Urban Studies Agglomeration, accessibility and Urban

Article

Urban Studies1–17! Urban Studies Journal Limited 2016Reprints and permissions:sagepub.co.uk/journalsPermissions.navDOI: 10.1177/0042098015624850usj.sagepub.com

Agglomeration, accessibility andproductivity: Evidence for largemetropolitan areas in the US

Patricia C MeloThe James Hutton Institute, Aberdeen, Scotland, UK

Daniel J GrahamImperial College London, UK

David LevinsonUniversity of Minnesota, Minneapolis, USA

Sarah AarabiMBA Candidate at Harvard Business School, Boston, MA, USA

AbstractThis paper estimates the productivity gains from agglomeration economies for a sample of thelargest metropolitan areas in the United States using measures of urban agglomeration based onemployment density and employment accessibility. The latter is a more accurate measure of eco-nomic proximity and allows testing for the spatial decay of agglomeration effects with increasingtravel time. We find that the productivity gains from urban agglomeration are consistent betweenmeasures, with elasticity values between 0.07 and 0.10. The large majority of the productivitygains occur within the first 20 minutes, and do not appear to exhibit significant nonlinearities.

Keywordsmetropolitan areas, productivity, spatial decay, transport accessibility, urban agglomerationeconomies

Received June 2015; accepted December 2015

Introduction

The existence of urban agglomerationexternalities implies that the allocation ofresources to cities delivers greater productiv-ity gains than non-urban areas. This has pol-icy implications, particularly the rationale

Corresponding author:Patricia C Melo, Social, Economic and GeographicalSciences, The James Hutton Institute, Craigiebuckler,Aberdeen AB15 8QH, Scotland, UK.Email: [email protected]

at University of Minnesota Libraries on March 8, 2016usj.sagepub.comDownloaded from

for investing in major infrastructure. Thedesign of agglomeration-based policiesrequires knowledge about the magnitudeand the spatial decay of the productivitybenefits from urban agglomeration acrossdifferent regions. In spite of abundantresearch on the size of productivity gainsfrom spatial agglomeration, there has beeninsufficient research on the spatial decaypattern of agglomeration effects and thepresence of nonlinearities. This study helpstowards finding an answer to some of thekey remaining questions in the literature,namely: How far and wide do the productiv-ity effects of spatial agglomeration spreadand how quickly do they attenuate overspace? Are there significant discontinuitiesin these effects within the urban hierarchy?

Previous studies have investigated howagglomeration economies attenuate overspace by using accessibility type measuressuch as market potential, economic mass andeffective density. These measures can bedescribed as a distance weighted sum ofopportunities (e.g. employment, population)between pairs of locations and have beenused to incorporate the notion of distancedecay into the measurement of agglomera-tion economies. They improve on the moreconventional measures based on populationand employment densities by providing abetter representation of spatial proximity.However, the majority of these studies mea-sure accessibility in terms of physical dis-tance and hence cannot account for the roleof (changes in) transport networks onimproved connectivity and the subsequentpositive effect on productivity. To ourknowledge, Graham (2007), Holl (2012),Lall et al. (2004), Le Nechet et al. (2012) andRice et al. (2006) are the only studies usingaccessibility type measures based on traveltimes derived from actual road networks.These studies, however, generally assume aconstant rate of decline in agglomerationeffects with increased distance/travel time.

Only a few studies allow for varying rates ofdecay with increased distance and overallthey suggest a steep decay of agglomerationeffects, although they can extend as far asthe boundaries of labour markets (e.g. DiAddario and Patacchini, 2008; Rice et al.,2006; Rosenthal and Strange, 2008).

Another limitation of the literature is thegeneralised adoption of a linear relationshipbetween urban agglomeration and produc-tivity, and hence the assumption that theproductivity effects of agglomerationincrease in a proportional way across theurban hierarchy. Some studies have allowedfor variable returns to urban agglomerationby using a quadratic function (e.g. Carlinoand Voith, 1992; Graham, 2007;Kawashima, 1975; Moomaw, 1983), butonly very few have relaxed the assumptionof a linear parametric fit. Exceptions includeGraham and Dender (2011) and Le Nechetet al. (2012) who used semiparametric tech-niques on firm level data for the UK andFrance, respectively, and found evidencesuggestive of nonlinearities in the relation-ship between productivity and urbanagglomeration.

This paper addresses the limitationsabove by examining the productivity gainsfrom urban agglomeration for the 50 largestmetropolitan statistical areas (MSA) in theUnited States using a transport-based mea-sure of agglomeration (i.e. employmentaccessibility by automobile) to investigatethe spatial decay of the productivity-agglomeration effects and semiparametrictechniques to test for nonlinearities inagglomeration effects across the urban hier-archy.1 To our knowledge this is the firstattempt to estimate productivity-agglomeration effects for the United Statesusing a transport-based measure of agglom-eration and semiparametric techniques.

