The Comparative Advantage of Cities
Donald R. Davis

Jonathan I. Dingel

Columbia University and NBER
Chicago Booth

October 2014

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The Comparative Advantage of Cities

October 2014

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Research questions

What determines the spatial distribution of. . .
SkillsOccupations
Industries

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Research questions

What determines the spatial distribution of. . .
SkillsOccupations
Industries
In particular, how are these related to cities’ sizes?

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A first look: Wood product manufacturing

Consider wood product manufacturing, whose employees average
11.8 years of schooling
Plot employment in wood products against population for 276
metropolitan areas
Will wood products be manufactured in every city?
Will wood product employment be decreasing in city size,
increasing in city size, or attain an interior maximum?

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5
Log employment (deviation from mean)-5 -4 -3 -2 -1 0 1 2 3 4
-6
-7

-7

-6

Log employment (deviation from mean)-5 -4 -3 -2 -1 0 1 2 3 4

56

Industries and city size

10

12
14
16
Metropolitan log population

18

10

12
14
16
Metropolitan log population

18

Wood products

Wood products

Machinery

MachineryComputer and electronic products

Computer and electronic products

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Adding more industries

Now consider:
Machinery manufacturing (12.9 years of schooling)
Computer and electronic products (14.1 years of schooling)

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5
Log employment (deviation from mean)-5 -4 -3 -2 -1 0 1 2 3 4
-6
-7

-7

-6

Log employment (deviation from mean)-5 -4 -3 -2 -1 0 1 2 3 4

56

Industries and city size

10

12
14
16
Metropolitan log population

18

10

12
14
16
Metropolitan log population

18

Wood products

Wood products

Machinery

MachineryComputer and electronic products

Computer and electronic products

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5
Log employment (deviation from mean)-5 -4 -3 -2 -1 0 1 2 3 4
-6
-7

-7

-6

Log employment (deviation from mean)-5 -4 -3 -2 -1 0 1 2 3 4

56

Industries and city size

10

12
14
16
Metropolitan log population

18

10

12
14
16
Metropolitan log population

18

Wood products

Wood products

Machinery

MachineryComputer and electronic products

Computer and electronic products

Davis & Dingel (Columbia/Chicago Booth)

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5
Log employment (deviation from mean)-5 -4 -3 -2 -1 0 1 2 3 4
-6
-7

-7

-6

Log employment (deviation from mean)-5 -4 -3 -2 -1 0 1 2 3 4

56

Industries and city size

10

12
14
16
Metropolitan log population

18

10

12
14
16
Metropolitan log population

18

Wood products

Wood products

Machinery

MachineryComputer and electronic products

Computer and electronic products

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Comparative Advantage of Cities: Theory

We describe comparative advantage of cities as jointly governedby individuals’ comparative advantage and locational choices
Cities endogenously di↵er in TFP due to agglomeration
More skilled individuals are more willing to pay for more
attractive locations
Larger cities are skill-abundant in equilibrium
By individuals’ comparative advantage, larger cities specialize inskill-intensive activities
Under a further condition, larger cities are larger in all activities

Davis & Dingel (Columbia/Chicago Booth)

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5

Log employment (deviation from mean)-5 -4 -3 -2 -1 0 1 2 3 4

Use US data on skills and sectors
Characterize the comparativeadvantage of cities with two tests
Elasticity test of variation in
relative population/employment

-6

-6

-7

-7

Compare elasticities ofdi↵erent skills, sectors
Steeper slope in log-log plot ishigher10 elasticity
12
14
16
18
MSA log
Elasticities may
bepopulation
positive forall sectorsWood products

Log employment (deviation from mean)-5 -4 -3 -2 -1 0 1 2 3 4

5

6Comparative Advantage of Cities: Empirics (1/2)

10

12

14
16
MSA log population

18

Wood products

Machinery

MachineryComputer and electronic products

Computer and electronic products

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Comparative Advantage of Cities: Empirics (2/2)
Pairwise comparison test (LSM)
The function f (!, c) is log-supermodular if
c > c 0 , ! > ! 0 ) f (!, c)f (! 0 , c 0 )f (! 0 , c)f (!, c 0 )Our theory says skill distribution f (!, c) and sectoral
employment distribution f ( , c) are log-supermodular
For example, population of skill ! in city c is f (!, c). Check
whether, for c > c 0 , ! > ! 0 ,f (!, c)f (! 0 , c)f (!, c 0 )f (! 0 , c 0 )Are larger cities larger in all sectors?
Check if c > c 0 ) f ( , c) f ( , c 0 )Davis & Dingel (Columbia/Chicago Booth)

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Related literature
Distribution of heterogeneous skills: Behrens, Duranton, andRobert-Nicoud (2014); Eeckhout, Pinheiro, and Schmidheiny (2014); Davis and Dingel(2012); Acemoglu and Autor (2011); Baum-Snow and Pavan (2011)

Assignment models of di↵erential rents: Ricardo (1817),
Alonso-Muth-Mills, Brueckner (1987); von Thünen (1826); Sattinger (1979); Fujita andThisse (2002); Behrens and Robert-Nicoud (2011); Behrens, Duranton, andRobert-Nicoud (2014)

Assignment models of comparative advantage: Sattinger (1975);
Teulings (1995); Costinot (2009); Costinot and Vogel (2010, 2014)

