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

Atsushi Yamagishi
Princeton

July 11, 2023

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Introduction

City structure often (but not always) exhibits remarkable resilience after adevastating shock
Rebuilding of destroyed areas after wars and natural disasters.

What drives the resilience of city structure?
Important for considering future rebuilding events (e.g., Ukraine)
More broadly, suggestive of the effects of place-based policies on cities.

To answer this, we analyze the atomic bombing of Hiroshima with newdata and a new model.

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Our paper
We analyze the atomic bombing of Hiroshima to investigate the resilienceof city structure and its underlying mechanisms
We newly digitize granular historical data on population, employment,
and locational characteristics within Hiroshima city.
Strong resilience: totally destroyed city center recovered in population
density just five years after the bombing.
Moreover, it is not the case that the city center could recover because it hadvery favorable locational characteristics (natural conditions, transportation
acccess etc).

To further understand the mechanisms behind the recovery, we develop andcalibrate a novel dynamic urban model.
Strong agglomeration forces and expectations in the recovery are
essential for the rebuilding of central Hiroshima.

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Literature
History (in)dependence in the spatial economy: Davis and Weinstein(2002, 2008); Bosker et al. (2007); Miguel and Roland (2011); Redding et al.
(2011); Bleakley and Lin (2012); Schumann (2014); Siodla (2015); Hornbeck and
Keniston (2017); Michaels and Rauch (2018); Brooks and Lutz (2019); Ahlfeldt etal. (2020); Heblich et al. (2021); Yamasaki et al. (2021); Allen and Donaldson(2022); Yamagishi and Sato (2022)
Fundamental locational characteristics shaping city structure: Alonso (1964);
Muth (1967); Mills (1969); Fujita (1989); Anas et al. (1998); Glaeser and Kahn
(2004); Saiz (2010); Lee and Lin (2018); Harari (2020)
Expectations in the spatial economy: Krugman (1991); Matsuyama (1991);
Fukao and Bénabou (1993); Ottaviano (2001); Baldwin (2001); Oyama (2009);
Barreda-Tarrazona et al. (2021)
Quantitative dynamic spatial economics models: Desmet et al. (2018); Caliendo
et al. (2019); Barboni (2021); Heblich et al. (2021); Kleinman et al. (2022); Allenand Donaldson (2022).
Studies on the recovery of Hiroshima: Hiroshima City Government (1971; 1983).
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1. Background
2. Descriptive and reduced-form evidence
3. Model4. Quantification
5. The role of agglomeration economies
6. The role of expectations in the recovery
7. Conclusion

Atomic bombing in Hiroshima

We analyze the atomic bombing of Hiroshima.
Mainly focus on Hiroshima due to data availability and city size, but we alsopresent similar reduce-form results for Nagasaki.

Since the construction of the Hiroshima castle in the Samurai era, Hiroshima
has been a major city in Japan.
Population around 1940 was about 400,000.

The atomic bomb (known as ”Little Boy”) was dropped by US Army Air
Forces on August 6, 1945, close to Hiroshima’s city center.
Soon after the bombing, radioactive contamination became not severe as it
mitigated rapidly
Especially after a large typhoon in September 1945 that washed away
contaminated substances.

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Atomic bombing in Hiroshima as a shock to city structure

Catastrophic damage, especially near the city center.
The death rate was near 100% for those within 1km from the epicenter.
Almost all buildings within 2km from the epicenter were totally destroyed.

But city outskirts avoided the severest destruction, and even experienced
population increase.
On November 1, 1945, areas more than 3km away from the epicenter had
142% of the pre-bombing population.
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1. Background
2. Descriptive and reduced-form evidence
3. Model4. Quantification
5. The role of agglomeration economies
6. The role of expectations in the recovery
7. Conclusion

Data
The unit of analysis is the “block” (cho cho moku). We use 174 blocks in
Hiroshima city.
Average block size is 0.32km2
Blocks tend to be larger as we move away from the CBD.

