data in both our main calibration and the absence of agglomeration forces.

34

6.1 Model with expectations in no recovery
We present a version of our theoretical model in which no recovery is expected. Specifically, when
individuals have opportunity to relocate, they choose optimally where to live and work in periodt + 1 while anticipating that the economic conditions of period t will persist. Applied to the recovery
period of Hiroshima, workers optimally decide their workplace and residence for 1950, assumingthat the population and employment distribution of 1945 would continue. This concept is similar to
the widespread idea that people would migrate from areas with low contemporaneous utility to thosewith high contemporaneous utility (e.g., Greenwood 1975; Krugman 1991 Section 2; Fujita et al.
1999). Intuitively, this situation approximates the case in which people heavily discount the payoffs
in the distant future so that they essentially consider only the current utility.⁴¹ Under this hypothesis,
the initial condition entirely determines the dynamics of location choices in the economy.⁴²
We operationalize the migration decision as follows. When individuals make decisions on locations for the period t + 1, they anticipate that population and employment distribution from theperiod t + 1 onward is identical to the current period t. If an individual ω is able to choose theresidence and workplace for t + 1 at the end of period t, she solves the following problem:
n
o
∗
vint
(ω ) = ln uint + max ρ ln Vj∗ℓt+1 + σε jℓt+1 ; ρ ln Vot∗ +1 + σε ot+1 ,(19)
where we modify the value function in the right-hand-side of (6) as follows. When individuals construct the value function {Vj∗ℓt+1 }, we suppose that they (i) believe that all future population { Rℓτ }τ =t+1,...,T and employment { L jτ }τ =t+1,...,T are identical to the level of period t;and (ii) correctly anticipate that location fundamentals of productivity { a jτ }τ =t+1,...,T , amenities{bℓτ }τ =t+1,...,T and commuting costs {κ jℓτ }τ =t+1,...,T as in our calibration. This assumption allows us to focus on the role of expectations about future population and employment. We also
assume that the mobility frictions {θτ }τ =t+1,...,T follow the same path in our calibration and the idiosyncratic shocks follow the same Type-I extreme value distribution. Importantly, (i) implies thatpeople expect population and employment to remain at the same level as in 1945 when choosing
their residence and workplace for 1950.
The migration probabilities are analogous to (9) by using the value function {Vj∗ℓt+1 }. Thesemigration probabilities for period t + 1 are determined by the population and employment density inthe current period t and previous period t − 1. In particular, we substitute the current population andemployment into the all future terms on the right-hand-side of the continuation value of amenities(14) and productivity (15). Then, the dynamics of employment and population are described using(11) and (12). See Section F of the online appendix for further details.
⁴¹Note that in our formulation of the model, as in Caliendo et al. (2019), lowering the discount factor ρ implies thatboth the payoffs in the nearest future (period t + 1) and those further ahead (periods t + 2 and onward). Thus loweringρ does not represent such a situation in which people care only about the current utility.
⁴²Although the assumption of expectations in no recovery may be extreme, we make this assumption to obtain a clean
comparison benchmark to determine the role of expectations in the recovery. This strategy is analogous to Krugman(1991) that first presented a model with adaptive expectations in Section 2 and then contrasted it with a forward-looking
model developed in the rest of the paper.

35

6.2 The counterfactual predictions expecting no recovery
We now analyze how different expectations about recovery affect the ability of our model to accountfor the recovery of central Hiroshima. For this purpose, we calculate the counterfactual populationand employment distribution by using the model in Subsection 6.1. In order to focus on the population and employment within the city, we assume that the total population matches the observed
data. We also use the parameters and fundamentals obtained in Section 5. In particular, given that
our calibrated model explains well the resurgence due to agglomeration forces and that the alternative model here includes agglomeration economies (i.e., α1 , α2 , β 1 , β 2 are the same as our main
calibration), the failure to explain the recovery implies that expectations in recovery are crucial for
agglomeration economies to rationalize the recovery.

Log employment density (per square km)

Log population density (per square km)

Figure 6: Population and Employment Density in 1950 If Recovery was Not Expected
12
10
8
6
4
2

0

2
4
Distance to CBD (km)19451950 (prediction)1950 (prediction)

6
1950 (data)
1950 (data)

12
10
8
6
4
2
0

2
4
Distance to CBD (km)1945(a) Population density in 1950

1950 (prediction)1950 (prediction)

6
1950 (data)
1950 (data)(b) Employment density in 1950

Note: Each panel plots the results of local polynomial regressions of the log population density (Panel a) or employment
density (Panel b) on the distance from the city center. We conduct three regressions separately for the 1945 population
density in data, the 1950 population density in data, and the 1950 population or employment density under the counterfactual scenario of the model in which no recovery is expected.

Figure 6 depicts population and employment density in the counterfactual scenario in which
no recovery is expected. The left panel 6a plots the predicted population density in 1950 against
the distance to the city center. In contrast to the observed data, we find that the monocentric city
structure does not re-emerge. A similar pattern is observed for employment in the right panel 6b.
The failure of the resurgence of central Hiroshima can be intuitively explained as follows. Since
individuals anticipate that the city center would remain as its current state so that the populationand employment density remains low in 1950, they suppose that the city center in 1950 is unattractive as a residence and workplace in terms of positive contemporaneous spillovers (i.e., α1 > 0
and β 1 > 0). Therefore, although the model with expectations of no recovery includes agglomeration economies, agglomeration economies provide an incentive to live and work in the peripheral

36

areas that had relatively high density immediately after the bombing. Taken together, the contemporaneous positive spillovers both in population and employment density render the central areaof Hiroshima unattractive under the counterfactual scenario, which fails to account for the strong
incentive to reside and work in the city center during the recovery period.
Figure 7: Population Density in 1960 and 1975 If Recovery was Not Expected

Log population density in data (1975)

Log population density in data (1960)

10

8

6

4

2

10
8
6
4
2
0

2

4
6
8
10
Log predicted population density (1960)

0(a) Population density in 1960

2
4
6
8
10
Log predicted population density (1975)(b) Population density in 1975

Note: This figure plots against the observed log population density the log population density in the counterfactual
scenario when no recovery is expected. Each dot represents a block and the dot size is proportional to the population
size in 1945 (i.e., right after the bombing). The dashed line represents the 45-degree line, implying that the predictionof the model and the observed data coincide. Panel 7a is for 1960 and Panel 7b is for 1975.

In addition to failing to account for data from the recovery period (1945-1950), the model withno recovery expectations fails to account for data after 1950. Figure 7 depicts the population densityof each location in 1960 and 1975 based on the adaptive expectation model in Section 6.1 on thehorizontal axis and the observed population density on the vertical axis. The size of each dot reflects
the population immediately after the bombing, which is generally small near the city center. If theadaptive model accounts for the data, then each observation lies on the 45-degree line represented
by the dashed line. We find that observations substantially deviate from the 45-degree line in both1960 and 1975, implying that the adaptive model fails to account for the data in periods following theinitial recovery period. There are two additional takeaways. First, a smaller dot tends to appear to the
far left of the 45-degree line, indicating that the population density in the data is higher than in theadaptive counterfactual scenario. This suggests that the city center, with its low initial population,
keeps failing to recover its population density beyond 1950. Second, the adaptive counterfactual
scenario has a larger variation in population density across locations, which appears to be growing
over time. Intuitively, the adaptive model implies that initially populated areas are more attractive

37

due to net positive externalities and vice versa. In contrast to the observed data, the impact of history(i.e., the initial population and employment distribution) would be amplified over time.
The failure of the model of Subsection 6.1 to predict the recovery is suggestive of the selffulfilling nature of expectations in the spatial economy (Krugman 1991; Matsuyama 1991). The
comparison of Figures 5 and 6 suggests that the model predicts the recovery of the city center when
individuals expect the recovery and vice versa. In this sense, under the degree of agglomeration
economies that we calibrate, optimistic expectations about the future of central Hiroshima played acrucial role in inducing the recovery despite the initial low density due to the shock of the atomic
bombing.
6.3 Discussion: Origins of expectations in the recovery
Our analysis has demonstrated that expectations for the recovery are essential for explaining therecovery of central Hiroshima. However, we have remained agnostic as to why individuals could
believe in the recovery despite its catastrophic shock. In this subsection we discuss several factorsthat may have influenced the coordination of individuals’ expectations.
First, the presence of the recovery plan by the government would have facilitated the formationof expectations, despite the fact that the plan was published in the midst of the recovery and wassubstantially underfunded (see Subsection 3.4).⁴³ Another possible factor is the tangible presenceof infrastructure, particularly the train and tram systems. While the direct benefit of access to train
stations does not appear to be crucial for the recovery (see Table 1 that controls for transportation
access), the continuity of the pre-war train network may have anchored people’s expectations forthe reconstruction. Land ownership is a further consideration. People could reasonably anticipate
the recovery if they believed that landowners had a strong attachment to the location and that someof them would return despite the miserable conditions. However, the direct effect of this channel
may be limited in our context because of the low ownership rate. In particular, landownership rate
in urban areas of pre-WW2 Japan was likely to be less than 10 percent (Kato 1988).⁴⁴ Consistent
with the limited importance of attachment due to property ownership, Hiroshima City Government(1983b) conducted a survey on tenure of current residence in 1965 and concluded that “many individuals settled in the current location after being forced to move by the bombing.”⁴⁵ Lastly, thenarrative of “rebuilding from the atomic bombing” may have sounded like a compelling success
⁴³Zoning laws are a related factor, but their importance was limited in explaining the recovery because the first postwar zoning of Hiroshima was not published until 1949. The recovery was nearly complete by that point. In addition,
there were only three types of zones (commercial use, residential use, and industrial use) and the center did not receive
particularly preferential zoning treatment.
⁴⁴The fraction of households owning a home was quite low in urban areas of pre-WW2 Japan at around 25 percent(Hinokidani and Sumita 1988).
⁴⁵Moreover, the turnover of business owners was also active. According to Hiroshima City Government (1983a), in
1958, approximately 28 percent of stores on a shopping street (Hondori) remained in the same location as during the
pre-war period, while the remaining 72 percent started operating after the bombing. Although the majority of them arenewcomers, land ownership may have influenced their expectations for the recovery of business activities.

38

story from the tragedy and been shared widely (Shiller 2017).⁴⁶ As long as individuals were awarethat many others shared this narrative, it might lead to self-fulfilling “memory-based” expectations
that the city would return to how they remembered it (Malmendier and Wachter 2022).⁴⁷
These underlying factors may influence the attractiveness of each location through the directchannel and the expectations channel. In the expectations channel, these factors may alter people’s expectations regarding the future population and employment distribution after the bombing,thereby affecting the attractiveness of each location via agglomeration economies. Our results in
Subsection 6.2 have highlighted the importance of this expectation channel. For the direct channel,
these factors may directly stimulate the recovery of central Hiroshima by increasing its attractiveness, which corresponds to an increase in location-specific amenities (bnt ) and productivity (ait ) in
the model. However, our results in Subsection 5.4 imply the limited importance of this channel.
First, Figure 5a highlights that agglomeration economies, not location-specific amenities and productivity, induced the recovery. Second, our estimates of location-fixed amenities and productivity,
which may be higher in the city center if the bombing has made the city center attractive for somereason, are homogeneous with respect to the distance from the city center (see Figure E.1). Finally,
Figure 5 shows that our model can explain the recovery without structural residuals of amenities
and productivity, which may include the direct channel of the above-mentioned factors. In sum,
although their direct impact on the attractiveness of each location would be limited in our context,
the aforementioned factors may have a significant impact on the spatial distribution of economic
activities by contributing to the formation of recovery expectations.

7 Conclusion
This paper has examined the evolution of city structure through the experience of Hiroshima. We
have used the atomic bombing as an unprecedentedly large shock to the city structure that allows
us to study the mechanisms underlying the dynamics of city structure. We have newly collectedgranular data on population, employment, and fundamental characteristics at the block level within
Hiroshima. Using this data, we have found the strong path independence in Hiroshima: the completely destroyed city center recovered just five years after the atomic bombing. Moreover, ourreduced-form analysis has revealed that the fundamental location advantages of the city center do
not plausibly explain the rebuilding. Thus, the initial condition and location fundamentals, two key
determinants of city structure emphasized in urban economics, do not adequately explain central
Hiroshima’s rapid and strong recovery after the bombing.
⁴⁶It is challenging to assess how powerful and widespread such a narrative was. The 1946 Statistical Abstract ofHiroshima was suggestive in stating ‘...rumors like “nothing will grow here for 75 years” immediately disappeared
among people with their burning desire to rebuild...’ (p4, translated by the authors).
⁴⁷We can calculate the predicted population and employment density when everyone has “purely memory-based
expectations.” Specifically, we can proceed with the model simulation as in Subsection 5.4, assuming that workers
expect the population distribution in 1936 and employment distribution in 1938 to be realized again in 1950. The
simulation shows that such purely memory-based expectations also induce the recovery of the city center.