Models of cities’ industrial structure: Henderson (1974); Duranton andPuga (2001); Helsley and Strange (2012)

A structural interpretation of prior estimates of sectors’
population elasticities: Henderson (1983, 1991, 1997); Holmes and Stevens(2004)

Davis & Dingel (Columbia/Chicago Booth)

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Outline
1

Theory2

Empirical approach and data description

3

Empirical results
Elasticities tests
Pairwise comparisons tests
Larger cities are larger in all skills and sectors

4Conclusions

Davis & Dingel (Columbia/Chicago Booth)

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TheoryModel components
Producers
Skills: Continuum of skills indexed by ! (educational attainment)
Sectors: Continuum of sectors (occupations, industries)
Goods: Freely traded intermediates assembled into final good
All markets are perfectly competitive
PlacesCities are ex ante identical
Locations within cities vary in their desirability
TFP depends on agglomeration of “scale and skills”✓ ˆ◆A(c) = J L,
j(!)f (!, c)d!
!2⌦

Analytical tool: log-supermodularity
The skill distribution f (!, c) is log-supermodular if
c > c 0 , ! > ! 0 ) f (!, c)f (! 0 , c 0 ) f (! 0 , c)f (!, c 0 )Davis & Dingel (Columbia/Chicago Booth)

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Individual optimization
Perfectly mobile individuals simultaneously choose
A sector of employment
A city with total factor productivity A(c)A location ⌧ (distance from ideal) within city c
The productivity of an individual of skill ! isq(c, ⌧, ; !) = A(c)T (⌧ )H(!, )Utility is consumption of the numeraire final good, which is income
minus locational costU(c, ⌧, ; !) = q(c, ⌧, ; !)p( ) r (c, )= A(c)T (⌧ )H(!, ))p( ) r (c, )Davis & Dingel (Columbia/Chicago Booth)

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Sectoral choice

Individuals’ choices of locations and sectors are separable:
arg max A(c)T (⌧ ) H(!, )p( ) r (c, ) = arg max H(!, )p( )| {z } |{z}locational

sectoralH(!, ) is log-supermodular in !, and strictly increasing in !
Comparative advantage assigns high-! individuals to highsectors (Costinot, 2009; Costinot and Vogel, 2010)
Absolute advantage makes more skilled have higher incomes(G (!) = max H(!, )p( ) is increasing)

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Locational choice
A location’s attractiveness = A(c)T (⌧ ) depends on c and ⌧T 0 (⌧ ) < 0 may be interpreted as commuting to CBD, proximity
to productive opportunities, or consumption value
More skilled are more willing to pay for more attractive locations
Equally attractive locations have same rental price and skill type
Location in higher-TFP city is farther from ideal desirability= A(c)T (⌧ ) = A(c 0 )T (⌧ 0 )A(c) > A(c 0 ) ) ⌧ > ⌧ 0
Locational hierarchy: A smaller city’s locations are a subset oflarger city’s in terms of attractiveness: A(c)T (0) > A(c 0 )T (0)Davis & Dingel (Columbia/Chicago Booth)

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Equilibrium distributions
Skill and sectoral distributions reflect distribution of locational
attractiveness: Higher- locations occupied by higher-!
individuals who work in higher- sectors
Locational hierarchy ) hierarchy of skills and sectors
The distributions f (!, c) and f ( , c) are log-supermodular if andonly if the supply of locations with attractiveness in city c,s( , c), is log-supermodular⇣⌘(
1
V A(c)
if  A(c)T (0)s( , c) = A(c)0otherwise@
where V (z) ⌘ @z
S (T 1 (z)) is the supply of locations withinnate desirability ⌧ such thatT (⌧ ) = z
Davis & Dingel (Columbia/Chicago Booth)

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When is s( , c) log-supermodular?
Proposition (Locational attractiveness distribution)
The supply of locations of attractiveness in city c, s( , c), is
log-supermodular if and only if the supply of locations with innate
desirability T 1 (z) within each city, V (z), has a decreasing elasticity.
Links each city’s exogeneous distribution of locations, V (z), toendogenous equilibrium locational supplies s( , c)Informally, ranking relative supplies is ranking elasticities of V (z)
⇣
⌘
✓
◆
@
ln
V
A(c)
@ ln s( , c)s( , c) / V
)
=
A(c)
@ ln
@ ln zSatisfied by the canonical von Thünen geography
Davis & Dingel (Columbia/Chicago Booth)

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The Comparative Advantage of Cities
Corollary (Skill and employment distributions)
If V (z) has a decreasing elasticity, then f (!, c) and f ( , c) are
log-supermodular.
Larger cities are skill-abundant in equilibrium (satisfies Assumption 2
in Costinot 2009)
Locational productivity di↵erences are Hicks-neutral in equilibrium(satisfies Definition 4 in Costinot 2009)
H(!, ) is log-supermodular (Assumption 3 in Costinot 2009)

Corollary (Output and revenue distributions)
If V (z) has a decreasing elasticity, then sectoral output Q( , c) andrevenue R( , c) ⌘ p( )Q( , c) are log-supermodular.
Davis & Dingel (Columbia/Chicago Booth)

