Skill-Biased Agglomeration
Jonathan Dingel

Skill-Biased Agglomeration

Economic geography of human capital: Where do skilled workers live and why?
My goal today is to tackle four questions:▶ Why should we care about the spatial distributions of skills and sectors?
▶ How do we know that agglomeration is skill-biased?
▶ How should we characterize skills when modeling cities?
▶ What tools are relevant for building and estimating models?

Dingel – Skill-Biased Agglomeration – UEA Summer School 2024 – 2

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 are often used as exogenous variation
4. They should help us understand how cities work

Dingel – Skill-Biased Agglomeration – UEA Summer School 2024 – 3

Spatial distributions of skills and sectors▶ Public discussion describes US cities in terms of skills and sectors▶ Ranking cities by educational attainment is a popular media exercise▶ Place names are shorthand for sectors

Dingel – Skill-Biased Agglomeration – UEA Summer School 2024 – 4

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

Dingel – Skill-Biased Agglomeration – UEA Summer School 2024 – 5

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

Dingel – Skill-Biased Agglomeration – UEA Summer School 2024 – 6

They covary with city characteristics

-1

-.5

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

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

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

18

Dingel – Skill-Biased Agglomeration – UEA Summer School 2024 – 7

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

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

Dingel – Skill-Biased Agglomeration – UEA Summer School 2024 – 7

Data source: Occupational Employment Statistics 2000

10

12
14
16
Metropolitan log population18

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

1

2
Log (demeaned) employment share
0
-1
1

-1

-1

-.5

-2

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

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

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 ofnational employment and GDP
Dingel – Skill-Biased Agglomeration – UEA Summer School 2024 – 7

They are often used as exogenous variation
It is common to see the following theory-empirics pairing:▶ Model: all locations produce a homogeneous good
▶ Estimation by shift-share design: exogenous shifts in local labor demand via
local industrial composition × national changes in industrial employment
What variation does this shift-share design exploit?
▶ GPSS: employment shares are IVs measuring exposure to shifts▶ AKM & BHJ: sectoral shifters are randomly assigned and independent▶ Skill mix vs industry mix (e.g., endogenous local SBTC of Beaudry, Doms,
Lewis 2010)▶ City characteristics covarying with skills and sectors highlight
exclusion-restriction assumptions
Dingel – Skill-Biased Agglomeration – UEA Summer School 2024 – 8

They should help us understand how cities work
▶ Why do different people and different businesses locate in different places?
▶ The answers should be crucial to understanding how cities work
▶ Lucas (1988): “the ‘force’ we need to postulate account for the central role ofcities in economic life is of exactly the same character as the ‘external humancapital’ I have postulated as a force to account for certain features ofaggregative development.”▶ Which elements of the Marshallian trinity imply we’ll find finance anddot-coms in big cities?
▶ Coagglomeration (Ellison Glaeser Kerr 2010) and heterogeneous
agglomeration (Faggio, Silva, Strange 2015) can provide clues▶ Eckert, Ganapati, Walsh (2024): Wage growth since 1980 has been faster inlarger cities and it’s all in business services
Dingel – Skill-Biased Agglomeration – UEA Summer School 2024 – 90.4
2004-71999

An introduction to skill-biased agglomeration
0.3

1989

▶ Central fact: Larger cities have higher college-graduate shares (Berry &

1979

0.2

Glaeser 2005, Moretti 2012) and higher college wage premia (Baum-Snow &Pavan 2013, Davis & Dingel 2019)
0.1

0

2

4

6

8

10

CitySize

Figure 3: Relative Skill Levels and Wages by City Size Over Time
Panel A: Fraction College or More by City Size

Panel B: College Log Wage Premium by City Size

2004-70.4
2004-7
1999
0.3

0.6
1999

1989
1979

0.2

1989

0.4

1979

0.1

0.2
0

2

4

6

8

10

0

CitySize

2

4

6

8

10

CitySize

Panel B: College Log Wage Premium by City Size

Notes: Panel A shows the fraction of total hours worked by all men and women with at least a college degree ineach location type in each year. Panel B shows relative mean log wages for white men ages 25-54 working fullBaum-Snow and Pavan, “Inequality
and
City
2013
time and full year withversus withoutcollegeSize”,
degrees.
2004-7▶ How to explain spatial variation in relative prices and relative quantities?
▶ Start from “canonical model” with two skill types and spatial variation in
0.6

1999

0.4

1989

relative supply
and relative demand
Dingel – Skill-Biased Agglomeration – UEA Summer School 2024 – 10
1979

0.2

Spatial equilibrium with two skill groups
A simple starting point
1. Two skill groups, s ∈ {L, H}
2. Elastic labor supply: Us (Ac , ws,c , pc ) = Us (Ac′ , ws,c′ , pc′ ) ∀c, c′ ∀s
3. Homothetic preferences: Us (Ac , ws,c , pc ) =ws,c Ac
pc

These jointly imply that relative wages are spatially invariant:wH,c′ Ac′wL,c′ Ac′
wH,c AcwL,c Ac
=
and
=
pc
pc′
pc
p c′
wH,c′
wH,c
′
=⇒
=
∀c, c
wL,c
wL,c′

Dingel – Skill-Biased Agglomeration – UEA Summer School 2024 – 11Spatial equilibrium with two skill groups
A simple starting point
1. Two skill groups, s ∈ {L, H}
2. Elastic labor supply: Us (Ac , ws,c , pc ) = Us (Ac′ , ws,c′ , pc′ ) ∀c, c′ ∀s
3. Homothetic preferences: Us (Ac , ws,c , pc ) =ws,c Ac
pc

These jointly imply that relative wages are spatially invariant:wH,c′ Ac′wL,c′ Ac′
wH,c AcwL,c Ac
=
and
=
pc
pc′
pc
p c′
wH,c′
wH,c
′
=⇒
=
∀c, c
wL,c
wL,c′

Dingel – Skill-Biased Agglomeration – UEA Summer School 2024 – 11Spatial equilibrium and skill premia (two types; homothetic prefs)
wH /wL

Relative supply
Rosen(1979), Roback(1982)

Relative demand
QH /QL
Differences in productivity “tend to show up exclusively in changes in quantities of skilled people, not in
different returns to skilled people across space” (Glaeser 2008)
Dingel – Skill-Biased Agglomeration – UEA Summer School 2024 – 12

Spatial equilibrium and skill premia (two types; homothetic prefs)
wH /wL

Relative supply
Topel (1986), Moretti (2011),
Diamond (2016)