39

To further investigate the mechanism underlying the recovery of central Hiroshima, we havedeveloped and calibrated a novel dynamic quantitative urban model. Our model is the first quantitative spatial model that accommodates commuting, forward-looking location choices, and historydependence through migration frictions and lagged agglomeration economies in productivity andamenities. The calibration of the model has demonstrated that it adequately explains the resurgenceof population and employment in the city center after the bombing, and agglomeration economies
are the key to making central Hiroshima again an attractive place to live and work. Furthermore, bycontrasting with an alternative version of our model in which people do not foresee future populationand employment when choosing their residence and workplace, we have illustrated that expectationsin the recovery are essential for the recovery of the city center to be realized. Taken together, ourquantitative findings highlight the role of agglomeration economies and expectations in shaping the
dynamics of city structure.
This paper has highlighted agglomeration economies and expectations as the key drivers of theresurgence of central Hiroshima. Our analysis suggests the potential importance of these factors
in determining the dynamics of city structure in general contexts. Yet, there are some caveats toapplying our results to different places. First, the strength of agglomeration economies may varydepending on the spatial scale and particular underlying microfoundations. Second, a more systematic understanding of how expectations about the future spatial distribution of economic activities
can emerge is necessary for determining which spatial equilibrium is realized in a particular context.
We have pointed out in Subsection 6.3 that a combination of different factors may have contributed
to forming expectations in the recovery. Since these factors are likely to be present in varying degrees in other contexts of wartime destruction, our findings suggest that expectations regarding therecovery may be essential for the path-independence after wartime destruction often documented
in empirical research. However, it is less clear how people form expectations about future changes
in city structure beyond wartime contexts, which may lead to different patterns of the evolution ofcity structure. Understanding this would be an important future research agenda.

40

References
Ahlfeldt, Gabriel M, Stephen J Redding, Daniel M Sturm, and Nikolaus Wolf, “The economics
of density: Evidence from the Berlin Wall,” Econometrica, 2015, 83 (6), 2127–2189.
Allen, Treb and Dave Donaldson, “Persistence and Path Dependence in the Spatial Economy,”
mimeo, 2022.
Ambrus, Attila, Erica Field, and Robert Gonzalez, “Loss in the time of cholera: long-run impactof a disease epidemic on the urban landscape,” American Economic Review, 2020, 110 (2), 475–
525.
Anas, Alex, Richard Arnott, and Kenneth A Small, “Urban spatial structure,” Journal of Economic Literature, 1998, 36 (3), 1426–1464.
Arthur, W Brian, Increasing returns and path dependence in the economy, University of Michigan
Press, 1994.
Balboni, Clare, “In harm’s way? infrastructure investments and the persistence of coastal cities,”
mimeo, 2021.
Baldwin, Richard E, “Core-periphery model with forward-looking expectations,” Regional Science and Urban Economics, 2001, 31 (1), 21–49.
Barreda-Tarrazona, Iván, Tapas Kundu, and Stein Østbye, “On rational forward-looking behavior in economic geography: An experimental analysis,” Regional Science and Urban Economics,
2021, 87, 103654.
Bleakley, Hoyt and Jeffrey Lin, “Portage and path dependence,” The Quarterly Journal of Economics, 2012, 127 (2), 587–644.
Bosker, Maarten, Steven Brakman, Harry Garretsen, and Marc Schramm, “Looking for multiple equilibria when geography matters: German city growth and the WWII shock,” Journal of
Urban Economics, 2007, 61 (1), 152–169.
Brakman, Steven, Harry Garretsen, and Marc Schramm, “The strategic bombing of German
cities during World War II and its impact on city growth,” Journal of Economic Geography, 2004,
4 (2), 201–218.
Brooks, Leah and Byron Lutz, “Vestiges of transit: Urban persistence at a microscale,” Review of
Economics and Statistics, 2019, 101 (3), 385–399.
, Jonathan Rose, and Stan Veuger, “Destruction, Policy, and the Evolving Consequences of
Washington, DC’s 1968 Civil Disturbance,” FRB of Chicago Working Paper, 2022.
Caliendo, Lorenzo, Maximiliano Dvorkin, and Fernando Parro, “Trade and labor market dynamics: General equilibrium analysis of the china trade shock,” Econometrica, 2019, 87 (3),741–835.
Carvalho, Leandro S, Stephan Meier, and Stephanie W Wang, “Poverty and economic decisionmaking: Evidence from changes in financial resources at payday,” American Economic Review,
2016, 106 (2), 260–284.
Davis, Donald R and David E Weinstein, “Bones, bombs, and break points: the geography of
economic activity,” American Economic Review, 2002, 92 (5), 1269–1289.
and , “A search for multiple equilibria in urban industrial structure,” Journal of Regional
Science, 2008, 48 (1), 29–65.

41

Desmet, Klaus, Dávid Krisztián Nagy, and Esteban Rossi-Hansberg, “The geography of development,” Journal of Political Economy, 2018, 126 (3), 903–983.
Diamond, Douglas W and Philip H Dybvig, “Bank runs, deposit insurance, and liquidity,” Journalof Political Economy, 1983, 91 (3), 401–419.
Dingel, Jonathan I and Felix Tintelnot, “Spatial economics for granular settings,” Technical Report, National Bureau of Economic Research 2020.
Feigenbaum, James, James Lee, and Filippo Mezzanotti, “Capital destruction and economic
growth: The effects of Sherman’s March, 1850–1920,” American Economic Journal: Applied
Economics, 2022, 14 (4), 301–42.
Foley-Fisher, Nathan, Borghan Narajabad, and Stéphane Verani, “Self-fulfilling runs: Evidence from the us life insurance industry,” Journal of Political Economy, 2020, 128 (9), 3520–
3569.
Fujita, Masahisa, Urban economic theory, Cambridge university press, 1989.
, Paul R Krugman, and Anthony Venables, The spatial economy: Cities, regions, and international trade, MIT press, 1999.
Fukao, Kyoji and Roland Bénabou, “History versus expectations: a comment,” The Quarterly
Journal of Economics, 1993, 108 (2), 535–542.
Garcia-Cicco, Javier, Roberto Pancrazi, and Martin Uribe, “Real business cycles in emerging
countries?,” American Economic Review, 2010, 100 (5), 2510–2531.
Glaeser, Edward L, “Urban resilience,” Urban Studies, 2022, 59 (1), 3–35.
and Matthew E Kahn, “Sprawl and urban growth,” in “Handbook of Regional and Urban economics,” Vol. 4, Elsevier, 2004, pp. 2481–2527.
Greenwood, Michael J, “Research on internal migration in the United States: A survey,” Journalof Economic Literature, 1975, pp. 397–433.
Halleck Vega, Solmaria and J Paul Elhorst, “The SLX model,” Journal of Regional Science,
2015, 55 (3), 339–363.
Harari, Mariaflavia, “Cities in bad shape: Urban geometry in India,” American Economic Review,
2020, 110 (8), 2377–2421.
Hayakawa, Kazuo and Michiko Nakaouji, “Toshi no jinko kibo to chika no kankei ni tsuite (On therelationship between population size and land prices),” Nihon kenchiku gakkai ronbun houkoku
shu, 1965, extra volume. (In Japanese).
Heblich, Stephan, Alex Trew, and Yanos Zylberberg, “East-Side Story: Historical Pollution and
Persistent Neighborhood Sorting,” Journal of Political Economy, 2021, 129 (5), 1508–1552.
Hinokidani, Mieko and Shyoji Sumita, “Jutaku Syoyu Keitai No Henyo Katei Ni Kansuru Kenkyu(A Study on the Changing Process of Housing Tenure),” Journal of Architecture and Planning,
1988, 392, 136–146. (The main text is in Japanese. The English title and abstract are included.).
Hiroshima City Government, “Hiroshima Genbaku Sensai-Shi (The Hiroshima Atomic Bombing
Damage Records),” 1971. (In Japanese).
, “Hiroshima Shin-Shi: Chiri-hen (The New History of Hiroshima: The Geography),” 1983. (InJapanese).

42

, “Hiroshima Shin-Shi: Shimin-seikatsu-hen (The New History of Hiroshima: The Citizen’sLife),” 1983. (In Japanese).
Hornbeck, Richard and Daniel Keniston, “Creative destruction: Barriers to urban growth and theGreat Boston Fire of 1872,” American Economic Review, 2017, 107 (6), 1365–98.
Inami, Etsuji, “Toshi Henbou ron Danshou: Hiroshima to Nagasaki no baai (Conditions of thereconstruction in the atombombed cities, Hiroshima and Nagasaki),” Japanese Journal of Human
Geography, 1953, 5 (3), 195–204. (In Japanese. An English abstract is available).
Kato, Yuriko, “On the ownership of land and housing in pre-war Tokyo (Senzen no toukyou ni
okeru tochi kaoku no shoyuu jyoukyou ni tsuite),” Journal of Aoyama Gakuin Woman’s JuniorCollege, 11 1988, 42, 99–114. (In Japanese).
Kleinman, Benny, Ernest Liu, and Stephen J Redding, “Dynamic spatial general equilibrium,”
Econometrica, 2023, 91 (2), 385–424.
Kline, Patrick and Enrico Moretti, “People, places, and public policy: Some simple welfare economics of local economic development programs,” Annual Review of Economics, 2014, 6 (1),629–662.
Kocornik-Mina, Adriana, Thomas KJ McDermott, Guy Michaels, and Ferdinand Rauch,“Flooded cities,” American Economic Journal: Applied Economics, 2020, 12 (2), 35–66.
Krugman, Paul, “History versus expectations,” The Quarterly Journal of Economics, 1991, 106(2), 651–667.
Lee, Sanghoon and Jeffrey Lin, “Natural amenities, neighbourhood dynamics, and persistence inthe spatial distribution of income,” The Review of Economic Studies, 2018, 85 (1), 663–694.
Lin, Jeffrey and Ferdinand Rauch, “What Future for History Dependence in Spatial Economics?,”
Regional Science and Urban Economics, 2022, 94, 103628.
Malmendier, Ulrike and Jessica A Wachter, “Memory of Past Experiences and Economic Decisions,” Available at SSRN, 2022.
Matsuyama, Kiminori, “Increasing returns, industrialization, and indeterminacy of equilibrium,”
The Quarterly Journal of Economics, 1991, 106 (2), 617–650.
Michaels, Guy and Ferdinand Rauch, “Resetting the urban network: 117–2012,” The Economic
Journal, 2018, 128 (608), 378–412.
Miguel, Edward and Gerard Roland, “The long-run impact of bombing Vietnam,” Journal of
Development Economics, 2011, 96 (1), 1–15.
Murphy, Kevin M, Andrei Shleifer, and Robert W Vishny, “Industrialization and the big push,”
Journal of Political Economy, 1989, 97 (5), 1003–1026.
Nozawa, Hiroshi, “Hiroshima-shi no Hattatsu to sono Zinbun Gensyo no Chiri-teki Kousatsu (AGeographical Consideration on the Development of Hiroshima city and its Humanilistic Issues),”
Chiri Ronso, 1934, 5, 47–91. (In Japanese).
Ohshima, Munao, “Fukkou no ashidori (The path of the recovery),” Shin Toshi, 1950, 4 (8), 6–13.
(In Japanese. A special issue of Hiroshima Peace Memorial City Construction).
Ottaviano, Gianmarco IP, “Monopolistic competition, trade, and endogenous spatial fluctuations,”
Regional Science and Urban Economics, 2001, 31 (1), 51–77.

43

Oyama, Daisuke, “History versus expectations in economic geography reconsidered,” Journal of
Economic Dynamics and Control, 2009, 33 (2), 394–408.
Rauch, James E, “Does history matter only when it matters little? The case of city-industry location,” The Quarterly Journal of Economics, 1993, 108 (3), 843–867.
Redding, Stephen J and Esteban Rossi-Hansberg, “Quantitative spatial economics,” Annual Review of Economics, 2017, 9, 21–58.
, Daniel M Sturm, and Nikolaus Wolf, “History and industry location: Evidence from German
airports,” Review of Economics and Statistics, 2011, 93 (3), 814–831.
Saiz, Albert, “The geographic determinants of housing supply,” The Quarterly Journal of Economics, 2010, 125 (3), 1253–1296.
Schumann, Abel, “Persistence of Population Shocks: Evidence from the Occupation of West Germany after World War II,” American Economic Journal: Applied Economics, 2014, 6 (3), 189–
205.
Shiller, Robert J, “Narrative economics,” American Economic Review, 2017, 107 (4), 967–1004.
Siodla, James, “Razing San Francisco: The 1906 disaster as a natural experiment in urban redevelopment,” Journal of Urban Economics, 2015, 89, 48–61.
Takahashi, Hiroko, “Genbaku touka ippungo: kesareta zanryuu housyasen no eikyou (One-minuteafter atomic bombing: The hidden effect of remaining radiation),” Amerika kenkyuu, 2008, 42,
1–19. (In Japanese. An English abstract is available.).
Takano, Keisuke, “Path-dependence in the location of business agglomeration: The impact of the
postwar land requisition in Yokohama,” mimeo, 2022.
Takezaki, Yoshihiko and Ryoji Soda, Hiroshima Genbaku Dezitaru Atorasu (The Digital Atlas of
Atomic Bombing in Hiroshima), Research center for regional geography, Hiroshima University,
2001. (In Japanese).
Tsivanidis, Nick, “Evaluating the impact of urban transit infrastructure: Evidence from bogota’stransmilenio,” mimeo, 2022.
Yamagishi, Atsushi and Yasuhiro Sato, “Persistent Stigma in Space: 100 Years of Japan’s Invisible Race and Their Neighborhoods,” mimeo, 2023.
Yamasaki, Junichi, Kentaro Nakajima, and Kensuke Teshima, “From samurai to skyscrapers:
How historical lot fragmentation shapes Tokyo,” mimeo, 2022.