The findings for the effect of urbanagglomeration on labour productivity arevery similar regardless of whether we use

2 Urban Studies


employment density or employment accessi-bility to measure agglomeration. This sug-gests that, in the context of our study,metropolitan density seems to have a stron-ger role than road network speed in the rea-lisation of urbanisation externalities. Thepreferred estimates indicate an elasticityvalue between 0.07 and 0.10, suggesting thata 10% increase in urban agglomeration isassociated with a 0.7%–1% increase inlabour productivity. The results further indi-cate that the productivity effects of urbanagglomeration can extend up to 60 minutesdriving time, although the large majorityoccur within the first 20 minutes and henceare spatially very localised. The semipara-metric analysis does not reveal any signifi-cant ‘threshold effects’ within our sample oflarge and very large metropolitan areas,therefore indicating that a linear parametricfit seems to be a reasonable assumption.

The remainder of the paper is organised asfollows. We next present the empirical metho-dology and the main estimation issues, whilethe following section describes the data andvariables used in the analysis. The main resultsare then presented and discussed, and the finalsection draws together the main conclusions.

Empirical methodology

Under the standard assumption that inputfactors are paid the value of their marginalproducts, local input factors will have higherprices in more productive areas. In this con-text, wage rates should reflect, even if par-tially, labour productivity. Wage models canbe used to investigate spatial variation inlabour productivity. The literature offersseveral explanations for the differences inlabour productivity across space. Under spa-tial equilibrium real wages should be equalacross space, however this is rarely observedin the real world. Spatial inequalities inlabour productivity and wages can resultfrom exogenous and endogenous factors.

These include differences in human capital(e.g. Glaeser and Mare, 2001; Moretti,2004b; Rauch, 1993); differences in the costof living and in the availability and qualityof local amenities (e.g. Glaeser and Gottlieb,2009; Roback, 1982); and agglomerationexternalities (e.g. Fujita and Thisse, 2002).To measure the effect of urban agglomera-tion on labour productivity we thereforeneed to specify wage models that control forother determinants of labour productivity.This is illustrated in the general wage model:

wit = f (Uit,Eit,Kit,Hit, lt,mi) ð1Þ

where the subscripts i and t denote the MSAand year, respectively. wit is the average realwage, Uit represents urban agglomeration,Eit measures educational attainment, Kit

denotes the Krugman index of relative indus-trial specialisation and Hit is a proxy forlocal cost of living. To account for unob-served shocks that are common to all areasbut vary across time we include year specificeffects lt. To account for additional MSAspecific unobserved heterogeneity (e.g. valu-able natural resources) we also include met-ropolitan area effects mi.

The log-linearised wage models are esti-mated using the two separate measures ofurban agglomeration (Uit): employment den-sity (Uit = Dit) and employment accessibility(Uit = Ait). The term eit in equation (2) is theresidual error, which is assumed to be nor-mally distributed while allowing for hetero-skedasticity and spatial clustering on MSA.

ln (wit)=a+b ln (Uit)+s ln (Eit)

+ dKit + gHit + lt +mi + eit

ð2Þ

To investigate the spatial decay of urbanagglomeration effects we separate the mea-sure of employment accessibility into a seriesof contiguous travel time bands k, as shownin equation (3).

Melo et al. 3


ln (wit)=a+X

k

bk ln (Akit)+s ln (Eit)

+ dKit + gHit + lt +mi + eit

ð3Þ

Finally, to examine the presence of nonli-nearities in the productivity effects of urbanagglomeration across MSA, we use a semi-parametric partially linear model (e.g.Ruppert et al., 2003; Wood, 2006), whereurban agglomeration enters the equationnonlinearly according to a smooth functionf estimated using penalised spline regressiontechniques and the other terms are definedas in the equations above. This is illustratedin equation (4).

ln (wit)=a+ f (Uit)+s ln (Eit)+ dKit

+ gHit + lt +mi + eit

ð4Þ

There are important identification issuesthat need to be considered in the estimationof the models above, namely possible endo-geneity of urban agglomeration due toomitted variable bias or unobserved heteroge-neity, and reverse causality between urbanagglomeration, human capital and labourproductivity. Individual unobserved heteroge-neity is generally addressed through the useof the random-effects (RE) and fixed-effects(FE) estimators. The RE estimator assumesthat unobserved heterogeneity is not corre-lated with the observed covariates, which iffalse leads to inconsistent and biased para-meter estimates. On the other hand, althoughthe FE estimator allows for correlationbetween unobserved heterogeneity and themodel covariates, it can result in a great lossof efficiency in the presence of highly persis-tent data, as is typically the case of spatialagglomeration. A more flexible approach isthe correlated random-effects (CRE) estima-tor, which includes the mean of the covariatesand allows testing the assumption of no cor-relation between unobserved heterogeneityand model covariates (Chamberlain, 1982;

