Spatial Sorting of Skills and Sectors
Jonathan I. Dingel
Chicago Booth

Frontiers in Urban Economics
November 2015

Spatial Sorting of Skills and Sectors

My goal is to tackle three questions:I

Why should we care?

I

How should we characterize skills and sectors?

I

What tools are available to model builders?

Spatial distributions of skills and sectors

Why should we care about the spatial distributions of skills and sectors?
1. They vary a lot
2. They covary with city characteristics
3. They’re often the basis for identification
4. They should help us understand how cities workSpatial distributions of skills and sectors
I

Public discussion describes US cities in terms of skills and sectors

I

Ranking cities by educational attainment is a popular media exercise

I

Place names are shorthand for sectors

Educational attainment varies a lot across cities
Share of population 25 and older with bachelor’s degree or higher

0.28 − 0.63
0.23 − 0.28
0.19 − 0.23
0.16 − 0.19
0.14 − 0.16
0.07 − 0.14

Data source: American Community Survey, 2005-2009, Series S1501 Plot: CBSAs for maptile

Sectoral composition varies a lot across cities
Employment share of Professional, Scientific, and Technical Services

0.06 − 0.26
0.04 − 0.06
0.03 − 0.04
0.03 − 0.03
0.02 − 0.03
0.01 − 0.02

Data source: County Business Patterns, 2009, NAICS 54

Plot: CBSAs for maptile

They covary with city characteristics

-1

-.5

Log (demeaned) skilled population share
.5
-.5
0

Log (demeaned) skilled population share
.25
-.25
0

1

.5

Populations of three educational groups across US metropolitan areas

10

12
14
16
Metropolitan log population

18

10

12
14
16
Metropolitan log population

Bachelor's degree

Bachelor's degree

College dropout

College dropout

High school graduate

High school graduate

Data source: 2000 Census of Population microdata via IPUMS-USA

18

They covary with city characteristics
1
-1

-2

Log (demeaned) employment share-101

Log (demeaned) employment share
-.5
.5
0

2

Employment in three occupations across US metropolitan areas

10

12
14
16
Metropolitan log population

18

10

12
14
16
Metropolitan log population

18

Computer and mathematicalComputer and mathematical

Office and administrative support

Office and administrative support

Installation, maintenance and repair

Installation, maintenance and repair

Data source: Occupational Employment Statistics 2000

10

12
14
16
Metropolitan log population

18

1
Log (demeaned) employment share
-.5
0
.5

2
Log (demeaned) employment share
0
-1
1

-1

-1

-.5

-2

Log (demeaned) skilled population share
.5
-.5
0

Log (demeaned) skilled population share
-.25
0
.25

1

.5

They covary with city characteristics

10

12
14
16
Metropolitan log population

18

10

12
14
16
Metropolitan log population

18

10

12
14
16
Metropolitan log population

18

Bachelor's degree

Bachelor's degree

Computer and mathematicalComputer and mathematical

College dropout

College dropout

Office and administrative support

Office and administrative support

High school graduate

High school graduate

Installation, maintenance and repair

Installation, maintenance and repair

Skills and sectors are strongly linked to cities’ sizes(a) Confounds inference: Agglomeration benefits vs compositional effects(b) Confounds counterfactuals: Making NYC 10x larger raises finance’s
share of national employment and GDP

They’re often the basis for identification

Recent JMPs by Notowidigdo, Diamond, and Yagan
I

Theory: all locations produce a homogeneous goodI

Empirics: exploit variation in industrial composition to estimate
model parameters via shifts in local labor demandI

Shift-share instrument: local composition × national changes

What variation does the instrument exploit?
I

Skill mix vs industrial mix (e.g. endogenous local SBTC - Beaudry,Doms, Lewis 2010)

I

City characteristics covarying with skills and sectors highlight
exclusion-restriction assumptions

They should help us understand how cities workI

Why do different people and different businesses locate in different
places?

I

The answers should be crucial to understanding how cities work

I

Which elements of the Marshallian trinity imply we’ll find financeand dot-coms in big cities?

I

Coagglomeration (Ellison Glaeser Kerr 2010) and heterogeneous
agglomeration (Faggio, Silva, Strange 2015) can provide clues

I

Theory is laggard: Most models of sectoral composition arepolarized, with specialized cities that have only one tradable sector
and perfectly diversified cities that have all the tradable sectors(Helsley and Strange 2014)

Spatial distributions of skills and sectors

How should we characterize skills and sectors?
I

Important question for both theory and empirics

A richer depiction of firms and workers improves realism, but. . .
I

more types threaten to make theoretical models intractableI

more types increase the burden of finding instruments

While the trade-offs are specific to the research question underinvestigation, we can start by asking: Are two skill groups enough?

Spatial equilibrium with two skill groups

A simple starting point
1. Two skill groups, s ∈ {L, H}
2. Spatial equilibrium: Us (Ac , ws,c , pc ) = Us (Ac 0 , ws,c 0 , pc 0 ) ∀c, c 0 ∀sw

3. Homotheticity: Us (Ac , ws,c , pc ) = Acs,cpc
These jointly imply that relative wages are spatially invariant
wH,c 0wL,c 0
wH,c
wL,c
=
=
and
Ac pc
Ac 0 pc 0
Ac pc
Ac 0 pc 0wH,cwH,c 0=∀c, c 0⇒wL,cwL,c 0Spatial equilibrium with two skill groups

A simple starting point
1. Two skill groups, s ∈ {L, H}
2. Spatial equilibrium: Us (Ac , ws,c , pc ) = Us (Ac 0 , ws,c 0 , pc 0 ) ∀c, c 0 ∀sw