Relative demand
QH /QL
Dingel – Skill-Biased Agglomeration – UEA Summer School 2024 – 12

Spatial equilibrium and skill premia (two types; homothetic prefs)
wH /wL

Relative supply
Topel (1986), Moretti (2011),
Diamond (2016)

Skill-biased agglomeration
Relative demand
QH /QL
Dingel – Skill-Biased Agglomeration – UEA Summer School 2024 – 12

Why not a story about relative supply?
Preferences are not homothetic. What happens if we relax that assumption?
Relative prices of income-elastic goods are lower in larger cities:▶ Income elasticity of housing demand is less than one:
Albouy, Ehrlich, and Liu (2016), Finlay and Williams (2023)▶ Larger cities specialize in producing income-elastic tradable goods:
Dingel (2017), Handbury (2021), Onoda (2023)
These are empirically relevant forces, but they increase the relative supply of skill
in larger cities

Dingel – Skill-Biased Agglomeration – UEA Summer School 2024 – 13

Spatial equilibrium and skill premia (two types)
wH /wL
wH,c′ wL,c
wL,c′
wH,c
PH,c = PH,c′ , PL,c = PL,c′ , PH,c ̸= PL,cRelative supply
Big-city relative supply(BKT 2009, Lee 2010)

Relative demand
QH /QL

Black, Kolesnikova, Taylor (2009): “if the income elasticity of housing is less than one. . . thereturn to education is lower in cities that are more expensive”
Dingel – Skill-Biased Agglomeration – UEA Summer School 2024 – 14

Spatial equilibrium and skill premia (two types)
wH /wL
Relative supply
Big-city relative supply

Skill-biased agglomeration
Relative demand
QH /QLWith two types, the explanation for spatial variation in relative prices and relative
quantities lies in skill-biased agglomeration shifting relative demand.
Dingel – Skill-Biased Agglomeration – UEA Summer School 2024 – 14

What is skill-biased agglomeration?

The canonical model is one way of interpreting the central fact
▶ In two-type model, larger cities have higher relative demand for skill▶ With more than two underlying types, these relative quantities and relative
prices may reflect compositional differences (i.e., spatial sorting)▶ I read the available empirical evidence as saying two types are not enough

Dingel – Skill-Biased Agglomeration – UEA Summer School 2024 – 15

Two types in theory and practiceTwo-type models can be simple – but what about two-type empirics?
▶ Omit types: Davis & Dingel (2019) plot of college wage premia showsbachelor’s vs HS diplomas – use only 45% of population to test price prediction▶ Convert quantities to “equivalents”: “one person with some college isequivalent to a total of 0.69 of a high school graduate and 0.29 of a college
graduate” (Katz & Murphy 1992, p.68)
Results may be sensitive to dichotomous definitions▶ Diamond (2016): “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”▶ Baum-Snow, Freedman, Pavan (2015): “Diamond’s result does not hold for
CBSAs if those with some college education are included in the skilled group.”
Dingel – Skill-Biased Agglomeration – UEA Summer School 2024 – 16

Two types in theory and practiceTwo-type models can be simple – but what about two-type empirics?
▶ Omit types: Davis & Dingel (2019) plot of college wage premia showsbachelor’s vs HS diplomas – use only 45% of population to test price prediction▶ Convert quantities to “equivalents”: “one person with some college isequivalent to a total of 0.69 of a high school graduate and 0.29 of a college
graduate” (Katz & Murphy 1992, p.68)
Results may be sensitive to dichotomous definitions▶ Diamond (2016): “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”▶ Baum-Snow, Freedman, Pavan (2015): “Diamond’s result does not hold for
CBSAs if those with some college education are included in the skilled group.”
Dingel – Skill-Biased Agglomeration – UEA Summer School 2024 – 16

Dichotomous approach misses relevant variation▶ In labor economics, the canonical two-skill model “is largely silent on anumber of central empirical developments of the last three decades”, such as
wage polarization and job polarization (Acemoglu and Autor 2011)▶ In the urban context, there is systematic variation across cities in terms offiner 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 2020)

Dingel – Skill-Biased Agglomeration – UEA Summer School 2024 – 17

How much should we worry about spatial sorting?
Contrasting views. Suggestions of sorting:▶ “Workers in cities with a well-educated labor force are likely to have unobserved
characteristics that make them more productive than workers with the same level ofschooling in cities with a less-educated labor force. For example, a lawyer in New
York is likely to be different from a lawyer in El Paso, TX.” (Moretti 2004, p.2246)▶ Within occupations, job postings in larger cities require more interactive tasks
and using newer technologies, especially for college graduates (Atalay, Sotelo,
Tannenbaum 2021)
Claim of little sorting (e.g., de la Roca, Ottaviano, Puga 2023) stems from:▶ Cognitive test scores in NLSY79 (11,000 US individuals)▶ Estimated finite-mixture model using NLSY79 (Baum-Snow & Pavan 2012)▶ Individual fixed effects from AKM-style regressions
Dingel – Skill-Biased Agglomeration – UEA Summer School 2024 – 18

Evidence of little spatial sorting from US NLSY79
National Longitudinal Survey of Youth 1979 (NLSY79)▶ Bacolod, Blum, Strange (2009): “The mean AFQT scores do not vary much
across [four] city sizes” within occupational categories▶ BBS observe only one sales person in MSAs with 0.5m – 1.0m residents (10thand 90th percentiles of AFQT are equal)

table▶ Baum-Snow & Pavan (2012): Estimated finite-mixture model implies “sortingon unobserved ability within education group. . . contribute little to observed
city size wage premia.”▶ 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

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Bringing more US data to bear on sorting▶ Baccalaureate and Beyond tracks a cohort graduating from four-year colleges
in 1993▶ In 2003, look at 2,300 white individuals who obtained no further education
after bachelor’s degree and now live in a MSA▶ Look at variation in SAT scores across cities – all variation is within the finest
age-race-education cell in typical public data sets
▶ Mean SAT score in metros with more than 3.25m residents is 40 points higher
than metros with fewer than 0.57m residents

Dingel – Skill-Biased Agglomeration – UEA Summer School 2024 – 20

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

0

.0005

Density.001 .0015

.002

.0025

than metros with fewer than 0.57m residents▶ Full distribution suggests stochastic dominance