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The Comparative Advantage of Cities
Corollary (Skill and employment distributions)
If V (z) has a decreasing elasticity, then f (!, c) and f ( , c) are
log-supermodular.
Larger cities are skill-abundant in equilibrium (satisfies Assumption 2
in Costinot 2009)
Locational productivity di↵erences are Hicks-neutral in equilibrium(satisfies Definition 4 in Costinot 2009)
H(!, ) is log-supermodular (Assumption 3 in Costinot 2009)

Corollary (Output and revenue distributions)
If V (z) has a decreasing elasticity, then sectoral output Q( , c) andrevenue R( , c) ⌘ p( )Q( , c) are log-supermodular.
Davis & Dingel (Columbia/Chicago Booth)

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When are bigger cities bigger in everything?
We identify a sufficient condition under which a larger city has alarger supply of locations of a given attractivenessProposition
For any A(c) > A(c 0 ), if V (z) has a decreasing elasticity that is lessthan -1 at z = A(c) , s( , c) s( , c 0 ).
Now apply this result to the least-attractive locations, so larger cities
are larger in all skills and sectors

Corollary
If V (z) has a decreasing elasticity that is less than -1 at
1 (!)
z = KA(c)= A(c) , A(c) > A(c 0 ) implies f (!, c) f (!, c 0 ) andf (M(!), c) f (M(!), c 0 ) 8! 2 ⌦.
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Empirical approach anddata description

Empirical tests
Our theory says f (!, c) and f ( , c) are log-supermodular.
Two tests to describe skill and sectoral employment distributions:
Elasticities test:
Compare population elasticities estimated via linear regression
More skilled types should have higher population elasticities
More skill-intensive sectors should have higher population
elasticities

Pairwise comparisons test:
Compare any two cities and any two skills/sectors
Relative population of more skilled should be higher in larger(!,c)
f (!,c 0 )city: c > c 0 , ! > ! 0 ) ff (!
0 ,c)f (! 0 ,c 0 )Relative employment of more skill-intensive sector should bef ( ,c 0 )higher in larger city: c > c 0 , > 0 ) ff(( 0,c),c)f ( 0 ,c 0 )“Bin” together cities ordered by size and compare bins similarly
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Data: Skills
Proxy skills by educational attainment, assuming f (edu, !, c) is
log-supermodular in edu and ! (Costinot and Vogel 2010)
Following Acemoglu and Autor (2011), we use a minimum of
three skill groups.
Skill (3 groups)
High school or lessPopulation Percent
share
US-born.35.77

Some college

.32

.88

Bachelor’s or more

.33

.85

Skill (9 groups)
Less than high school
High school dropout
High school graduate
College dropout
Associate’s degree
Bachelor’s degree
Master’s degree
Professional degree
Doctoral degree

Population Percent
share
US-born
.03
.21
.07
.69
.24
.87
.24
.89
.08
.87
.21
.86
.08
.83
.03
.81
.01
.69

Population shares and percentage US-born are percentages of full-time, full-year prime-age workers.
Source: Census 2000 microdata via IPUMS-USA
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Data: Sectors
21 manufacturing industries (3-digit NAICS, 2000 County Business Patterns)
22 occupations (2-digit SOC, 2000 BLS Occupational Employment Statistics)
Infer sectors’ skill intensities from average years of schooling ofworkers employed in them
Skill
Occupational category
intensity Manufacturing industry
Farming, Fishing, and Forestry
9.3
ApparelBuilding & Grounds Cleaning & Maintenance
10.9
Textile Product Mills
Food Preparation and Serving
11.4
Leather and Allied ProductConstruction and Extraction
11.5
Textile Mills
Production
11.6
Furniture and Related Products
Healthcare Practitioners and Technical
15.6
Beverage and Tobacco Products
Community and Social Services
15.8
Transportation Equipment
Education, Training, and Library
16.5
Petroleum and Coal Products
Life, Physical, and Social Science
17.1
Computer & Electronic Products
Legal
17.3
Chemical
Data source: Census 2000 microdata via IPUMS-USA
Davis & Dingel (Columbia/Chicago Booth)

The Comparative Advantage of Cities

Skill
intensity
10.7
11.4
11.7
11.7
11.7
13.1
13.2
13.5
14.1
14.1

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Empirical results

Elasticities tests

Three skill groups

Table: Population elasticities of educational groups

Dep var: ln f (!, c)!1 HS or less
⇥ log population!2 Some college⇥ log population!3 BA or more
⇥ log population

All
0.96

US-born
0.90(0.011)(0.016)

1.00

0.97

(0.010)(0.012)

1.10

1.07

(0.015)(0.017)

Standard errors, clustered by MSA, in parentheses.

Sample is all full-time, full-year employees residing in metropolitan areas.