We have collected and digitized a variety of historical sources on
Hiroshima, beginning in the 1930s. Data sources
Fraction of destroyed buildings by atomic bombing in each block
Population in each block from 1933 to 1975
Employment and establishment from 1938 to 1975
Commuting pattern
Proxies of fundamental locational amenities and productivity
Other Geographical Information System (GIS) data
Population and employment over time

We focus on the administrative Hiroshima city as of the bombing (1945)
throughout our analysis.
Approximately equals the metropolitan area of Hiroshima in the pre-war period.
7 / 26

Dynamics of population density
Log Population Density (per square km)

9

8

7

6

5
0

2

4

Distance to CBD (km)

6

1936

Note: The figure shows the non-parametric regression of the log of population density on the distance to the
CBD using the block-level data for different years.

The monocentric city structure in the pre-war period.
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Dynamics of population density
Log Population Density (per square km)

9

8

7

6

5
0

2

4

Distance to CBD (km)
1936

6

1945

Note: The figure shows the non-parametric regression of the log of population density on the distance to the
CBD using the block-level data for different years.

The monocentric city structure was reversed in 1945.
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Dynamics of population density
Log Population Density (per square km)

9

8

7

6

5
0

2

4

6

Distance to CBD (km)

1936

1945

1950

Note: The figure shows the non-parametric regression of the log of population density on the distance to the
CBD using the block-level data for different years.

The monocentric city structure recovered already in 1950.

Considering pre-war trend

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Reduced-form evidence
We estimate the following reduced-form model analogous to Davis andWeinstein (2002):()()
Popdensi,1945
Popdensi,t= γ × ln
+ ηXi + vi ,ln
Popdensi,1945
Popdensi,1936
Descriptive regression of the post-war population growth rate on thedestruction rate of the population.
γ describes how the shock is persistent in the data.
γ = 0 suggests no recovery:ln Popdensi,t = ln Popdensi,1945 + ηXi + vi ,γ = −1 suggests complete recovery:ln Popdensi,t = ln Popdensi,1936 + ηXi + vi

Xi is the locational characteristics of block i, such as natural conditions andtransportation access
If fundamentals explain the post-war population growth (i.e., the recovery),then controlling for them would drive γ closer to zero. List of controls
11 / 26

Change in log population density, 1945-50

Reduced-form evidence
5
4
3
2
1
0
-1
-4

-3

-2

-1

0

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

Slope of -1

γ is far from 0 but close to -1 (strong recovery).
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Reduced-form evidence

Change in log population density 1936-1945
p-value from testing γ = −1
Control variables
Within 3 km from the city center
Number of blocks
R-squared

(1)
(2)
(3)
Change in log population density
1945 - 1950

(4)
(5)
(6)
Change in log population density
1945 - 1960

-0.712(0.026)0.000-0.931(0.100)0.499✓-0.688(0.030)0.000-0.929(0.101)
0.492
✓

174
0.809

174
0.862

174
0.772

174
0.854

-0.979(0.097)
0.835
✓
✓
158
0.880

-1.007(0.117)
0.949
✓
✓
158
0.862

Controlling for locational characteristics, we cannot reject γ = −1 (complete
recovery) List of controls
Therefore, it is unlikely that the city center could recover because it isinnately an attractive place
γ = −1 even by focusing on smaller homogeneous areas (within 3km from the
CBD)
Other robustness checks lead to similar conclusion Further robustness on reduced-form analysis
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When the bomb hit the outskirts: 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

The bomb hit an outskirt of Nagasaki, while it hit the city center in Hiroshima
But we obtain γ = −1 (complete recovery) also for Nagasaki.
Recovery despite lacking potential locational advantages of pre-war city center
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Summary of the reduced-form findings

Extremely large shock on city structure – the city had a monocentric city
structure but the atomic bombing reversed the pattern.
The center became the least populated place.