Mundlak, 1978). In the case of reverse causal-ity, the concern is that more productive met-ropolitan areas may attract workers withhigher education, thus further increasingurban agglomeration and educational attain-ment. The remedial strategy adopted in theliterature is to use instrumental variable (IV)estimators. The most common instrumentsused in the agglomeration literature includelong-lagged values of urban agglomeration(Ciccone and Hall, 1996; Combes et al., 2010;Rice et al., 2006) and geological and geogra-phical instruments (Ciccone, 2002; Combeset al., 2010; Glaeser and Gottlieb, 2009;Rosenthal and Strange, 2008). Given thechanges in MSA boundaries over time, it isdifficult to construct an instrument for urbanagglomeration based on deep time lags.Alternatively, we follow an approach similarto that of Fingleton (2003, 2006) and use afive-group method which ranks the endogen-ous variable into one of five quintiles accord-ing to its size and then defines the instrumentas the rank order (i.e. quintiles). The rationaleis that there is strong association between therankings of urban agglomeration and urbanagglomeration size, but there is no relationbetween the relative rankings and labour pro-ductivity other than through the value ofurban agglomeration. To instrument humancapital, we follow Moretti (2004a) who useda deep time lag for the presence of collegesand universities as created in the 19th centuryby The Land Grant Movement.

Data

The dataset consists of a balanced panel ofthe 50 largest MSAs in the United Stateswith a population of at least 1 million. Thetime horizon of the study is limited by dataavailability for employment accessibility,which is available for 1990, 1995, 2001 and2009. The data sources and variables used inthe study are described in the followingparagraphs.

4 Urban Studies


Labour productivity

To represent labour productivity, we usedata for average MSA wage per job, avail-able from the Regional EconomicInformation System (REIS) of the Bureauof Economic Analysis (BEA). To calculatereal average wage per job (w) we use theGDP deflator with base year for 1990.

Urban agglomeration: Employment densityvs. employment accessibility

We consider two measures of urban agglom-eration: employment density and employ-ment accessibility. The former has beenextensively used in the empirical literatureand although it is generally preferred to sim-ple measures of total population andemployment, its main limitation is that itassumes a uniform distribution of peopleacross space and it does not account for therole of the transport network on actual spa-tial proximity, which our measure ofemployment accessibility does. Employmentaccessibility is defined in equation (5) asthe number of jobs a representative travellercan reach within a certain travel timethreshold.

Ak, t =pVn, tk

Ct

! "Dt ð5Þ

where,

# Dt = metropolitan area employmentdensity at year t

# k = time band (in minutes)# Vn,t = average network speed in km/h

at year t# Ct = average circuity at year t

Because we do not have microdata onspeeds by link going back to 1990 (this isonly widely available, for a fee, in recentyears with the advent of GPS), average met-ropolitan speeds estimated from a variety ofdata by the Texas A&M Transportation

Institute (TTI) in their Urban MobilityReport are used, comprising a weightedaverage of arterial and freeway speeds.Similarly, micro level employment (at theblock level) is not available consistentlybefore the Census LEHD datasets becameavailable in 2003, so urban employment den-sity is used. The average circuity is the ratioof the shortest path network distance to theEuclidean distance and has been computedin a separate study (Levinson andEl-Geneidy, 2009). For more details aboutthe calculation of employment accessibilitysee Levinson (2012).

The representative traveller experiencesuniform metropolitan average employmentdensity, metropolitan average network speedand circuities that vary by trip length. Allvariables change with year. The maximumdistance (or time) travelled is constrained sothat once the representative traveller reachesa band where s/he passes all metropolitanjobs, the accessibility is capped (i.e. theregion does not go on infinitely, only so longas all jobs at average density are available).

The distribution of employment across thetravel time bands between 10 and 90 minutesindicates that 15% of employment is accessi-ble within the first 10 minutes, and this valueincreases to 54% for 20 minutes, 83% for 30minutes, 94% for 40 minutes, 98% for 50minutes and 99% for 60 minutes. As a result,on average, the full majority of employmentis accessible within one hour’s travel time.Unfortunately, our measure of employmentaccessibility is solely based on the road trans-port network and hence does not account forthe role of public transport, which is likely tobe important in the largest urban areas.2 Theaverage mode share for work trips in the USfor 2013 is 76.4% drive alone and 9.4% car-pool, compared with 73.2% and 13.4% in1990. It is lower in the largest metro areas,but even there automobile dominates (e.g.59% for metropolitan New York, 73.6% forSan Francisco) (McKenzie, 2015).

Melo et al. 5


Economic structure

To account for differences in the economicstructure of metropolitan areas that mightalso affect their wage composition we use ameasure of relative economic specialisationbased on the Krugman Specialisation Index(K) (Krugman, 1991).

Kit =XO

o=1

soi $ soij j ð6Þ

where soi is the local employment share inindustry o and soi is the average employmentshare in industry o for the group of metropoli-tan areas. Industry employment data areobtained from the BEA REIS database for 14different industries. The index values rangebetween K = 0 (no specialisation) and K =2*(I-1)/I (maximum specialisation). Thehigher the index the more the economic struc-ture of the local economy deviates from thatof the reference group (i.e. sample average)and the more it is considered to be specialised.

Human capital

Human capital (E) is measured by the per-centage of population aged 25 years and overholding a bachelor’s degree or higher. Datafor educational attainment were obtainedfrom the decennial Census (for 1990 and2000) and from the American CommunitySurvey (ACS) for 2009. Using 2000 data for2001, we had data for 1990, 2001 and 2009.Unfortunately, data were not available for1995 as the ACS was conducted for the firsttime in 1996 in four counties only. To avoidlosing a quarter of the observations we inter-polated the 1995 educational data using acompound annual growth rate between 1990and 2000.