Davis & Dingel (Columbia/Chicago Booth)

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Three skill groups

.9

.95

Population elasticity
1
1.05

1.1

1.15

Figure: Population elasticities of educational groups

High school or less
Davis & Dingel (Columbia/Chicago Booth)Some college

The Comparative Advantage of Cities

BA or more
October 201428 / 45

Nine skill groups

.9

.95

Population elasticity
1
1.05
1.1

1.15

Figure: Population elasticities of educational groups

LHS

HSD

HSG

CD

AA

BA

MA

Pro

PhD

Table
Davis & Dingel (Columbia/Chicago Booth)

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Nine skill groups

.9

.95

Population elasticity
1
1.05
1.1

1.15

Figure: Population elasticities of educational groups

All individuals
LHS

HSD

HSG

CD

AA

BA

US-born individuals
MA

Pro

PhD

Table
Davis & Dingel (Columbia/Chicago Booth)

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Cities, skills, and birthplaces

Why the di↵erence between skill distribution of population as a wholeand US-born individuals?
One possibility: Extreme-skill complementarity (Eeckhout,Pinheiro, and Schmidheiny, 2014)
Another possibility: Ethnic enclaves
In 1980 foreign-born were 6% of US population; in 2000, 11%
In 1980 foreign-born were 32% of lowest skill group; in 2000,
they were 79%

Davis & Dingel (Columbia/Chicago Booth)

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Spatial distribution of skills in 1980

.9

Population elasticity
.95
1
1.05

1.1

1.15

Figure: Population elasticities of educational groups, 1980

LHS

Gr 9-11Gr 12

All individuals

US-born individuals

0-1 yr col 2-3 yr col

4 yr col5+ yr colTable
Davis & Dingel (Columbia/Chicago Booth)

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.8

Population elasticity of employment
1
1.2

1.4

Occupations’ elasticities and skill intensities
Computer & Mathematical

Architecture & Engineering
Legal

Business & Financial Operations

Life, Physical & Social Science
Arts, Design, Entertainment, Sports & Media
Protective Service
Management
Office & Administrative Support
Personal Care & Service
Transportation & Material Moving
Production
Bldg/Grnds Cleaning & Mntnce
Sales & Related
Construction & Extraction
Education, Training & Library
Installation, Maintenance & Repair
Healthcare Practitioners & TechnicalCommunity & Social Services
Food Preparation & Serving
Healthcare Support

Farming, Fishing & Forestry

10
12
14
16
18
Skill intensity (employees' average years of schooling)

231 elasticity comparisons yield 80% success rate
Davis & Dingel (Columbia/Chicago Booth)

The Comparative Advantage of Cities

Table
October 201432 / 45

Computer and Electronic Product Manufacturing

Chemical Manufacturing
Transportation Equipment Manufacturing
Miscellaneous Manufacturing
Printing and Related Support Activities

Apparel ManufacturingandAppliance,
Tobacco Product
Manufacturing
ElectricalBeverage
Equipment,
and Component
Manufacturing
Textile Product Mills

Textile Mills
Fabricated Metal Product Manufacturing
Food Manufacturing
Machinery Manufacturing
Primary Metal Manufacturing
Nonmetallic Mineral Product Manufacturing

Plastics and Rubber Products Manufacturing

Petroleum and Coal Products Manufacturing
Paper Manufacturing

Wood Product Manufacturing
Furniture and Related Product Manufacturing.8

Population elasticity of employment
1
1.2
1.4

1.6

Industry population elasticities and skill intensities

Leather and Allied Product Manufacturing

11

12
13
14
Skill intensity (employees' average years of schooling)

210 elasticity comparisons yield 87% success rate
Davis & Dingel (Columbia/Chicago Booth)

The Comparative Advantage of Cities

Table
October 201433 / 45

Pairwise comparisons tests

Pairwise comparisons test
If f (⌫, c) is log-supermodular, where ⌫ = ! or ⌫ = ,c > c 0 , ⌫ > ⌫ 0 ) ln f (⌫, c) + ln f (⌫ 0 , c 0 ) ln f (⌫ 0 , c) + ln f (⌫, c 0 )if C and C 0 are distinct sets and C s C 0 , then 8⌫ > ⌫ 0
X
X
X
X
ln f (⌫, c) +ln f (⌫ 0 , c 0 )ln f (⌫ 0 , c) +ln f (⌫, c 0 )c2C

c 0 2C 0c2C

c 0 2C 0

Example: Chicago > Kalamazoo; Bachelor’s degree > HS graduate(!,c)
f (!,c 0 )c > c 0 , ! > ! 0 ) ff (!
0 ,c)f (! 0 ,c 0 )f (BA,Chicago)(BA,Kalamazoo)= 642,776> 24,178= f f(HSG
is truef (HSG ,Chicago)
611,054
36,425,Kalamazoo)

If there are n (bins of) cities and m skills/sectors, there aren(n 1)⇥ m(m2 1) pairwise comparisons.
2
Davis & Dingel (Columbia/Chicago Booth)

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Pairwise weights
With idiosyncratic errors, comparisons of cities of similar sizeand sectors of similar skill intensity are less informative
Comparing Chicago (population 9 million) to Des Moines(population 456 thousand) is much more informative about therelevance of our theory than Des Moines vs Kalamazoo(population 453 thousand)In addition to simple success rate, we also report a weighted
average of the success rate, weighting by di↵erences in cities’ log
populations and di↵erences in skill intensities.2ifference
Density
.6
.4
.2
0
2
4
D
6
Difference(2000
Population
CMSA)
in logdifferences
populations

Population differences(2000 CMSA)

Density
.4
0

0

0

.05

.2

.2

.1

DensityDensity
.15

.4

.6

.2

.8

.25

.6

.2ifference in schooling
Density
.8
.6
.4
.2
0
1
2
3
D
4
Difference

02
4Difference in log populations

Davis & Dingel (Columbia/Chicago Booth)