3. Homotheticity: Us (Ac , ws,c , pc ) = Acs,cpc
These jointly imply that relative wages are spatially invariant
wH,c 0wL,c 0
wH,c
wL,c
=
=
and
Ac pc
Ac 0 pc 0
Ac pc
Ac 0 pc 0wH,cwH,c 0=∀c, c 0⇒wL,cwL,c 0Spatial variation in skill premia
Collegewage premia are higher in larger cities
Abilene,Akron,
Albany,Albany--Schenectady--Troy,
Albuquerque,
Alexandria,
Allentown--Bethlehem--Easton,
Altoona,
Amarillo,
Anchorage,
Ann
Anniston,Appleton--Oshkosh--Neenah,
Asheville,
Athens,Atlanta,Atlantic--CapeAuburn--Opelika,
Augusta--Aiken,
Austin--San
Bakersfield,
Baltimore,
Bangor,Barnstable--Yarmouth,
Baton
Beaumont--Port
Bellingham,
BentonBergen--Passaic,
Billings,
Biloxi--Gulfport--Pascagoula,
Binghamton,
Birmingham,
Bloomington,
Bloomington--Normal,
Boise
Boston,Boulder--Longmont,
Brazoria,
Bremerton,
Bridgeport,
Brockton,
Brownsville--Harlingen--San
Bryan--College
Buffalo--Niagara
Burlington,
Canton--Massillon,
Casper,
Cedar
Champaign--Urbana,Charleston--North
Charleston,Charlotte--Gastonia--RockCharlottesville,
Chattanooga,
Cheyenne,
Chicago,Chico--Paradise,
Cincinnati,
Clarksville--Hopkinsville,
Cleveland--Lorain--Elyria,
Colorado
Columbia,
Columbus,
CorpusCumberland,
Dallas,Danbury,
Danville,
Davenport--Moline--RockDayton--Springfield,
Daytona
Decatur,
Denver,Des
Detroit,
Dothan,Dover,
Duluth--Superior,
Dutchess
Eau
El
Elkhart--Goshen,
Elmira,Erie,
Eugene--Springfield,
Evansville--Henderson,
Fargo--Moorhead,
Fayetteville,
Fayetteville--Springdale--Rogers,
Fitchburg--Leominster,Flagstaff,
Flint,
Florence,
Fort
Fresno,Gadsden,Gainesville,
Galveston--Texas
Gary,
Glens
Goldsboro,
Grand
Great
Greeley,
Green
Greensboro--Winston-Salem--High
Greenville,
Greenville--Spartanburg--Anderson,
Hagerstown,
Hamilton--Middletown,
Harrisburg--Lebanon--Carlisle,
Hartford,
Hattiesburg,
Hickory--Morganton--Lenoir,
Honolulu,
Houma,
Houston,
Huntington--Ashland,
Huntsville,
Indianapolis,
Iowa
Jackson,Jacksonville,
Jamestown,
Janesville--Beloit,
JerseyJohnsonJohnstown,
Joplin,Kalamazoo--Battle
Kankakee,KansasKenosha,Killeen--Temple,
Knoxville,
Kokomo,La
Lafayette,
Lake
Lakeland--WinterLancaster,
Lansing--East
Laredo,Las
Lawrence,
Lawton,Lewiston--Auburn,Lexington,
Lima,
Lincoln,
LittleLongview--Marshall,
Los
Louisville,
Lowell,Lubbock,
Lynchburg,
Macon,
Madison,Manchester,Mansfield,
McAllen--Edinburg--Mission,
Medford--Ashland,
Melbourne--Titusville--Palm
Memphis,Merced,Miami,
Middlesex--Somerset--Hunterdon,
Milwaukee--Waukesha,
Minneapolis--St.
Missoula,
Mobile,Modesto,Monmouth--Ocean,Monroe,Montgomery,
Muncie,MyrtleNaples,Nashua,Nashville,
Nassau--Suffolk,
New
Newark,Newburgh,
Norfolk--Virginia
Oakland,
Ocala,
Odessa--Midland,
Oklahoma
Olympia,
Omaha,
OrangeOrlando,Owensboro,
PanamaParkersburg--Marietta,
Pensacola,
Peoria--Pekin,
Philadelphia,
Phoenix--Mesa,
Pine
Pittsburgh,
Pittsfield,
Portland,Portland--Vancouver,Portsmouth--Rochester,
Providence--Fall
Provo--Orem,
Pueblo,Punta
Racine,Raleigh--Durham--Chapel
Rapid
Reading,
Redding,
Reno,
Richland--Kennewick--Pasco,
Richmond--Petersburg,
Riverside--San
Roanoke,
Rochester,Rockford,
Rocky
Sacramento,
Saginaw--BaySt.
Salem,
Salinas,
Salt
San
Santa
Sarasota--Bradenton,
Savannah,
Scranton--Wilkes-Barre--Hazleton,
Seattle--Bellevue--Everett,Sharon,Sheboygan,
Sherman--Denison,
Shreveport--Bossier
Sioux
South
Spokane,Springfield,
Stamford--Norwalk,State
Steubenville--Weirton,
Stockton--Lodi,
Sumter,
Syracuse,
Tacoma,Tallahassee,
Tampa--St.
Terre
Texarkana,
Toledo,Topeka,Trenton,Tucson,Tulsa,
Tuscaloosa,Tyler,
Utica--Rome,
Vallejo--Fairfield--Napa,
Ventura,Victoria,
Vineland--Millville--Bridgeton,
Visalia--Tulare--Porterville,
Waco,
Washington,
Waterbury,
Waterloo--Cedar
Wausau,West
Wheeling,
Wichita,Wichita
Williamsport,
Wilmington--Newark,
Wilmington,
Worcester,
Yakima,Yolo,
York,
Youngstown--Warren,
Yuba
Yuma,
.8
.7
.6
.5
.4
.3
.2
Skill
11
12
13
14
15
16
MSA
Paso,
Crosse,Cloud,
Joseph,Louis,
Cruces,Vegas,Angeles--Long
Claire,Angelo,Antonio,
Diego,
Francisco,
Jose,
Luis
Moines,Lake
Arbor,
Bluff,
Collins--Loveland,
Lauderdale,
Myers--Cape
Pierce--Port
Smith,
WaltonWayne,
Worth--Arlington,
Bedford,Haven--Meriden,
London--Norwich,
Orleans,
York,
PA
City,
Charles,
MI
City,
CA
PA
Palm
IN
Rock--North
City,
Falls,
Haute,
OH
College,
NV
TX
Barbara--Santa
Cruz--Watsonville,
Fe,
Rosa,
Gorda,
Rapids,Bay,
Forks,
Junction,
Rapids--Muskegon--Holland,
Rouge,Bend,
OK
Mount,FL
AZ
TX
Beach,
MO
TX
City,
DE
OH
OR
NY
MA--NH
Christi,
AL
City,
GA
WI
Harbor,County,FL
COCA
Falls,
OH
WY
MT
GA
TX
IN
PA
NE--IALA
NE
ME
WA
MA--NH
CO
MI
City,
GA
AZ
AL
CA
SC
NH
KS
GA
TX
NJ
LA
OK
CO
City--Kingsport--Bristol,
VA
Obispo--Atascadero--Paso
FL
Beach,
WI
TX
PA
IL
AL
WA
CA
NJ
MI
MS
TN
TX
WI
IN
Springs,
CT
ME
MT
TX
AL
SC
WA
VA
WI
City--Ogden,
HI
CA
County,TN--AR--MS
TN
NM
MO--IL
AZ--UT
NC
MA
CA
AL
IL
NY
WV--OHKY--IN
MN
MO
SC
City,
IA
premium
OH
NY
AR
MD
IL
GA
KS
MA--NHCANC
OH--KY--IN
AL
GA--AL
OH
WI
LA
IN
WY
WI--MN
PA
FL
KY
Beach--Boca
IA--NE
ID
CA
MN
NY
SD
NC
NY--PAWIVT
TX--Texarkana,MI
NV--AZ
MA--CT
FL
SD
LA
PA
NY
Petersburg--Clearwater,
log
MT
MO
CT
VA
IL
MA
AR--OK
WA
WV
AK
PA
NM
CA
Marcos,
WI
AL
NJ
CA
NC
Beach,
KY
TX
IA
NY
FL
IN
NH
NC
PA--NJ
MO--KSAL
MS
DC--MD--VA--WVFLNC
MD--WVND--MN
NY
MD
IN
CA
TX
PA
NY
FL
TX
LA
IN
NM
AL
LA
UT
City--Midland,
TN--GA
Lansing,
MA
NC
IA
IL
SC
PA
Bernardino,
CA
May,
Station,
TX
VA
AZ
OK
MI
CA
CO
FL
River--Warwick,Paul,
Arthur,CA
TX
GA--SC
Falls,
Beach--Newport
NYFL
Falls,
IN
NJ
St.
AL
TX
Haven,
MN--WI
Coral,City,
WI
CO
ND--MNNY
Charleston,
LittleOH
OR
ME
Creek,
Beach,
TX
NJ
FL
CT
TX
NJ
population
City,
OH
CO
TX
OR
IL
Lucie,
DE--MDCT
OR--WA
MN--WI
WV--KY--OH
FL
Maria--Lompoc,
OH
NY
IL
IA
OH--WVCOOH
TX
WV--OHWIMI
IN--KYMAUTCT--RI
VA
MA
TX
CA
FL
TN--KY
TX
Raton,
Rock,
NH--MEFLCA
Hill,
Island,
OH
LA
MI
Hill,
CA
CA
AR
WA
FL
Bay,
Benito,
TX
MI
NY
NC
MS
WA
WI
NC
NJ
PA
SC
AR
NC--SCFLPA
IA--IL
RI--MAFLAR
TN--VANews,
NJ
Point,PA
MI
TX
Robles,SC
FLCAVA--NC
NCCA