However, strong resilience: the city center recovered just in five years
Moreover, we find little evidence that the fundamental locational
advantages of the city center explain the recovery
People chose to live in the city center again not because it was innately agood place

To further explore the mechanisms behind the recovery, we now take astructural approach

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1. Background
2. Descriptive and reduced-form evidence
3. Model4. Quantification
5. The role of agglomeration economies
6. The role of expectations in the recovery
7. Conclusion

Overview of our structural analysis
We first construct a novel dynamic quantitative urban model, which cancaptureHeterogeneity in locational characteristics
Initial distribution of population and employment (history)
Expectations in the future city structure

We calibrate it to the post-recovery data (1950–1975)
Due to data unavailability, we could not use the pre-war period data forcalibration

Show that the calibrated model can well explain the data of therecovery period (1945–1950).
Through counterfactual analyses, we highlight that agglomeration
economies and expectations in the recovery are they key for therebuilding of central Hiroshima.

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Model overview

A first quantitative urban model with all of the following key features:
1. Commuting: Workplace and residence can be different.
2. Forward-looking migration decisions: Workers solve the dynamic problem of
workplace and residence choice.
3. History dependence in migration frictions and history-dependent fundamentals.

At the same time, the model is parsimonious in many aspects due to therelatively limited data availability in Hiroshima around the atomic bombing.

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Model overview

Details of the model

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1. Background
2. Descriptive and reduced-form evidence
3. Model4. Quantification
5. The role of agglomeration economies
6. The role of expectations in the recovery
7. Conclusion

Overview of model quantification
The quantification of the model proceeds in steps:
1. Calibrating parameters κint , ρ, σ, θt , uot .

Details

2. From the observed flow of population and employment, back out the“attractiveness” of each block as residence and workplace. Details
3. Estimate the amenity and productivity spillovers (α1 , α2 , β1 , β2 ) by GMM.
Details

Identification assumption: changes in amenities and productivity of each block
over time are best explained by the model, not by structural errors.
Net positive agglomeration forces: (α1 , α2 , β1 , β2 ) = (0.24, -0.07, 0.20, 0.02)

Remark:For estimation, we use population and employment data 1950–1975 with the
5-years interval.
We then examine how much the model can explain the 1945-1950 data, whichreflects the response to the historical shock. This period is not used for
estimation.

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Model fit: Accounting for the recovery period 1945–1950.

How well does our model explain the recovery of central Hiroshima in
1945–1950?
We assess how well our model can explain the recovery without structural
errors of the model.
Assumptions:
The spillover parameters (β1 , β2 ), the block-fixed amenities b̄n , and composite
amenities in 1955 Ξn,55 are the same as our calibration from 1955-1975.
Higher mobility right after the war (θ1950 = 0.9).
At 1945, people evaluate the amenities of each location while anticipating thatthe 1950 population distribution observed in data would realize

The employment distribution is simulated under analogous assumptions on
productivity.

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Model fit: Accounting for the recovery period 1945–1950.

12
10
8
6
4
2

0

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

Population density

6
1950 (data)
1950 (data)

Log employment density (per square km)

Log population density (per square km)

Our calibrated model successfully predicts the rebuilding during
1945–1950. Method
12
10
8
6
4
2

0

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

6
1950 (data)
1950 (data)

Employment density

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1. Background
2. Descriptive and reduced-form evidence
3. Model4. Quantification
5. The role of agglomeration economies
6. The role of expectations in the recovery
7. Conclusion

The role of agglomeration economies
When shutting down the agglomeration forces (positive spillovers of populationand employment density), the model fails to predict the recovery of the city center
Method

12
10
8
6
4
2

0

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

Population density

6
1950 (data)
1950 (data)

Log employment density (per square km)

Log population density (per square km)⇒ The attractiveness of destroyed city center was coming from density,
not other locational characteristics (natural conditions, infrastructure etc.)
12
10
8
6
4
2

0

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

6
1950 (data)
1950 (data)

Employment density
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1. Background
2. Descriptive and reduced-form evidence
3. Model4. Quantification
5. The role of agglomeration economies
6. The role of expectations in the recovery
7. Conclusion

Expectations in the recovery

We have highlighted that the key incentive for living and working in the city
center is coming from agglomeration forces.
This implicitly assumes that people expect in the recovery of the city
center when choosing their workplace and residence.
To show the importance of expectations in the recovery, we contrast our
main model with the case in which people do not expect in therecovery.