6

0

2

4
Difference in schooling

6

The Comparative Advantage of Cities

8

0

1

2
Difference in schooling

October 20143

4

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0.5

0.6
0.7
0.8
0.9
1.0
Pairwise comparison success rate

Pairwise comparisons: Three skill groups

270
108,94590
12,015301305

Unweighted, all
Unweighted, US born

10
135

5
30

3
9

2 Bins3 Comparisons

Population-difference weighted, all
Population-difference weighted, US born

Table
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0.5

0.6
0.7
0.8
0.9
1.0
Pairwise comparison success rate

Pairwise comparisons: Three skill groups

270
108,94590
12,015301305

Unweighted, all
Unweighted, US born

10
135

5
30

3
9

2 Bins3 Comparisons

Population-difference weighted, all
Population-difference weighted, US born

Table
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0.5

0.6
0.7
0.8
0.9
1.0
Pairwise comparison success rate

Pairwise comparisons: Three skill groups

270
108,94590
12,015301305

Unweighted, all
Unweighted, US born

10
135

5
30

3
9

2 Bins3 Comparisons

Population-difference weighted, all
Population-difference weighted, US born

Table
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0.5

0.6
0.7
0.8
0.9
1.0
Pairwise comparison success rate

Pairwise comparisons: Three skill groups

270
108,94590
12,015301305

Unweighted, all
Unweighted, US born

10
135

5
30

3
9

2 Bins3 Comparisons

Population-difference weighted, all
Population-difference weighted, US born

Table
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0.5

0.6
0.7
0.8
0.9
1.0
Pairwise comparison success rate

Pairwise comparisons: Nine skill groups

270
1,307,340

90
144,18030
15,660

Unweighted, all
Pop-diff-weighted, US born

10
1620

5
360

3
108

2 Bins36 Comparisons

Unweighted, US born
Pop-diff-edu-share-weighted, US born

Table
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0.5

0.6
0.7
0.8
0.9
1.0
Pairwise comparison success rate

Pairwise comparisons: Nine skill groups

270
1,307,340

90
144,18030
15,660

Unweighted, all
Pop-diff-weighted, US born

10
1620

5
360

3
108

2 Bins36 Comparisons

Unweighted, US born
Pop-diff-edu-share-weighted, US born

Table
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0.5

0.6
0.7
0.8
0.9
1.0
Pairwise comparison success rate

Pairwise comparisons: Nine skill groups

270
1,307,340

90
144,18030
15,660

Unweighted, all
Pop-diff-weighted, US born

10
1620

5
360

3
108

2 Bins36 Comparisons

Unweighted, US born
Pop-diff-edu-share-weighted, US born

Table
Davis & Dingel (Columbia/Chicago Booth)

The Comparative Advantage of Cities

October 201438 / 45

0.5

0.6
0.7
0.8
0.9
1.0
Pairwise comparison success rate

Pairwise comparisons: Nine skill groups

270
1,307,340

90
144,18030
15,660

Unweighted, all
Pop-diff-weighted, US born

10
1620

5
360

3
108

2 Bins36 Comparisons

Unweighted, US born
Pop-diff-edu-share-weighted, US born

Table
Davis & Dingel (Columbia/Chicago Booth)

The Comparative Advantage of Cities

October 201438 / 45

0.5

0.6
0.7
0.8
Pairwise comparison success rate

0.9

Pairwise comparisons: 22 occupations

276
8,073,382

90
925,15530
100,485

Unweighted

10
10,39552,310

3
2 Bins693 231 ComparisonsPop-diff-skill-diff weighted

Table
Davis & Dingel (Columbia/Chicago Booth)

The Comparative Advantage of Cities

October 201439 / 45

0.5

0.6
0.7
0.8
Pairwise comparison success rate

0.9

Pairwise comparisons: 21 manufacturing industries

276

90

30

10

5

6,183,770

817,344

91,350

9,450

2,100

Unweighted

3
2 Bins630 210 ComparisonsPop-diff-skill-diff weighted

Table
Davis & Dingel (Columbia/Chicago Booth)

The Comparative Advantage of Cities

October 2014

40 / 45

Larger cities are larger in all skills and sectors
Larger cities are more populous in all educational attainment
categories and employ more people in all sectors
Every estimated population elasticity is strongly positive
For manufacturing industries, the prediction thatc > c 0 ) f ( , c) f ( , c 0 ) is true in 77% of 796,950 cases
16 industries attain maximal size in NYC, LA, or Chicago
Only industry outside top ten is textile mills (maximal in #52
Greenville-Spartanburg-Anderson)
For occupations, c > c 0 ) f ( , c) f ( , c 0 ) true for 88%
19 of the 22 occupations attain their maximal size in NYC

Davis & Dingel (Columbia/Chicago Booth)

The Comparative Advantage of Cities

October 201441 / 45

Conclusions

Conclusions: Theory
Urban
Extends systems-of-cities approach to incorporate substantive
locational heterogeneity within cities
Predicts that cities are neither completely specialized norcompletely diversified
Predicts the pattern of economic activity based on observablecharacteristics of cities and sectors
Trade
Integrate endogenous spatial distribution of skills withhigh-dimensional theory of comparative advantage
At equilibrium, economy exhibits properties of Costinot (2009)
F-economy
Links ordering of locations by skills to city size
Predict distributions of skills and sectors across cities are
log-supermodular
Derive empirically implementable tests of the theory
Davis & Dingel (Columbia/Chicago Booth)