.7

.8

Stamford--Norwalk, CT

McAllen--Edinburg--Mission, TX

Skill premium.5.6Danbury, CT Brownsville--Harlingen--San Benito, TX

San Jose, CA

.2

.3

.4

OrangeDallas,
County,TXCA
Houston,TX
Bridgeport, CT
Binghamton, NY
Richland--Kennewick--Pasco,
WA
El Paso, TX
San Francisco, CA
Odessa--Midland,
TX AL
Huntsville,
Miami, FL
Birmingham,
AL
Ventura,CA
Dothan,Panama
ALCity, FL
Newark, NJ
Santa
Cruz--Watsonville,
CA
Jackson,TN
Fayetteville--Springdale--Rogers,AR
Los York,
Angeles--Long
Beach, CA
Ocala,FL
Lawrence,
MA--NH
New
NY
Rochester,
MN
Austin--San Marcos, TX
Gadsden,AL
Trenton, NJ
Sherman--Denison,
TXWaco,TX TXFortWorth--Arlington,
TX NC--SCSan
Antonio,
TX
Amarillo,
Corpus Augusta--Aiken,
Christi, TX
GA--SC
West
New
Palm
Charlotte--Gastonia--Rock
Orleans,
Beach--Boca
LA Raton,
FL Hill,
FortAL
AZ
WaltonBeach,
FL
Atlanta, GA
Memphis,TN--AR--MS
Decatur,Decatur,
IL Yuma,
Sacramento,NJTampa--St.
CAHill, NC Petersburg--Clearwater,
Santa
Fe, NM
Raleigh--Durham--Chapel
FL
Visalia--Tulare--Porterville,
Jersey City,
CANJ
TX
Melbourne--Titusville--Palm
Bay,
FLBergen--Passaic,
Fort
Lauderdale,FL
San Diego, CA
Sioux City, IA--NELongview--Marshall,Orlando,FLOH--KY--IN
Washington, DC--MD--VA--WVColumbus,
Lowell,MA--NHGA--AL
Shreveport--BossierCity, LATN
Cincinnati,
Victoria, TX
BoiseChattanooga,
City,
ID
Bakersfield,
Knoxville,
TN--GACA
Oakland,CA
Fort
Smith,
AR--OK
Fort
Pierce--PortSt.
Lucie,
FL
Phoenix--Mesa,
AZ
Galveston--Texas
FL
City, TX Little Rock--North
LittleCA
Rock, AR
Alexandria,
BentonLA Manchester,
Harbor,Naples,
MI NH
Fresno,Greenville--Spartanburg--Anderson,
SC
Cumberland,
Parkersburg--Marietta,
MD--WV
Las
Cruces,NM
WV--OH
Hamilton--Middletown,
OH
Greensboro--Winston-Salem--High
Point, NC
Bloomington--Normal,
IL
TX
Kalamazoo--Battle
Creek, MI
Glens
Falls,
NYLaredo,
Akron,
Boston,MA--NH
Chicago, IL
Albany,Wichita
GA Falls,
TXNCLubbock,
Macon,
GA
Middlesex--Somerset--Hunterdon,
NJ
PA
TX Tallahassee,
Beaumont--Port
Lafayette,
FLJackson,
LA
Columbia,
Mobile,AL
SC Tulsa,
TXOH OK NM
Jacksonville,FL
Pensacola,FL
Albuquerque,
Monmouth--Ocean,
NJ Pittsburgh,
Baltimore,
MD
Philadelphia, PA--NJSanAngelo, Jacksonville,
TX
MSArthur,
Allentown--Bethlehem--Easton,PA
Goldsboro,
NC
Savannah,Montgomery,GA
ALCharleston--North
Roanoke,NH
Charleston,VA
OH
SC Columbus,
St.Nassau--Suffolk,
Louis, MO--IL NY
Abilene,
TX Nashua,
Brazoria,
VA
TX WV
Des
JohnsonMoines,Colorado
City--Kingsport--Bristol,
IASprings,Albany--Schenectady--Troy,
COCharleston,Hartford,
TN--VACT Kansas
Yuba
Tuscaloosa,
City,
CA Lynchburg,
AL
NYCity,MO--KSRiverside--San
Killeen--Temple,
Harrisburg--Lebanon--Carlisle,
PA
Indianapolis,
Cleveland--Lorain--Elyria,
IN Beach--Newport
OH
Vineland--Millville--Bridgeton,
NJ
Canton--Massillon,
Stockton--Lodi,
OH
CA
VA
Detroit,
Bernardino,MI
CA
Hattiesburg,
Jackson,MSMI
Asheville,
Dutchess
NC
County,Saginaw--Bay
NYTX
City--Midland,
Omaha,
Syracuse,
NE--IA
MIRichmond--Petersburg,
NY
Norfolk--Virginia
News,
VA--NC
Williamsport,
Florence,
SC
PA
Gainesville,
FL Peoria--Pekin,
Provo--Orem,ILNY--PA
UT
Salt
Lake
City--Ogden,
UT
Rocky
Tyler,
Mount,
Merced,TX
NC
CA
Newburgh,
Daytona
Beach,
FLTucson,Louisville,
Rochester,
KY--INNY
TX--Texarkana,AR
SantaModesto,Barbara--Santa
Sarasota--Bradenton,
CA
Maria--Lompoc,
Oklahoma
FL
CA
City,
OK
Pine
Lewiston--Auburn,
Bluff, AR Texarkana,ME
Redding,
MyrtleSpringfield,
CA
Beach,ILSC
AZCharlottesville,
VA
Fort
Myers--Cape
Coral, FL
Nashville,
TN River--Warwick,
Cedar
Waterbury,
Rapids,Anchorage,
IA OR
CT AK
Grand
Providence--Fall
Rapids--Muskegon--Holland,
Denver, CO MI
RI--MA
South
Bend,
IN
Lexington,
Worcester,Wilmington--Newark,
KYMA--CT
DE--MD
PuntaWI
Gorda,
Medford--Ashland,
OR--WA
Johnstown,
PA
Reading,
Salinas,PA
CA WA
OHPortland--Vancouver,
Wausau,Hagerstown,
MDFLYakima,
WA
Hickory--Morganton--Lenoir,
Davenport--Moline--RockAnn Arbor,
Island,NC
MIMSDayton--Springfield,
IA--IL
Spokane,Milwaukee--Waukesha,
WI
Bremerton,
Utica--Rome,WA
Biloxi--Gulfport--Pascagoula,NY
Boulder--Longmont,York,
PALakeland--WinterCO
Lansing--East
Lansing,
Haven,MI FL
Greenville,
Wheeling,
NC Clarksville--Hopkinsville,
WV--OH
Fayetteville,
NC
Wichita,
KS OH
Flint,MI
Brockton,
NC
Salem,MA NV
TN--KYOR
Toledo,Seattle--Bellevue--Everett,Joplin,
MO Wilmington,
Portland,ME
Reno,
Vallejo--Fairfield--Napa,
Scranton--Wilkes-Barre--Hazleton,
PA
Minneapolis--St. Paul,WA
MN--WI
Elmira,Danville,
Owensboro,
NY Dover,KY VA
Anniston,
Bryan--College
AL
DE
Station,TX
Atlantic--Cape
May,
Baton
NJ Rouge, LA CA
MT
Las Vegas, NV--AZ
Green
Lancaster,PA
Bangor,
ME Billings,
Portsmouth--Rochester,
NH--ME
Kankakee,
ILMonroe,
Elkhart--Goshen,
LA Charles,
San Bay,Luis
INWI
Obispo--Atascadero--Paso
London--Norwich,
Wayne,
CT--RI
Robles,IN
CA CT Buffalo--Niagara
Springfield,
MOFortNew
Youngstown--Warren,
Haven--Meriden,
OH
Falls, NY
La Jamestown,
Crosse,Pueblo,WI--MN
CO
Lake
LANew
Mansfield,
NY
OH
Santa Rosa,CA
Sumter, SCFlorence,
Kenosha,
WI
Erie,
Huntington--Ashland,
PA
WV--KY--OH
Casper, WY
NewAL
Bedford,MA
Eau
Claire,WIEvansville--Henderson,
IN--KY
Honolulu, HI
Pittsfield, MA
Altoona,PA
Grand
Junction,
Barnstable--Yarmouth,
Champaign--Urbana,CO
Houma,
MAIL
Topeka,Fargo--Moorhead,
KS LA
ND--MN
Springfield,
Tacoma,MAWA
Sheboygan,
WI
Auburn--Opelika,
Fitchburg--Leominster,Yolo,ALCAMA
Olympia,
Flagstaff,
Rockford, IL
Kokomo,IN Terre
St.Haute,
Cloud,INMN WA
Lawton,OK AZ--UTAppleton--Oshkosh--Neenah,
WI
Columbia,
Burlington,
MO
Racine,WIVT
Greeley,
Fort
Collins--Loveland,
CO
Sioux
Falls,CO
SD
Great
Rapid
Falls,St.
City,
Joseph,MTSDSteubenville--Weirton,
MO College,
OH--WVNE
Eugene--Springfield,
Gary, IN
State
Chico--Paradise,
PA Lincoln,CA
Madison, WIOR
Athens, GA
Janesville--Beloit,
WI
Duluth--Superior,
MN--WI
Sharon,PA
Waterloo--Cedar
Falls, IA
Bloomington,IN
Muncie,IN
Lima, OH
Missoula,
Cheyenne,
WY MT
Grand Forks, ND--MNLafayette, IN
Iowa City, IA Bellingham, WA
Lawrence, KS