500

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

1500
15 > log pop > 14.3
log pop < 13.25

Dingel –Observations:
Skill-Biased
Agglomeration– UEA Summer School 2024 – 21740, 710,
680, 640
Sample selection: TOOKSAT==1 & B3HDG03==1 & white==1

Evidence from wage regressions with worker fixed effects
de la Roca and Puga (2017) use Spanish tax data on 2004-2009 earnings:▶ 157,113 workers and 40,809 cross-city moves▶ Assume random migration conditional on observables▶ eijt is worker i’s experience in city j through time t▶ Estimating equation:ln wict = σc + µi +CXδjc eijt + βxit + ϵict

j=1

▶ If one only estimates a static specificationln wict = σc + µi + βxit + ζictPσ̂c may be biased if Cov (ιict − ῑic ), C
δ
(e
−
ē
)
̸= 0 (if workers’
jc
ijt
ij
j
experience is higher when they are in c)
Dingel – Skill-Biased Agglomeration – UEA Summer School 2024 – 22

de la Roca and Puga (2017) on dynamics and sorting▶ Experience in larger cities is more valuable and portable

35%
30%
20%

25%

Madrid always

10%

15%

Madrid 5 years,
then Santiago
Sevilla always

0%

5%

Sevilla 5 years,
then Santiago
0

1

2

3

4

5

6

7

8

9

Years worked
Dingel – Skill-Biased Agglomeration – UEA Summer School 2024 – 23
Panel (a) Profiles allowing for learning benefits of bigger cities

10

Downloaded from http://restud.oxfordjo

Earnings premium,relative to Santiago — median size

40%

122
REVIEW
OF ECONOMICSTUDIES and Sevilla (fourth largest)
Earnings of equivalent
workers
in Madrid(largest)
relative to Santiago de Compostela (median)de la Roca and Puga (2017) on dynamics and sorting

25%

30%

35%

Madrid always,thworker fixed-effect at 75 percentile

15%

20%

Madrid always,thworker fixed-effect at 25 percentile

10%

Sevilla always,thworker fixed-effect at 75 percentile

0%5%

Sevilla always,thworker fixed-effect at 25 percentile

0

1

2

3

4

5

6

7

8

9

Years worked
Figure 7
Earnings profiles relative to median-sized city, high- and low-ability worker

Dingel – Skill-Biased Agglomeration – UEA Summer School 2024 – 23
TABLE 5

10

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Earnings premium,relative to Santiago — median size

40%

▶ Experience in larger cities is more valuable and portable
ROCA & PUGALEARNING BY WORKING IN BIG CITIES
135▶ Big-city experienceDEisLAmore
valuablefor workers with higher ability

50%

de la Roca and Puga (2017) on dynamics and sorting
0

1

2

3

4

5

6

7

8

9

10

Years worked▶ Experience in larger cities is more valuableand portable
Figure 7▶ Big-city experienceis more valuable for workers with higher ability
Earnings profiles relative to median-sized city, high- and low-ability worker▶ There is sorting across five occupational categories
TABLE 5Comparison of occupational groups across cities of different sizes
Occupational groups (%)

First to second biggest cities
Third to fifth biggest cities
Other cities

Very-highskilled

Highskilled

Medium-highskilledMedium-low
skilledLowskilled

10.9
6.3
3.5

13.8
10.9
7.9

24.2
21.0
18.4

41.7
48.2
54.0

9.4
13.8
16.1

Notes: Employers assign workers into one of ten social security categories which we regroup into five occupational skill
categories. Shares are averages of monthly observations in the sample.

sorting based on observable worker characteristics. Big cities have more engineers, economists,
Dingel – Skill-Biased Agglomeration – UEA Summer School 2024 – 23
and lawyers than small cities. However, is it also the case that big cities attract the best withinde la Roca and Puga (2017) on dynamics and sorting▶ Experience in larger cities is more valuable and portable▶ Big-city experience is more valuable for workers with higher ability▶ There is sorting across five occupational categories

136
REVIEW OF ECONOMIC STUD
▶ Little sorting within these categories whenusing full dynamic
specification

Downloaded from http://restud.oxfordjournals.org/ b

Figure 8Comparisons of worker fixed-effects distributions across cities

Dingel – Skill-Biased Agglomeration – UEA Summer School 2024 – 23

Notes: Experience in cities refers to work experience accumulated in the respective citygroup (the largest city Oslo or the six other large cities). Other explanatory variables aredeﬁned in the notes to Table 2. Robust standard errors (clustered by worker) are given
in parenthesis. All regressions include a constant term.
⁎ Indicate signiﬁcance at the 10% level.
⁎⁎ Indicate signiﬁcance at the 5% level.
⁎⁎⁎ Indicate signiﬁcance at the 1% level.

Norway (above 150,000 inhabitants). We investigate the robustness of
this deﬁnition by introducing a cutoff population size of 100,000 anddistinguishing between Oslo and twelve other cities. As expected, theOslo wage premium is higher when the comparison is regions withfewer than 100,000 inhabitants. The main difference compared to a cutoff of 150,000 inhabitants (Table 4) is that the return to experience incities outside Oslo is no longer increasing with education level. Our interpretation is that the higher return to experience for collegeeducated workers requires larger cities. Similarly, the different job tenure effects across education groups are reduced when we expand theNorweigan wage regressions with worker fixed effects

Carlsen Rattsø & Stokke (2016) use 2003-2010 data on Norway:

literature, Matano and Naticchioni (2016) show similar differences be▶ College-educatedhaveforhigher
tween the top and the bottom ofworkers
the wage distribution
job change return to big-city experienceand separating between high- and low-density regions.

▶ The city wage premium trajectories depend on job tenure

Fig. 1. Urban wage premium trajectories for primary- and college-educated workers, years after move to Oslo.