44

Online Appendix to: “The Economic Dynamics of City Structure: Evidence from Hiroshima’s Recovery”
Kohei Takeda

Atsushi Yamagishi

A Data Appendix

A1

B Nagasaki

A 12

C Additional Reduced-form Evidence

A 13

D Theoretical Appendix

A 17

E Calibration Appendix

A 25

F When Individuals Expect No Recovery

A 31

A Data Appendix
This section describes the details of data construction. Table A.1 provides summary statistics.
A.1 Basic data
Maps (spatial units) and sample selection. We use the city block (cho cho moku) as our spatial
unit of analysis. As our main definition of geography and city blocks, we use the GIS data ofblock boundaries as of the bombing constructed by Takezaki and Soda (2001). We make several
adjustments to create our final sample. First, although Takezaki and Soda (2001) follows the map ofofficially-published block boundaries (Hiroshima shin-shi), it was constructed after the war and a
few blocks do not correspond to our population data. We address this issue by suitably aggregating
blocks in Takezaki and Soda (2001).¹ Second, we drop some blocks that experienced exceptional
events that are outside the scope of our model. We first drop blocks that later constitute Hiroshima
Peace Memorial Park, Hiroshima-shi Chuo Park, and Hijiyama Park. Second, we drop three blocks
that exhibit unusually large changes in population or employment in some periods, which is likely
due to idiosyncratic events outside of the model.² Third, we drop observations that have missing
observations in the destruction rate of buildings or the establishment counts in 1938. Finally, to¹We aggregate two blocks (Akebomo-machi and Kougo kita-machi) that are recorded in a disaggregated way in
Takezaki and Soda (2001). We also combine the Yaga machi and Yaga shin-machi, and Funairi minami-machi andFunairi kawaguchi-machi.
²We drop Hakushima kita-machi, Iwamiya-cho, and Toriya-cho. Although we are not completely sure of why
these there blocks exhibit a sudden change in population or employment, we speculate that the presence of schools
in Hakushima kita-machi and Iwamiya-cho, and a very small size of Toriya-cho (less than 0.0025km2 ) made themprone to idiosyncratic shocks.

A1

ensure that our geographical scope is small, we drop two blocks whose centroids are more than 6kilometers from the city center. In our final sample, there are 174 blocks. We also digitize the blockboundaries as of 1966 and 1976 to deal with changes in the block boundaries. For 1966, we use
the map found in the report of the 1965 block-level population of Hiroshima (Hiroshima-shi machibetsu jinkou setai shiryou shouwa 40-nen kokusei chosa yori). For 1976, we use the Hiroshima citymap (Hiroshima shigai chizu) issued by a private publisher (Shobun-sya) in 1976.
Destruction by the atomic bombing. The severity of destruction can be measured primarily in
two ways: the destruction ratio of buildings and the kill ratio of people. Hiroshima City Government(1971), which is our key source of data on the bombing damage, provides both measures at the blocklevel. However, we primarily focus on the building data for two reasons. First, the kill ratio is lessreliable because it was extremely difficult to check who was killed in the totally destroyed city.
Indeed, Hiroshima City Government (1971) has many missing values for the kill ratio precisely
because no reliable data on the kill rate was available. In contrast, the destruction rate of buildings
was easier to record even a while after the bombing and hence has way fewer missing values. Second,Hiroshima City Government (1971) records the “immediate” death rate by the bombing, but thedefinition of the “immediate” is unclear and seemingly inconsistent across blocks in Hiroshima
City Government (1971). This is important in the context of Hiroshima because many people diedmany days, months, or even years after the bombing due to the atomic-bomb sickness caused by
the radiation. Third, prior studies about the impact of bombing on the city population (Davis andWeinstein 2002; Brakman, Garretsen and Schramm 2004) note that the damage to buildings isa better measure of the damage level than casualties. We base our analysis on the digitization ofHiroshima City Government (1971) by Takezaki and Soda (2001), but we consulted Hiroshima City
Government (1971) to (i) correct errors in Hiroshima City Government (1971) or Takezaki and Soda
(2001) and (ii) obtain the building destruction rate or the kill rate when they can be credibly inferredfrom the text information. We plot the building destruction rate against the distance from the CBD
in Figure A.1a. The strong heterogeneity within the city is apparent. Blocks within 2 kilometersof the CBD were quite severely destroyed, while those more than 2 kilometers away from the CBDtend to experience much less destruction. See also Figure 1b for the representation of a map. A
similar plot for the kill rate is in Figure A.1b. The severest damage tends to concentrate in a smallerarea (particularly within 1 kilometer of the CBD) and the data has more variation conditional on thesame distance from the CBD, partially because the data is noisier.
A.2 Population and employment
Population. We collect and digitize block-level population data. For 1933–1936, we use the Statistical Handbook of Hiroshima city (Hiroshima-shi toukei sho) that reports the population at theblock level. For 1945–1953, we use the Statistical Abstract of Hiroshima City (Hiroshima shisei
youran). Since 1955, we use the population census data. The time-series data is summarized in Fig-

A2

ure 2a. Two issues must be addressed to make the population data comparable from 1933 to 1975.
First, the block boundaries changed over time and the city’s shape also changed due to landfills andflood control. Second, prior to 1951, population data is available only at a less spatially-granularlevel than blocks. We address these issues using various data and construct block-level population
data that are comparable between 1933 and 1975.
To address these issues, we first base our definition of blocks as of 1945 and focus on blockareas that existed from 1945 to 1975. Then, when the block boundary changes since 1945, weevenly distribute the population based on the overlapping area. To address the changes in the sizeof blocks due to landfills and flood control, we focus on land areas between 1945 and 1975. Our
focus on the 1945 blocks allows us to ignore new landfills. However, flood control, especially theredesign of the ota river, which started at full scale in 1961 and was almost completed in 1965, isstill an issue because some land areas in 1945 later went under the river. This implies that someblocks in our data are smaller than their original size as of 1945. To address this, we calculate thepercentage change in the area before and after this flood control and multiply by this percentage
all population variables prior to 1965, which again implicitly assumes that the population is evenly
distributed within each block. Second, prior to 1951, population data is available only at a lessspatially-granular level than the blocks. To construct the block-level population data in 1945, we
combine the block-level information on the rate of totally destroyed buildings from Hiroshima City
Government (1971) and the population change ratio from the pre-bombing period to November 11945 from the Statistical Abstract of Hiroshima City for each distance bin from the epicenter of theatomic bomb. We first calculate the fraction of totally destroyed buildings by the distance to thecity center by aggregating the data from Hiroshima City Government (1971). We then regress the
population change ratio onto the quadratic function of the fraction of totally destroyed buildings. As
seen in Figure A.2a regression model fits the data well. We use this model to predict the population
change ratio by using the block-level total destruction of buildings. Finally, we multiply this ratiowith the 1936 block-level population to approximate the 1945 block-level population. We validate
our method of imputing the 1945 population after the bombing using different data. The 1946
edition of Hiroshima shisei youran reports in a map the population level before (August of 1945)
and after (August of 1946) the bombing for each school district. While we do not know the exact
border of school districts, we can compute the population change ratio between the two periods,
which we expect to be highly correlated with the population change due to the atomic bombing.
We then compare the population change rate of each school district with that of the census blockthat appears closest to the relevant school district on the map. Figure A.3 shows the scatter plot andthe fitted line. We obtain a very high correlation (ρ ≃ 0.86) between these two despite the data
limitations that the population was measured at different timing and the correspondence of school
districts and the block was measured with error.
To construct the block-level population data in 1949 and 1950, we use population data that isrecorded at a less spatially granular level, called shucchojo, taken from the 1949 and 1950 Statistical

A3

Abstract of Hiroshima.³ Shucchojo divides the city into 18 districts based on the administrative areaof each branch of the city government office. In principle, each shucchojo district is aggregatedfrom blocks.⁴ Assuming that within each shucchojo, the population share is the same as in 1951,
we approximate the block-level population data by multiplying this share by the population of the
shucchojo.
Our main analysis does not use population data from 1946–1948 because the block-level datais hard to construct. However, the population data for 1946, 1947, and 1948 is available in theStatistical Abstract of Hiroshima City separately for distance categories from the epicenter of thebombing. In Figure A.4, we plot the time series of the population share of areas within 1 kilometerof the epicenter using this data. The figure shows that the recovery process had already started
strongly in 1946.
Employment. We collect and digitize block-level employment data. For 1938, we use the Survey of Commerce and Industry in Hiroshima City (Hiroshima-shi shoukou-gyou keiei chousa) thatrecords the number of establishments at the block level. For 1946, we take from the Statistical
Abstract of Hiroshima City (Hiroshima shisei youran) the number of buildings used for businesspurposes. For 1953, we use the Survey on the Daytime Population of Hiroshima (Hiroshima-shi
chukan jinko chosa). From 1957 to 1975, we use the Business Establishment Statistical Survey (jigyousho toukei chousa). Throughout this paper, we focus on employment in the manufacturing orservice sectors and ignore agricultural employment. This is a relatively moderate restriction because
we focus on an urban area throughout our sample period.⁵ The time-series data is summarized in
Figure 2b.
Three issues must be addressed to make the block-level employment data comparable between
1938 and 1975. First, similar to population, the block boundary and the land area changed over time.
Second, for 1945–1963, the employment information is available only at a less spatially granularlevel than blocks. Third, for 1938 and 1945, we know the number of establishments but not the
number of workers. For the first issue, we address it using the same strategy as the population data.
We now describe how we address the second issue. We calculate the number of establishments as of³Similar to the block-level data, we have also adjusted the shrink in the area of shucchojo districts by defining thearea change of each district before and after the ota river flood control. We multiply the original population by this areachange rate to obtain the shicchojo level population.
⁴There are a few exceptions in which a block overlaps multiple shucchojo districts. In this case we assume that a
block belongs to the district in which more of the block residents live.
⁵While most of our data already focus on non-agricultural employment, the 1953 data report total employment,
including agricultural employment. To adjust for this, we estimate the number of agricultural workers in 1953 using
the following procedure: First, we obtain the share of agricultural households from the 1950 Statistical Abstract ofHiroshima. Combined with the number of agricultural workers from the 1950 Population Census, we estimate thatabout half of the agricultural household members are counted as working. This allows us to calculate the fraction ofagricultural workers in the overall population. We multiply it by the 1953 block-level population to approximate theblock-level agricultural employment in 1953. This adjustment of relatively minor importance because even in 1950,
when agricultural employment was significant in the Japanese economy, the Population Census suggests that less than
10 percent of workers are in the agricultural sector in Hiroshima city.

A4

November 1945, which is the time at which our first post-war population data is available. For this,
we first take from the 1946 Statistical Abstract of Hiroshima City the number of buildings for shops,
restaurants, banks, hotels, associations, and entertainment facilities before and after the bombing(August 1946). We also approximate the establishment distribution right after the bombing (August1945) by multiplying the number of establishments before the bombing and the ratio of totally
destroyed buildings.⁶ Using linear interpolation, we can approximate the number of establishments
for each distance bin as of November 1945 from the numbers as of August 1945 and 1946. Second,
we regress the change rate of the number of establishments from the pre-war period to November
1945 on the ratio of totally destroyed buildings and its square. Figure A.2b shows that the regression
model exhibits a good fit. Finally, we multiply the number of establishments in 1938 by the predictedchange rate using the block-level ratio of the totally destroyed buildings and the estimated regression
model shown in Figure A.2b.⁷
To construct the block-level employment distribution for 1950–1963, we rely on the employment distribution that is recorded at a less spatially granular level (shucchojo).⁸ Since our 1957
employment data aggregates seven peripheral districts into one, we define it as the “others” district
and use 12 shucchojo areas. The number of workers at the shucchojo level is available for 1953,
1957, and 1963. To calculate the employment at the block level, we multiply the number of workers
in the shucchojo and the employment share of that block in 1966. This procedure assumes that theemployment share within the shucchojo district is approximated by the 1966 distribution, but allows
for the employment changes across shucchojo districts. Finally, to approximate the employment distribution in 1950, we assume that the employment distribution in 1950 is the same as in 1953 except
for the total number of workers, which we scale down by the growth rate in the total population.
Finally, we need to construct the block-level employment data from the block-level establishment data. Following prior studies (e.g., Ahlfeldt, Redding, Sturm and Wolf 2015), we assume that
employment is proportional to the number of establishments. To determine the total size of employment in 1938 and 1945, we multiply the total population by the labor force participation rate in 1936,
which is 44.2 percent according to the 1936 Statistical Handbook of Hiroshima City (Hiroshima-shi
toukei sho).⁹
⁶We compute the average fraction of totally destroyed buildings for each bin from the block-level data of the fractionof totally destroyed buildings (Hiroshima City Government 1971), using the 1938 number of establishments as weights.
⁷The predicted model yields a negative change rate in the number of establishments for a 100 percent total destruction
rate. To address this, we use the change rate predicted for the 99 percent destruction rate for blocks with a 100 percent
destruction rate.
⁸The issues of some blocks belonging to two shucchojo and changing land areas are addressed in the same way as
the population data.
⁹In our structural estimation, however, the total employment equals the total population because our model assumes
that everyone works. We normalize the total population to the total employment.