11

12

13
14
MSA log population

15

Davis and Dingel, “A Spatial Knowledge Economy”, 201316

Spatial variation in skill premia
This pattern is getting stronger over time
Figure 3: Relative Skill Levels and Wages by City Size Over Time
Panel A: Fraction College or More by City Size

0.4
2004-7
1999
0.3

1989
1979

0.2

0.1
0

2

4

6

8

10

CitySize
Panel B: College Log Wage Premium by City Size

2004-7
0.6
1999
1989

0.4

1979

0.2
0

2

4

6

8

10

CitySize

Notes: Panel A shows the fraction of total hours worked by all men and women with at least a college degree in
Baum-Snow
and
and
City
Size”,
2013
each location type in eachyear. Pavan,
Panel B shows “Inequality
relative mean log wages forwhite menages 25-54
working fulltime and full year with versus without college degrees.

How to proceed?

The data reject our simple model; skill premia are higher in larger cities
wH,c
wH,c 06=
wL,c
wL,c 0Three possible routes to take
1. Non-homothetic preferences
2. Upward-sloping local labor supplies
3. More than two skill groups

How to proceed?

The data reject our simple model; skill premia are higher in larger cities
wH,c
wH,c 06=
wL,c
wL,c 0Three possible routes to take
1. Non-homothetic preferences (Black, Kolesnikova, Taylor 2009)
2. Upward-sloping local labor supplies (Topel, Moretti, Diamond)
3. More than two skill groups (My focus today)How to proceed?

The data reject our simple model; skill premia are higher in larger cities
wH,c
wH,c 06=
wL,c
wL,c 0Three possible routes to take
1. Non-homothetic preferences (Black, Kolesnikova, Taylor 2009)⇒ Do more skilled people find big cities less attractive for
consumption? (Albouy, Ehrlich, Liu 2015, Handbury 2012)
2. Upward-sloping local labor supplies (Topel, Moretti, Diamond)
3. More than two skill groups (My focus today)How to proceed?
The data reject our simple model; skill premia are higher in larger cities
wH,c
wH,c 06=
wL,c
wL,c 0Three possible routes to take
1. Non-homothetic preferences (Black, Kolesnikova, Taylor 2009)⇒ Do more skilled people find big cities less attractive for
consumption? (Albouy, Ehrlich, Liu 2015, Handbury 2012)
2. Upward-sloping local labor supplies (Topel, Moretti, Diamond)⇒ Relative prices and quantities imply higher relative demand forskilled in larger cities
3. More than two skill groups (My focus today)How to proceed?
The data reject our simple model; skill premia are higher in larger cities
wH,c
wH,c 06=
wL,c
wL,c 0Three possible routes to take
1. Non-homothetic preferences (Black, Kolesnikova, Taylor 2009)⇒ Do more skilled people find big cities less attractive for
consumption? (Albouy, Ehrlich, Liu 2015, Handbury 2012)
2. Upward-sloping local labor supplies (Topel, Moretti, Diamond)⇒ Relative prices and quantities imply higher relative demand forskilled in larger cities
3. More than two skill groups (My focus today)
Both 2 and 3 push us towards thinking about the complementarity
between agglomeration and skills

A continuum of skills

Recent research works with a continuum of skills
I

High-dimensional: Infinite types of individualsI

One-dimensional: Skills are ordered

A few reasons to take this route
1. Dichotomous results depend on dichotomous definitions
2. Broad categories miss important variation
3. Continuum case can be quite tractableTwo types in theory and practiceTwo-type models can be simple – but what about two-type empirics?
I

Omit types: Our plot of college wage premia was bachelor’s degrees
vs HS diplomas – use only 45% of population to test price prediction

I

Convert quantities to “equivalents”: “one person with some college
is equivalent to a total of 0.69 of a high school graduate and 0.29 ofa college graduate” (Katz & Murphy 1992, p.68)

