today chapter 7 –cities and congestion: economies of scale, urban systems and zipf’slaw more on...
TRANSCRIPT
Today
• Chapter 7– Cities and congestion: economies of scale, urban systems and
Zipf’sLaw
• More on the role of geographical space– relevance of non-neutral space for urban systems– background paper Stelder (2005) on Nestor
Issues
• Typical outcome of CP model is agglomeration into just a few cities (of equal size)
• reality: urban hierchies=many cities of different size with some regularities accross countries and time
• VL model and the Bell Shape curve better in this respect but does not allow interregional migration
• How can Geographical Economics account for this?
Sources of agglomeration economies
• Marshall (1920) (remember box 2.1)• Knowledge spill-overs
• Labour pool
• Backward linkages– 1: pure/technological– 2: pecuniary
Scope of agglomeration economies
• Rosenberg & Strange (2004)– industrial scope (locailzation<->urbanization)– temporal scope (path dependency)– geographical scope (density inside city<->proximity to other
cities)– organisation and business culture/competitiveness scope
(diversity -> competition)
People or firms?
• Florida (2002)– "creative class" concept – spill-overs between people rather than between firms
• Gleaser (2004)– "bohemien" index insignificant when modelled
together with human capital indices
Scope of scale economies
• MAR (Marschall/Arrow/Romer) externalities: spill-overs between jointly located firms/industries of the same type; also known as localization economies (Sillicon Valley/ Detroit); a firm is more productive in the vicinity of many identical firms
• Jacobs externalities: urban spill-overs between all types; also known as urbanisation economies; a firm is more productive in the vicinity of many firms whatsoever/ in a larger city
• Duranton (2007): current consensus is that both are relevant and of comparable importance
• CP model:– firms group together because local demand is high, and demand is high
because firms have grouped together ->– positive externality is associated with the number of firms, not with
specialization ->– models urbanization rather than localization
Interdependence?
• main focus of empirical studies on (samples of) individual cities
• "free floating islands"• agglomeration forces get more attention than
spreading forces• no role for interdependence between cities and
between cities and their hinterland
Urban versus Geographical economics
• Combes, Duranton & Overman (2005)– wage curve– cost of living curve– net wage curve – labor supply curve
The urban modelprototype Henderson (1974)
• Only cities no hinterland• Industry-specific spill-overs• Counter force: negative economies of scale (congestion) (non-
industry specific)• fig 7.3: will lead to full specialization of each city into one industry
(p285-286)– all cities specializing in industry x must be of the same size
– cities specializing in an industry with higher scale economies will be larger (higher wage can bear more congestion costs)
– inter-city trade
--> urban system of specialized cities of different size trading with each other
Figure 7.3 Core urban economics model
Labor supply curve
A
B
Wage curveindustry 2
Wage curveindustry 1
NA NB
NA NB
HA
HB
Net Wage A =Net Wage B
W(N)-H(N)
H(N)
W(N)
WA
WB
Net Wage Industry 2
Net Wage Industry 1
Cost of Living Curve
Figure 7.4 Core geographical economics model
A
B
Nf = NH = 0.5
Low transport cost:Net Wage Home =Net Wage Foreign
Low Transport costHome
Low Transport costForeign
High Transport costForeign
High Transport costHome
High transport cost:Net Wage Home =Net Wage Foreign
Low Transport cost
High Transport cost
Cost of living curves
Wage curves
NH = 1NF = 1
W(N)
Wh
Hh
W(N)-H(N)
Net wage curves Home
Foreign
H(N)
unstable stable
The CP model in fig 7.4
• difference with the urban model of fig 7.3– cost of living falls with city size– real wage may or may not increase with city size,
depending on transport costs
Scale and relevance
Combes, Duranton & Overman:• urban model more relevant for cities, local externalities
more important than long-distance inter-city relations • CP model more relevant for regions and countries,
market access and inter-region/country interdependencies more important\
• critique: is inter-location interdependency more important at larger distances?