Cost of living and local amenities

Wages are generally higher in larger urbanareas, even after correcting for differences in

housing costs. Spatial variation in real wagescan reflect differences in the availability andquality of urban amenities. To account fordifferences in the cost of living we use theFederal Housing Finance Agency (FHFA)house price index (H) for each MSA. Weadjust the original index to be centred on themean value of the index for our sample ofmetropolitan areas and to have 1990 as thebaseline year. Lower real wages might bemore acceptable where climate is pleasur-able, while areas with hostile climate mighthave to offer higher real wages to attractpeople (Glaeser et al., 2001). To account forthis we use controls for the climate region agiven MSA belongs to based on the nine cli-mate regions identified by the NationalClimatic Data Center (Karl and Koss, 1984).

Table 1 provides basic descriptive statisticsfor the variables, while Figure 1 shows scatterplots for the relationship between metropoli-tan area average wage and the measures ofurban agglomeration (i.e. employment densityand employment accessibility) and humancapital. There is a strong positive correlationbetween average wages and employment den-sity (0.60) and educational attainment (0.74),and a relatively less strong correlation foremployment accessibility, especially within 20minutes’ travel time (0.15). The latter mightresult from greater congestion effects in thecore urban areas of metropolitan areas. Thecorrelation between average wages andemployment accessibility is very similar acrossthe travel time bands for 30, 60 and 90 min-utes – 0.45, 0.54 and 0.55, respectively. This isexpected because the number of jobs accessi-ble within 30 and 60 minutes’ travel time cor-responds to approximately 83% and 99% ofthe MSA employment accessible within 90minutes, respectively.

Results and discussion

This section presents and discusses the mainfindings. The results obtained from the IV

6 Urban Studies


and non-IV models using RE, FE and CREestimators are presented in Tables 2 to 4,respectively. Table 2 shows the models in

which urban agglomeration is measured byemployment density, while Table 3 reportsthe results for the models based on

Table 1. Descriptive statistics of variables.

Variable Min Mean Median CV Max SDB/SDW

Real average wage (w) 20,268 27,918 26,995 0.20 53,182 1.15Emp. accessibility, 10 min (A10) 48,012 126,331 117,833 0.38 275,360 1.19Emp. accessibility, 20 min (A20) 192,046 478,833 456,453 0.33 1,101,442 1.19Emp. accessibility, 30 min (A30) 371,128 834,306 792,804 0.43 2,333,749 1.83Emp. accessibility, 40 min (A40) 371,128 1,069,420 884,454 0.71 3,377,059 3.08Emp. accessibility, 50 min (A50) 371,128 1,205,735 884,454 1.02 5,276,655 4.27Emp. accessibility, 60 min (A60) 371,128 1,293,838 884,454 1.33 7,598,383 5.17Emp. accessibility, 90 min (A90) 371,128 1,342,600 884,454 1.55 8,550,473 7.33Employment density (D) 16 138 114 0.91 560 6.99Krugman specialisation index (K) 0.07 0.18 0.16 0.47 0.45 5.53Educational attainment (E) 14 27 26 0.23 47 1.54House price index (H) 0.80 1.45 1.28 0.39 3.19 0.40

Notes: CV: coefficient of variation (i.e. ratio of standard deviation to the mean). SDB/SDW: ratio of between-MSAstandard deviation over within-MSA standard deviation. Wages are expressed in real USD; employment accessibility isexpressed in number of people; employment density is expressed in terms of people per square kilometre; Krugman’sindex of relative specialisation ranges between 0 (no specialisation) and 2 (maximum specialisation); Educationalattainment consists of the percentage of population with bachelor’s or higher degree; the cost of living index is based onthe MSA house price index with 1990 as the reference year.

Figure 1. The relationship between real average wages, urban agglomeration and educational attainment.

Melo et al. 7


Tab

le2.

Res

ults

oft

hew

age

mode

lsus

ing

empl

oym

ent

dens

ity.

Mode

lR

EFE

CR

E(1

)C

RE

(2)

RE-

IVFE

-IV

CR

E-IV

(1)

CR

E-IV

(2)

Cons

tant

8.99

50***

10.0

361*

**8.

6019***

8.58

65***

9.19

73***

10.9

582***

8.57

51***

8.48

55***

ln(D

)0.

1139***

0.03

020.

0302

0.03

360.

1453

***

0.02

580.

0579

0.09

90***

ln(E

)0.

1373***

20.

0541

20.

0541

20.

0441

0.02

532

0.33

50*

20.

2908

20.

2476

**K

0.15

092

0.18

282

0.18

280.

0763

0.18

032

0.28

312

0.26

152

0.23

72H

0.09

98***

0.11

37***

0.11

37***

0.11

26***

0.09

89***

0.11

92***

0.11

51***

0.10

66***

mea

nofln

(D)

0.07

60*

0.07

16*

0.04

83m

ean

ofln

(E)

0.35

80***

0.36

10***

0.59

46***

0.54

21***

mea

nofK

0.41

500.