Results may be sensitive to dichotomous definitions
I

Diamond (2015): “A MSA’s share of college graduates in 1980 is
positively associated with larger growth in its share of college
workers from 1980 to 2000”

I

Baum-Snow, Freedman, Pavan (2015): “Diamond’s result does nothold for CBSAs if those with some college education are included in
the skilled group.”Two types in theory and practiceTwo-type models can be simple – but what about two-type empirics?
I

Omit types: Our plot of college wage premia was bachelor’s degrees
vs HS diplomas – use only 45% of population to test price prediction

I

Convert quantities to “equivalents”: “one person with some college
is equivalent to a total of 0.69 of a high school graduate and 0.29 ofa college graduate” (Katz & Murphy 1992, p.68)

Results may be sensitive to dichotomous definitions
I

Diamond (2015): “A MSA’s share of college graduates in 1980 is
positively associated with larger growth in its share of college
workers from 1980 to 2000”

I

Baum-Snow, Freedman, Pavan (2015): “Diamond’s result does nothold for CBSAs if those with some college education are included in
the skilled group.”Dichotomous approach misses relevant variation

I

In labor economics, the canonical two-skill model “is largely silent on
a number of central empirical developments of the last three
decades”, such as wage polarization and job polarization (Acemoglu
and Autor 2011)I

There is systematic variation across cities in terms of finer
observable categories: population elasticities for high school
graduates (.925), associate’s degree (0.997), bachelor’s degree(1.087), and professional degree (1.113) (Davis and Dingel 2015)

Do broad categories miss important variation?
Contrasting views
I“Workers in cities with a well-educated labor force are likely to haveunobserved characteristics that make them more productive thanworkers with the same level of schooling in cities with a less-educatedlabor force. For example, a lawyer in New York is likely to bedifferent from a lawyer in El Paso, TX.” (Moretti 2004, p.2246)

I“Within broad occupation or education groups, there appears to be
little sorting on ability” (de la Roca, Ottaviano, Puga 2014)

Data sources for “no sorting” evidenceI

NLSY79: Longitudinal study of about 11,000 US individuals

I

Spanish tax data 2004-2009: 150,375 workers (de la Roca and Puga
2015)

Do broad categories miss important variation?
National Longitudinal Survey of Youth 1979
I

Bacolod, Blum, Strange (2009): “The mean AFQT scores do notvary much across [four] city sizes” within occupational categoriesI

BBS observe only one sales person in MSAs with 0.5m – 1.0m
residents (10th and 90th percentiles of AFQT are equal) tableI

Baum-Snow & Pavan (2012): Structural estimation of finite-mixture
model implies “sorting on unobserved ability within educationgroup. . . contribute little to observed city size wage premia.”I

BSP use NLSY79 data on 1754 white men; 583 have bachelor’s
degree or more; college wage premia don’t rise with city size table

Spanish tax data (de la Roca and Puga 2015)
I

150,375 workers and 37,443 migrations

I

Identification of sorting relies on random migration conditional on
observables

I

Little sorting within five educational categories

Bringing more data to bear on sortingI

Baccalaureate and Beyond tracks a cohort graduating from four-yearcolleges in 1993I

In 2003, look at 2300 white individuals who obtained no further
education after bachelor’s degree and now live in a PMSA

I

Look at variation in SAT scores across cities – all variation is within
the finest age-race-education cell in typical public data sets

I

Mean SAT score in metros with more than 3.25m residents is 40
points higher than metros with fewer than 0.57m residents

Sorting within observable demographic cells
Mean SAT score in metros with more than 3.25m residents is 40
points higher than metros with fewer than 0.57m residents

I

Full distribution suggests stochastic dominance

0

.0005

Density.001 .0015

.002

.0025

I

500

1000
SAT scorelog pop > 15
14.3 > log pop > 13.25

Observations: 740, 710, 680, 640
Sample selection: TOOKSAT==1 & B3HDG03==1 & white==1

1500
15 > log pop > 14.3
log pop < 13.25

The continuum case
Why work with a continuum?
I

Evidence for sorting on characteristics that are typically not observed

I

Need at least five types to capture sorting on observables in thesense of de la Roca and Puga (2015)

I

Modeling a finite, particular number of types is potentially painfulContinuum case can be quite tractableI

Recent work: Behrens, Duranton, Robert-Nicoud (2014), Davis andDingel (2013, 2015), Gaubert (2015), Behrens and Robert-Nicoud(Handbook 2015)

I

These papers rely on tools from the assignment literature

I

Assignments of individuals/firms to cities, with endogenous citycharacteristics determined in equilibrium

I

Davis and Dingel (2015) speak to both skills and sectors

Assignment models
Many markets concern assignment problems
I

Who marries whom? (Becker)

I

Which worker performs which job? (Roy)I

Which country makes which goods? (Ricardo)

If relevant objects are well ordered, we can use tools from mathematics ofcomplementarity to characterize equilibrium prices and quantities
I

Supermodularity (Topkis 1998)

I

Log-supermodularity (Athey 2002)

Basis for today’s introduction
I

Sattinger - “Assignment Models of the Distribution of Earnings”

I

Costinot & Vogel - “Beyond Ricardo: Assignment Models inInternational Trade”

I

Davis & Dingel - “The Comparative Advantage of Cities”

Differentials rents model

In the spirit of Ricardo’s analysis of rent, start with land and labor:I

A plot of land has fertility γ ∈ RIA farmer has skill ω ∈ R

IProfits are π(γ, ω) = p · y (γ, ω) − r (γ)

Which farmer will use which plot of land?
I

Farmers optimize: γ ∗ (ω) ≡ arg maxγ π(γ, ω)IEquilibrium prices r (γ) must support the equilibrium assignment offarmers to plots

Supermodularity

Definition (Supermodularity)
A function g : Rn → R is supermodular if ∀x, x 0 ∈ Rn
g (max (x, x 0 )) + g (min (x, x 0 )) ≥ g (x) + g (x 0 )where max and min are component-wise operators.
I

Supermodularity means the arguments of g (·) are complementsIg (x) is SM in (xi , xj ) if g (xi , xj ; x−i,−j ) is SMI

g (x) is SM ⇐⇒ g (x) is SM in (xi , xj ) ∀i, j

Ig≥ 0 ⇐⇒ g (x) is SM in (xi , xj )If g is C 2 , ∂x∂i ∂xj2Supermodularity implies PAM
Positive assortative matching:I

If g (x, t) is supermodular in (x, t), then x ∗ (t) ≡ arg maxx∈X g (x, t)
is increasing in t

I

If y (γ, ω) is strictly supermodular (fertility and skill arecomplements), then γ ∗ (ω) is increasing

I

More skilled farmers are assigned to more fertile land

Why? Suppose not:I

Suppose ∃ω > ω 0 , γ > γ 0 where γ 0 ∈ γ ∗ (ω), γ ∈ γ ∗ (ω 0 )I

γ 0 ∈ γ ∗ (ω) ⇒ p · y (γ 0 , ω) − r (γ 0 ) ≥ p · y (γ, ω) − r (γ) ∀γ

Iγ ∈ γ ∗ (ω 0 ) ⇒ p · y (γ, ω 0 ) − r (γ) ≥ p · y (γ 0 , ω 0 ) − r (γ 0 ) ∀γ 0I

Summing: p · (y (γ 0 , ω) + y (γ, ω 0 )) ≥ p · (y (γ, ω) + y (γ 0 , ω 0 ))I

Would contradict strict supermodularity of y (·)