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The role of expectations in the recovery

12
10
8
6
4
2

0

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

Population density

6
1950 (data)
1950 (data)

Log Employment Density (per square km)

Log Population Density (per square km)

When people do not expect the recovery of the city center, the recovery does not
happen as they avoid living and working in the city center Method⇒ People indeed chose to live and work in the center again because highdensity was expected in the near future
12
10
8
6
4
2
0

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

6
1950 (data)
1950 (data)

Employment density

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On the emergence of expectations in the recovery
What we have highlighted: expectations in the recovery are essential in
explaining the recovery of Hiroshima.
Our model and data do not allow us to investigate why the expectations in
the recovery emerged.
Potential explanations:
The presence of public recovery plan
Surviving tram system
Remaining property rights
Narratives of rebuilding
Memory of the pre-war Hiroshima

The direct impacts of these factors seem limited because of limited
importance of fundamental amenities and productivity in explaining therecovery.
However, they may have induced it indirectly through forming expectations in
the recovery.
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1. Background
2. Descriptive and reduced-form evidence
3. Model4. Quantification
5. The role of agglomeration economies
6. The role of expectations in the recovery
7. Conclusion

Conclusion
What is driving the remarkable resilience of the city structure after acatastrophic shock?
We investigate the atomic bombing of Hiroshima, with new data and a new
dynamic urban model.
The totally-destroyed central Hiroshima recovered just five years after thebombing.
The incentive to rebuild the destroyed central Hiroshima was coming fromagglomeration economies, rather than its locational advantages.
People chose to live and work in the city center again because they expected
the high density in the near future
If they had not expected the recovery, the destroyed city center would nothave recovered.

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Appendix slides

Data sources
Population (newly digitized)
1933-1936. Hiroshima-shi toukei sho
1945–1953. Hiroshima shisei youran
1955–. Population census.
Block-level population in 1945 is estimated using less granular population data
and the damage records.

Employment/Establishment (newly digitized)
1938. Hiroshima-shi shoukou gyou keiei chosa1946. Hiroshima shisei youran
1953. Hiroshima chukan jinko chosa1957-. Business establishment statistical survey
We use a less granular level in 1946 and the destruction of buildings, and the1938 distribution of establishments to estimate the block-level employment in
1945.
We use a less granular level in 1953, 1957, 1963 and the block-level data in
1966 to approximate the block-level employment 1945–1963.
Back

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Data sources
Damage by atomic bombing.
Hiroshima genbaku sensai-shi on the kill ratio and the ratio of destructedbuildings.
Takezaki and Soda (2001) provides the GIS version.

Commuting.
1987 person-trip survey. Microdata provided by the Chugoku Region
Development Bureau.

Proxies of fundamental locational amenities and productivity.
Various sources, but mainly from digital national land information (theMinistry of Land, Infrastructure, Transport and Tourism) and the Hiroshimacity government.

Maps.
As our main definition of geographic units, we use the block boundaries as of
the bombing (Takezaki and Soda 2001).
Newly-digitized commercial maps published in 1966 and 1976 to deal with the
redrawing of the block boundaries.
Back
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400
.1
300

200
.05
100

0

0
33343536

454950515253 55

Year

60

Total Number

65

70

75

Number within 1km from CBD

Share within 1km from CBD (right axis)

Population

250

.25

200

.2

150

.15

100
.1
50

Share in 1km from CBD.15

Employment in Hiroshima city (thousands)

500

Share in 1km from CBD

Population in Hiroshima city (thousands)

Population and employment over time

.05
0
38

45

53

57

Year

Total Number

63

66

75

Numbers within 1km from CBD

Share within 1km from CBD (right axis)

Employment

Back

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Dynamics of population density
Log Population Density (per square km)

9

8

7

6

5
0

2

4

6

Distance to CBD (km)

1936

1945

1950

1950(counterfactual)

Note: The figure shows the non-parametric regression of the log of population density on the distance to the
CBD using the block-level data for different years.