Introducing congestion
• L = Nτ(1-τ) ( α + βx) -1 < τ < 1
• if 0 < τ < 1 negative externalities• if -1 < τ < 0 (additional) positive externalities• if τ = 0 no congestion effects
1. Yr = δ λr Wr + φr ( 1 – δ)
2. Ir = ( Σs λs1-τε Trs
1-ε Ws1-ε )1/(1-ε)
3. Wr = λ-τ ( Σs Ys Trs1-ε
Isε-1 )1/ε
with τ =0 (1)-(3) reduces to the CP model
0
1
2
3
4
0 1 2 3 4 5
output
total N = 100 average N = 100 total N = 400
average N = 400 total no cong. average no cong.
Figure 7.5 Total and average labor costs with congestion
Parameter values: = 1, = 0.2; = 0.1 for N = 100 and N = 400, = 0 for "no cong."
Figure 4.1 The relative real wage in region 1
2-region base scenario
0,97
1
1,03
0 0,2 0,4 0,6 0,8 1
lambda 1
w1
/w2
A
D
CB
E
F
ws = Ws Is-δ
stable unstable
T =1.7
Figure 4.2 The impact of transport costs
Variations in transport costs T
0.9
1
1.1
0.000 0.200 0.400 0.600 0.800 1.000
lambda 1
w1
/ w
2
1.3
1.5
1.7
1.9
2.1
Higher T: spreading more likely
Figure 7.6 The 2-region core model with congestion ( = 5; = 0.4; = 0.01)
a. T = 1.9
0,92
1
1,08
0 0,5 1
w 1/w 2
c. T = 1.61
0,94
0,96
0,98
1,00
1,02
w1/w2
b. T = 1.7
0,93
0,965
1
1,035
0 0,5 1
w1/w2
0 0,5 1
Figure 7.6 (cont)-
d. T = 1.4
0,95
1
1,05
0 0,5 1
w 1/w 2
e. T = 1.1
0,975
1
1,025
0 0,5 1
w 1/w 2
f. T = 1.07
0,985
1
1,015
0 0,5 1
w 1/w 2
Figure 7.6 (cont)
g. T = 1.05
0,992
1
1,008
0 0,5 1
w 1/w 2
h. T = 1.03
0,98
1
1,02
0 0,5 1
w 1/w 2
i. T = 1.01
0,97
1
1,03
0 0,5 1
w 1/w 2
CP- congestion model
• range of possible outcomes wider• partial agglomeration as stable equilibrium
possible -> less “black hole” results
Figure 7.7 The racetrack economy with congestion ( = 5; = 0.7; = 0.1)
a. T = 1.21
23
4
5
6
7
8
9
10
1112
1314
15
16
17
18
19
20
21
22
2324
initial final b T = 1.31
23
4
5
6
7
8
9
10
1112
1314
15
16
17
18
19
20
21
22
2324
initial final
Figure 7.7 continued
c. Final distribution; T = 1.2
0
0.04
0.08
0.12
1 3 5 7 9 11 13 15 17 19 21 23
Figure 7.7 continued
d. Final distribution; T = 1.3
0
0.03
0.06
0.09
1 3 5 7 9 11 13 15 17 19 21 23
Zipf’s Law
• A special case of the power law phenomenon: uneven distribution with few (very) large values and many small values
• log (Mi) = c – q log(Ri)
• Perfect Zipf: q=1• Research: some countries q>1 some q<1, some quite
close to 1 (USA)• Depends strongly on data, definitions and sample size• City proper versus agglomeration• The “tail” of the distribution does not work• The role of the primate city
Table 7.3 Primacy ratio, selected countries*
France (1982) 0.529 UK (1994) 0.703
Austria (1991) 0.687 Egypt (1992) 0.499
Mexico (1990) 0.509 Chili (1995) 0.769
Peru (1991) 0.753 South Korea (1990) 0.532
Indonesia (1995) 0.523 Vietnam (1989) 0.570
Czech Republic (1994) 0.550 Hungary (1994) 0.726
Romania (1994) 0.605 Russian Federation (1994) 0.504
Iran 0.556 Iraq (1987) 0.643
Sample Mean 0.500
Year of observation in between brackets. Source: own calculations based on UN data that can be found at http://www.un.org/Depts/unsd/demog//index/html
Table 7.4 Primacy ratio, selected countries
Table 7.5 Summary statistics for q
City proper Urban agglomeration
Mean 0.88 1.05
Standard Error 0.030 0.046
Minimum 0.49 0.69
Maximum 1.47 1.54
Average R2 0.94 0.95
# observations 42 22
Estimated q for 48 countries
q ≠ 1 more often than not; Zipf's law rarely holds
Figure 7.4 Frequency distribution of estimated coefficients*
0
2
4
6
8
10
12
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 More
city proper urban agglomeration
A theory on Zipf?