4938*

0.46

65*

mea

nofH

20.

1201*

20.

1189

20.

1214

Obs

erva

tions

200

200

200

200

200

200

200

200

Hau

sman

test

(p-v

alue

)19

.17

(0.0

039)

10.3

0(0

.244

5)Fi

rst

stag

ePa

rtia

l/She

aR

2

-ln

(E)

(1)

0.85

/0.8

00.

34/0

.12

0.28

/0.0

60.

27/0

.26

-ln

(D)

(1)

0.84

/0.7

90.

27/0

.10

0.15

/0.0

30.

80/0

.79

Und

erid

entific

atio

nte

st(2

)50

.087***

11.6

31***

4.81

6**

9.18

3***

Wea

kid

entific

atio

nte

st(3

)28

4.97

5.96

82.

476

7.20

3W

eak-

inst

rum

ent-

robu

stin

fere

nce(4

)81

.73***

14.2

0***

2.38

24.0

42***

R2–

ove

rall

0.82

180.

4365

0.84

810.

8443

0.78

840.

1529

0.84

440.

8384

R2–

withi

n0.

9355

0.94

100.

9410

0.94

030.

9356

0.93

150.

9331

0.93

29R

2–

betw

een

0.72

990.

0170

0.76

960.

7632

0.66

390.

3097

0.76

960.

7586

Year

cont

rolv

aria

bles

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Not

es:***

,**

and*

indi

cate

sign

ifica

nce

at1%

,5%

and

10%

,res

pect

ivel

y.St

anda

rder

rors

are

clus

ter-

robu

st.C

lust

erin

gis

on

met

ropo

litan

area

s.D

epen

dent

vari

able

:log

ofM

SAre

alav

erag

ew

age

rate

.The

mode

lsal

soin

clud

eco

ntro

lvar

iabl

esfo

rcl

imat

ere

gions

,but

for

the

FEm

ode

lsth

ese

vari

able

sdr

op

due

tom

ultico

lline

arity

with

the

met

ropo

litan

area

fixed

-effe

cts.

(1)

Und

erid

entific

atio

nte

st(K

leib

erge

n-Pa

aprk

LMst

atis

tic)

.(2

)W

eak

iden

tific

atio

nte

st(K

leib

erge

n-Pa

aprk

Wal

dF

stat

istic)

.Sto

ck-Y

ogo

wea

kid

entific

atio

nte

stcr

itic

alva

lues

are

avai

labl

efr

om

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-Yogo

(200

5).

(3)

Wea

k-in

stru

men

t-ro

bust

infe

renc

e(S

tock

-Wri

ght

LMS

stat

istic)

.

8 Urban Studies


Tab

le3.

Res

ults

oft

hew

age

mode

lsus

ing

empl

oym

ent

acce

ssib

ility

.

Mode

lR

EFE

CR

E(1

)C

RE

(2)

RE-

IVFE

-IV

CR

E-IV

(1)

CR

E-IV

(2)

Cons

tant

8.31

52***

10.2

467***

7.62

29***

7.54

97***

8.22

77***

10.1

331***

7.59

39***

7.52

63***

ln(A

E,6

0)

0.08

04***

20.

0013

20.

0013

20.

0007

0.11

54***

0.06

520.

0688

0.09

53***

ln(E

)0.

1620***

20.

0720

20.

0720

20.

0710

0.03

202

0.31

96***

20.

3148***

20.

2979

**K

0.22

092

0.19

482

0.19

482

0.19

360.

2948**

20.

2740

20.

2718

20.

2615

H0.

1040***

0.11

73***

0.11

73***

0.11

51***

0.10

39***

0.11

47***

0.11

43***

0.10

91***

mea

nofl

n(A

E,6

0)

0.09

54***

0.09

58***

0.02

53m

ean

ofl

n(E)

0.40

33***

0.38

70***

0.64

62***

0.61

47***

mea

nofK

0.54

03*

0.54

08*

0.61

73**

0.60

91**

mea

nofH

20.

0771

20.

0740

Obs

erva

tions

200

200

200

200

200

200

200

200

Hau

sman

test

39.6

0(0

.000

0)17

.28

(0.0

273)

Firs

tst

age

Part

ial/S

hea

R2

-ln

(E)

(1)

0.85

/0.8

00.

32/0

.31

0.27

/0.1

20.

27/0

.27

-ln

(AE,6

0)

(1)

0.86

/0.8

10.

34/0

.33

0.04

/0.0

20.

51/0

.51

Und

erid

entific

atio

nte

st(2

)49

.185***

45.8

86***

2.95

3*10

.454***

Wea

kid

entific

atio

nte

st(3

)34

6.83

731

.292

1.37

97.

979

Wea

k-in

stru

men

t-ro

bust

infe

renc

e(4)

80.9

9***

15.6

0***

9.47***

42.0

4***

R2–

ove

rall

0.81

370.

3054

0.85

090.