Ricardian trade model

Costinot and Vogel (2015) survey Ricardo-Roy models
I

Ricardo: Linear production functions

I

Roy: Multiple factors of production (ω)

Output in sector σ in country c isZ
Q(σ, c) =A(ω, σ, c)L(ω, σ, c)dωΩ

Ricardo 1817: England = c > c 0 = Portugal and cloth = σ > σ 0 = wineA(σ, c)/A(σ 0 , c) ≥ A(σ, c 0 )/A(σ 0 , c 0 )Log-supermodularity (1/2)
Definition (Log-supermodularity)
A function g : Rn → R+ is log-supermodular if ∀x, x 0 ∈ Rn
g (max (x, x 0 )) · g (min (x, x 0 )) ≥ g (x) · g (x 0 )where max and min are component-wise operators.
I

Example: A : Σ × C → R+ , where Σ ⊆ R and C ⊆ R, with σ > σ 0
and c > c 0A(σ, c)A(σ 0 , c 0 ) ≥ A(σ 0 , c)A(σ, c 0 )Ig (x) is LSM in (xi , xj ) if g (xi , xj ; x−i,−j ) is LSM

I

g (x) is LSM ⇐⇒ g (x) is LSM in (xi , xj ) ∀i, j

I∂ ln g
g > 0 and g is C 2 ⇒ ∂x
≥ 0 ⇐⇒ g (x) is LSM in (xi , xj )
i ∂xj

2

Log-supermodularity (2/2)

Three handy properties:
1. If g , h : Rn → R+ are log-supermodular, then gh is
log-supermodular.
2. If g : Rn → R+ is log-supermodular, then G (x−i ) ≡is log-supermodular.

R

3. If g : Rn → R+ is log-supermodular, thenxi∗ (x−i ) ≡ arg maxxi ∈R g (xi , x−i ) is increasing in x−i .

g (xi , x−i )dxi

Assignments with factor endowments (Costinot 2009)
Primitives:
I

Technologies A(ω, σ, c) = A(ω, σ) ∀c

IEndowments L(ω, γL,c )Profit maximization by firms:
p(σ) ≤ min{w (ω, c)/A(ω, σ)}ω∈ΩΩ(σ, c) ≡ {ω ∈ Ω : L(ω, σ, c) > 0)} ⊆ arg min{w (ω, c)/A(ω, σ)}ω∈ΩA(ω, σ) is strictly log-supermodular in (ω, σ) ⇒IΩ(σ, c) is increasing in σ by property 3 of LSM

I

High-ω factors are employed in high-σ activities

Equilibrium:I

FPE w (ω, c) = w (ω)

IContinuum ⇒ Σ(ω, c) = Σ(ω) singleton

Output quantities (Costinot 2009)
Labor market clearing:Z
L(ω, σ, c)dσ = L(ω, γL,c ) ∀ω, cΣ

L(ω, γL,c ) is strictly log-supermodular: High-γL,c locations are relatively
abundant in high-ω factors
Z
Q(σ, c) =A(ω, σ)L(ω, σ, c)dωZΩ=
A(ω, σ)L(ω, γL,c )dωby Σ(ω, c) singletonΩ(σ)

Rybczynski: A(ω, σ) and L(ω, γL,c ) SLSM ⇒ Q(σ, γL,c ) SLSM byproperties 1 and 2 of LSM

Comparative Advantage of Cities: Theory

I

Davis and Dingel (2015) describe comparative advantage of cities as
jointly governed by individuals’ comparative advantage andlocational choices

I

Cities endogenously differ in TFP due to agglomeration

I

More skilled individuals are more willing to pay for more attractive
locationsI

Larger cities are skill-abundant in equilibriumI

By individuals’ comparative advantage, larger cities specialize inskill-intensive activities

I

Under a further condition, larger cities are larger in all activities

1

0

-1

-3

-2

Compare elasticities of different
skills, sectors
I Steeper slope in log-log plot ishigher elasticity
10
12
14
16
18
Metropolitan
log population
I Elasticities may
be positive
for all
Professional, Scientific & Technical Services
sectorsI.5

Elasticity test of variation in
relative population/employment

0

I

-.5

Characterize the comparativeadvantage of cities with two tests

-1

I

2

Use US data on skills and sectors
Log (demeaned) employment shareI

Log (demeaned) employment share

1

3

Comparative Advantage of Cities: Empirics (1/2)

10

12
14
16
Metropolitan log population

18

Professional, Scientific & Technical Service

Finance & Insurance

Finance & Insurance

Manufacturing

Manufacturing

Comparative Advantage of Cities: Empirics (2/2)
Pairwise comparison test (LSM)I

The function f (ω, c) is log-supermodular if
c > c 0 , ω > ω 0 ⇒ f (ω, c)f (ω 0 , c 0 ) ≥ f (ω 0 , c)f (ω, c 0 )I

Our theory says skill distribution f (ω, c) and sectoral employment
distribution f (σ, c) are log-supermodularI

For example, population of skill ω in city c is f (ω, c). Check
whether, for c > c 0 , ω > ω 0 ,f (ω, c)f (ω, c 0 )≥0f (ω , c)f (ω 0 , c 0 )Are larger cities larger in all sectors?
I

Check if c > c 0 ⇒ f (σ, c) ≥ f (σ, c 0 )TheoryModel components
Producers
I

Skills: Continuum of skills indexed by ω (educational attainment)

I

Sectors: Continuum of sectors σ (occupations, industries)

I

Goods: Freely traded intermediates assembled into final goodI

All markets are perfectly competitive

PlacesI

Cities are ex ante identical

I

Locations within cities vary in their desirability

I

TFP depends on agglomeration of “scale and skills”
 Z
A(c) = J L,
j(ω)f (ω, c)dωω∈Ω

Individual optimization
Perfectly mobile individuals simultaneously chooseI

A sector σ of employment

I

A city with total factor productivity A(c)I

A location τ (distance from ideal) within city c

The productivity of an individual of skill ω isq(c, τ, σ; ω) = A(c)T (τ )H(ω, σ)Utility is consumption of the numeraire final good, which is income minus
locational cost:U(c, τ, σ; ω) = q(c, τ, σ; ω)p(σ) − r (c, τ )= A(c)T (τ )H(ω, σ))p(σ) − r (c, τ )Sectoral choiceI

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

sectoralI

H(ω, σ) is log-supermodular in ω, σ and strictly increasing in ω

I

Comparative advantage assigns high-ω individuals to high-σ sectors

I

Absolute advantage makes more skilled have higher incomes(G (ω) = maxσ H(ω, σ)p(σ) is increasing)Locational choiceI

A location’s attractiveness γ = A(c)T (τ ) depends on c and τI

T 0 (τ ) < 0 may be interpreted as commuting to CBD, proximity to
productive opportunities, or consumption value

I

More skilled are more willing to pay for more attractive locations

I

Equally attractive locations have same rental price and skill typeI

Location in higher-TFP city is farther from ideal desirability
γ = A(c)T (τ ) = A(c 0 )T (τ 0 )A(c) > A(c 0 ) ⇒ τ > τ 0