The case for the recovery is stronger once we account for the pre-war trendof population density.
Back
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List of controls
Natural conditions: Altitude, slope, distance to water area, soil condition,
geographical coordinates.
Human-made conditions: Distance to the nearest train station, distance tothe nearest cultural asset (bunkazai), housing stock conditions after thebombing (fraction of half-destructed, moderately-destructed, and intact
buildings).
Pre-trend + catch-all for unobserved attractiveness: Pre-war trend(1933-1936) of the population.
(Robustness) The spatial lag of (i) the population change rate 1936–1945,(ii) the spatial lag of natural conditions and human-made conditions, and (iii)
1945 population
The spatial weight matrix is set based on the spatial decay of spillovers in
Ahlfeldt et al. (2015) or a gravity model estimate based on geographicaldistance in 1987 Hiroshima Person Trip Survey Data.

(Robustness) The number of public housing units.
Back
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Further results on reduced-form results
Recovery in employment distribution. γ ≃ −0.86 ∼ −1.
Recovery in land prices. The location with the highest land price in a city is
the same before and after the war.
Timing of the recovery: the population increase of the center had alreadystarted in 1946.
The characteristics of neighboring blocks (the spatial lag of explanatory
variables in the “SLX” model).
Wartime population change rate of neighboring blocks
Locational characteristics of neighboring blocks
1945 population of neighboring blocks (proxy for market access)Public recovery policies (public housing): controlling for public housing does
not change the results. Other plans were not well implemented right after the
war due to budget shortage.
Back

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Production
Discrete blocks in a city, and continuum of individuals living for finite time up
to period T.
We assume that the last period is approximately the steady state.

Competitive firms producing homogeneous tradable goods and workers
commute between blocks subject to commuting costs.
Firms in block i in period t has the linear production technology:
yit = Ait Lit
Contemporaneous and lagged productivity spillovers with respect toemployment density (Allen and Donaldson 2022): microfoundations)α( )α 1 (Lit−1 2Lit
Ait = ait
Si
Si
Perfect competition implies the wage rate in i: wit = Ait .
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Preferences

Period utility of workers living in n and working in i in period t:
ln uint = ln Bnt + ln wit − ln κint ,where κint is the bilateral commuting cost.
Contemporaneous and lagged spillovers in amenities with respect topopulation density (Allen and Donaldson 2022): microfoundation(
Bnt = bnt

RntSn

)β 1 (

Rnt−1
Sn

)β 2

Workers also have an option to live and work outside the city that yields
exogenous utility uot .

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Migration
With probability θt+1 , people get a migration opportunity at the end of
period t to choose new workplace and residence in t + 1.
Calvo-style migration friction (Heblich et al. 2021).

Following Caliendo et al. (2019), the forward-looking migration decision ismade to solve the following:{}max ρVjℓt+1 + σεjℓt+1 ; ρVot+1 + σεot+1 ,Vjℓt+1 is the value function of living in ℓ and working in j.
ρ is the discount factor.
εjℓt+1 is the idiosyncratic preference to the workplace-residence pair following
the Gumbel distribution and σ governs its variance. Bellman equations

Agents expect all future variables, including the location choices of the otherworkers, from t + 1 in making the migration decision at the end of period t.
Workplace-residence choice probability:
λjℓt+1 = ∑exp(Vjℓt+1 )ρ/σ
ρ/σι∈{(j′ ,ℓ′ ),o} exp(Vιt+1 )35 / 26

Equilibrium
Mass of workers living in n and working in i is
Lint+1 = (1 − θt+1 )Lint + λint+1 θt+1 M,
where M is the total mass of agents in this economy including those living
outside Hiroshima.
Equilibrium conditions:
1. Value functions solve the Bellman equation.