Dingel – Skill-Biased Agglomeration – UEA Summer School 2024 – 24

d Puga (forthcoming). In a dyexperience and job tenure areobserved abilities in cities is shifted 5% to the right compared to the restof the country, the estimatedof the country. The sorting based on worker ﬁxed effects is driven by
served ability when enteringcollege-educated workers. Aggregate studies miss this heterogeneity.
ow in panel A, the distributionWe show the comparison of worker ﬁxed effects distributions betweenc model differs between citiescities and other regions for the three education groups in Fig. 2. As seen,gion distribution is 4% to thethe distributions for cities and the rest of the country are similar fore la Roca and Puga's ﬁndingsprimary-educated and secondary-educated workers, while the distribuis no sorting when includingtion for college-educated workers is shifted to the right for city regions.
effects. We ﬁnd signiﬁcant dif-The larger dispersion in city regions observed for all workers disappears
entering the labor market, andwhen we consider each education category (the estimated dilation
parameters are not signiﬁcantly different from 1). The observed heteroeffect in cities.
ributions of estimated workergeneity with respect to education explains the higher dispersion in citpanel B, the estimated shiftsies for all workers.
own for each of the education The effects discussed above may reﬂect generational effects or career
ducated workers, the distribu-development. We distinguish between young (those under 35 years ofhift when comparing cities andage) and old workers (those above 45 years of age). The age cutoff refers
6ucated, the distribution of un-to the average age of the worker when included in the sample. The rethe right compared to the restsults are documented in panel C of Table 5. We begin by reproducing, inrker ﬁxed effects is driven bya static model, the ﬁndings of Combes et al. (2012b) that sorting is moreudies miss this heterogeneity.important in the old worker group. This is shown in the ﬁrst and the
d effects distributions betweensecond rows of panel C. There is a signiﬁcant shift in the distributions
ation groups in Fig. 2. As seen,between cities and the rest of the country for both young and oldof the country are similar forworkers, but the shift is larger for the old workers (9.4% compared to
ed workers, while the distribu-5.2% for the young). When we control for experience and job tenure
ed to the right for city regions.and allow the value of experience and tenure to vary according to city
ved for all workers disappearssize, the sorting among old workers disappears (comparing the third
gory (the estimated dilationand fourth rows of panel C). This follows from old workers in cities havfrom 1). The observed hetero-ing more experience and higher return to experience compared to old
ns the higher dispersion in cit-workers in the rest of the country. Our understanding is that differencesin unobserved abilities are more important early in a worker's career. Itt generational effects or careershould be noted that Combes et al. (2012b) estimate a ﬁxed effect foroung (those under 35 years ofaverage ability over time. We ﬁnd that sorting matters for ability uponrs of age). The age cutoff refersentering the labor market. The dilation parameter in the second column
cluded in the sample.6 The re-is signiﬁcantly higher than 1 for old workers in both the static and the
5. We begin by reproducing, indynamic speciﬁcation. The wage dispersion for old workers is larger inl. (2012b) that sorting is morecities compared to the rest of the country.

Norweigan wage regressions with worker fixed effects
Carlsen Rattsø & Stokke (2016) use 2003-2010 data on Norway:▶ College-educated workers have higher return to big-city experience▶ The city wage premium trajectories depend on job tenure▶ Sorting on unobserved abilities is driven by the college educatedFig. 2. Comparison of worker ﬁxed effects across education groups, cities vs. rest of
country.

▶ Sorting by young: no sorting on worker fixed effects among older workers

is shown in the ﬁrst and thecant shift in the distributions

Dingel – Skill-Biased Agglomeration – 6.UEA
SummerSchool2024 – 24
Continuous
population
densityUS wage regressions with worker fixed effects
Card, Rothstein, Yi (2023) use Longitudinal Employer-Household Dynamics data:▶ Abowd-Kramarz-Margolis wage regression with worker FEs, establishment
FEs, and controls for age and time
▶ Commuting Zone effect is average of establishment FEs in the CZ(specification with worker FEs and CZ FEs biased by “hierarchy effect”)▶ “We find some evidence of the kind of dynamic returns to ‘big city’ experiencehighlighted by de la Roca and Puga (2017) but the addition of this channel has little
impact on the static returns to different CZs”

▶ Half of the observed large-CZ earnings premium reflects worker sorting▶ 2/3 of spatial variation in college wage premia is variation in relative skills▶ Much of the remaining 1/3 is because of enhanced sorting of college-educatedworkers to high-wage industries in larger CZs
Dingel – Skill-Biased Agglomeration – UEA Summer School 2024 – 25

Modeling a spatial economy with a continuum of skills
Why work with a continuum?
▶ Evidence for sorting on characteristics that are typically not observed▶ Need at least five types to capture sorting on observables in the sense of de laRoca and Puga (2017)▶ Modeling a finite, particular number of types is potentially painfulContinuum case can be quite tractable▶ See Behrens, Duranton, Robert-Nicoud (2014), Davis and Dingel (2019, 2020),
Behrens and Robert-Nicoud (Handbook 2015)▶ These papers rely on tools from the assignment literature▶ Assignments of individuals/firms to cities, with endogenous citycharacteristics determined in equilibrium▶ Davis and Dingel (2020) speak to both skills and sectors
Dingel – Skill-Biased Agglomeration – UEA Summer School 2024 – 26

Davis & Dingel - A Spatial Knowledge Economy (2019)
We have models of:▶ Knowledge spillovers as a pure externality (one interpretation of Henderson
1974, Black 1999, Lucas 2001)▶ Endogenous exchange of ideas in a single (or symmetric) location(s) (Helsley
and Strange 2004, Berliant, Reed III, and Wang 2006, Berliant and Fujita
2008, Lucas and Moll 2014)
Our contribution:▶ Model a system of cities in which costly idea exchange is the agglomerationforce▶ Our model replicates a broad set of facts about the cross section of cities▶ We provide a spatial-equilibrium explanation of why skill premia are higher inlarger cities and how this emerges from symmetric fundamentals
Dingel – Skill-Biased Agglomeration – UEA Summer School 2024 – 27

Model summary
Our model’s core components:▶ Spatial equilibrium – zero mobility costs▶ Heterogeneous workers – continuum of abilities▶ Two sectors:▶ Tradables: Labor heterogeneity matters for productivity▶ Non-tradables: Homogeneous productivity▶ Skilled tradables sector has local learning opportunities▶ Workers choose to spend time exchanging ideas▶ Gains from interactions increasing in own ability and peers’ ability▶ Congestion costs make housing more expensive in larger cities▶ Workers choose locations, occupations, and time spent exchanging ideas
Dingel – Skill-Biased Agglomeration – UEA Summer School 2024 – 28

Preferences and congestion▶ Preferences: Unit demand for housing and n̄-unit demand for non-tradable:
V (pn,c , ph,c , y) = y − pn,c n̄ − ph,c .
▶ Each individual in a city of population Lc pays a net urban cost (in units of
the numeraire) of
ph,c = θLγc
▶ Individuals are perfectly mobile across cities and jobs, so their locational andoccupational choices maximize V (pn,c , ph,c , y).