A5

A.3 Other data
Commuting and transportation network. We use the trip-level microdata of the 1987 Hiroshima
City Person-Trip Survey for residents of the Hiroshima metropolitan area. It was large-scale (about
7 percent of the population was surveyed) and representative. To further enhance the representativeness based on residence, age, and gender, we use the sampling weights provided in the survey.
The unit of observation is a trip and for each trip, it collects information on the origin, destination,and mode(s) of transportation. We use the representative mode of transportation in the trip: walk,bicycle, car, bus, and train. The representative mode is defined as follows. First, the representativemode is “train” if the trip uses a train or tram. Then, for trips that have not been coded, we codethem as “bus” if it uses buses. We code trips that have not been coded as “car” if it uses a motorcycle
or automobile. We code trips that have not been coded as “bicycle” if it uses a bicycle. Finally, we
code it as “walk” if it uses walking.
Using the microdata of 1987 person-trip survey, we estimate the mode choice model using travels of workers from home to workplace.¹⁰ To measure the travel time between each workplaceresidence pair, we also collect and digitize road networks in 1987, bus networks, and train networks
in Hiroshima city, and compute the bilateral travel time between blocks for each mode: walk, bike,car, bus, and train.¹¹ The travel time in each travel mode between the areas is also obtained using
the centroid of each area. Although public transportation networks were generally stable during oursample period, there were a few notable changes, including the discontinuation of the Ujina line
in 1966. To address this, we also digitize the bus and train networks in 1950. Prior to 1966, we
use the public transportation networks of 1950, and after that, we use those of 1987. Throughout
our sample period, we use the 1987 road network for data quality, which is reasonable given thatthe road network in Hiroshima has not changed significantly from the pre-war period. To formallyverify this, we digitize the road networks on the published city maps prior to the bombing and in1950.¹² We then calculate the travel times to the city center under these networks and compare themwith the travel time under the 1987 road network. The correlation between the pre-bombing period
and 1987 is around 0.95 and the correlation between 1950 and 1987 is around 0.97.
Location characteristics. We collect various information on the locational characteristics of eachblock. We first explain the natural locational characteristics: altitude, ruggedness and soil condition.
¹⁰As an alternative measure of a bilateral commuting matrix, we also try the geographical distance between blocks.
We measure the bilateral distance by the geographical distance between the centroids of two areas. We estimate the gravity equation by constructing a bilateral commuting matrix between 66 areas within our sample area, using individuallevel information on the residence and the workplace. The 66 areas are constructed by suitably aggregating blocks. Our
main conclusions do not change.
¹¹We use QGIS to compute the travel time. Based on available evidence, we assume the following travel speeds: 5km/h for walking, 12 km/h for bicycling, 25 km/h for driving a car, 15 km/h for bus, 12 km/h for tram, and 36 km/h forother trains. In calculating the travel time by bicycle, car, bus, and train, we assume walking occurs outside its network.
¹²For the pre-bombing map, we digitize a map created by the US army based on pre-bombing resources (https://maps.
lib.utexas.edu/maps/ams/japan_city_plans/). For 1950, we digitize the Geospatial Information Authority of Japan Map.

A6

The altitude and the ruggedness are taken from the Digital National Land Information.¹³ For each
250 m × 250m squares, the data record the average altitude and the average degree of slopes. We
assign the value at the centroid of each block. Second, we obtain the location of water areas separately for the pre-war and post-war periods. We use the digital map of Takezaki and Soda (2001) forthe pre-war period and the Basic National Land Information data for the post-war period. Finally,
we take the soil condition from the Land Classification Basic Investigation.¹⁴ We use the data on
the surface strata and assign the soil condition to each block using the centroid location.
We next explain our data on non-natural locational characteristics. We collect information on
the location of train stations in 1950 from the Digital National Land Information.¹⁵ The list ofcultural assets (bunkazai) in the city is taken from the Hiroshima Metropolitan Area and Hiroshima
Prefecture Open Data Portal Site.¹⁶ Finally, we digitize the location and the number of units of eachpublic housing from the 1949 and 1950 Statistical Abstract of Hiroshima City (Hiroshima shisei
youran).¹⁷ The data cover all public housing units constructed in Hiroshima from 1946 to 1950.
Land prices. We obtain the location with the highest unit land price within Hiroshima city.¹⁸ For
1931, this is reported in the 1931 Statistical Yearbook of Hiroshima City. For 1959, the National Tax
Agency reports the location with the highest land price in each prefecture.¹⁹ Since the highest land
price in Hiroshima prefecture was in Hiroshima city, we know that this place also had the highest
land price in Hiroshima city.
Migration rate. In order to assess the degree of mobility friction, we use information on migration rates. Our primary data source is the 1960 population census. It asks whether a respondentchanged their address, including moving within the same municipality. In densely populated areasof Hiroshima prefecture, 85.9 percent of people in prime-age answered they did not.²⁰ Converting
this into a 5-year interval, we calculate the rate of moving within five years is θ ≃ 0.53. However, this migration probability seems too small for the period right after the war. Many people
reallocated for wartime reasons and they would have lower mobility costs (e.g., lower attachment¹³Source: https://nlftp.mlit.go.jp/ksj/gml/datalist/KsjTmplt-G04-d.html, in Japanese. Last accessed on September
9, 2022¹⁴Source is map with a scale of 1 to 50,000; https://nlftp.mlit.go.jp/kokjo/inspect/landclassification/land/l_national_
map_5-1.html, in Japanese. Last accessed on September 7, 2022.
¹⁵Source: https://nlftp.mlit.go.jp/ksj/gml/datalist/KsjTmplt-N05-v1_3.html, in Japanese. Last accessed on September 7, 2022.
¹⁶Source: https://hiroshima-opendata.dataeye.jp/resources/9843, last accessed on September 9, 2022.
¹⁷In some cases, the location information in the data does not allow us to pin down the block the public housing islocated in. We still assign the single block based on our best guess on the location of that public housing.
¹⁸In Japan, to our knowledge, digitized comprehensive land price data in the pre-WWII period is available only inTokyo and Kyoto (Yamagishi and Sato 2023).
¹⁹This can be found in Weekly Tax Communication (Shukan zeimu tsushin), volume 444, issue of February 22, 1960.
²⁰The prime-age means between the ages of 15 and 59. Data source: https://www.e-stat.go.jp/stat-search/files?
page=1&layout=datalist&toukei=00200521&tstat=000001036867&cycle=0&tclass1=000001038047&tclass2val=0,in Japanese. Last accessed on September 8, 2022.

A7to their current residence, higher probability of intending job switching). According to the city
population registry (reported in Hiroshima shisei youran), more than 50,000 of people moved outof Hiroshima city in 1949. Since the population of Hiroshima city at the end of 1948 was about
24,000 (1952 Hiroshima shisei youran), this implies an annual migration rate of 21 percent even if
intra-city migration is ignored. We assume that the relative frequency of intra-city migration andinter-city migration right after the war is similar to that in 1960.²¹ Then, this suggests an annual
rate of staying of 0.64, corresponding to a rate of moving within five years θ ≃ 0.9. Note that our
migration rate for the period 1945–1950 is primarily based on the migration data from 1949. Thismight understate the migration rate if the mobility right after the war was even higher than the 1949
migration rate.

100.0

100.0

Percentage of death by bombing

Percentage of destroyed buildings by bombing

Figure A.1: Damage to buildings and Death of people

80.0

60.0

40.0

20.0

0.0

80.0

60.0

40.0

20.0

0.0
0

1

2

3

4

Distance to CBD (km)

5

6

0

(a) Damage to Buildings

1

2

3

4

Distance to CBD (km)56(b) Death Rate of People

Note: The left panel plots percentage of totally destroyed buildings by the atomic bombing in each block. The rightpanel plots percentage of people killed by the atomic bombing in each block. Source is Hiroshima City Government(1971).

²¹For the prime-aged people, this ratio in the densely-populated area of Hiroshima prefecture is around 7:10, implyingthat the annual migration rate is roughly 0.36.

A8

Figure A.2: The population and establishment change on the rate of totally-destroyed buildings
1.5
Establishment change rate due to the bombing

Population change rate due to the bombing

1

1

.5

.8

.6

.4

.2

0

0
0.0

20.0

40.0
60.0
80.0
Percentage of totally destroyed buildings

100.0(a) Population change

0.0

20.0

40.0
60.0
80.0
Percentage of totally destroyed buildings

100.0(b) Establishment change

Note: The left panel shows the scatter plot of the percentage of totally destroyed buildings and the population change
rate due to the bombing for distance categories from the epicenter (within 1km, 1-1.5km, 1.5-2km, 2-2.5km, 2.5-3km,
more than 3km away). The population change is from the 1946 Statistical Abstract of Hiroshima City and the destruction
rate is a population-weighted average of the block-level destruction rate from Hiroshima City Government (1971). The
right panel shows the scatter plot of the percentage of totally destroyed buildings and the establishment change rate dueto the bombing, for distance categories from the epicenter (0.5km grids up to 5km). The establishment change is fromthe 1946 Statistical Abstract of Hiroshima City. In both panels, we fit the quadratic model and plot it.

Figure A.3: Validation of our 1945 population data with alternative population data in 1946

Population change rate (as of August 1946)

1.5

1

.5

ρ＝0.855

00.51
Imputed population change rate (as of November 1945)

1.5

Note: We validate our method of imputing the 1945 population after the bombing using different population data takenfrom the 1946 edition of Hiroshima shisei youran at the school district level. The horizontal axis shows the predicted
population change rate as of November 1945 based on the imputed destruction rate of buildings for each school district.
The vertical axis shows the population change rate as of August 1946, taken from the data. We also plot a linear
regression line.

A9

.25

.2

.15

.1

.05

1960

1955

1951
1952
1953

1945
1946
1947
1948

0
1933
1934
1935
1936

Population share, within 1km from the epicenter

Figure A.4: Actual and counterfactual population share within 1km from the epicenter

Year
ActualCounterfactual

Note: This figure shows the population share of areas within 1 kilometer of the epicenter of the atomic bombing. For
1945–1948, we observe the population in the Statistical Abstract of Hiroshima. For the remaining years, we aggregate
the block-level population to the distance bins from the epicenter according to the definition of Hiroshima City Government (1971). The counterfactual population share extrapolates the pre-war linear trend to the post-WWII period,
analogous to Figure 2 of Davis and Weinstein (2002).

A 10

Table A.1: Summary statistics

Population 1936
Population 1936 per 1km2
Population 1945
Population 1945 per 1km2
Population 1950
Population 1950 per 1km2
Population 1960
Population 1960 per 1km2
Population 1975
Population 1975 per 1km2
Employment 1938
Employment 1938 per 1km2
Employment 1945
Employment 1945 per 1km2
Employment 1953
Employment 1953 per 1km2
Employment 1966
Employment 1966 per 1km2
Employment 1975
Employment 1975 per 1km2
Block area (km2 )Distance to the CBD (km)Distance to the nearest station (m)Distance to the nearest water area (m)Distance to the nearest cultural asset (m)Altitude (m)Average slope (degree)
Dummy of bad soil condition
LatitudeLongitude
Annual population growth rate 1933–1936
Rate of total destroyed Building
Rate of half-damaged buildings
Rate of mildly-damaged buildings
Rate of intact building
Observations

Full sample
mean
sd
count
1880 2153
17423761 14104 174
917
2927
174
3566 5496
174
1495 2683
174
11877 6616
174
2215 3648
174
16725 8548
174
2625 5423
174
12758 5046
174
978
835
174
42517 41449 174
405
1056
174
5507 8035
174
669
965
174
7358 6083
174
1277 1516
174
18499 17408 174
1515 1880
174
21017 21948 174
.321
.971
174
1.66
1.06
174
336
319
174
248
229
174
808
637
174
5.91
14.4
174
.814
2.4
174
.96
.197
174
34.4 .0104 174
132.0167 174
1.03
.0355 174
74.5
35.4
174
18.6
26
174
6.65
17.7
174
.685
3.99
174
174

A 11

Within 3km from the CBD
mean
sd
count
1642
1103
158
25752 13138
158
459
916
158
3374
5158
158
1026
1091
158
12583 6374
158
1537
1689
158
17737 8188
158
1501
2694
158
13065 4906
158
949
626
158
46512 41422
158
259
420
158
5602
8072
158
505
465
158
7909
6099
158
1060
792
158
20111 17463
158
1211
993
158
22821 22243
158
.132
.39
158
1.4
.652
158
285
232
158
226
185
158
684
412
158
4.25
7.56
158
.611
2.07
158
.981
.137
158
34.4 .00917
158
132
.0123
158
1.03
.0344
158
81.1
29.8
158
15.2
23.6
158
3.38
12.1
158
.316
1.66
158
158

B Nagasaki
Throughout the paper, we focus on Hiroshima: the first city hit by the atomic bomb in our history.
Our focus on Hiroshima is motivated by better data availability and city size: Hiroshima was about
twice as large as Nagasaki in the pre-war period. That said, this section analyzes Nagasaki, thesecond and last city that experienced an atomic bombing as of the time this paper is written, basedon available data.
The case of Nagasaki is useful to distinguish the role of war-time destruction from the locational
fundamentals because the atomic bomb hit a different part of the city. In Hiroshima, we have shownin Section 3 that the atomic bombing of Hirohsima results in a populaton decline in the city’s core,
while the city’s outskirts experienced an increase in population. In contrast, as shown in the damage
map of Nagasaki in Figure B.1a, the atomic bomb hit the outskirts of Nagasaki and the epicenter ismore than 2 kilometers away from the city center, where the Nagasaki City Hall and the Nagasaki
Prefectural Office are located. Consequently, the city center of Nagasaki, areas to the south-east ofNagasaki station, was damaged relatively mildly. Some of the outskirts of Nagasaki experienced
destruction and a decrease in population, while the center, which experienced less destruction, experienced an increase in population as people escaped into the center (Inami 1953). Therefore, incontrast to Hiroshima where the monocentric city structure was reversed, the concentration in thecenter was augmented by the bombing in Nagasaki. This contrasting pattern of population change
after the atomic bombing allows us to distinguish between the importance of the destruction due
to the bombing and its fundamental characteristics. If the destruction rate determines the post-war
population growth, then the outskirts should experience a substantial increase in population. In contrast, if being the (pre-war) city center is what matters in explaining the post-war population growthof central Hiroshima, then we would not expect the recovery of the pre-war population distribution
on the outskirts of Nagasaki.
To investigate the post-war population growth in Nagasaki after the bombing, we use the population data in May 1945 (pre-bombing), October 1945 (post-bombing), and March 1954 at the school
district level, taken from Nagasaki City Government (1983). We estimate the following equation
similar to equation (1):!
!
Popdensi,1954
Popdensi,1945 Octln= γ ln+ vi .
(B.1)
Popdensi,1945 Oct
Popdensi,1945 May
The unit of observation is the school district i and there were 24 school districts.²²
Figure B.1b shows the estimation result. Despite the fact that the atomic bomb hit a different
part of the city, the figure looks very similar to the case of Hiroshima in Figure 4. The estimated²²Strictly speaking, we cannot calculate population density because we have no information on the size of each school
district. However, this does not prevent us from implementing (B.1) as long as the size does not change throughout oursample period. We do not include control variables because Nagasaki City Government (1983) does not show a map of
school districts and we could not collect precise locational characteristics.

