Discussion of “Walled Cities in Late Imperial China”
by Yannis Ioannides and Junfu Zhang
Yueran Ma
Harvard University
July 20, 2015
Yueran Ma (Harvard University)
Walled Cities in Late Imperial China
July 20, 2015
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This Paper
Interesting paper with thought-provoking facts about walled cities in late
imperial China.
Historical snapshots: late Ming Dynasty (circa early 1600s) and late Qing
Dynasty (circa late 1800s – early 1900s).
1
Size distribution of walled cities:
Empirical evidence: close to Zipf’s law in the upper tail.
A static model with near power law distribution of city size given power
law distribution of urban production amenities.
2
Characteristics of city walls:
Area inside the wall positively correlated with jurisdiction population.
Quality of the wall increasing in probability of being attacked.
Yueran Ma (Harvard University)
Walled Cities in Late Imperial China
July 20, 2015
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This Discussion
Highlights:
Walled cities in history sheds further light on the size distribution of
cities.
—City boundaries are well-defined by city walls.
—“City walls last for hundres of years and thus city size rarely grows over a
long period of time.”
Dynamic (random growth) vs. static theories of Zipf’s law.
Plan of discussion:
Brief review of evidence on the size distribution of walled cities.
The model in a nutshell.
Thoughts on the mechanisms.
Possible extensions.
Yueran Ma (Harvard University)
Walled Cities in Late Imperial China
July 20, 2015
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Size Distribution of Walled Cities: Ming Dynasty
Yueran Ma (Harvard University)
Walled Cities in Late Imperial China
July 20, 2015
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The Model in a Nutshell
Key element: R—Urban production amenity.
Urban production (clothing): Yc = RN α .
Rural production (food): every farmer has λ units of land; produces x
units of food.
(1 − α) ln N + 2βτ D(N, λ, τ, β) = ln α + ln R +
1
β
ln x − ln V
1−β
β
R increases → The city is able to support both a larger urban population
N, and a larger rural hinterland D.
R follows a power law distribution → N follows a power law distribution if
D grows at the speed of ln N.
Yueran Ma (Harvard University)
Walled Cities in Late Imperial China
July 20, 2015
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The Model in a Nutshell
Results similar if instead model rural production amenity:
Urban production (clothing): Yc = N α .
Rural production (food): every farmer has λ units of land; produces Rx
units of food.
A challenge: How to get power law exponent close to −1?
(1 − α) ln N + 2βτ D(N, λ, τ, β) = ln α + ln R +
Yueran Ma (Harvard University)
Walled Cities in Late Imperial China
1
β
ln x − ln V
1−β
β
July 20, 2015
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Thoughts on the Mechanisms
What determines city size distribution at any given point in time?
Random growth
Locational fundamentals
Political hierarchy
Yueran Ma (Harvard University)
Walled Cities in Late Imperial China
July 20, 2015
7 / 18
Scope for Random Growth?
Walled cities are not static. They grow and change, although very slowly.
Walls of Beijing:
— Liao (916–1165 AD), — Jin (1115–1234 AD), — Yuan (1271–1368 AD),
— Ming (1368–1644 AD) & Qing (1644–1911 AD).
Yueran Ma (Harvard University)
Walled Cities in Late Imperial China
July 20, 2015
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Can We Know More?
1
Size distribution of walled cities in China 2,500 years ago.
Formative years of cities in ancient China.
Random growth forces could be weak.
But static mechanisms should be at play. City size distribution would
be near power law if driven by power law distribution of locational
amenities.
Modern sources:
Qu, Yingjie (1991) Reconstructing Cities in Pre-Qin Era;
Zhou, Changshan (2001) Research on Cities in Han Dynasty...
Historical sources:
Book of Han: Volume on Geography (Han Dynasty);
Yuanhe Junxian Tuzhi (Tang Dynasty)...