8485

0.77

320.

2385

0.84

490.

8416

R2–

withi

n0.

9302

0.94

080.

9408

0.94

070.

9284

0.92

770.

9278

0.92

49R

2–

betw

een

0.73

530.

2181

0.77

500.

7706

0.64

540.

0516

0.77

500.

7713

Year

cont

rolv

aria

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Melo et al. 9


Table 4. Results of the wage models testing the spatial decay of urban agglomeration.

Model RE FE CRE

Constant 8.6951*** 10.3749*** 7.5708***ln(AE,20) 0.0530*** 20.0106 20.0106ln(AE,20-30) 0.0011 0.0003 0.0003ln(AE,30-40) 0.0021** 20.0017 20.0017ln(AE,40-60) 0.0039** 0.0001 0.0001ln(AE,60-90) 0.0023* 20.0002 20.0002ln(E) 0.1628*** 20.0727 20.0727K 0.2017 20.2162 20.2162H 0.1040*** 0.1214*** 0.1214***mean of ln(AE,20) 0.1091**mean of ln(AE,20-30) 0.0047mean of ln(AE,30-40) 0.0031mean of ln(AE,40-60) 0.0085**mean of ln(AE,60-90) 20.0007mean of ln(E) 0.4035***mean of K 0.5316*mean of H 20.0881Observations 200 200 200Hausman test 54.15***R2– overall 0.7933 0.2622 0.8570R2– within 0.9286 0.9417 0.9417R2– between 0.7175 0.3518 0.7855Year control variables Yes Yes Yes

Notes: ***, ** and * indicate significance at 1%, 5% and 10%, respectively. Standard errors are cluster-robust. Clusteringis on metropolitan areas. Dependent variable: log of MSA real average wage rate. The models also include controlvariables for climate regions, but for the FE models these variables drop due to multicollinearity with the metropolitanarea fixed-effects.

Figure 2. Spatial decay of urban agglomeration effects based on employment accessibility.

10 Urban Studies


employment accessibility. Table 4 and Figure2 refer to the models testing the spatial decayof the productivity gains from urbanagglomeration across a set of successivetravel time bands. The last part of the sectiondiscusses the analysis of nonlinearities in therelation between productivity and urbanagglomeration (Figure 3).

Productivity gains from urbanagglomeration

We first discuss the results in Table 2.Overall the models have good explanatorypower with generally high coefficients ofdetermination (R2). The first four columnsof the table refer to the non-IV models,

Figure 3. Nonparametric fit of the relation between metropolitan area wages (vertical axis) and urbanagglomeration (horizontal axis): employment density (top) and employment accessibility (bottom).

Melo et al. 11


while the last four columns refer to the IVmodels.3 The discussion focuses on the pre-ferred models selected using appropriatetests for model comparison.4 The elasticityof wage with respect to employment densityobtained from the preferred model CRE (2),which includes correlated random-effects foremployment density, educational attainmentand housing costs index, is 0.072; this indi-cates that increasing employment density by10% increases wages, all else equal, by0.72%. Correcting for reverse causalityappears to have a minor impact on the effectof urban agglomeration, which increasesfrom 0.072 to 0.099 (CRE-IV (2)).

The models in Table 3 are based on the 60minutes’ travel time band accounting for thelarge majority of metropolitan employment.The results obtained from the preferredmodel CRE (2), which includes correlatedrandom-effects for employment density, edu-cational attainment and relative industrialspecialisation, are in line with those obtainedin Table 2 for employment density.5 Raisingemployment accessibility by 10% is associ-ated with an increase in wages of 0.96%.Similarly, correcting for reverse causalitydoes not seem to change the elasticity esti-mate for employment accessibility, which isequal to 0.095 (CRE-IV (2)).

The findings reported above for the effectof urban agglomeration on average labourproductivity are consistent between the twomeasures used and suggest that incorporat-ing information on network speeds does notseem to affect the results much, which seemto be mainly driven by density effects. Thismay be partly due to the fact that employ-ment accessibility is based on average metro-politan speeds, which do not vary as muchas density. Our preferred estimates indicatean elasticity value between 0.07 and 0.10.Corroborating other studies (e.g. Ciccone,2002; Ciccone and Hall, 1996), we find thatcorrecting for reverse causality does notmuch affect the magnitude of the estimates.

Overall, the magnitudes of the urbanagglomeration elasticity estimates appear tobe slightly higher than those obtained in pre-vious studies using aggregate regional leveldata for the United States; however, thesedifferences are considered reasonable becauseour analysis is focused on the 50 largest met-ropolitan areas for which we expect toobserve stronger returns to urban agglomera-tion. Ciccone and Hall (1996), using data for1988, found that doubling county employ-ment density increased productivity by about6%. More recent evidence for the UnitedStates based on metropolitan area data sug-gests that the urban agglomeration elasticityranges between 5 and 8%. Glaeser et al.(2001) and Glaeser and Resseger (2010)found that doubling metropolitan area popu-lation leads to an increase in average labourproductivity of about 5% for 1980 and 8%in 1990 and 2001.