Dingel – Skill-Biased Agglomeration – UEA Summer School 2024 – 29

Production▶ An individual can produce tradables (t) or non-tradables (n)▶ An individual working in sector σ earns income equal to the value of her
output, which is
(
y=

pn,c
z̃(z, Zc )if σ = nif σ = t▶ Tradables production depends on own ability (z), time spent producing (β),
time spent exchanging ideas (1 − β), and local learning opportunities (Zc ):z̃(z, Zc ) = max B(1 − β, z, Zc )β∈[0,1]

Dingel – Skill-Biased Agglomeration – UEA Summer School 2024 – 30

Idea exchange
Tradables production:z̃(z, Zc ) = max B(1 − β, z, Zc )β∈[0,1]▶ Scalar Zc depends on time-allocation decisions of all agents in c.
▶ Denote idea-exchange time of ability z in city c by 1 − βz,c
▶ Denote local ability distribution µ(z, c), where µ(z,c)µ(z) is the share of z in c.
Zc = Z({1 − βz,c }, {µ(z, c)}).
▶ Denote total time devoted to learning by tradables producers in city c by McZ(1 − βz,c )µ(z, c)dz.
Mc = Lz:σ(z)=t
Dingel – Skill-Biased Agglomeration – UEA Summer School 2024 – 31

Idea exchange: General assumptions▶ Assumption 1. The production function for tradables B(1 − β, z, Zc ) is continuous,strictly concave in 1 − β, strictly increasing in z, and increasing in Zc .
B(1 − β, z, 0) = βz and B(0, z, Zc ) = z ∀z.
▶ Assumption 2. Tradables output z̃(z, Zc ) is supermodular and is strictlysupermodular on ⊗ ≡ {(z, Z) : z̃(z, Z) > z}.
▶ Assumption 3. The idea-exchange functional Z({1 − βz,c }, {L · µ(z, c)}) is
continuous, equal to zero if Mc = 0, and bounded above bysup{z : 1 − βz,c > 0, µ(z, c) > 0}. If Mc > Mc′ and {(1 − βz,c )µ(z, c)} stochasticallydominates {(1 − βz,c′ )µ(z, c′ )}, thenZ({1 − βz,c }, {L · µ(z, c)}) > Z({1 − βz,c′ }, {L · µ(z, c′ )}).

Dingel – Skill-Biased Agglomeration – UEA Summer School 2024 – 32

Idea exchange: Special case
For some of our analysis, we focus on particular functional forms for B(·) and Z(·):
B(1 − β, z, Zc ) = βz(1 + (1 − β)AZc z)
Z({(1 − βz,c ), µ(z, c)}) = (1 − exp(−νMc )) z̄c( R(1−βz,c )zR
if Mc > 0z:σ(z)=t z:σ(z)=t (1−βz,c )µ(z,c)dz µ(z, c)dzz̄c =0otherwise▶ Random matching: Probability of encounter during each moment of timespent seeking idea exchanges is (1 − exp(−νMc ))▶ Mc is the total time devoted to idea exchange▶ z̄c is the average ability of the individuals encountered
Dingel – Skill-Biased Agglomeration – UEA Summer School 2024 – 33

Two lemmas
Lemma (Comparative advantage)
Suppose that Assumption 1 holds. There is an ability level zm such that individualsof greater ability produce tradables and individuals of lesser ability produce
non-tradables.
(
t if z > zm
σ(z) =
n if z < zmLemma (Spatial sorting of tradables producers engaged in idea exchange)
Suppose that Assumption 2 holds. For z > z ′ > zm , if µ(z, c) > 0, µ(z ′ , c′ ) > 0,β(z, Zc ) < 1, and β(z ′ , Zc′ ) < 1, then Zc ≥ Zc′ .
Dingel – Skill-Biased Agglomeration – UEA Summer School 2024 – 34

Spatial equilibrium

Proposition (Heterogeneous cities’ characteristics)
Suppose that Assumptions 1 and 2 hold. In any equilibrium, a larger city has higher
housing prices, higher non-tradables prices, a better idea-exchange environment,
and higher-ability tradables producers. If Lc > Lc′ in equilibrium, then ph,c > ph,c′ ,pn,c > pn,c′ , Zc > Zc′ , and z > z ′ > zm ⇒ µ(z, c)µ(z ′ , c′ ) ≥ µ(z, c′ )µ(z ′ , c) = 0.

Dingel – Skill-Biased Agglomeration – UEA Summer School 2024 – 35

Spatial equilibrium: Two-city example
1.8
1.6
1.4

Nominal wage

1.2
zb

1
0.8

Utility

zm
2

0.6
0.4

2

1

1

0.2
0
0

0.1
Ls,1

0.2

0.3

Ls,2
Non-tradables

0.4

0.5

0.6

0.7

Lt,1

Lt,2
Tradables

Ability (z)

0.8

0.9

Dingel – Skill-Biased Agglomeration – UEA Summer School 2024 – 36

1

Differences in average wages▶ Differences in tradables producers’ wages are the sum of three components:
composition, learning, and compensation effects▶ Denote zb the “boundary” ability of indifferent tradables producer▶ Define inframarginal learning∆(z, c, c′ ) ≡ [z̃(z, Zc ) − z̃(z, Zc′ )] − [z̃(zb , Zc ) − z̃(zb , Zc′ )]▶ Define the density of tradables producers’ abilities in city c byµ(z,c)µ̃(z, c) ≡ R′′
z ′ :σ(z ′ )=t µ(z ,c)dz
RR′′
z:σ(z)=t z̃(z, Zc )µ(z, c)dz
z:σ(z)=t z̃(z, Zc )µ(z, c )dz
RR′w̄c − w̄c ≡−′z:σ(z)=t µ(z, c)dz
z:σ(z)=t µ(z, c )dz
Z ∞
Z ∞
=
[µ̃(z, c) − µ̃(z, c′ )]z̃(z, Zc′ )dz +µ̃(z, c)∆(z, c, c′ )dz
zm
zm
|
{z
} |
{z
}
composition

inframarginal learning

Dingel – Skill-Biased Agglomeration – UEA Summer School 2024 – 37

+ pn,c − pn,c′| {z }

compensation

Skill premia▶ Define a city’s observed skill premium as its average tradables wage divided bycits (common) non-tradables wage, pw̄n,c▶ When a tradables producer of ability zb is indifferent between cities c and c′ ,this skill premium is higher in c if and only ifZ ∞ w̄c′[µ̃(z, c) − µ̃(z, c′ )]z̃(z, Zc′ )dz +µ̃(z, c)∆(z, c, c′ )dz ≥ pn,c − pn,c′
−1
pn,c′
{z
}
| zm
{z
} | zm{z} |Z ∞composition

inframarginal learning

relative compensation▶ Helpful to define a production-function property:

Conditionc)
The ability elasticity of tradable output, ∂ ln∂z̃(z,Z, is non-decreasing in z and Zc .
ln z

Dingel – Skill-Biased Agglomeration – UEA Summer School 2024 – 38

Larger cities have higher skill premia
Proposition (Skill premia)
Suppose that Assumptions 1 and 2 hold. In an equilibrium in which the smallest
city has population L1 and the second-smallest city has population L2 > L1 ,1. if the ability distribution is decreasing, µ′ (z) ≤ 0, z̃(z, Zc ) is log-convex in z,
2
1
and z̃(z, Zc ) is log-supermodular, then pw̄n,2> pw̄n,1;
2. if the ability distribution is Pareto, µ(z) ∝ z −k−1 for z ≥ zmin and k > 0, and2
1
the production function satisfies Condition 1, then pw̄n,2> pw̄n,1;
3. if the ability distribution is uniform, z ∼ U (zmin , zmax ), the production
max −zmin )1> L1 z(1−n̄)(z, thenfunction satisfies Condition 1, and L2L−L
2min +n̄(zmax −zmin )
1
w̄2
w̄1
pn,2 > pn,1 .
Dingel – Skill-Biased Agglomeration – UEA Summer School 2024 – 39

Larger cities have higher skill premia▶ The three cases in Proposition 2 trade off stronger assumptions about the
production function with weaker assumptions about the ability distribution▶ Paper contains numerical results for more than two cities for special case ofB(1 − β, z, Zc ) = βz(1 + (1 − β)A (1 − exp(−νMc )) z̄c z)▶ Paper contains illustrative example with 275 cities that quantitatively matches
Zipf’s law, premia-population correlation, and size-invariant housing
expenditure shares▶ Numerical comparative static: 10% increase in A leaves the power-law
exponent virtually unchanged and increases both the economy-wide averageskill premium and the population elasticity of skill premia by 7%–8%.

Dingel – Skill-Biased Agglomeration – UEA Summer School 2024 – 40

Davis and Dingel (2019) summary
A microfounded account of skill-biased agglomeration that matches the facts:▶ Cities facilitate idea exchange, more skilled value learning opportunities more,
and more skilled are more valuable idea-exchange partners▶ Spatial sorting of skilled explains spatial variation in skill premia▶ Nests Black, Kolesnikova, Taylor (2009) two-type logic
Related to recent job-market papers on spatial sorting of heterogeneous agents▶ Lhuillier (2024): Spatial sorting based on human capital accumulation⋆ Absent migration costs, model with supermodular learning function and t + 1
payoff works just like model with instantaneous supermodular benefits▶ Oh (2024): Cities are too large when worker-firm matching opportunities arerationed by congestion costs (cities as platforms)⋆ Normative analysis of model akin to worker-worker matching when ν → ∞ soidea-exchangeDingel
benefits
depend only on composition, not scale– Skill-Biased Agglomeration – UEA Summer School 2024 – 41

Skill-biased agglomeration around the world
Most evidence is for United States or Western Europe.
Dingel, Miscio, Davis (JUE 2021):▶ Use lights at night in satellite imagery to define metropolitan areas for Brazil,
China, and India▶ In all three developing economies, larger cities are skill-abundant (using yearsof schooling as proxy for skills)▶ In Brazil, college wage premia are higher in more populous cities, consistent
with developed-economy patterns

Dingel – Skill-Biased Agglomeration – UEA Summer School 2024 – 42

Agglomeration has become more skill-biased since 1980
486

Panel B1

0.6
BostonChicagoNew York
Detroit Philadelphia San Francisco
DallasMinneapolis
Los Angeles
Washington

0.5

Houston

0
−0.5

−2

−1.5

−1

−0.5

β = 0.17(0.027)
R2 = 0.13∆ ln rent
1980–2000∆ ln college employment
ratio 1980−2000

Panel A

0

Panel C

Boston
New York
San Francisco

0.4

Philadelphia
ChicagoWashington
DetroitLos Angeles
Dallas Minneapolis

0.2
0Houstonβ = 0.70(0.044)
R2 = 0.49

−0.2

−0.4
−0.5

0

0.5

1

∆ ln college employment ratio, 1980−2000

In college employment ratio, 1980

Panel D
0.6

0.3
0.2

Boston
New York
San Francisco
Washington
Philadelphia
DallasMinneapolis
Chicago

0.1

Los Angeles
Detroit0

Houstonβ = 0.237

−0.1
−0.2

(0.026)
R2 = 0.24

−0.5

0

0.5

1

∆ ln college employment ratio, 1980−2000∆ ln college wage
1980−2000∆ ln noncollege wage
1980−2000

MARCH 2016

THE AMERICAN ECONOMIC REVIEW

BostonSan Francisco

0.4

Dallas New York
ChicagoPhiladelphia
Los Angeles
Minneapolis
HoustonWashington

0.2

Detroitβ = 0.30(0.025)
R2 = 0.36

0
−0.2
−0.5

Davis and Dingel (2019):
spatially neutral SBTC (↑ A)
raises skill premia in larger
cities, consistent with
1990-2007 increase

0

0.5

1

∆ ln college employment ratio, 1980−2000

Figure 1. Changes in Wages, Rents, and College Employment Ratios, 1980–2000
Notes: Weighted by 1980 population. Largest 15 MSAs in 1980 labeled.