A 12

Figure B.1: The map and the reduced-form result of Nagasaki(a) Map of Physical Damages Causedby the Atomic Bombing (Nagasaki)(b) Change in Population Density (Nagasaki)
Change in Log Population Density, 1945-54

4

3

2

1

0

-1
-3

-2

-1

Change in Log Population Density, before and after bombed
Fitted line

0

Slope of -1

Note: The map of Figure B.1a shows the epicenter of the bombing in Nagasaki, as well as major facilities and theextent of the damage to structures. This map is provided by the Atomic Bomb Disease Institute at Nagasaki University.
Figure B.1b plots the change in the log of population density from 1945 to 1954 compared to those from May 1945 to
October 1945 in Nagasaki. Each circle represents a school district (i.e., an observation), where the size of the circle is
proportional to the population density in May 1945. We plot the (unweighted) linear fit between these two variables(solid line) as well as the slope of -1 (dashed line).

slope of the fitted line is −0.882 with a standard error 0.101. While we can strongly reject thenull of γ = 0, we cannot reject the null of γ = −1 at the conventional level. Therefore, similar
to Hiroshima, we obtain evidence of the path independence within Nagasaki. This evidence from
Nagasaki suggests that the population distribution in the city would resemble the pre-war one, even
if the atomic bomb hit a different place within the city. Combined with the result from Hiroshima,
it is difficult to attribute the recovery to the fundamental advantages of particular locations within acity.

C Additional Reduced-form Evidence
Employment. We repeat the same reduced-form analysis as Section 3 for employment data in
1938, 1945, and 1966. Figure C.1 shows the scatter plot of the log employment change rates in thesame way as Figure 4 for population data. Similar to the population, we find those areas that experienced a significant decline in employment due to the bombing had a high employment growth ratein the post-war period. Moreover, the magnitude of this recovery is close to, albeit not exactly, thecase of the complete path independence shown in the dashed line. Table C.1 reports the regression
results of the equation (1) for employment, in the same manner as Table 1 for population. Column

A 13

1 reports the result of the simple regression in Figure C.1. We find the coefficient around -0.86,
which indicates a stronger recovery than the case of the population in Table 1 (around -0.7). Adding
control variables, column 2 shows that the coefficient is now almost -1, i.e., the path independence.
The path independence result after adding control variables is the same as in the case of the population. Finally, column 3 shows that focusing on blocks within 3 kilometers of the epicenter, whichis expected to have more homogeneous locational characteristics, still implies path independence.
This is again similar to the pattern of the population in Table 1.
Characteristics of neighboring blocks. We suppose that post-war population growth of block i
may depend not only on own characteristics but also on the characteristics of neighboring blocks
j ̸= i. To consider the characteristics of neighbors, we adopt the so-called “SLX model” in spatial
econometrics literature (Halleck Vega and Elhorst 2015) and control for the spatial lag of the twoPopdens
types of dependent variables in our main regression equation (1). The spatial lag of ln Popdensi,1945
i,1936summarizing the wartime destruction rate of surrounding blocks and the spatial lag of Xi summarizes the locational characteristics of neighboring blocks. We use the exponential spatial weighting
matrix by using geographical distances between centroids of blocks in kilometers, implying thatthe characteristics of blocks that are close to block i are given more weights.²³ We also construct
the spatial lag of population right after the bombing, which is meant to capture the market accessof a given block.²⁴ In addition to our baseline control variables on block characteristics, We additionally control for these spatial lag variables in our main regression analysis in Table 1. Table
C.2 shows that the inclusion of these
spatial lag
 Popdens variables does not change our conclusion about thei,1945coefficient γ associated with ln Popdens. In particular, we cannot reject the null of complete
i,1936
path independence (γ = −1) in all specifications. Overall, the results suggest that considering thecharacteristics of neighboring blocks does not change our path-independence result.
Public housing. To assess how much the recovery of central Hiroshima was driven by governmental policies, we explore the role of public housing, which was a primary policy target right after
the war. To investigate whether the provision of public housing directly leads to the recovery, we
control for the number of public housing units on top of our main reduced-form regressions in Table
1. Table C.3 reports the results, showing that controlling for public housing does not change ourconclusion.²⁵²³Following the decay of spillovers in Ahlfeldt et al. (2015), we set the spatial decay parameter at 4.32.
²⁴We set the spatial decay parameter at 0.05 given the commuting cost estimate with respect to geographical distancein Hiroshima, which was reported in a previous version of this paper (Takeda and Yamagishi 2023).
²⁵The result that public housing provision does not explain the recovery of central hiroshima is natural because wefind that public housings were more likely to be supplied in locations away from the CBD.

A 14

Change in log employment density, 1945-66

Figure C.1: Change in employment density
6

4

2

0

-2
-5

-4

-3

-2

-1

0

Change in log employment density, 1938-45 (after bombed)
Fitted line

Slope of -1

Note: This figure plots the log employment change rate from 1938 to 1945 against the log employment change ratefrom 1945 to 1966. Each circle represents a block (i.e., an observation), where the size of the circle is proportional tothe employment density in 1938. We plot the (unweighted) linear fit between these two variables (solid line) as well as
the slope of -1 (dashed line).

Table C.1: Change in employment density
(1)
(2)
(3)
Change in log employment density 1945-66
Change in log employment density 1938-45 -0.8571 -0.9978-0.9420(0.0324) (0.0586)(0.0642)p-value from testing γ = −1
0.000
0.970
0.368
Control variables✓✓
Within 3km from the city center✓
Number of blocks
174
174
158
R-squared
0.828
0.892
0.915
Note: We report the OLS estimation result of the equation (1) for employment density. Fundamentals consist of thequadratics of the distance to the nearest station, the distance to the nearest cultural asset, the distance to the nearest water
area, the altitude, and the slope. We also include a dummy for a bad soil condition. We also control for the quadraticsof the pre-war (1933-1936) population growth rate, the fractions of the half-destroyed, moderately-destroyed, and intact
buildings, and the geographical coordinates (the latitude, the longitude, and their interaction). In columns 3, we confine
the sample to blocks within 3km from the city center, in which fundamental conditions are more homogeneous. We
also test the null that γ = −1 (i.e., the complete path independence) and report its p-value. Robust standard errors inparentheses.

A 15

Table C.2: Controlling for characteristics of neighboring blocks
(1)
(2)
(3)
Change in log population density 1945-50-0.9385a -0.9345a-0.9568a(0.0990) (0.1046)(0.1036)

Change in log population density 1936-45
p-value from testing γ = −1
Control variables (block characteristics)
Spatial lag of change in log population density 1936-45
Spatial lag of control variables (block characteristics)
Spatial lag of population right after the bombing
N
R2

0.536
✓
✓

0.533
✓

174
0.863

174
0.890

✓

0.677
✓

✓
174
0.863

Standard errors in parenthesesc p < 0.1, b p < 0.05, a p < 0.01

Note: We report the OLS estimation result of the equation (1) for population density, while controlling for a spatial lagof dependent variables based on geographic distances between centroids of blocks. As control variables, we include thequadratics of the distance to the nearest station, the distance to the nearest cultural asset, the distance to the nearest water
area, the altitude, and the slope. We also include a dummy for a bad soil condition. We also control for the quadraticsof the pre-war (1933-1936) population growth rate, the fractions of the half-destroyed, moderately-destroyed, and intact
buildings, and the geographical coordinates (the latitude, the longitude, and their interaction). The spatial lags of thechange in log population density 1936-45 and block characteristics are constructed using exponential weights, where thedecay parameter is set at 4.32. We construct the spatial lag of each control variable (except for latitudes and longitudes)
and use them as separate controls, using the decay parameter 4.32. The spatial lag of population right after the bombing
is constructed using the decay parameter 0.05. Column 1 includes the spatial lag of the population density change
due to the war. Column 2 controls for the spatial lag of block characteristics. Column 3 controls for the spatial lag of
population level right after the bombing. We also test the null that γ = −1 (i.e., the complete path independence) andreport its p-value. Robust standard errors in parentheses.

Table C.3: Change in population density (controlling for public housing)

Change in log population density 1936-45
p-value from testing γ = −1
Control variables (other than public housing)Within 3km from the city center
Number of blocks
R-squared

(1)
(2)
(3)
Change in log population density 1945-50-0.7270 -0.9453-0.9839(0.0270) (0.0986)(0.0992)
0.000
0.580
0.871
✓
✓
✓
174
174
158
0.816
0.866
0.880

Note: We report the OLS estimation result of the equation (1) for population density, while controlling for the numberof units of public housing in each block for all specifications. Fundamentals consist of the quadratics of the distanceto the nearest station, the distance to the nearest cultural asset, the distance to the nearest water area, the altitude, andthe slope. We also include a dummy for a bad soil condition. We also control for the quadratics of the pre-war (19331936) population growth rate, the fractions of the half-destroyed, moderately-destroyed, and intact buildings, and thegeographical coordinates (the latitude, the longitude, and their interaction). In columns 3, we confine the sample toblocks within 3km from the city center, in which fundamental conditions are more homogeneous. We also test the nullthat γ = −1 (i.e., the complete path independence) and report its p-value. Robust standard errors in parentheses.

A 16

D Theoretical Appendix
This section provides detailed derivations in the model.
D.1 Value function
When an individual ω is able to change the location choices, she solves the problem of location
choice (6) in the main text. The idiosyncratic taste shocks are drawn from the time-invariant andindependent mean-zero Type I extreme distribution:
F (ε) = exp(− exp(−(ε + Γ))),f (ε) = exp(−(ε + Γ)) F (ε)

R∞
where Γ is Euler-Mascheroni constant: Γ ≡ − 0 ln xe− x dx. For d ∈ {C × C , o }, we have
distribution functions:

 

s − ρVdt+1+Γ.
Gdt+1 (s) = Prob[ρVdt+1 + σε dt+1 ≤ s] = exp − exp −σ
Therefore, ρVjℓt+1 + σε jℓt+1 follows Gumbel distribution with mean ρVjℓt+1 and scale parameter
σ. The large value of σ leads to large variation. LetVt∗+1 ≡ max ρVjℓt+1 + σε jℓt+1 ; ρVot+1 + σε ot+1
Then, we have
Ht+1 (s) = Prob[Vt∗+1 ≤ s] = ∏ Gjℓt+1 (s) × Got+1 (s)( j,ℓ)

which corresponds to the maximum of the Gumbel random variables. It can be shown that this also
follows the Gumbel distribution with mean
µt+1 = E t+1 [s] = σ ln  ∑ exp(Vjℓt+1 )ρ/σ + exp(Vot+1 )ρ/σ (D.1)( j,ℓ)

Therefore, for d ∈ {C × C , o }, we have value functions (7) and (8) in the main text.
D.2 Location choice
We transform the variable such that z = ε + σΓ. Suppose that an agent can switch the location.
Then, the probability that an individual chooses location pair of workplace j and residential place ℓin period t + 1 is:






Z ∞
1
1
 ∏ exp −e− σ z+ρVjℓt+1 −ρVj′ ℓ′ t+1 exp −e− σ z+ρVjℓt+1 −ρVot+1  1 e− σz dz
λ j ℓ t +1 =σ
− ∞ ( j ′ ,ℓ ′ )A 17

Letting s = e−z/σ ,
Z ∞










1
ρVjℓt+1 − ρVdt+1  dsσ0d∈{( j′ ,ℓ′ ),o } ∞
exp −s ∑d∈{( j′ ,ℓ′ ),o} exp − σ1 ρVjℓt+1 − ρVdt+1


=

1
− ∑d∈{( j′ ,ℓ′ ),o} exp − σ ρVjℓt+1 − ρVdt+1

λ j ℓ t +1 ==exp −s

∑

exp −

(D.2)

0

exp(Vjℓt+1 )ρ/σ∑d∈{( j′ ,ℓ′ ),o} exp(Vdt+1 )ρ/σ

Analogously, the probability that workers live outside of the city is:
λot+1 =

exp(Vot+1 )ρ/σ∑d∈{( j′ ,ℓ′ ),o} exp(Vdt+1 )ρ/σ

(D.3)

An individual can change the residential place and workplace with the exogenous probability, θt ∈(0, 1). Using the probabilities of location choice, the mass of workers choosing location i as aworkplace and location n as a residential place in period t + 1 can be expressed by:
Lint+1 = (1 − θt+1 ) Lint + θt+1 λint+1 Lt + θt+1 λint+1 (M − Lt )= (1 − θt+1 ) Lint + θt+1 λint+1 M
We can use the same idea to derive the dynamics of population (11) and employment (12):Rnt+1 = ∑ Lint+1 = (1 − θt+1 ) Rnt + θt+1 ∑ λint+1 M(D.4)

Lit+1 = ∑ Lint+1 = (1 − θt+1 ) Lit + θt+1 ∑ λint+1 M

(D.5)

i ∈C

i ∈C

and
n∈C

n∈C

The total population in the city is
L t +1 =∑Lint+1 = (1 − θt+1 ) Lt + θt+1 (1 − λot+1 )M(i,n)∈C×C

D.3 Equilibrium
eint = Vint − Vot and ueint ≡ uint /uot . Bellman equation implies
Let V
eint = ln ueint + (1 − θt+1 )ρV
eint+1
V

A 18

(D.6)

Iterating this, we obtaineint = ln ueint +V= ln ueintT∑ ρτ −tτ = t +1T∏

τ = t +1ueinτβ

∏ (1 − θ s )s = t +1ρτ−t ∏τs=t+1 (1−θs )ait bnt
α + α2 β 1 + β 2
Sn

Si 1

T

β

= ln Cint Litα1 Litα2−1 Rnt1 Rnt2−1
where Cint ≡

!