Bellman equations

2. Commuting market clear in the city: the employment and population at eachblock are consistent with the flow equation above.
3. Workers optimally choose their workplace and residence.
4. Firms maximize their profits and zero profit condition.

We can analytically show:

Proposition

the existence of equilibrium and the steady state
the uniqueness of the steady state when the net agglomeration economies arenegative (α1 + α2 < 0 and β1 + β2 < 0)
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Microfoundations of spillovers

Spillovers for productivity
Production capital supply: Infrastructure depreciation or increased cost of
new construction (α2 < 0)
Idea creation: New ideas are less likely to be adopted when there are moreincumbents (α2 < 0).
Spillovers for amenity
Housing market: More housing stock implies lower housing cost (β2 > 0)
Back

37 / 26

Bellman equations
The expected value of living in n and working in i at time t and the expectedvalue of living and working outside Hiroshima solve the following:
Vint = ln uint + (1 − θt+1 )ρVint+1 + θt+1 µt+1
Vot = ln uot + (1 − θt+1 )ρVot+1 + θt+1 µt+1 ,
where



∑
exp(Vjℓt+1 )ρ/σ + exp(Vot+1 )ρ/σ  .
µt+1 = σ ln (j,ℓ)µt+1 is the “option value of moving,” that is, the expected utility at time t bymaking the migration decision for t + 1.
We assume VinT = ln uinT and VoT = ln uoT for values in the last period.
Back38 / 26

Characterization of the equilibria and the steady states

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 andLit ≥ (1 − θt )Lit−1 , exists. (ii) The steady-state equilibrium exists when
α1 + α2 ̸= σ/ρ and β1 + β2 ̸= σ/ρ. (iii) A suﬀicient conditions for the uniquesteady state are negative net spillovers: α1 + α2 ≤ 0 and β1 + β2 ≤ 0.
When α1 + α2 > 0 or β1 + β2 > 0, the steady states can be multiple.
We have numerically found multiple steady states under our estimates of(α1 , α2 , β1 , β2 ).
Back

39 / 26

Step 1: Calibration of parameters
We obtain the bilateral commuting cost κint by a nested logit model ofcommuting mode choice estimated by 1987 trip survey data (c.f., Tsivanidis2022). Details
Based on the commuting gravity equation at the steady state, we estimate
the commuting elasticity ρ/σ = 8. Estimation results
Close to the estimate of Dingel and Tintelnot (2022) and Ahlfeldt et al.
(2015).

We set ρ = 0.66 based on popular discount factor in developing countries(e.g., Garcia-Cicco et al. 2010).
The Calvo migration friction is set to θt = 0.53 after 1950.
Calibration is based on census data about the fraction of people changing theirresidence.

uot is matched to the total population of the city.
Our focus is the population and employment distribution within the city.
Back

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Step 2: Back out residence and workplace attractivenessThe population and employment flow and the migration probabilities imply
Rnt − (1 − θt )Rnt−1 =Lit − (1 − θt )Lit−1 =∑ Kint Ξρ/σnt
[L − (1 − θt )Lit−1 ]∑ρ/σ it
K
Ξ
ijt
i
jt
j

∑
n

ρ/σ

Kint Ωit[Rnt − (1 − θt )Rnt−1 ]∑ρ/σj Kjnt Ωjt(Ξnt , Ωit ) captures residence and workplace attractiveness.
We can solve the above equations for Ξnt and Ωit
The unique up-to-scale solution with a normalization for the geometric meanof Ξnt and Ωit .