Dingel – Skill-Biased Agglomeration – UEA Summer School 2024 – 43

Two-type touchstone: Diamond (AER 2016)
Since 1980, college graduates have been concentrating in more skilled US cities.
Those cities have faster wage and housing-price growth. Questions:▶ Why are college graduates choosing already-skilled cities?
▶ Is this spatial divergence associated with greater welfare inequality?
Read Diamond (2016) to learn about a bunch of relevant concepts and tools:▶ Great Divergence (Berry Glaeser 2005, Moretti’s New Geography of Jobs)▶ Endogenous amenities (Milena Almagro’s 2023 summer school slides)▶ Inferring welfare with multiple types (c.f. Moretti 2013)▶ “Bartik (1991)” shift-share instruments (AKM 2019, BJH 2022, GPSS 2020)▶ Housing supply elasticities (Glaeser Gyourko 2005, Saiz 2010)
This paper uses shift-share IVs to estimate parameters of a one-sector model
Dingel – Skill-Biased Agglomeration – UEA Summer School 2024 – 44

1

2

Explaining sectors: The Comparative Advantage of Cities▶ Davis and Dingel (2020) describe comparative
Log (demeaned) employment share0-11

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

advantage of cities as jointly governed by individuals’
comparative advantage and locational choices▶ City-level TFP is endogenous outcome of
agglomeration economies and locations within cities
vary in their desirability▶ Larger cities are skill-abundant in10 equilibrium
12
14

16
Metropolitan log population

Computerand mathematical▶ By individuals’ comparative advantage,largercitiesspecialize in skill-intensive activities-1

more attractive locations-2▶ More skilled individuals are more willing to pay for

18

10

12
14
16
Metropolitan log population

18

Computer and mathematical

Office and administrative support

Office and administrative support

Installation, maintenance and repair

Installation, maintenance and repair

Dingel – Skill-Biased Agglomeration – UEA Summer School 2024 – 45

One key sector: Business services (Eckert, Ganapati, Walsh 2024)
F IGURE 1: T HE US WAGE -D ENSITY G RADIENT IN 1980 AND 2015

Average Wage

Relative to Decile 1(A) Aggregate(B) By Sector

2.2

2.2

2

2

1.8

2015

2015

Business Services
Other Sectors

1.8
1.6

1.6
1.4

1980

1.2

1.2

1

1
1

2

3

4

5

6

7

8

9 10

1980
2015
1980

1.4

1

2

3

4

5

6

7

8

9 10

Commuting Zone Population Density Decile
Notes: This figure shows average wages across commuting zones (Tolbert and Sizer, 1996) sorted into
Dingel – Skill-Biased Agglomeration – UEA Summer School 2024 – 46
deciles of increasing
population density. Each decile accounts for one-tenth of the US population inOne key sector: Business services (Eckert, Ganapati, Walsh 2024)
F IGURE 6: T HE R OLE OF E DUCATION IN U RBAN -B IASED G ROWTH( A ) Business Services

1.4
1.3

Non-College:
1980
2015

1.2

1.5
Average Wage

Average Wage

Relative to Decile 1

1.5

1.6

College:
1980
2015
Relative to Decile 1

1.6( B ) Other Sectors

1.4
1.3

Non-College:
1980
2015

1.2

1.1

1.1

1

1
1 2 3 4 5 6 7 8 9 10
Commuting Zone Density Decile

College:1980
2015

1 2 3 4 5 6 7 8 9 10
Commuting Zone Density Decile

Dingel – Skill-Biased
2024
– 46
( C ) Business
Services Agglomeration – UEA Summer( D School) Other
Sectors

1 2 3 4 5 6 7 8 9 10
Commuting Zone Density Decile

1 2 3 4 5 6 7 8 9 10
Commuting Zone Density Decile

One key sector: Business services (Eckert, Ganapati, Walsh 2024)
1980
2015

.6
.5
.4
.3
.2
.1
1

2 3 4 5 6 7 8 9 10
Commuting Zone Density Decile

College Share of Employment.7( D ) Other Sectors
Within Commuting Zone Decile and Sector

College Share of Employment

Within Commuting Zone Decile and Sector( C ) Business Services
.7

1980
2015

.6
.5
.4
.3
.2
.1
1

2 3 4 5 6 7 8 9 10
Commuting Zone Density Decile

Notes: This figure shows average annual wages and college employment shares across commuting zones
Dingel – Skill-Biased Agglomeration – UEA Summer School 2024 – 46
(Tolbert and Sizer, 1996)
sorted into deciles of increasing population density, separately for BusinessEckert, Ganapati, Walsh (2024)
Empirical patterns:▶ Business Services sector accounts for almost all urban-biased wage growth▶ Large (> 100 emp) Business Services establishments account for 70%▶ IT investment is concentrated in large, urban Business Services firms
Quantitative model:▶ Scale effect from complementarity between firm size and capital▶ Investment-specific technical change reduces price of IT▶ Growth accounting exercise: observed decline in IT capital prices alone
explains most urban-biased growth since 1980
▶ Absent scale effect, very little urban-biased growth
See also Chen, Novy, Perroni, Wong (2023) on urban-biased structural change
Dingel – Skill-Biased Agglomeration – UEA Summer School 2024 – 47

Skill-biased agglomeration and dynamics
My (static) account with continuum of types:▶ Davis & Dingel (2019): Endogenous process is idea exchange between
heterogenous agents with skill complementarity▶ Davis & Dingel (2020): Larger cities are skill-abundant and specialize in moreskill-intensive industries and occupations
Some of the benefits are dynamic (Glaeser & Maré 2001, Carlsen Rattsø & Stokke
2016, de la Roca & Puga 2017, Card Rothstein & Yi 2024)▶ Large cities have faster wage growth and human capital is portable
Models of human-capital dynamics with heterogeneous agents in recent JMPs:▶ Paolo Martellini: Life-cycle model of spatial sorting▶ Hugo Lhuillier: Spatial variation in peer effects on human-capital growth▶ Levi Crews: Aggregate growth rate depends on spatial distribution
Dingel – Skill-Biased Agglomeration – UEA Summer School 2024 – 48

Agglomeration and dynamics
Cities as engines of growth in human capital and human-capital-driven growth:▶ Lucas (1988): “But from the viewpoint of a technology through which the averageskill level of a group of people is assumed to affect the productivity of each individual
within the group, a national economy is a completely arbitrary unit to consider.”▶ Estimates from dlRP, CRS, CRY all say that workers learn more in big cities▶ Models of knowledge diffusion as source of growth (Lucas 2009; Lucas, Moll
2014; Perla, Tonetti 2014; Buera, Lucas 2018) neglect cities▶ Optimal spatial policy should account for growth effects
Other life-cycle components of spatial choices I’ll neglect today:▶ Kids and suburbs: delayed childbearing explains half of urban revival (Moreno-Maldonado,
Santamaria 2024)▶ Retirees value amenities and prices, not wages (Komissarova 2022; c.f. Albert, Monras 2022)
Dingel – Skill-Biased Agglomeration – UEA Summer School 2024 – 49