Table 4 presents the results for the spatialdecay models using a series of consecutivetravel time bands between 20 and 90 min-utes. The CRE model is selected as the pre-ferred model because it provides consistentand more efficient parameter estimates thanthe FE model.6 The results suggest that thespatial scope of the productivity effects ofagglomeration can extend up to 60 minutes’driving time, although the bulk of the effectsoccur within the first 20 minutes. The mag-nitude of the effect reduces dramatically forthe following travel time bands and tends tobe statistically insignificant (with the excep-tion of the travel time band between 40 and60 minutes). This pattern of a steep spatialdecay is illustrated in Figure 2, and supportsthe view of very localised benefits from spa-tial agglomeration while at the same timereaching as far as, but not necessarily in acontinuous way, the boundaries of labourmarket areas.

In a report describing commuting pat-terns in the United States, McKenzie andRapino (2011) show that the average one-

12 Urban Studies


way travel time to work was about 22 min-utes in 1990 and 25 minutes in 2000, andremained at 25 minutes in 2009. This com-muting pattern is in line with stronger urbanagglomeration effects within 20 and 30 min-utes of travel time, as found in our analysis.In addition, similar findings of a steep spa-tial decay of urban agglomeration effectswere also obtained from wage models basedon driving time accessibility measures forGreat Britain (Rice et al., 2006) and physicaldistance accessibility measures for the US(Rosenthal and Strange, 2008), Italy (DiAddario and Patacchini, 2008) and the UK(Melo and Graham, 2009).

Finally, we consider the results obtainedfrom the semiparametric analysis. Thisapproach does not make any assumptionson the functional form of the relationshipbetween productivity and urban agglomera-tion, and allows the shape of the curve to bedrawn as much as possible from the data.This provides a good way of investigating ifthere are ‘size’ thresholds above which thebenefits from additional agglomerationbecome disproportionally greater or smaller.

The sample used consists of the 50 largestmetropolitan areas, and hence contains con-siderably less variation than a full sample oflarge, medium and small metropolitan areas.As a result, the findings should be consid-ered in the context of large and very largeurban areas. Nonetheless, there is still morethan an order of magnitude (about 20-fold)variation in the size of the metropolitanareas in the sample. Taking the year 2009 asreference, the latest year in our dataset, weobserve that 60% of the sample consists ofmetropolitan areas with a populationbetween 1–2.5 million, 22% of the sampleconsists of areas with a population between2.5–5 million, 14% of the sample consists ofareas with a population between 5–9 millionand only 4% of the sample consists of met-ropolitan areas with a population of 10 mil-lion or more.

Figure 3 illustrates the nonparametric fitof the metropolitan area average real wageand urban agglomeration, where urbanagglomeration is measured by employmentdensity (top panel) and employment accessi-bility (bottom panel).7 The vertical axisshows the value of the nonparametric fit ofthe dependent variable and the horizontalaxis shows the values of urban agglomera-tion. The shaded area corresponds to theinterval determined by the two standarderror lines above and below the estimate ofthe smooth curve. The shape of the curvesdoes not reveal significant nonlineareffects, and indeed we cannot reject the testwith null hypothesis that the nonpara-metric fit can be approximated by a para-metric linear fit.8 This indicates that it isoverall reasonable to assume a linear rela-tion between spatial agglomeration andproductivity for urban areas with andabove 1 million people, and that there areno significant ‘threshold effects’ acrossurban areas of these sizes. It also suggeststhat there is no ‘wider economic benefits’or ‘agglomeration economies’ rationale forallocating disproportionally more publicinvestment to the top larger metropolitanareas compared to other large and verylarge metropolitan areas.

The main difference between the twocurves is the downward sloping trend for themetropolitan areas with the highest employ-ment density, although this effect appears tobe statistically insignificant. One partialexplanation for this difference might be theinability to disentangle congestion from highdensities. It has been shown elsewhere(Levinson, 2012) that there is often a trade-off between high densities and lower mobi-lity resulting from increased travel times andcongestion. However, accessibility levelsmay vary between high density urban areasas a result of differences in the spatial orga-nisation (e.g. urban form) and the planningand quality of transport systems. This

Melo et al. 13


implies that transport-based measures ofurban agglomeration such as our measure ofemployment accessibility may be better ableto disentangle, even if only partially, theeffect of increased congestion from that ofincreased density.

Human capital, economic structure andcost of living

As expected, educational attainment helpsexplain spatial differences in average wagesacross metropolitan areas. The effect is con-sistent across the models reported in Tables2 to 4 and suggests that increasing educa-tional attainment by 10% is associated withan increase in wages between 3–4%. As foreconomic structure, our analysis based onthe Krugman index of relative specialisationcould not identify any conclusive effect forits relationship with average metropolitanarea wage. Future analysis on this topiccould attempt to combine this indicator witha measure of the type of industrial speciali-sation as a way to further explore issuesrelating to industry mix. However, for thepurpose of our analysis we were mainlyinterested in separating the effects of urbanclustering from those of industrial clustering.The models also show that an increase of 1point in the house price index is associatedwith a less than proportional increase inaverage wage.