The Comparative Advantage of Cities

October 201443 / 45

Conclusions: Empirics
More disaggregated examination of distributions of skills and sectoral
employment across cities than existing literature
Provide evidence that LSM a good description of skills and cities
Theory-consistent elasticities in 35/36 comparisons with nineUS-born skill groups
Stronger than simple correlation of city size and college share
1980 data contra EPS’s “extreme skill complementarity”
Provide evidence that LSM plays a substantive role in cross-city
distributions of sectoral employment
Theory-consistent elasticities in more than 80% of comparisonsfor both occupations and manufacturing industries

Davis & Dingel (Columbia/Chicago Booth)

The Comparative Advantage of Cities

October 201444 / 45

Thank you

Consumption interpretation

q(c, ⌧, ; !) = A(c)H(!, )U(c, ⌧, ; !) = T (⌧ ) [A(c)H(!, )p( )r (c, ⌧ )]Lower-⌧ locations complement consumption of the final good
Higher-income individuals more willing to pay for more attractive
location
This consumption interpretation changes the expression forequilibrium rental prices
This interpretation does not change the two propositions
describing cities’ sizes, skills, and sectors
Davis & Dingel (Columbia/Chicago Booth)

The Comparative Advantage of Cities

October 201446 / 45

Equilibrium (1/2)
Denote the quantity of individuals of skill ! residing in city c at
location ⌧ and working in sector by L ⇥ f (!, c, ⌧, ).
Individuals maximize utilities by choices of city, location, andsectorf (!, c, ⌧, ) > 0 () {c, ⌧, } 2 arg max U(c, ⌧, ; !)Final-good producers maximize profits by demanding⇣ p( ) ⌘ ✏Q( ) = I
B( )

(1)

(2)

Absentee landlords maximize profits in Bertrand competition sothat unoccupied locations have rental prices of zero✓0r (c, ⌧ ) ⇥ S (⌧ )Davis & Dingel (Columbia/Chicago Booth)

L

ˆ

2⌃

ˆ

f (!, c, ⌧, )d!d!2⌦

The Comparative Advantage of Cities◆= 0 8c 8⌧ (3)October 2014

47 / 45

Equilibrium (2/2)
Agglomeration occurs and markets clear:ˆˆ
0S (⌧ ) Lf (!, c, ⌧, )d d! 8c 8⌧
!2⌦
2⌃
ˆ
Xˆ
Q( ) = Lq(c, ⌧, ; !)f (!, c, ⌧, )d!d⌧ 8
c2C

f (!) =

X

!2⌦

(5)

⌧ 2T

f (!, c) =

c2C

(4)

Xˆ
c2C

2⌃

ˆ

8!

(6)

j(!)f (!, c)d!) 8c(7)f (!, c, ⌧, )d⌧ d⌧ 2TA(c) = J(Lˆ!2⌦

A competitive equilibrium is a set of functions Q : ⌃ ! R+ ,f : ⌃ ⇥ C ⇥ ⇥ ⌦ ! R+ , r : C ⇥ ! R+ , and p : ⌃ ! R+ suchthat conditions (1) through (7) hold.
Back to Casual
Davis & Dingel (Columbia/Chicago Booth)

The Comparative Advantage of Cities

October 2014

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Nine skill groups
Population Percent
share
US-born
.03
.21
.07
.24
.24
.08
.21
.08
.03
.01

.69
.87
.89
.87
.86
.83
.81
.69

For US-born, only reject
Davis & Dingel (Columbia/Chicago Booth)!

Dep var: ln f (!, c)!1 Less than high school⇥ log population!2 High school dropout⇥ log population!3 High school graduate⇥ log population!4 College dropout⇥ log population!5 Associate’s degree⇥ log population!6 Bachelor’s degree⇥ log population!7 Master’s degree⇥ log population!8 Professional degree⇥ log population!9 PhD⇥ log population
!0

() !

! 0 inThe Comparative Advantage of Cities

Population elasticities
All
US-born
1.17
0.91(0.039)(0.028)

1.03

0.94

(0.017)(0.020)

0.93

0.90

(0.013)(0.016)

1.00

0.98

(0.011)(0.013)

1.00

0.96

(0.014)(0.016)

1.10

1.07

(0.015)(0.017)

1.12

1.09

(0.018)(0.019)

1.12

1.09

(0.018)(0.019)

1.11

1.06

(0.035)(0.033)!3 <!2 comparison.
October 201449 / 45

Spatial distribution of skills in 1980
Population Percent
share
US-born
.06
.67
.11
.33
.08
.13
.13
.13

.91
.94
.94
.92
.92
.90

Dep var: ln f (!, c)!1 Less than grade 9⇥ log population!2 Grades 9-11
⇥ log population!3 Grade 12⇥ log population!4 1 year college⇥ log population!5 2-3 years college⇥ log population!6 4 years college⇥ log population!7 5+ years college⇥ log population

Population elasticities
All
US-born
0.99
0.89(0.028)(0.030)

1.00

0.98

(0.019)(0.021)

0.97

0.95

(0.013)(0.015)

1.04

1.03

(0.018)(0.018)

1.09

1.07

(0.018)(0.018)

1.10

1.08

(0.018)(0.018)