Yueran Ma (Harvard University)
Walled Cities in Late Imperial China
July 20, 2015
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Zhou, Changshan (2001) Research on Cities in Han Dynasty
Han Dynasty: 202BC–220AD
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Walled Cities in Late Imperial China
July 20, 2015
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5
4
Log Rank
2
3
1
0
10
11
12
13
Log Population
14
15
Population in Han Dynasty Administrative Areas in 2AD
Source: Ge, Jianxiong (1986) Population Geography in West Han Dynasty,
based on Book of Han: Volume on Geography
Yueran Ma (Harvard University)
Walled Cities in Late Imperial China
July 20, 2015
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Locational Fundamentals
If R captures locational fundamentals, and if locational fundamentals
are stable over time, then would expect relative city size to be quite
stable over time.
Davis and Weinstein (2002): Evidence of strong persistence
throughout the history of Japan. But a) they measure population not
at city level but at region level, b) population in early periods
measured by number of archaeological sites.
Yueran Ma (Harvard University)
Walled Cities in Late Imperial China
July 20, 2015
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Persistence of Chinese Regional Population: Ming – 2010
Data on population in 208 Chinese prefecture-level cities in Ming Dynasty
and in 2010. Raw correlation of log population (all cities): 0.39.
14
15
Log Population (2010)
17
16
18
100 largest cities by population in Ming:
12
13
14
15
Log Population (Ming)
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Walled Cities in Late Imperial China
July 20, 2015
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Can We Know More?
2
How did walled cities evolve over time?
–From early imperial China to late imperial China.
Degree of persistence?
How much did the accumulation of (random) past shocks play a role?
–From late Ming Dynasty to late Qing Dynasty.
Match cities in Ming and Qing using the current dataset.
Should expect extremely high persistence in this case.
3
Analyze local production amenities
Detailed local level tax data available for Ming Dynasty and for various
other periods in time. Have been used to back out GDP of agricultural
and manufacturing sectors.
Does R follow a power law distribution? Does it connect to city size?
Yueran Ma (Harvard University)
Walled Cities in Late Imperial China
July 20, 2015
14 / 18
Political Hierarchy
The notion of a hierarchy of cities has ancient roots:
“The king’s city is 9 li by 9 li... the duke’s city is 7-by-7... the baron’s city
is 5-by-5... the knight’s city is 3-by-3...”
—Zuo Zhuan, approx 400BC
Same arrangement found in commentaries to Rites of Zhou, and other
historical documents from 2,000+ years ago.
Edge (li)
Area (li 2 )
Level 1
9
81
Yueran Ma (Harvard University)
Level 2
7
49
Level 3
5
25
Level 4
3
9
Walled Cities in Late Imperial China
Level 5
1.8
3.24
Level 6
1
1
July 20, 2015
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Political Hierarchy
Approximates a thought experiment of the social planner sitting down
to lay out the arrangement of his cities. Probably not just about
“putting people in their place”.
Echoes hierarchy of cities based on their functions. Hsu (2012):
“Goods with substantial scale economies, e.g., stock exchanges or symphony
orchestras, will be found in only a few locations, whereas those with small
scale economies, e.g., gas stations or convenience stores, will be found in
many.”
In ancient China, hierarchy dictated by administrative functions →
Governance + provision of public goods and services.
Yueran Ma (Harvard University)
Walled Cities in Late Imperial China
July 20, 2015
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Political Hierarchy
Every level i city governs k level i + 1 cities, each of which is δ/k
fraction of the size of the city at level i. Then the approximate slope
of the Zipf plot is:
ln(Ri+1 /Ri )
ln(k)
ln(k)
≈
=−
ln(Si+1 /Si )
ln(δ/k)
ln(k) − ln(δ)
Yueran Ma (Harvard University)
Walled Cities in Late Imperial China
July 20, 2015
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Summary
Interesting paper.
—Helps to understand city walls as a historical and economic
phenomenon.
—Sheds new light on the size distribution of cities.
Might be able to extend the analysis to better understand the
economic mechanisms.
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Walled Cities in Late Imperial China
July 20, 2015
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