I

Locational hierarchy: A smaller city’s locations are a subset of larger
city’s in terms of attractiveness: A(c)T (0) > A(c 0 )T (0)Equilibrium distributions
I

Skill and sectoral distributions reflect distribution of locational
attractiveness: Higher-γ locations occupied by higher-ω individuals
who work in higher-σ sectors

I

Locational hierarchy ⇒ hierarchy of skills and sectors

I

The distributions f (ω, c) and f (σ, c) are log-supermodular if andonly if the supply of locations with attractiveness γ in city c, s(γ, c),
is log-supermodular



γ
 1 V
if γ ≤ A(c)T (0)
A(c)
A(c)
s(γ, c) =0otherwise∂
where V (z) ≡ − ∂z
S T −1 (z) is the supply of locations with innate
desirability τ such thatT (τ ) = z

When is s(γ, c) log-supermodular?
Proposition (Locational attractiveness distribution)
The supply of locations of attractiveness γ in city c, s(γ, 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.
I

Links each city’s exogeneous distribution of locations, V (z), toendogenous equilibrium locational supplies s(γ, c)

I

Informally, ranking relative supplies is ranking elasticities of V (z)


γ


∂
ln
V
A(c)
∂ ln s(γ, c)γ⇒=s(γ, c) ∝ V
A(c)∂ ln γ∂ ln zI

Satisfied by the canonical von Thünen/monocentric geography

The Comparative Advantage of Cities
Corollary (Skill and employment distributions)
If V (z) has a decreasing elasticity, then f (ω, c) and f (σ, c) are
log-supermodular.
I

Larger cities are skill-abundant in equilibrium (satisfies Assumption 2 inCostinot 2009)I

Locational productivity differences are Hicks-neutral in equilibrium(satisfies Definition 4 in Costinot 2009)

I

H(ω, σ) is log-supermodular (Assumption 3 in Costinot 2009)

Corollary (Output and revenue distributions)
If V (z) has a decreasing elasticity, then sectoral output Q(σ, c) andrevenue R(σ, c) ≡ p(σ)Q(σ, c) are log-supermodular.

The Comparative Advantage of Cities
Corollary (Skill and employment distributions)
If V (z) has a decreasing elasticity, then f (ω, c) and f (σ, c) are
log-supermodular.
I

Larger cities are skill-abundant in equilibrium (satisfies Assumption 2 inCostinot 2009)I

Locational productivity differences are Hicks-neutral in equilibrium(satisfies Definition 4 in Costinot 2009)

I

H(ω, σ) is log-supermodular (Assumption 3 in Costinot 2009)

Corollary (Output and revenue distributions)
If V (z) has a decreasing elasticity, then sectoral output Q(σ, c) andrevenue R(σ, c) ≡ p(σ)Q(σ, c) are log-supermodular.

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

Corollary
If V (z) has a decreasing elasticity that is less than -1 at−1γ(ω)
z = K A(c)= A(c) , A(c) > A(c 0 ) implies f (ω, c) ≥ f (ω, c 0 ) andf (M(ω), c) ≥ f (M(ω), c 0 ) ∀ω ∈ Ω.

Empirical approach anddata description

Empirical tests
Our theory says f (ω, c) and f (σ, c) are log-supermodular.
Two tests to describe skill and sectoral employment distributions:
I

Elasticities test:
Compare population elasticities estimated via linear regression
More skilled types should have higher population elasticities
I More skill-intensive sectors should have higher population elasticities

I

I

I

Pairwise comparisons test:
Compare any two cities and any two skills/sectors
Relative population of more skilled should be higher in larger city:f (ω,c 0 )(ω,c)
c > c 0 , ω > ω 0 ⇒ ff(ω0 ,c) ≥ f (ω 0 ,c 0 )I Relative employment of more skill-intensive sector should be higher(σ,c)
f (σ,c 0 )in larger city: c > c 0 , σ > σ 0 ⇒ ff(σ0 ,c) ≥ f (σ 0 ,c 0 )I “Bin” together cities ordered by size and compare bins similarly
I

I

Data: Skills
I

Proxy skills by educational attainment, assuming f (edu, ω, c) is
log-supermodular in edu and ω (Costinot and Vogel 2010)

I

Following Acemoglu and Autor (2011), we use a minimum of threeskill groups.
Population
share
.37

Share
US-born.78

Some college

.31

.89

Bachelor’s or more

.32

.85

Skill (3 groups)
High school or less

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
Doctorate

Population
share
.04
.08
.25
.23
.08
.20
.08
.03
.01

Share
US-born
.29
.73
.88
.89
.87
.86
.84
.81
.72

Notes: Sample is individuals 25 and older in the labor force residing in 270 metropolitan
areas. Data source: 2000 Census of Population microdata via IPUMS-USA

Data: Sectors
I
I
I

SOC
45
37
35
47
51
29
21
25
19
23

19 industrial categories (2-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
Occupational category
Farming, Fishing & Forestry
Cleaning & MaintenanceFood Preparation & Serving Related
Construction & Extraction
Production
Healthcare Practitioners & TechnicalCommunity & Social Services
Education, Training & Library
Life, Physical & Social Science
Legal Occupations

Skill
intensity
8.7
10.8
11.5
11.5
11.5
15.6
15.8
16.3
17.2
17.3

NAICS
11
72
23
56
48
52
51
55
54
61

Industry
Forestry, fishing, hunting & agriculture support
Accommodation & food services
Construction
Admin, support, waste mgt, remediation
Transportation & warehousing
Finance & insurance
Information
Management of companies & enterprises
Professional, scientific & technical services
Educational services

Data source: 2000 Census of Population microdata via IPUMS-USA

Skill
intensity
10.5
11.8
11.9
12.2
12.6
14.1
14.1
14.6
15.3
15.6

Empirical results

Three skill groups

Dependent variable: ln f (ω, c)βω1 High school or less × log populationβω2 Some college × log populationβω3 Bachelor’s or more × log population

(1)
All

(2)
US-born

Population
share

Share
US-born

0.954

0.895

.37

.78

(0.0108)(0.0153)

.31

.89

.32

.85

0.996

0.969

(0.0105)(0.0122)

1.086

1.057

(0.0153)(0.0162)

Nine skill groups
Dependent variable: ln f (ω, c)βω1 Less than high school × log populationβω2 High school dropout × log populationβω3 High school graduate × log populationβω4 College dropout × log populationβω5 Associate’s degree × log populationβω6 Bachelor’s degree × log populationβω7 Master’s degree × log populationβω8 Professional degree × log populationβω9 PhD × log population

(1)
All

(2)
US-born

Population
share

Share
US-born

1.089

0.858

.04

.29

(0.0314)(0.0239)

.08

.73

.25

.88

.23

.89

.08

.87

.20

.86

.08

.84

.03

.81

.01

.72

1.005

0.933

(0.0152)(0.0181)

0.925

0.890

(0.0132)(0.0163)

0.997

0.971

(0.0111)(0.0128)

0.997

0.965

(0.0146)(0.0157)

1.087

1.059

(0.0149)(0.0164)

1.095

1.063

(0.0179)(0.0181)

1.113

1.082

(0.0168)(0.0178)

1.069

1.021

(0.0321)(0.0303)