τ

∏



τ = t +1

ln ueinτ
!
(D.7)
β

β

α1 α2
Cinτ LiτLiτ −1 Rnτ1 Rnτ2 −1ρτ−t ∏τs=t+1 (1−θs )

!

−1 −1
uot > 0.
κint

The probability (D.2) can be expressed as
λint =

eint )ρ/σexp(Vejℓt )ρ/σ + 1∑ j,ℓ exp(V(D.8)

Therefore, we obtain population in location n:eint )ρ/σexp(VMejℓt )ρ/σ + 1∑ j,ℓ exp(V(D.9)

eint )ρ/σexp(VMejℓt )ρ/σ + 1
n ∑ j,ℓ exp(V(D.10)

Rnt = (1 − θt ) Rnt−1 + θt ∑iand employment in location i:
Lit = (1 − θt ) Lit−1 + θt ∑The equilibrium is characterized by { Rnt , Lit } solving (D.7), (D.9) and (D.10) jointly.
We show the existence of the forward-looking competitive equilibrium in which population andemployment satisfy Rnt ≥ (1 − θt ) Rnt−1 and Lit ≥ (1 − θt ) Lit−1 given θt . To simplify thenotation, we suppose (1 − θt )ρ → 0. Yet, our following augment can be applied for the generalcase. When (1 − θt )ρ → 0, the forward-looking equilibrium is characterized by ({ Rnt }, { Lit })solving the system of equations:
Rnt = (1 − θt ) Rnt−1 + ∑

ρ/σ

β̃

β̃

Cint Rnt1 Rnt2−1( Lit − (1 − θt ) Lit−1 ),ρ/σ β̃ 1 β̃ 2i ∑ℓ Ci ℓ t R ℓ t R ℓ t −1
ρ/σCint Litα̃1 Litα̃2−1( Rnt − (1 − θt ) Rnt−1 )ρ/σ α̃ α̃n ∑ j C jnt L jt1 L jt2−1(D.11)

Lit = (1 − θt ) Lit−1 + ∑where α̃1 ≡ α1 ρ/σ, α̃2 ≡ α2 ρ/σ, β̃ 1 ≡ β 1 ρ/σ and β̃ 2 ≡ β 2 ρ/σ.
We suppose that Rnt ≥ (1 − θt ) Rnt−1 and Lit ≥ (1 − θt ) Lit−1 for any {θt }. Therefore, wecharacterize the equilibrium in which population and employment are increasing given the friction

A 19

of mobility. This is in line with our quantification in the next section. Letting z = (R, L) be avector of population and employment and we define the operator J (z ) such that ι-th element Jι (z )corresponds to the right-hand side of (D.11). When Rnt ≥ (1 − θt ) Rnt−1 and Lit ≥ (1 − θt ) Lit−1 ,we can define the convex subset of R2N++ where the operator J is mapping from the subset to itself.
The operator J is continuous mapping. Therefore, by Brouwer’s fixed-point theorem, there exist
forward-looking equilibrium such that they satisfy Rnt ≥ (1 − θt ) Rnt−1 and Lit ≥ (1 − θt ) Lit−1 .
D.4 Steady-state equilibrium
If the steady state equilibrium exists, it is stationary steady state where all variables in the model are
not changing over time. In such stationary steady state, the conditional probabilities that workers
commute to i given residential place n become:α̃ρ/σãin Liλin=α̃ρ/σ∑ j∈C λ jnã jn L∑

λiL|n =j∈Cjwhere we let α̃ ≡ α1 + α2 , β̃ ≡ β 1 + β 2 , and ãin ≡ ( āi /κin )ρ/σ > 0, where ãin summarizes thetime-invariant fundamental productivity consistent with the steady-state. Analogously the conditional probabilities that workers live in n given workplace i become:β̃ρ/σλnR|i =

λinb̃in Rn=β̃ρ/σ∑ℓ∈C λiℓb̃ R∑ℓ∈C i ℓ ℓ

where b̃in ≡ (b̄n /κin )ρ/σ > 0. In sum, the steady state equilibrium is characterized by variables{ Rn , Li , Φi , Υn } solving the system of equations:1− β̃ρ/σRnΦi = ∑ b̃in Rn

1= ∑ ãin Υ−n Rn ,

Υn = ∑ ãin Lii1−α̃ρ/σLiβ̃ρ/σ= ∑ b̃in Φi−1 Li ,
n

n

α̃ρ/σ

,
(D.12)i

To exploit the result of Allen, Arkolakis and Li (2020), we define the following matrix C and D thatsummarize the parameters from the left and right-hand sides of the system of equations, respectively:




0
−1
1
0
1 − β̃ρ/σ



1
0
0 
 , D =  β̃ρ/σ 0

C=
 1

1 − α̃ρ/σ 
0
0
−1
1
0
0 α̃ρ/σ 0
Matrix C is diagonal matrix and invertible when α1 + α2 ̸= σ/ρ and β 1 + β 2 ̸= σ/ρ, and steadystate equilibrium exists when these conditions hold. Then, we define matrix Γ = |DC−1 |. Using
the results in Allen et al. (2020), the system of equations has a unique up-to-scale solution if all

A 20

eigenvalues of the matrix Γ are no larger than one. In our case the sufficient conditions for a unique
up-to-scale solution are:| β̃ρ/σ| + 1|α̃ρ/σ| + 1≤1≤ 1,|1 − α̃ρ/σ||1 − β̃ρ/σ|These conditions hold if and only if:β̃ = β 1 + β 2 ≤ 0,α̃ = α1 + α2 ≤ 0(D.13)The net agglomeration in productivity (α1 + α2 ) and net neighborhood externality in amenities(β 1 + β 2 ) are negative so that congestion force is dominating the agglomeration force in both workplace and residential place to ensure the unique up-to-scale solution. The level of the solution ispinned down by the total population in the city, and we obtain a unique stationary steady state.
D.5 Microfoundations of productivity spillovers
In this section we present two different microfoundations of productivity spillovers. The first subsection considers the local production capital and the second subsection discusses the innovation
by local firms.
D.5.1

Local production capital

Capital in final good production. The production function is given by yit = kνit1 lit with a parameter ν1 ∈ (0, 1). k it stands for local production capital (e.g., floor space) and ν1 governs thedecreasing returns to scale in its contribution to labor productivity. The technology is linear in its
labor, so the equilibrium wage wit = kνit1 .²⁶ Firms also choose their local capital input taking its unit
price pit as given, leading to pit = ν1 lit kνit1 −1 . Since the production technology is linear in labor, at
this profit maximizing point, firms that earn negative profits may stop operating if the cost of local
capital is incurred by them. To simplify the discussion, we assume that firms do not exit, possibly
because they receive a lump-sum transfer from the government or other sources that cover the costof local capital.²⁷
Local capital supply. Capital is supplied locally in each location. The production technology ofthe supplier is Cobb-Douglas technology: k it = eit nitν2 S̄it1−ν2 , where eit is the efficiency of productionof local capital, nit is input of numeraire (final goods) and S̄it is land used for business. The supplier²⁶Due to the linear technology both in tradable final goods production and capital production, the wage rate must be
equalized across both sectors for both sectors to be active. We focus on such a situation and assume as a tie-breaking
rule that a fixed ϱ ∈ (0, 1) fraction of Lit workers work in the capital sector and the remaining work in the final goods
sector.
²⁷Alternatively, firms may earn positive profits in equilibrium and have no incentive to exit when they can exert aνmonopsony power in the labor market and set a lower wage than the marginal revenue: wit = k it1 /(1 + mit ), which isisomorphic to the perfect competition case multiplied by 1/(1 + mit ). In particular, since the local labor supply curve
has the iso-elastic form with elasticity ρ/σ when θt = 1, mit equals ρ/σ so that markup rate is constant and common
across all locations.

A 21

of local capital decides input of numeraire given commercial land (S̄it ). The local capital supplierbid for commercial land and absentee land owner extract all profit from the suppliers, implying thatfirms earn zero profit in equilibrium. In equilibrium market clearing condition for the local capitalleads to:k it = k̄0 eitλ1 ( Ait lit )λ2 S̄itλ1 −λ2 ,where k̄0 is a constant, λ1 ≡ 1/(1 − ν1 ν2 ) and λ2 ≡ ν2 /(1 − ν1 ν2 ).
We now specify the efficiency of local capital supply (eit ) and land allocation for commercial use(S̄it ). First, efficiency is related to the infrastructure invested by the government. If infrastructure
depreciates more when firms use it intensively in period t − 1, while infrastructure increases morewhen the government’s investment is increasing based on production in period t − 1. The timeψdifference is intuitive since replacing infrastructure takes time. Then, we can argue eit = ēit Lit1−1 ,where ēit is fundamental quality. Next, commercial land use is also related to land allocation by thegovernment or absentee landowners based on economic activities in the previous period. On theother hand, land for commercial use can be negatively associated with employment in the previous
period through lot size adjustment costs (Yamasaki, Nakajima and Teshima 2022). More workers inperiod t − 1 may imply a smaller lot size and that increases development costs or adjustment costsof land for large-scale construction, limiting the efficient land allocation toward business. In sum,ψ
we can write: S̄it = Si Lit2−1 where ψ2 can be negative or positive.
Equilibrium wages. Combining them, we can represent the wage equation in location i:(ψ +ψ2 )λ̃1 −ψ2 λ̃2 λ̃1 −λ̃2,Siwit = kνit1 = Āit Litλ̃2 Lit−11

where Āit conflates fundamentals, λ̃1 = λ1 ν1 and λ̃2 = λ2 ν1 . Manipulating this, we have: λ̃2 Lit
Lit−1 (ψ1 +ψ2 )λ̃1 −ψ2 λ̃2wit = Ait,
(D.14)
Si
Si
where Ait absorbs fundamentals. The wage is increasing in current employment density (Lit /Si ).
The effect of previous employment density (Lit−1 /Si ) depends on the sign of parameters. Assumingthat the firm profit goes outside of the economy, the rest of the model behaves the same as our mainmodel in Section 4 with Ait is given by the right-hand-side of (D.14).
D.5.2

Innovation by incumbent workers in local firms

The technology of final good producers is linear in labor, yit = Ait Lit where Lit is total employment.
Productivity of firms in location i is determined by:
Ait = (ϕit − δA ) Lit χ Āt−1 ,(D.15)

which has three different components. First, productivity grows at rate ϕit − δA . ϕit is innovation
between period t − 1 and t and δA is the obsolescence rate of previous idea. Second, there is scale effects in innovation and parameter χ captures the return to employment size in knowledge spillovers.