This strategy is conditional on the observed equilibrium and it works even if
the model has multiple equilibria.
Back

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Step 3: Estimate the spillover parameters
Identification strategy: Minimize the role of time-varying idiosyncratic
fundamentals (=structural errors) in accounting for the attractiveness of eachblock.
We first separate exogenous fundamentals and spillover effects.
Given (β1 , β2 ), we use(
Ξnt = bnt

RntSn

)β 1 (

Rnt−1
Sn

)β 2

ρ(1−θ

Ξnt+1 t+1)

to solve for exogenous part of amenities bnt .
Do analogous thing to recover fundamental productivity ait from Ωnt given(α1 , α2 ).
Back

42 / 26

Step 3: Estimate the spillover parameters

As moment conditions, we posit that changes in the fundamental amenities
and productivity are mean zero within the same distance bin k from the CBD(c.f., Ahlfeldt et al. 2015; Heblich et al. 2020):
E[∆ ln ant × In (k)] = 0, E[∆ ln bit × Ii (k)] = 0.
Note that the first-difference means that we allow for any block-fixedamenities and productivity.
We iterate over guessed (α1 , α2 , β1 , β2 ) to minimize the deviation from themoments.
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Step 3: Estimate the spillover parameters

We get(α1 , α2 , β1 , β2 ) = (0.24, −0.07, 0.20, 0.02)
which are all statistically different from zero.

Table

The first estimate of Allen-Donaldson spillovers in a within-city setting.
α1 + α2 > 0 and β1 + β2 > 0 imply possibility of multiple steady-states.
We can show that α1 + α2 ≤ 0 and β1 + β2 ≤ 0 are suﬀicient for the uniquesteady state.
We numerically found multiple steady states because of positive net
agglomeration forces.
Back

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Estimating commuting cost

Given the workplace i and residence n, a worker chooses a travel mode (walk,bus, train, bike, car) to minimize the travel cost.
Nested logit: Public modes (walk, bus, train) and private modes (bike, car)
Travel time negatively impacts travel cost.
Strong substitution within nests (λ ≃ 0.1).

We use the expected travel cost as the (log of the) bilateral travel cost.
To calculate the commuting cost prior to 1987, we assume lower car
ownership rate in prior years.
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Estimation results of the commuting gravity equation

The following standard gravity equation holds in a steady state:ρln Lin = − Din + Wi + Hn + ξin ,σ
The results from the 1987 person-trip survey of Hiroshima:

Average commuting cost (c̄in )Estimation
Number of observations
More than 20 commuters
R-squared or Pseudo R-squared(1)(2)
Log Commuting Flow
-4.082-3.976(0.156)(0.170)
OLS
2,473
1,635
✓
0.543
0.522

(3)
(4)
log (Commuting Flow + 1)
-5.758-3.931(0.179)(0.169)
OLS
4,356
1,635
✓
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

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Estimation results of spillover parameters

Elasticity of employment density (α1 )Elasticity of past employment density (α2 )Elasticity of population density (β1 )Elasticity of past population density (β2 )(1)(2)
All blocks
Productivity Amenities
0.237(0.0010)-0.065(0.0008)
0.198(0.0014)0.023(0.0009)(3)(4)
Blocks in 3 km to CBD
Productivity Amenities
0.239(0.0001)-0.066(0.0001)
0.222(0.0046)
0.006(0.0043)

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 (allblocks) or 158 blocks (blocks in 3 kilometers to CBD). 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.

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Making predictions for 1945–1950.
We calculate the composite amenities Ξn1950 to predict population
distribution in 1945–1950.
The system of equations used in Step 2 of calibration determines the predicted
population and employment Step2 equations

When predicting the 1950 population without structural errors:
(
)β (
)β
Rn,1950 1 Rn,1945 2 ρ(1−θ1955 )Ξn,1950 = b̄nΞn,1955
SnSn
For the case of no agglomeration, we can formulate Ξn1950 as the sum of
discounted values of amenities.
Ξn1950 = Bn1950 ≡ bn1950

T
∏

∏τ

(bnτ )

s=t+1 ρs (1−θs )τ =1955

In the case of no expectations in the recovery, we use
∏τ
(
)β (
)β +(β +β ) ∑T
ρ (1−θs )Rn1945 2 Rn1945 1 1 2 τ =t+1 s=1955 s
Ξn1950 = Bn1950
SnSn
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