Conclusions

This paper contributes to ongoing researchon the productivity gains from urbanagglomeration by empirically examining thespatial decay and nonlinearity of theseeffects using a new transport-based measureof urban agglomeration and semiparametrictechniques. To the best of our knowledgethis paper provides the first attempt to testfor potential nonlinearities in the productiv-ity gains from urban agglomeration for the

United States using semiparametrictechniques.

The findings suggest that theproductivity-agglomeration effects obtainedfor our sample of MSA are generally consis-tent between the two measures of urbanagglomeration used – employment densityand road transport-based employmentaccessibility. This suggests that, in the con-text of our study, metropolitan areas’ densi-ties seem to have a stronger role than roadnetwork speeds in the realisation of urbanagglomeration externalities. The secondmain finding is that the large majority of theproductivity-agglomeration effects occurwithin the first 20 minutes, which is in agree-ment with previous evidence on very loca-lised benefits, while remaining significantbut small at wider distances encompassingthe boundaries of labour markets.Furthermore, the analysis suggests that thereturns to additional spatial agglomerationfor our sample of large and very large met-ropolitan areas appear to be constant; how-ever, this result should not be generalised tothe more heterogeneous population of met-ropolitan areas in the United States, forwhich there may be significant ‘thresholdeffects’.

Some policy implications can be drawnfrom our findings. Evidence of a localisednature of spatial agglomeration effects sug-gests that within metropolitan areas imme-diate access (within 20 minutes) to jobs isvery important for productivity, which inturn highlights the importance of investingin efficient transport networks. In addition,the lack of evidence in favour of nonlineari-ties in the relationship between productivityand urban agglomeration suggests there isno economic argument for allocating dis-proportionally more public money, toimprove density and (road) transport acces-sibility, to the larger regions in our sampleof metropolitan areas with 1 million peopleor more.

14 Urban Studies


Funding

This research received no specific grant from anyfunding agency in the public, commercial, or not-for-profit sectors.

Notes

1. MSA can be defined as functional economicareas with a strong degree of economic inte-gration and are generally centred around acore urban area of at least 50,000 people.

2. Data for public transport revenue vehiclemiles are available from the National TransitDatabase for urbanised areas, but not formetropolitan areas. In a recent studyChatman and Noland (2014) look at the rela-tionship between transit services, physicalagglomeration and productivity for urbanisedareas in the US. Huang and Levinson (2015)have measured transit circuity for recentyears, and Owen and Levinson (2014) havemeasured accessibility.

3. The first stage partial R2 and Shea R2 havemoderate to high values and tend to be higherfor urban agglomeration. Moreover, theKleibergen-Paap rank LM statistic test rejectsthe null hypothesis of model underidentifica-tion, indicating that our models are identified.In addition, the Kleibergen-Paap Wald rankF weak identification test statistic is generallyhigher than the Stock and Yogo critical val-ues, suggesting that the instruments are notweak. Finally, the Stock-Wright LM S statis-tic also generally indicates that the instru-ments are valid.

4. The Hausman test rejects the null hypothesisof no correlation between MSA specificunobserved heterogeneity and the model cov-ariates, suggesting the FE estimator shouldbe preferred over the RE estimator as onlythe former provides consistent estimates.However, the FE estimator can result in greatloss of efficiency for variables with relativelysmall time variation, as tends to be the caseof education and agglomeration. The CREestimator allows for greater flexibility; it pro-vides consistent but more efficient parameterestimates than the FE estimator. CRE (1)model suggests there is correlation foremployment density, educational attainment

and housing cost index. Hence, model CRE(2) allows for correlation between MSA spe-cific unobserved heterogeneity and these cov-ariates. Turning to the IV models, modelCRE-IV (1) indicates there is correlation foreducational attainment and the relativeindustrial specialisation index. Model CRE-IV (2) allows for correlation between thesevariables and MSA specific unobservedheterogeneity.

5. For both the non-IV and IV models, theHausman test suggests there is correlationbetween metropolitan area specific unob-served heterogeneity and the observed covari-ates. Model CRE (1) indicates this is the casefor employment accessibility, educationalattainment and relative industrial specialisa-tion. Model CRE (2) allows for correlationfor these variables and produces an elasticityestimate for employment accessibility equalto 0.096. Model CRE-IV (1) suggests there iscorrelation for educational attainment andrelative industrial specialisation, which isallowed for in model CRE-IV (2) and pro-duces an elasticity estimate for employmentaccessibility equal to 0.095.

6. The Hausman test rejects the null hypothesisof consistency of the RE model. Issues of littletime variability in the measures of educationalattainment and employment accessibility ren-der most of the coefficients insignificant inthe FE model. To avoid the loss of efficiencyof the FE model, we estimate a CRE modelwhich we select as our preferred model. IVmodels were not estimated because of themany time bands but given the results inTables 2 and 3 we would not expect to findgreat differences between the IV and non-IVestimates.

7. The full set of results can be obtained fromthe authors upon request.

8. Similar results were obtained for the IV mod-els, which can be obtained from the authorsupon request.

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