1.13

1.11

(0.022)(0.022)Standard errors, clustered by MSA, in parentheses
Sample is all full-time, full-year employees residing in 253 metropolitan areas.
Davis & Dingel (Columbia/Chicago Booth)

The Comparative Advantage of Cities

October 2014

50 / 45

Occupations’ population elasticities
0.803
1 Farming, Fishing, and Forestry Occupations
12 Sales and Related Occupations⇥ log population(0.048)⇥ log population
Building
andGrounds
Cleaning
and
MaintenanceOccupations
1.039
2
13 Management occupations⇥ log population(0.011)⇥ log population
Food
Preparation
andServing
Occupations
0.985
3
14 Arts, Design, Entertainment, Sports, and Media Occupations⇥ log population(0.011)⇥ log population
1.037
4 Construction and Extraction Occupations
15 Business and Financial Operations Occupations⇥ log population(0.014)⇥ log population
1.045
5 Production Occupations
16 Architecture and Engineering Occupations⇥ log population(0.025)⇥ log population
1.061
6 Transportation and Material Moving Occupations
17 Computer and Mathematical Occupations⇥ log population(0.014)⇥ log population
1.015
7 Installation, Maintenance, and Repair Workers
18 Healthcare Practitioners and Technical Occupations⇥ log population(0.011)⇥ log population
0.980
8 Healthcare Support Occupations
19 Community and Social Services Occupations⇥ log population(0.013)⇥ log population
1.065
9 Personal Care and Service Occupations
20 Education, Training, and Library Occupations⇥ log population(0.017)⇥ log population
1.081
10 Office and Administrative Support Occupations
21 Life, Physical, and Social Science Occupations⇥ log population(0.010)⇥ log population
Protective
ServiceOccupations
1.123
11
22 Legal Occupations⇥ log population(0.014)⇥ log population
Observations
5943 Observations
R-squared
0.931 R-squared
Occupation FE
Yes
Occupation FE
Standard errors, clustered by MSA, in parentheses

Davis & Dingel (Columbia/Chicago Booth)

The Comparative Advantage of Cities

October 2014

1.037
(0.010)1.082(0.015)1.158(0.019)1.204(0.018)1.209(0.026)1.395(0.034)1.001(0.014)0.986(0.020)1.011(0.017)1.170(0.030)1.200(0.022)

5943
0.931
Yes

51 / 45

Industries’ population elasticities
1 Apparel Manufacturing⇥ log population
2 Textile Product Mills⇥ log population
3 Leather and Allied Product Manufacturing⇥ log population
4 Furniture and Related Product Manufacturing⇥ log population
5 Textile Mills⇥ log population
6 Wood Product Manufacturing⇥ log population
7 Fabricated Metal Product Manufacturing⇥ log population
8 Food Manufacturing⇥ log population
9 Plastics and Rubber Products Manufacturing⇥ log population
10 Primary Metal Manufacturing⇥ log population

Observations
R-squared
Industry FE
Only uncensored obs

Davis & Dingel (Columbia/Chicago Booth)

1.237

1.024

1.018

0.955

(0.070)(0.148)11 Nonmetallic Mineral Product Manufacturing⇥ log population
1.125 0.905
12 Paper Manufacturing(0.056) (0.135) ⇥ log population
0.743 0.147
13 Printing and Related Support Activities(0.099) (0.284) ⇥ log population
1.120 1.000
14 Electrical Equipment, Appliance & Component(0.050) (0.076) ⇥ log population
0.823 0.352
15 Machinery Manufacturing(0.105) (0.208) ⇥ log population
0.848 0.608
16 Miscellaneous Manufacturing(0.055) (0.085) ⇥ log population
1.094 1.036
17 Beverage and Tobacco Product Manufacturing(0.048) (0.050) ⇥ log population
0.953 0.864
18 Transportation Equipment Manufacturing(0.050) (0.067) ⇥ log population
1.105 0.975
19 Petroleum and Coal Products Manufacturing(0.056) (0.070) ⇥ log population
0.997 0.449
20 Computer and Electronic Product Manufacturing(0.078) (0.107) ⇥ log population
21 Chemical Manufacturing⇥ log population
5406
2130 Observations
0.564 0.541 R-squared
Yes
Yes
Industry FE
Yes
Only uncensored obs
Standard errors, clustered by MSA, in parentheses(0.036)(0.042)The Comparative Advantage of Cities

0.901

0.539

(0.063)(0.104)

1.202

1.122

(0.036)(0.047)

1.159

0.813

(0.074)(0.111)

1.071

0.960

(0.055)(0.069)

1.224

1.208

(0.044)(0.059)

1.168

1.010

(0.065)(0.147)

1.254

0.940

(0.075)(0.101)

0.951

0.393

(0.074)(0.308)

1.453

1.254

(0.075)(0.108)

1.325

0.992

(0.065)(0.098)

5406
0.564
Yes

2130
0.541
Yes
Yes

October 201452 / 45

Pairwise comparisons: 3 skill groups
Bins
2
2
2
2
3
3
3
3
5
5
5
5
10
10
10
10
30
30
30
30
90
90
90
90
270
270
270
270

BirthplaceAll
All
US-born
US-bornAll
All
US-born
US-bornAll
All
US-born
US-bornAll
All
US-born
US-bornAll
All
US-born
US-bornAll
All
US-born
US-bornAll
All
US-born
US-born