• should accept and explain deviations from q=1• should allow for changing q over time• can congestion-CP model do this?
Other approaches
• Simon (1955): – Random growth on a random distribution predicts that q =1
• Gabaix (1999):– Gibrat' s law: city growth is independent of its size– uniform growth rate with normal distribution variance leads to
q=1– only when either assuming CRS or with DRS and IRS levelling
out
• problem: no q ≠ 1 possible• Shirky (2005): networks create power laws
– http://www.shirky.com/writings/powerlaw_weblog.html
Zipf simulation
• 24-location racetrack model• feed with random history• three periods:
– pre-industrialization δ=0.5 ; ε=6 ; T=2 ; τ=0.2
– industrialization δ=0.6 ; ε=4 ; T=1.25 ; τ=0.2
– post-industrialization δ=0.6 ; ε=4 ; T=1.25 ; τ=0.33
Figure 7.10 Simulating Zipf
N-shape over time: q increases and later decreases
The role of geography
• Extra literature: stelder.pdf on nestor
• geography=neutral simulate how history matters
• history=neutral simulate how geography matters
• “no history assumption” = “in the beginning there were only little villages” or: initial distribution=equal distribution
• only possible in non-neutral space because no history in neutral space = immediate long term equilibrium (real wage identical everywhere)
symmetric space asymmetric space
Hotelling beach
racetrack
Equilibrium distribution in a racetrack economy
with 12 locations. =0.4, =4, =0.4
Equilibrium distribution in a Hotelling economy
with 12 locations. =0.4, =4, =0.4
Equilibrium distribution in a Hotelling economy
with 12 locations. =0.4, =4, =0.4 (no history)
Equilibrium distribution in a Hotelling economy
with 371 locations. =0.4, =4, =0.3 (no history)
Equilibrium distribution in symmetric space
with 3x3=9 locations. =0.4, =6, =0.4
Equilibrium distribution in symmetric space
with 3x3=9 locations. =0.1, =4.8, =0.52
Equilibrium distribution in symmetric space
with 9x9=81 locations. =0.4, =6, =0.4
Equilibrium distribution in symmetric space
with 10x10=100 locations. =0.4, =6, =0.4
Equilibrium distribution in symmetric space
with 11x11=121 locations. =0.4, =6, =0.4
Equilibrium distribution in symmetric space
with 51x51=2601 locations. =0.5, =5, =0.4
Equilibrium distribution in symmetric space
with 51x51=2601 locations. =0.5, =5.5, =0.4
Equilibrium distribution in symmetric space
with 51x51=2601 locations. =0.5, =6, =0.4
rank size distribution A - B - C
A two-dimensional grid in geographical space
AB=1; AC=2; AF=2+2 2 (shortest path)
Asymmetrical space with 98 locations =0.3, =5, =0.2
The USA model: “going to Miami”
USA =0.3, =6, =0.3
USA =0.3, =6, =0.4
Asia
Canada
Latin-America
Europe
USA
Adding foreign trade
USA =0.3, =6, =0.3 with foreign trade
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The European grid extended with sea transport
Figure 5. Simulation B1: basic model (n=130) =0.45, =0.55, =5
Figure 6. Simulation B2: basic model (n=115), no altitude, =0.45, =0.55, =5
Figure 7. Simulation B3: basic model (n=208) =0.45, =0.5, =5.5
Figure 8 Simulation B4: extended model (n=193) =0.45, =0.5, =5.5, =0.25
δ(Bn,An) versus number of predicted cities
Conclusions
• geography matters• more differentiated urban hierarchies with
– increasing number of regions– increasing non-neutrality