Spatial distribution of skills in 1980

Dependent variable: ln f (ω, c)βω1 Less than high school × log populationβω2 High school dropout × log populationβω3 Grade 12 × log populationβω4 1 year college × log populationβω5 2-3 years college × log populationβω6 4 years college × log populationβω7 5+ years college × log population

(1)
All

(2)
US-born

Population
share

Share
US-born

0.975

0.892

.09

.72

(0.0236)(0.0255)

.12

.91

.33

.93

.10

.94

.12

.91

.12

.92

.12

.90

1.006

0.983

(0.0157)(0.0179)

0.989

0.971

(0.00936)(0.0111)

1.047

1.033

(0.0144)(0.0151)

1.095

1.076

(0.0153)(0.0155)

1.091

1.073

(0.0153)(0.0157)

1.113

1.093

(0.0202)(0.0196)

1.4

Occupations’ elasticities and skill intensities

Population elasticity
1
1.2

Computer & MathematicalBusiness & Financial Operations

Architecture & Engineering
Legal
Life, Physical, & Social Science
Arts, Design, Entertainment, Sports, & Media

Protective Service
Office & Administrative Support
Management
Transportation & Material Moving
Personal Care & Service
Cleaning & MaintenanceConstruction & Extraction

Production

Food Preparation & Serving Related

Sales & Related
Education, Training, & Library
Installation, Maintenance, & Repair
Healthcare Practitioners & Technical
Healthcare Support
Community & Social Services.8

Farming, Fishing, & Forestry

6

8
10
12
14
16
18
Skill intensity (employees' average years of schooling)

20

1.6

Industry population elasticities and skill intensities

Population elasticity
1.2
1.4

Management of companies and enterprises

Professional, scientific and technical services
Admin, support, waste mgt, remediation services
Educational services
Finance and insurance Information
Transportation and warehousing
Real estate and rental and leasing
Wholesale tradeArts, entertainment and recreation
Construction

1

Other services (except public administration)
Accommodation and food services

Utilities
Manufacturing
Retail trade

Health care and social assistance.8

MiningForestry, fishing, hunting, and agriculture support

10

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

SummaryI

Spatial distributions of skills and sectors are prominent in public
discussion of cities, exploited for identification in empirical work, andpotentially key to understanding agglomeration processesI

We need models with more than two skills groups and more thanperfectly specialized/diversified cities

I

Recent research exploits tools from assignment literature tocharacterize spatial sorting of skills and sectors

I

Assignment mechanisms can be used in quantitative work via
assumptions on components observed and unobserved by the
econometrician – Fréchet distribution is most popularThank youBacolod, Blum, Strange on AFQT scores
Table 5
Agglomeration and the AFQT and Rotter scores: Distributions for selected occupations and city size categories.
Panel A. 10th & 90th Percentiles of AFQT Score
MSA Size

Panel B. 10th & 90th Percentiles of Rotter Score
MSA Size

Occupation

Small

MediumLarge

Very Large

Small

MediumLarge

Very Large

Managers

51.99
69.65
62.92
79.22
60.75
60.9
74.1
81.43
60.32
68.81
69.74
81.45
47.48
58.01
39.73
57.01
42.4
51.75
34.54
45.41
75.67
75.67
57.33
58.88
38.52
52.54
67.28
79.89
34.18
55.98
60.54
68.11
56.78
66.61

42.02
64.81
79.22
86.96
70.92
72.93
59.79
81.77
63.82
75.67
82.27
82.27
21.05
54.9
29.72
61.59
26.8
42.58
35.99
55.4
53.53
77.7
61.02
65.34
54.14
57.04
52.01
81.6
37.9
70.32
34.46
57.92
52.77
69.49

36.37
82.29
62.95
87.59
44.98
60.03
70.4
88.25
50.88
81.96
62.92
86.18
27.21
64.57
24.13
67.99
15.22
63.56
11.83
53.21
47.25
58.03
61.97
76.31
57.37
69.24
46.84
85.74
34.05
75.89
19.58
65.6
44.92
74

24.6
91.72
49.67
94.93
41.62
82.56
45.13
93.61
34.51
86.44
66.41
96.12
10.71
80.6
12.71
74.14
8.89
68.33
5.55
64.15
63.06
92.92
51.23
83.92
34.1
77.37
30.44
93.88
14.65
83.85
14.74
73.21
33.86
84.39

0.47
0.55
0.47
0.53
0.57
0.57
0.45
0.49
0.51
0.54
0.49
0.56
0.53
0.58
0.51
0.56
0.46
0.51
0.52
0.55
0.52
0.52
0.53
0.54
0.49
0.5
0.47
0.55
0.49
0.6
0.51
0.56
0.5
0.54

0.46
0.52
0.49
0.53
0.6
0.6
0.47
0.6
0.45
0.52
0.42
0.42
0.49
0.64
0.45
0.55
0.48
0.58
0.48
0.63
0.45
0.51
0.48
0.51
0.52
0.54
0.42
0.61
0.45
0.62
0.5
0.59
0.48
0.56

0.43
0.65
0.42
0.58
0.49
0.62
0.46
0.55
0.43
0.62
0.44
0.5
0.42
0.66
0.41
0.62
0.46
0.7
0.43
0.67
0.47
0.49
0.46
0.59
0.53
0.58
0.42
0.62
0.41
0.62
0.44
0.67
0.45
0.6

0.37
0.68
0.41
0.63
0.42
0.62
0.4
0.6
0.38
0.62
0.42
0.59
0.38
0.7
0.38
0.68
0.39
0.69
0.4
0.72
0.44
0.6
0.41
0.57
0.4
0.63
0.38
0.67
0.37
0.7
0.39
0.68
0.4
0.65

Engineers
Therapists
College Professors
Teachers
Sales Persons
Food Services
Mechanics
Construction Workers
Janitors
Natural Scientists
NursesSocial Workers
Technicians
Administrative Support
Personal Services
Total

Notes. The first row reports the 10th percentile, while the second row reports the 90th percentile. Small MSA size: population between 100,000 and 500,000; Medium:between 500,000 and 1 million; Large: between 1 million and 4 million; Very Large: more than 4 million.

College wage premia in NLSY vs Census
Baum-Snow & Pavan 2000 Census 2000 Census
Table 1, column 1
PMSA
CMSA
Non-Hispanic white males with fewer than 15 years of work experience
Medium-city college wage premium.09
0.09780.0937(0.00578)

Large-city college wage premiumN
Individuals observed
R2
p-value for equal premia

.05

17991
1257

(0.00613)

0.145

0.154

(0.00565)(0.00551)

3013263013260.197
03013263013260.202
0Robust standard errors in parentheses
Notes: This table describes full-time, full-year employees ages 18-55. Following BSP,
“college graduate” means anyone with a bachelor’s degree or greater educational attainment. Large means population greater than 1.5m. Medium means population .25m to
1.5m. Small includes rural areas. The premia in the first column are obtained by differencing the numbers for high-school and college graduates’ log wages in the first columnof BSP’s Table 1. Note that they report results for temporally deflated panel data, while
we report cross-sectional results. BSP assign individual to metropolitan statistical areasusing the 1999 boundary definitions, but they do not specify whether they use consolidated
MSAs or primary MSAs for large cities. Hence we report both.