Weights
Unweighted
Population di↵erence
Unweighted
Population di↵erence
Unweighted
Population di↵erence
Unweighted
Population di↵erence
Unweighted
Population di↵erence
Unweighted
Population di↵erence
Unweighted
Population di↵erence
Unweighted
Population di↵erence
Unweighted
Population di↵erence
Unweighted
Population di↵erence
Unweighted
Population di↵erence
Unweighted
Population di↵erence
Unweighted
Population di↵erence
Unweighted
Population di↵erence

Davis & Dingel (Columbia/Chicago Booth)College vssome college
1
1
1
1
1
1
1
1
1
1
1
1
.844
.927
.844
.927
.768
.887
.782
.893
.684
.804
.679
.799
.629
.717
.624
.712

College vs
HS or less
1
1
1
1
1
1
1
1
1
1
1
1
.844
.944
.889
.956
.726
.853
.784
.898
.667
.779
.693
.809
.616
.695
.635
.726

Some college
vs HS or less
1
1
1
1
1
1
1
1
.900
.955
.900
.955
.711
.852
.756
.870
.632
.716
.694
.812
.58
.627
.639
.727
.556
.588
.589
.647

The Comparative Advantage of Cities

Total
comparisons
3
3
3
3
9
9
9
9
30
30
30
30
135
135
135
135
1305
1305
1305
1305
12,01512,01512,01512,015
108,945
108,945
108,945
108,945

Average
1
1
1
1
1
1
1
1
.967
.985
.967
.985
.800
.908
.830
.918
.709
.819
.753
.868
.644
.737
.670
.778
.600
.667
.616
.695

October 2014

53 / 45

Pairwise comparisons: 9 skill groups
Table: Pairwise comparisons of nine skill groups with one city per bin
Unweighted comparisons
LHS HSD HS CD AA BA MA Pro
2 HSD .423
3 HS.399 .413
4 CD.428 .486 .587
5 AA
.43 .483 .571 .483
6 BA
.476 .555 .644 .619 .602
7 MA .484 .558 .643 .614 .615 .528
8 Pro .484 .57 .645 .617 .604 .524 .499
9 PhD .49 .548 .598 .576 .577 .521 .501 .511
Pop-di↵ weighted comparisons of US-born population
LHS HSD HS CD AA BA MA Pro
2 HSD .568
3 HS
.488 .435
4 CD.583 .569 .649
5 AA.552 .53 .616 .453
6 BA.644 .65 .738 .695 .682
7 MA .648 .651 .738 .686 .695 .544
8 Pro .654 .654 .73 .676 .676 .533 .493
9 PhD .611 .605 .651 .605 .617 .502 .476 .497
Davis & Dingel (Columbia/Chicago Booth)

The Comparative Advantage of Cities

October 2014

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Pairwise comparisons: 22 occupations
Bins Weights
Comparisons Success rate
2
Unweighted
231
.714
2
Population di↵erence
231
.714
2
Population di↵erence ⇥ skill di↵erence
231
.775
3
Unweighted
693
.688
3
Population di↵erence
693
.694
3
Population di↵erence ⇥ skill di↵erence
693
.736
5
Unweighted
2,310
.684
5
Population di↵erence
2,310
.71
5
Population di↵erence ⇥ skill di↵erence
2,310
.756
10
Unweighted
10,395.653
10
Population di↵erence
10,395.689
10
Population di↵erence ⇥ skill di↵erence
10,395.735
30
Unweighted
100,485.599
30
Population di↵erence
100,485.628
30
Population di↵erence ⇥ skill di↵erence
100,485.662
90
Unweighted
925,155.564
90
Population di↵erence
925,155.582
90
Population di↵erence ⇥ skill di↵erence
925,155.606
276 Unweighted
8,073,382.543
276 Population di↵erence
8,073,382.571
276 Population di↵erence ⇥ skill di↵erence
8,073,382.598
Davis & Dingel (Columbia/Chicago Booth)

The Comparative Advantage of Cities

October 201455 / 45

Pairwise comparisons: 21 manufacturing industries
Bins Weights
Comparisons Success rate
2
Unweighted
210
.648
2
Population di↵erence
210
.648
2
Population di↵erence ⇥ skill di↵erence
210
.767
3
Unweighted
630
.637
3
Population di↵erence
630
.64
3
Population di↵erence ⇥ skill di↵erence
630
.736
5
Unweighted
2100
.63
5
Population di↵erence
2100
.629
5
Population di↵erence ⇥ skill di↵erence
2100
.715
10
Unweighted
9450
.589
10
Population di↵erence
9450
.604
10
Population di↵erence ⇥ skill di↵erence
9450
.678
30
Unweighted
91,350.559
30
Population di↵erence
91,350.577
30
Population di↵erence ⇥ skill di↵erence
91,350.631
90Unweighted
817,344.536
90
Population di↵erence
817,344.545
90
Population di↵erence ⇥ skill di↵erence
817,344.576
276 Unweighted
6,183,770.529
276 Population di↵erence
6,183,770.538
276 Population di↵erence ⇥ skill di↵erence
6,183,770.558
Davis & Dingel (Columbia/Chicago Booth)

The Comparative Advantage of Cities

October 201456 / 45