Crews (2023) “Dynamic Spatial Knowledge Economy”: Overview
Theory: Local human capital externalities → agglomeration & growth▶ system of cities▶ heterogeneous workers learn & migrate over the life cycle▶ human capital process drives both agglomeration and growth▶ learn from others in your city, more if bigger or more skilled (local externalities)▶ learning → human capital dist. shifts right → output grows▶ characterize “cities drive growth”: growth rate = f (spatial distribution)
Solves the hard problem of regional econ (Breinlich, Ottaviano, Temple 2014)▶ “How to model growth and agglomeration as outcomes of a joint process”▶ Agents must know distribution of economic activity over time & space →high-dimensional▶ how? Equilibrium is a mean field game (Achdou et al 2022) → can track
distribution
Dingel – Skill-Biased Agglomeration – UEA Summer School 2024 – 50

Crews (2023) “Dynamic Spatial Knowledge Economy”: Overview
Theory: Local human capital externalities → agglomeration & growth▶ system of cities▶ heterogeneous workers learn & migrate over the life cycle▶ human capital process drives both agglomeration and growth▶ learn from others in your city, more if bigger or more skilled (local externalities)▶ learning → human capital dist. shifts right → output grows▶ characterize “cities drive growth”: growth rate = f (spatial distribution)
Solves the hard problem of regional econ (Breinlich, Ottaviano, Temple 2014)▶ “How to model growth and agglomeration as outcomes of a joint process”▶ Agents must know distribution of economic activity over time & space →high-dimensional▶ how? Equilibrium is a mean field game (Achdou et al 2022) → can track
distribution
Dingel – Skill-Biased Agglomeration – UEA Summer School 2024 – 50

Crews (2023) “Dynamic Spatial Knowledge Economy”: Overview
2. Quantitative: Using US data, jointly rationalize. . .
▶ . . . urban cross-section:▶ match city size distribution▶ big cities more productive, more expensive, more skilled on avg.

▶ . . . worker panels:▶ life-cycle of human capital investment (Ben-Porath 1967; Huggett, Ventura, Yaron
2006▶ migration driven by expected income; young & educated move more (Kennan,
Walker 2011)▶ city size wage premium = higher wage level + faster wage growth w/
permanent value▶ . . . aggregate growth: 2% per year on BGP
Dingel – Skill-Biased Agglomeration – UEA Summer School 2024 – 51

Crews (2023) “Dynamic Spatial Knowledge Economy”: Overview
3. Long-run effects of place-based policy▶ policy: relax land-use regulations in NYC and SF to US median▶ outcome: aggregate growth increases by 13bp
▶ through what channel?
▶ not syphoning skill from elsewhere▶ instead, stronger dynamic spillover → faster human capital accumulation

Spatial policy → ∆ spatial distribution → ∆ growth in two(complementary) ways:▶ by attracting more skilled workers to particular cities (e.g., push skilled to NYC)
▶ by producing more skilled workers for whole economy (e.g., push young to NYC)

For details of model (setup, equilibrium, balanced-growth path, and main result),
see slides on Levi’s webpage
Dingel – Skill-Biased Agglomeration – UEA Summer School 2024 – 52

Crews (2023) “Dynamic Spatial Knowledge Economy”: Overview
3. Long-run effects of place-based policy▶ policy: relax land-use regulations in NYC and SF to US median▶ outcome: aggregate growth increases by 13bp
▶ through what channel?
▶ not syphoning skill from elsewhere▶ instead, stronger dynamic spillover → faster human capital accumulation

Spatial policy → ∆ spatial distribution → ∆ growth in two(complementary) ways:▶ by attracting more skilled workers to particular cities (e.g., push skilled to NYC)
▶ by producing more skilled workers for whole economy (e.g., push young to NYC)

For details of model (setup, equilibrium, balanced-growth path, and main result),
see slides on Levi’s webpage
Dingel – Skill-Biased Agglomeration – UEA Summer School 2024 – 52

Crews (2023) “Dynamic Spatial Knowledge Economy” summary▶ A classic hypothesis (Jacobs 1969, Lucas 1988, Glaeser 2011) . . .
human capital spillovers+ human capital accumulation→ agglomeration (cities!)→ growth

human capital accumulation s.t. local spillovers → “cities drive growth”. . . but no models → no testing, no counterfactuals, no optimal
policy▶ Forward-looking dynamics + place-specific conditions → high-dimensional▶ Crews (2023): Introduce new tools/model + apply to U.S. data & policy
1. characterize “cities drive growth”: growth rate = f (spatial distribution)
2. rationalize patterns in U.S. data: worker panels, city cross-section, aggregate
BGP trend
3. policy counterfactual: relax LURs in NYC and SF → ↑ aggregate growth 13bp
Dingel – Skill-Biased Agglomeration – UEA Summer School 2024 – 53

Summary▶ Spatial distributions of skills and sectors are prominent in public discussion of
cities, exploited for variation in empirical work, and potentially key tounderstanding agglomeration processes▶ Agglomeration has skill-biased productivity benefits: larger cities have higher
relative quantities and relative wages for skilled▶ We need models with more than two skills groups and more than perfectly
specialized/diversified cities to understand empirical patterns▶ Agglomeration has become more skill-biased since 1980; business services seem
important driver of recent decades▶ Dynamics: Still much to investigate in the story of Lucas (1988, §6)
Dingel – Skill-Biased Agglomeration – UEA Summer School 2024 – 54

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.

Dingel – Skill-Biased Agglomeration – UEA Summer School 2024 – 55

College wage premia in NLSY vs Census
Baum-Snow & Pavan
Table 1, column 1

2000 Census
PMSA

2000 Census
CMSA

Non-Hispanic white males with fewer than 15 years of work experience
Medium-city (0.25–1.5m) college wage premium.09
0.09780.0937(0.00578)(0.00613)

Large-city (>1.5m) college wage premiumN
Individuals observed
R2
p-value for equal premia

.05

17991
1257

0.145

0.154

(0.00565)(0.00551)

3013263013260.197
03013263013260.202
0Notes: This table describes full-time, full-year employees ages 18-55. Following BSP, “college graduate” means abachelor’s degree or greater educational attainment. The premia in the first column are obtained by differencing thenumbers for high-school and college graduates’ log wages in the first column of BSP’s Table 1. Note that they reportresults for temporally deflated panel data, while we report cross-sectional results. BSP assign individual to metropolitan statistical areas using the 1999 boundary definitions, but they do not specify whether they use consolidated MSAs
or primary MSAs for large cities. Hence we report both. Robust standard errors in parentheses.
Dingel – Skill-Biased Agglomeration – UEA Summer School 2024 – 56