A 22

Third, all firms can access the productivity frontier of the last period, Āt−1 = maxi Ait−1 . In thefollowing, we discuss how we determine innovation, ϕit .
The innovation ϕit is equal to the average units of a blueprint of innovators in location i. In
period t, only incumbent workers who stay in the location from the period t − 1 can do innovation
since it requires experience in the local firms. Among workers in i at period t, incumbent workers
who do not have an opportunity of moving are (1 − θt ) Lit−1 . Each incumbent workers have one
unit of the blueprint of ideas at the end of period t − 1, zOld
it−1 = 1.
At the beginning of period t, all workers in location i draw new blueprints from Pareto distribution with support [1, ∞). Specifically, units of blueprints are drawn from 1 − z−ϱ and its average isϱ
ϱ−1 . Intuitively, all workers of Lit in location i including both incumbent and movers have new ideas
ϱ

relative to the incumbent ideas, and they acquire the average size of innovating ideas zNew
= ϱ −1 .
itIncumbent workers of (1 − θt ) Lit−1 can update their ideas or keep their obsolete ideas. To
update their ideas, they need to meet workers who draw new ideas and their matching function is
given by:P ((1 − θt ) Lit−1 , Lit ) = eit ((1 − θt ) Lit−1 )ϖ1 ( Lit )ϖ2 ,(D.16)
where eit controls matching efficiency and parameters are ϖ1 ∈ (0, 1) and ϖ2 ∈ (0, 1) as in standard
matching function. Then, the share of incumbent workers who update their blueprints is:
sNew
=
it

P ((1 − θt ) Lit−1 , Lit )= eit ((1 − θt ) Lit−1 )ϖ1 −1 ( Lit )ϖ2(1 − θt ) Lit−1

Then, the average units of blueprints per incumbent worker become:
ϕit = sNew
zNew
+ (1 − sNew
)zOld
it
it
it
it−1 = 1 +eit((1 − θt ) Lit−1 )ϖ1 −1 ( Lit )ϖ2
ϱ−1

Plugging this into (D.15) and setting δA = 1, we obtain productivity in location i:
Ait =

eit
((1 − θt ) Lit−1 )ϖ1 −1 ( Lit )ϖ2 +χ Āt−1
ϱ−1(D.17)

Productivity depends on matching efficiency (eit ), the number of incumbent workers who have
blueprints for innovation, a mass of workers in period t and the technology frontier in the previous period ( Āt−1 ). In particular, this is decreasing in the number of incumbent workers since they
are imperfectly updating their obsolete blueprints and more incumbent workers lead to a small shareof updating their blueprints. In contrast, this is increasing in the current number of workers sincemore workers lead to a large number of matching for updating blueprints of incumbent workers
and directly increase productivity through scale effects. Lastly, matching efficiency can absorb any
characteristics in location i. Among them, it is natural to assume that a small area is associated withhigher matching efficiency. Therefore, we can write the right-hand side of (D.17) as a function of
employment density.

A 23

D.6 Microfoundation of amenity spillovers
We consider local investment in housing. In each location there are homogeneous developers or
absentee landlords and each of them develops local amenities including housing or general amenities
for residents. In location n, they solve:max

cnt ,cnt+1 ,Xnt+1 ,Hnt+1v(cnt ) + ρv(cnt+1 )subject to
Xnt+1 1−η
Hnt+1 ≤,1−ηQHccnt + nt+1 + O( Xnt+1 , Hnt ) Hnt ≤ nt+1 nt+1
1 + r t +1
1 + r t +1SnHnt δH 

(1 − ς n ) Hntηη η ∈ (0, 1)

Developers consume numéraire and v(·) is a CRRA utility function. The stock of floor spaces forresidents at period t is Hnt . The developers live for two periods and choose consumption (cnt , cnt+1 )and investment in the first period (Xnt+1 ). We assume that the housing market is competitive so thatdevelopers take the housing price Qnt+1 as given.²⁸ In the budget constraint investing Xnt+1 unitsof numéraire requires adjustment costs O( Xnt+1 , Hnt ) per unit of the current stock of housing.
Specifically, we posit the function for the investment and adjustment costs:
Xnt+1 ψO( Xnt+1 , Hnt ) =,(D.18)
ψHnt
where we assume that ψ > 1 so that the investment costs are convex function of investment. This isa traditional functional form of investment costs in macroeconomics (see, for example Baxter andCrucini 1993). The production technology of floor space exhibits decreasing returns to investment.
Housing is durable with depreciation rate ς n and more housing stocks in the period t (Hnt ) save therequired investment to provide a given amount of housing units in period t + 1. The additional term
(Sn /Hnt )δH reflects the idea that available land measured by the land endowment per residential
floor space may affect the housing production cost. In particular, δH > 0 may hold if more available
land reduces the development cost.²⁹
We suppose that (1 + rt+1 )ρ = 1 and consumption is constant over time. First order conditions
for the problem imply:
1
ψHnt 1−ψ Xnt+1
Qnt+1 =
(D.19)
ρ(1 − η ) Xnt+1
Hnt+1²⁸Perfect competition in the housing market seems a reasonable assumption because there were many small developers in Hiroshima city after WW2. For example, the 1948 Statistical Abstract of Hiroshima City documents that there
were 1057 establishments classified as “construction industry” and the average number of workers per establishment
was about 9.
²⁹A several mechanisms can rationalize δH > 0. First, more land availability may imply lower land prices fordevelopers due to a larger amount of land supply. Second, the availability of a large land plot may facilitate a largescale development project through reduced transaction costs (Yamasaki et al. 2022).

A 24

Manipulating this, we obtain:
Qnt+1 = k̄ nSnHntδH ψ̃

( Hnt )1−ψ̃ ( Hnt+1 )ψ̃(1−ψ(1−η )) ,(D.20)

where k̄ n is constant and we define ψ̃ ≡ ψ/(1 − η ) > 1.
We suppose that each household requires one unit of floor space: therefore in equilibrium,
Hnt+1 = Rnt+1 and Hnt = Rnt . Using them, we can express the value of amenities in n atperiod t + 1 by:(1−ψ̃)+ψ̃(1−ψ(1−η ))Qnt+1 = k̄ n Sn



Rnt
Sn

(1−ψ̃)−δH ψ̃ 

Rnt+1
Sn

ψ̃(1−ψ(1−η )).

(D.21)

If the share of input in development (1 − η) is relatively small, the supply of residential amenities isinelastic and the price (Qnt+1 ) is increasing with population density in period t + 1 due to congestionin the housing market. In contrast, if δH is sufficiently small, the price is decreasing in population
density in period t. Intuitively, the large stock of housing in period t leads to a lower marginal costof investment in period t + 1. This turns out to be the positive spillover effects of current population
density (Rnt /Sn ) on the benefits from the local amenities. When we relate this microfoundation to
our representation in amenities and calibration results, this property is consistent with the positivecoefficient, β 2 > 0. In contrast, our estimation of β 1 > 0 suggests that housing and amenity supply
is likely relatively elastic.

E Calibration Appendix
We follow multiple steps to estimate structural parameters in the model. This section provides
details for Section 5 in the main text.
E.1

Step # 1: Travel mode choice and gravity equation for commuting

Travel mode choice (κint ) To estimate the commuting cost, we follow Tsivanidis (2022) by extending the model to incorporate multiple travel modes. Suppose that the bilateral travel cost ism ≡ exp( cm ) with (an inverse of) mode-specific travel cost:
κint
int
m
m
m
m
−cint
+1 ≡ − δτint+1 + γ + sint+1 ( ω ),mwhere τint
+1 is the travel time in minutes between i and n in period t + 1, δ captures the marginalincrease in travel cost when the travel time increases by one minute, γm is the mode-specific fixedmcost such as transfers and parking, and sint
+1 ( ω ) is an unobserved idiosyncratic shock to the commuting cost by the mode m between i and n. Workers choose the transit mode m to minimize themcommuting cost (i.e, maximize −cint
+1 ).

A 25

m
Assume that sint
+1 ( ω ) follows the Gumbel distribution with two nests: the nest of public modes
Bpub ≡ {Walk, Bus, Train} and the nest of private modes Bpri ≡ {Bike, Car}. The former nest
does not require owning a private vehicle while the latter does. Using the well-known log-sum
formula (Train 2009), we can write the expected commuting cost as


m
m
pub
pri
−(δτintk+1 − γ ) /νk
c̄car
=
−
ln
exp
(−
c̄
)
+
(−
c̄
exp
)
, c̄int+1 ≡ − νk ln ∑ e
int+1
int+1
int+1
m∈Bk

where νk is the dissimilarity parameter of nest k ∈ [pub, pri]. We use the microdata of the 1987
travel survey of Hiroshima to estimate (δ, γm , νpub , νpri ) in this nested logit model by the maximum
likelihood estimator. We obtain δ = 0.019 with standard error 0.002. We also estimate that νpub =0.129 with standard error 0.014 and νpri = 0.117 with standard error 0.013, implying the strong
substitution within each nest since both estimates are far from 1.
m ) = c̄ , which we use as the log bilateral travel cost ln κThen, we have E (ln κint
int
int in Section 4.
We suppose that with probability pcar , a worker can choose a car as a commuting mode. Otherwise,a car is unavailable so that the private nest is modified as Bpri,nocar ≡ {Bike}. We set pcar based on
the car ownership rate in Japan: 0.1 in 1950, 0.2 in 1955, 0.3 in 1960, 0.4 in 1965, 0.5 in 1970, and
0.7 in 1975. Note that we have implicitly assumed pcar = 1 in estimating the nested logit modelusing the 1987 travel survey data given the very high car ownership rate in 1987. Then, the expected
nocar
nocar
commuting cost is c̄int = pcar c̄car
int+1 + (1 − pcar ) c̄int+1 , where c̄int+1 is defined in the same was as
pri

c̄car
int+1 , except that the summation in c̄int+1 is over Bpri,nocar because car is unavailable.
Gravity of commuting (ρ/σ) In the steady state, the number of commuters from n to i becomes:
ρ/σLin = λin M =

ūin

ρ/σ

∑d ūdM

where ūin is ex-ante average utility for the location pair (i, n). Taking the logarithm of this,ρln Lin = (ln Bn + ln wi − ln κ̄in ) + ln M̄
(E.1)
σ
ρ/σ

where ln M̄ ≡ ln M − ln ∑d ūd

and

m,ω
m,ω
− ln κ̄in ≡ E [max − ln κin] = E [max −cin
] = −c̄inmmThis corresponds to the gravity equation (13) in the main text.
Table E.1 presents the results of the estimation of the gravity equation for commuting. Columns
1 and 2 provide OLS results. In Columns 3 and 4, we use OLS but we add 1 to commuting flow (Lin )so that we do not lose observations with zero commuting flows. We use the PPML for Columns 5
and 6. In each case, we also report a version of dropping the bilateral pair of less than 20 commuters
to assess the robustness to sampling noises. Our preferred specification is Column 5 that possesses
the theoretically desirable properties of the PPML (Santos Silva and Tenreyro 2006) and we set
ρ/σ = 8 in our calibration.

A 26

Table E.1: Gravity estimates for commuting
(1)
(2)
(3)
(4)
Log Commuting Flow log (Commuting Flow + 1)
Average commuting cost (c̄in )-4.082-3.976-5.758-3.931(0.156)(0.170)(0.179)(0.169)Estimation
OLS
OLS
Number of observations
2,473
1,635
4,356
1,635
More than 20 commuters✓✓
R-squared or Pseudo R-squared 0.543
0.522
0.551
0.521

(5)
(6)
Commuting Flow
-8.019 -7.031(0.195) (0.215)
PPML
4,290
1,635
✓
0.764
0.729

Note: We report estiamtes of gravity equation (13) for commuting by OLS in Columns 1 and 2. In Columns 3 and 4,
we use OLS but with adding 1 to commuting flows so that we do not drop observations with zero commuting flows.
We use the PPML in Columns 5 and 6. We use average commuting costs that we computed in mode choice and include
origin and destination fixed effects. Note that Column 5 has slightly fewer observations than Column 3 because ofcomputational issues in PPML (Correia et al. 2020). Standard errors in parentheses.

E.2

Step # 2: Back out continuation value of productivity and amenities

Our focus in this step is to back out the continuation value of amenities (14) and productivity (15).
eint )ρ/σ . Then, (D.9) and
The probability of location choices (D.8) becomes: λint = λot exp(V(D.10) can be expressed by:
!
ρ/σ
eint
Rnt − (1 − θt ) Rnt−1 = λot θt ∑ exp V
M
(E.2)
i

Lit − (1 − θt ) Lit−1 = λot θt∑ exp Veint

ρ/σ

!

M

(E.3)

n

for all locations (i, n) in a city and periods t = 1, 2, · · · . We also use the following notations forthe values of outside options and commuting costs:"T

vt = uot"∏ (uoτ )−ρτ −t∏τs=t+1 (1−θs )τ = t +1

Kint = κintT∏

τ = t +1−ρτ −t ∏τs=t+1 (1−θs )
κinτ

#−ρ/σ
,

#−ρ/σ

Then, (E.2) and (E.3) become:ρ/σRnt − (1 − θt ) Rnt−1 = λot θt vt MΞntρ/σLit − (1 − θt ) Lit−1 = λot θt vt MΩitρ/σ

∑ Kint Ωit ,

(E.4)

i ∈C

ρ/σ

∑ Kint Ξnt .

(E.5)

n∈C

for periods t = 1, 2, · · · . Intuitively, population increases in period t if the location exhibits highoption value of amenities (Ξnt ) and high commuting market access taking into account for the future

A 27

value of workplaces. Substituting (E.5) into (E.4) yields the system of equations (16) in the maintext. Solving the system conditional on observations of population and employment { Rnt , Lit } andparameter {θt }, we obtain {Ξnt , Ωit }. Given ρ/σ > 0, this system of equations is solved for uniquesolutions {Ξnt , Ωit } up to scale if Lit − (1 − θt ) Lit−1 ≥ 0 and Rnt − (1 − θt ) Rnt−1 ≥ 0 hold.
This step does not require the parameter values of agglomeration.
E.3

Step # 3: Estimation of parameters (α1 , α2 , β 1 , β 2 )Step 2 derives {Ξnt , Ωit } consistent with observed data to be an equilibrium. By construction, in
the last period T RnT β1 RnT −1 β2ΞnT = bnT
(E.6)
Sn
Sn
Given the observation of population { RnT , RnT −1 }, block size Sn and parameters (α1 , α2 , β 1 , β 2 ),we can invert this for fundamental amenities {bnT } in period T.
In period T − 1 we have: 
RnT −1 β1 RnT −2 β2 ρ(1−θT )ΞnT −1 = bnT −1
ΞnT
(E.7)
Sn
Sn
Given population density in period T − 1 and T − 2, parameter ρ, migration friction θ T and option
value {ΞnT }, we can invert this for the fundamental amenities in the previous period {bnT −1 }.
We continue this process and obtain the sequence of fundamental amenities: {bnt }t=1,··· ,T . For the
productivity, we can decompose {Ωit }t=1,2,··· ,T to obtain the sequence of fundamental productivity{ ait }t=1,··· ,T in analogous way.
The fundamental amenities and productivity { ait , bnt }t=1,··· ,T are uniquely given. These fundamentals are structural residuals in our calibration for the observation to be equilibrium. We assume that the fundamentals consist of location fixed components, time fixed components and variant
terms:
ln ait = ln aiF + ln a∗t + ln aVarit ,Varln bnt = ln bnF + ln bt∗ + ln bnt(E.8)

where ({ aiF }, {bnF }) are location fixed productivity and amenities, ({ a∗t }, {bt∗ }) are trend of proVar
ductivity and amenities and ({ aVarit }, { bnt }) are stochastic part of fundamental productivity andamenities. The location fixed productivity and amenities capture the first nature advantages of locations and trend of productivity and amenities reflect the change in levels over time.
Averaging out the trend yields:
ln ãit ≡ ln ait −1ln ait = ln ãiF + ln ãVar
it ,
N∑
i

ln b̃nt ≡ ln bnt −1
Varln bnt = ln b̃nF + ln b̃nt
,
N∑
n
A 28

Var
Var and b̃Var ≡ bVar / b̄Var are variables adjusted
where ãiF ≡ aiF / ā F , b̃nF ≡ bnF /b̄ F , ãVarntnttit ≡ ait / ātwith geometric mean. Then, taking the difference between periods and we suppose the following
moment conditions:E [∆ ln ãit × 1i (k )] = 0,E ∆ ln b̃nt × 1 n (k ) = 0,

(E.9)

Var
where ∆ ln ãit = ∆ ln ãVar
it and ∆ ln b̃nt = ∆ ln b̃nt are change in the idiosyncratic shocks in productivity and amenities between period t − 1 and t and 1 n (k ) is an indicator such that location n isin the grid k. The grid is defined based on the distance from CBD as in Ahlfeldt et al. (2015). Our
identification assumption is that any improvements or declines in the stochastic shocks of productivity and amenities over any six years period are unrelated to the distance from the city center. We
use the moment conditions (E.9) to estimate the set of parameters of agglomeration economies (α1 ,α2 , β 1 , β 2 ).

E.4

Calibrated amenities and productivity

In this section we present additional discussions on the amenities and productivity in our calibration.
Figure E.1 presents the estimated location-specific amenities and productivity. We adjust for theblock size since the fundamental amenities and productivity tend to be mechanically undervalued
for a smaller block (see Train 2009). Intuitively, other things being equal, a smaller block is likely tohave a higher population and employment density given the idiosyncratic preferences irrespectiveof the block size. Thus, the location-specific productivity and amenities may be undervalued insmaller blocks to offset such a small-block advantage. To adjust for this, we regress our estimate of
the log of the location-specific productivity and amenities on the log of area size, and we plot theresiduals from the regressions. Figure E.1a and E.1b shows the result for amenities and productivity,
respectively. Both are not strongly related to the distance from the CBD and if any, amenities andproductivity are relatively lower in areas closer to the CBD. We also find noisy estimated values forthe edge of the city.
Figure E.2 displays the changes in residuals of fundamental amenities (∆ ln b̃nt ) and productivity (∆ ln ãit ) for different periods, 1955-60 and 1965-70. During the early period, the changes
exhibit small variations across locations in the city and this confirms that the idiosyncratic part of
the fundamental location advantages in amenities is less important to explain the population changes
during this period. In the later period, 1965-70, we observe some increase of the residuals in thearea close to CBD while dropping in the periphery. This is consistent with the suburbanization thatproceeds not because of the fundamental locational advantages in the periphery but the expectationof moving toward the periphery. For residuals of productivity, their variation is relatively small
in the city for both periods. This implies that idiosyncratic shocks in fundamental productivity do
not account for the variation of employment distribution in the city and this is reassuring for ouridentification assumption.

A 29

Log value of fundamental productivity
adjusted with size

Log value of fundamental amenities
adjusted with area size

Figure E.1: Fundamental productivity and amenities (accounting for block size heterogeneity)

.2
.1
0
-.1
-.2
0

2
4
Distance to CBD (kilometers)
1955

1965

1975

.2
.1
0
-.1
-.2

6

0

Average between 1955-75

2
4
Distance to CBD (kilometers)
1955(a) Amenity

1965

1975

6

Average between 1955-75(b) Productivity

Note: These figures display fundamental productivity (āi ) and amenities (b̄n ) in our calibration, after netting out theblock size using the residual of the linear regression of the fundamentals on the block size. Each line shows a local
polynomial fitted line.

Figure E.2: Changes in fundamental amenities and productivity for different periods
Change in log of residual productivity

Change in log of residual amenities

.4

.2

0

-.2

-.4

0

2
4
Distance to CBD (kilometers)
1955-60

6

1965-70

.4

.2

0

-.2

-.4

0

2
4
Distance to CBD (kilometers)
1955-60(a) Change in fundamental amenities

6

1965-70(b) Change in fundamental productivity

Note: These figures show changes in fundamental amenities (∆ ln b̃nt ) and productivity (∆ ln ãit ) for two periods, 195560 and 1965-70. Each point represents different blocks and lines are local polynomial regressions.

E.5

Simulating population and employment density for 1945–1950.

Having estimated model parameters (α1 , α2 , β 1 , β 2 ) by exploiting the data from 1950 to 1975, we
can evaluate how much the model explains the population and employment change from 1945 to1950 after the atomic bombing. We compare the distribution of population and employment between
observations and simulated ones in 1950 when we abstract the structural errors. In particular, we
solve the system of equations:

A 30

Rn,50 = (1 − θ50 ) Rn,45 + ∑M
Kin,50 Ξn,50

ρ/σ

Li,50 − (1 − θ50 ) Li,45

M ρ/σ



∑ j Kij,50 Ξ j,50M ρ/σKin,50 Ωi,50
Li,50 = (1 − θ50 ) Li,45 + ∑Rn,50 − (1 − θ50 ) Rn,45 .
ρ/σn ∑ j K jn,50 Ω Mj,50i(E.10)

where we use Rn,50 β1 Rn,45 β2 ρ(1−θ55 )
,
Ξn,55
Sn
Sn

 

Li,50 α1 Li,45 α2 ρ(1−θ55 )MΩi,50 ≡ āi
Ωi,55
Si
Si

M
Ξn,50
≡ b̄n

(E.11)

on the right-hand side. They are constructed in the same way as equations (14) and (15), except that(ait , bnt ) are replaced by the average amenities and productivity over 1955-75 (āi , b̄n ), which are ourestimates of the block-specific amenities and productivity (aiF , bnF ) in equations (E.8). Importantly,
Varusing (āi , b̄n ) eliminates the idiosyncratic structural errors in amenities and productivity aVar
it , bit .³⁰
Since the structural errors in our model makes our model to perfectly match the observed populationand employment distribution, we can compare the importance of endogenous forces of the model andstructural errors in predicting the recovery by comparing the observed population adn employment
distribution and its prediction from equations (E.10) and (E.11).
We can similarly obtain the model prediction when there are no agglomeration economies by
setting α1 = α2 = β 1 = β 2 = 0 in equation (E.11). The comparison of model predictions withand without agglomeration economies indicates their importance in accounting for the recovery ofcentral Hiroshima.

F

When Individuals Expect No Recovery

We explain the details of the version of our model where workers do not have expectations forrecovery analyzed in Section 6 of the main text. At the end of period t = 0, 1, · · · , an individual ωsolves the problem (19) to choose their location for t + 1, where the idiosyncratic shocks have thesame distribution as in the baseline.
In particular, when individuals believe that the current state continues for the future, the option³⁰The year-fixed amenities and productivity (ā∗t , b̄t∗ ) in (E.8) are also excluded from (E.11), but this does not affectthe model prediction because they appear both in the denominator and the numerator of (E.10).

A 31

value of amenities (14) and productivity (15) for period t are changed to:! Tτ −t τ
T
Rnt−1 β2
Rnt−1 β1 +( β1 + β2 ) ∑τ=t+1 ρ ∏s=t+1 (1−θs )∗Ξnt ≡ ∏ bnτ ×
×
,
Sn
Sn
τ =t
! 
T
τ −t τ
T
Lit−1 α2
Lit−1 α1 +(α1 +α2 ) ∑τ=t+1 ρ ∏s=t+1 (1−θs )∗Ωit ≡ ∏ aiτ ×
×
Si
Si
τ =t

(F.1)

for periods t = 1, · · · . The important difference from our forward-looking model is that on theright-hand side, we replace a sequence of future population and employment with the current level.
In particular, when individuals make migration decisions for t = 1 at the end of period t = 0
after the shock, we suppose that individuals have no expectation for recovery and believe that the
population and employment distribution after the shock continues. Therefore, we substitute thepopulation and employment in the period in 1945, (Rn0 , Li0 ), into (Rnt−1 , Lit−1 ) in the right-handside of (F.1).
Using them, dynamics of population and employment are represented by:R∗nt − (1 − θt ) R∗nt−1 = λ∗ot θt v∗t MΞ∗nt ρ/σ ∑ Kint Ωit∗ ρ/σ ,i ∈CLit∗ − (1 − θt ) Lit∗ −1 = λ∗ot θt v∗t MΩit∗ ρ/σ∑ Kint Ξ∗nt ρ/σ ,

(F.2)

n∈C

where the utility of the outside of a city is adjusted such that the total population in a city is identicalto the observed data. The equilibrium is characterized by the following when we apply this to ourcontext. Given the initial employment and population { Li,45 , Rn,45 }, exogenous population in thelarge economy M, migration opportunities {θt }50,55,··· ,75 , fundamentals { ait , bnt }50,55,··· ,75 , valueof living outside of the city {u∗ot }50,55,··· ,75 and parameters (α1 , α2 , β 1 , β 2 , ρ/σ), (F.2) determine
the employment and population over time { Lit , Rnt }50,55,··· ,75 .
Manipulating the equilibrium conditions yields:
R∗nt − (1 − θt ) R∗nt−1 = ∑Kint Ξ∗nt ρ/σ( Lit∗ − (1 − θt ) Lit∗ −1 ),ρ/σ∗i ∈C ∑ℓ∈C Ki ℓt ΞℓtKint Ωit∗ ρ/σLit∗ − (1 − θt ) Lit∗ −1 =( R∗nt − (1 − θt ) R∗nt−1 ).
ρ/σ∗n∈C ∑ j∈C K jnt Ω jt

(F.3)

∑

Given predetermined employment and population and exogenous fundamentals, we can solve the2N equations in (F.3) for the unique solution.

References for the Appendix
Ahlfeldt, Gabriel M, Stephen J Redding, Daniel M Sturm, and Nikolaus Wolf, “The economics
of density: Evidence from the Berlin Wall,” Econometrica, 2015, 83 (6), 2127–2189.

A 32

Allen, Treb, Costas Arkolakis, and Xiangliang Li, “On the equilibrium properties of networkmodels with heterogeneous agents,” Technical Report, National Bureau of Economic Research
2020.
Baxter, Marianne and Mario J Crucini, “Explaining saving–investment correlations,” The American Economic Review, 1993, pp. 416–436.
Brakman, Steven, Harry Garretsen, and Marc Schramm, “The strategic bombing of German
cities during World War II and its impact on city growth,” Journal of Economic Geography, 2004,
4 (2), 201–218.
Correia, Sergio, Paulo Guimarães, and Tom Zylkin, “Fast Poisson estimation with highdimensional fixed effects,” The Stata Journal, 2020, 20 (1), 95–115.
Davis, Donald R and David E Weinstein, “Bones, bombs, and break points: the geography of
economic activity,” American Economic Review, 2002, 92 (5), 1269–1289.
Hiroshima City Government, “Hiroshima Genbaku Sensai-Shi (The Hiroshima Atomic Bombing
Damage Records),” 1971. (In Japanese).
Nagasaki City Government, “Nagasaki Genbaku Sensai-Shi Dai 5-kan Shiryouhen (The Nagasaki
Atomic Bombing Damage Records: Volume 5 Data),” 1983. (In Japanese).
Santos Silva, J.M.C. and Silvana Tenreyro, “The log of gravity,” The Review of Economics andStatistics, 2006, 88 (4), 641–658.
Takeda, Kohei and Atsushi Yamagishi, “History versus Expectations in the Spatial Economy:
Lessons from Hiroshima,” Mimeo, 2023.
Takezaki, Yoshihiko and Ryoji Soda, Hiroshima Genbaku Dezitaru Atorasu (The Digital Atlas of
Atomic Bombing in Hiroshima), Research center for regional geography, Hiroshima University,
2001. (In Japanese).
Train, Kenneth E, Discrete choice methods with simulation, Cambridge university press, 2009.
Tsivanidis, Nick, “Evaluating the impact of urban transit infrastructure: Evidence from bogota’stransmilenio,” mimeo, 2022.
Yamagishi, Atsushi and Yasuhiro Sato, “Persistent Stigma in Space: 100 Years of Japan’s Invisible Race and Their Neighborhoods,” mimeo, 2023.
Yamasaki, Junichi, Kentaro Nakajima, and Kensuke Teshima, “From samurai to skyscrapers:
How historical lot fragmentation shapes Tokyo,” mimeo, 2022.

A 33